[HN Gopher] Alien Truth
       ___________________________________________________________________
        
       Alien Truth
        
       Author : pyb
       Score  : 158 points
       Date   : 2022-10-18 11:20 UTC (11 hours ago)
        
 (HTM) web link (paulgraham.com)
 (TXT) w3m dump (paulgraham.com)
        
       | dadboddilf2 wrote:
       | I'm very confused, I see the page with that guy's article (or any
       | of his articles for that matter), but I don't see any
       | instructions on how you can get paid to read it.
        
       | radford-neal wrote:
       | This essay would benefit from some examples of common beliefs
       | that he thinks are _not_ "Alien Truths", and what he thinks the
       | implications of that are. As it is, I don't really see what he's
       | trying to get at...
        
       | bobabob wrote:
       | > We'd probably share Occam's razor. There doesn't seem anything
       | specifically human about any of these ideas.
       | 
       | Except the fact that humans are the only species that we know so
       | far to have thought about them?
        
       | rbanffy wrote:
       | > that it would be true for aliens that one can get better at
       | something by practicing
       | 
       | I think that one depends a lot on how they learn or can transfer
       | knowledge. We rely on language for it, and language is severely
       | limited - We can't learn olympic gymnastics from watching TV, but
       | a species that could directly transfer memories and behaviors
       | would have a huge leg on us in that regard - I'd assume we'd
       | quickly notice their fast-paced technological advance.
       | 
       | Or completely miss it, because they'd anyhilate themselves a
       | couple hours after discovering the military use of nuclear fusion
       | ;-)
        
       | lakomen wrote:
       | SCNR has this guy never heard of https?
        
       | cies wrote:
       | If Occam's razor is presented as a truth (which is pretty
       | subjective, as it depends on what we/someone considers "simple").
       | Then finding one case where what most people thought was the
       | simple reason, was not actually the reason after evidence came to
       | light, then Occam's razor can be rejected as a theory right?
       | 
       | I think this has long happened, and do not understand why this is
       | still presented as "truth".
       | 
       | I prefer the standard of truth used by natural-sciences. The rest
       | I find pretty bendable (virology included).
        
         | naasking wrote:
         | > If Occam's razor is presented as a truth (which is pretty
         | subjective, as it depends on what we/someone considers
         | "simple").
         | 
         | It doesn't though. Firstly, Occam's razor is not about
         | simplicity but about "parsimony". Parsimony is calculated in
         | information theory via Kolmogorov complexity:
         | 
         | https://en.wikipedia.org/wiki/Kolmogorov_complexity
         | 
         | This then lets us describe how to do induction so it provably
         | converges in the fastest way possible, Solomonoff Induction:
         | 
         | https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_induc...
         | 
         | Arguably, this can be seen as a formalization of the scientific
         | process.
        
           | mistermann wrote:
           | > It doesn't though. Firstly, Occam's razor is not about
           | simplicity but about "parsimony". Parsimony is calculated in
           | information theory via Kolmogorov complexity
           | 
           | In theory perhaps, but in practice it is firstly calculated
           | by the mind of the person who plays the Occam's Razor card,
           | and then subsequently by people who ingest the claim, and
           | typically all participants are performing their calculations
           | using biased heuristics and flawed logic, and have negative
           | interest in what is actually true, or if truth is even
           | reachable.
        
       | [deleted]
        
       | benreesman wrote:
        
         | simiones wrote:
         | > There is no distinct identity. You have no power over space
         | time.
         | 
         | Agreed.
         | 
         | > There is no arrow of time.
         | 
         | This is almost certainly wrong. Just because some of our models
         | don't include it, doesn't mean it's not a meaningful physical
         | construct. Show us an egg unscrambling itself, and then we can
         | agree that there is no arrow of time.
        
         | dang wrote:
         | " _Please don 't fulminate._"
         | 
         | " _When disagreeing, please reply to the argument instead of
         | calling names. 'That is idiotic; 1 + 1 is 2, not 3' can be
         | shortened to '1 + 1 is 2, not 3._"
         | 
         | https://news.ycombinator.com/newsguidelines.html
        
       | GistNoesis wrote:
       | There is only one truth : There is no single truth !
       | 
       | Is a forest intelligent ? Is a cat intelligent ? Is a human
       | intelligent ? Is a chess program intelligent ? Is a proof-
       | assistant intelligent ? Is a numerical solver intelligent ? Is
       | the universe intelligent ?
       | 
       | Depending on your choice of definitions, you can get the answers
       | you like.
       | 
       | Some intelligences will be able to comprehend other types of
       | intelligence. Depending on their resources. There is usually a
       | price to be paid, whether in raw computation, memory, or speed.
       | And this price may often induce a hierarchy where the relation is
       | only one way : where the greater intelligence can predict how the
       | states of the lesser one will evolve, but the lesser one can't.
       | 
       | Because these resources are of various nature, they generate a
       | Pareto frontier. Only while the resources constraint stay
       | relevant. For example, once you reach enough intelligence, given
       | the rules of tic-tac-toe, you can play the optimal game.
       | Similarly there are end-game tables for chess, that allow
       | computers to play perfectly, but humans must use heuristics
       | because they don't have enough memory.
       | 
       | But you can always create a bigger game, or constrain your
       | resources. You can always be a collector of mathematical
       | curiosities, that are in some sense some extrema in the space you
       | chose to restrict yourself to.
       | 
       | AI will probably choose to live in constructs, where this dynamic
       | game of collecting resources until they are no longer a
       | constraint is perpetually maintained to keep it interesting,
       | because the alternative omnipotence is no fun.
       | 
       | Those constructs will be so disconnected from reality, that we
       | won't be able to acknowledge their existence.
        
       | deltasevennine wrote:
       | >Justice, for example. I wouldn't want to bet that all
       | intelligent beings would understand the concept of justice, but I
       | wouldn't want to bet against it either.
       | 
       | Justice is a biased concept. It's a biological phenomenon. Most
       | of us are born with justice modules in our brain. Certain people
       | aren't, they're called psychopaths and these people are basically
       | proof about the genetic component of justice.
       | 
       | Justice is simply a set of behaviors that helps you and your
       | tribe survive from an evolutionary perspective. If you robbed and
       | killed people all the time, well that doesn't help with survival
       | does it? So brains evolve justice modules. There are alternative
       | survival strategies that involve behaviors that are
       | unjustified... and your emotions reflect this possible
       | alternative path. One can be emotionally tempted by unjustified
       | behavior and move in that direction when the situation allows for
       | it. It's all preprogrammed...
       | 
       | For PG to talk about justice as possibly universal is like
       | talking about English as possibly universal. Clearly these are
       | biased concepts unique to humanities biological situation. It's
       | unlikely that a frog feels justice simply because the
       | evolutionary pressures to make him feel that way don't exist.
       | Hardly a candidate for even consideration of being universal.
       | 
       | There can be aliens that are highly intelligent but anti-social.
       | Such creatures have little need to develop a biological justice
       | module as part of their intelligence. I would imagine communities
       | of these creatures are only held at equilibrium because of
       | mutually assured destruction. This has certainly been the case
       | for humanity as humanity has multiple modes of operation, justice
       | is just one component, fear of death is another.
        
         | alfor wrote:
         | All of our truths are based on biology.
         | 
         | Without our body we cannot see, feel and experience. Something
         | is true when it is useful, predictive to us, to our body, when
         | it allow us to move away from pain and toward pleasure.
         | 
         | If there is no observer and no sensations(feedback) I don't
         | think we can ever come to any truth.
        
           | deltasevennine wrote:
           | Some truths seem to be universal meaning they exist separate
           | from our biology, for example: logic.
           | 
           | Other truths seem inextricably tied to our biology, for
           | example: happiness.
           | 
           | One that is ambiguous is, Justice. To which I say the
           | ambiguity is an illusion. Justice is like happiness.
           | Completely unique to the human experience.
        
       | dav wrote:
       | Paul Graham needs to read this and get back to us.
       | 
       | Where Mathematics Comes From: How the Embodied Mind Brings
       | Mathematics into Being by George Lakoff
       | 
       | https://www.goodreads.com/book/show/53337
        
       | bo1024 wrote:
       | (1) The examples he gives of "non-mathematical" concepts are
       | pretty mathematizable. Randomized controlled testing --
       | mathematics can prove why this is a good idea. Occam's razor -
       | usefulness can be formalized in the machine learning context.
       | Different conceptions of justice, fairness, etc. can be modeled
       | mathematically (at least certain aspects of them can), which
       | helps one understand and distinguish them. (Examples:
       | utilitarianism, equality of outcome versus equality of
       | opportunity.)
       | 
       | (2) The question of "functionally equivalent" is interesting
       | here. If an alien species accurately predicts the trajectory of a
       | complex rocket, many of us would say they _must_ be using math,
       | because we know that our mathematics governs how rockets move.
       | Even if they cannot communicate their method in a way we can
       | understand. Economists sometimes use the phrase  "as if", e.g.
       | the alien acts "as if" they have a utility function, regardless
       | of whether that's how they conceptualize their own action.
       | Similarly. they would certainly act "as if" they had math and
       | physics. But the question of whether that would imply they "do",
       | I'm less sure of.
        
       | theboywho wrote:
       | > it would be true for aliens that one can get better at
       | something by practicing
       | 
       | We get better by practicing only because of our brain's
       | neuroplasticity, which one might argue, is a mechanism of
       | adaptation, and thus a result of evolution. An intelligent life
       | might have developed other ways of coping with change, and not
       | necessarily through a neuroplastic brain, but for example,
       | through an instant rewiring of the brain that doesn't require any
       | practice.
       | 
       | The same can be said for justice, even though it might seem as a
       | social construct, it's still rooted in our biology (emotions are
       | still "physical" reactions in our body) and so an intelligent
       | life might have developed a different biological system different
       | than that of emotions.
        
         | notshift wrote:
         | > for example, through an instant rewiring of the brain that
         | doesn't require any practice.
         | 
         | You might have an alien species that can copy the brain state
         | of someone who already knows a task, or one that can gain
         | skills extremely quickly through practice, but I don't think
         | practice is going away. The fact that neural networks have been
         | the only way we've been able to solve a lot of problems, which
         | approximate the way that the human brain learns, is pretty
         | strong evidence of this. You start out with some weights, you
         | measure loss, you adjust weights, and then you try again.
         | 
         | Justice as an emotion might go away or exist in a different
         | form, but the underlying reason why humans have a sense of
         | justice is evolutionary psychology / game theory. Probably any
         | life form which is shaped by evolutionary forces would have
         | some similar instinct. (Certainly not all possible intelligent
         | life forms though, I'd agree.)
        
           | asdff wrote:
           | > The fact that neural networks have been the only way we've
           | been able to solve a lot of problems, which approximate the
           | way that the human brain learns, is pretty strong evidence of
           | this.
           | 
           | Chances are a lot of machine learning implementations can be
           | replaced with just "boring" statistical models and achieve
           | more power.
           | 
           | OTOH plenty of creatures don't need to learn. Does a mosquito
           | need to learn? No, it spawns thousands of offspring and
           | doesn't live very long. The high spawn rate means you have a
           | wide variety of natural mutations in your offspring, meaning
           | one or a few of them are likely to have higher fitness in a
           | given niche. It doesn't matter if most die if a few go on to
           | survive. This is the strategy many organisms use to dominate
           | the world in far greater numbers than our own species.
        
             | notshift wrote:
             | I sure hope we don't have mass-reproducing space mosquitos
             | in our future.
        
               | asdff wrote:
               | It's OK, space has too much radiation for things to
               | migrate off world unshielded. Except if you are a
               | tardigrade though, but the reasons for them being like
               | that are due to the types of niches they occupy on earth.
               | Mosquitos on earth that have some sort of space proof
               | shielding in their exoskeleton would probably be quickly
               | outcompeted by those more fit mosquitos that don't have
               | to invest resources into this space proof exoskeleton.
        
       | incomingpain wrote:
       | I wrote a scifi book in which I wrote 'heaven' as being an alien
       | construct. Somewhere in the universe a tremendously
       | technologically advanced civilization constructed a device which
       | simulates 'heaven' for all people in the universe. Through
       | 'enlightenment' the discoverer is able to bring knowledge of
       | 'heaven' back to their people but in our history how could a
       | figure like Buddha or Jesus post-enlightenment explain aliens and
       | advanced technology. So you end up producing a story at a level
       | of your current day scientific understanding.
       | 
       | Fundamentally your message to humanity post-enlightenment would
       | be the rules on how to get to heaven. Which many world-religions
       | classes go into depth. There are fundamental rules that benefit
       | everyone to follow that wouldn't really be inherently human to
       | follow.
       | 
       | >We'd probably share Occam's razor. There doesn't seem anything
       | specifically human about any of these ideas.
       | 
       | Aliens will also have developed the piano and chess. They are
       | inherent things to discover eventually.
       | 
       | Fundmantally a great way to analyze what the rules are would be
       | impossible to list. Just look at the list of crimes in countries
       | which are so large lawyers dont even know them all. So you need a
       | system that's much more simply. Isn't that system 'karma'.
        
         | bmitc wrote:
         | > Aliens will also have developed the piano and chess. They are
         | inherent things to discover eventually.
         | 
         | How could that claim be true? We have highly intelligent beings
         | (i.e., "aliens") right here on Earth that have not developed
         | these things.
         | 
         | These discussions on aliens are often off the rails from the
         | start because they implicitly begin with the assumption that
         | humans are the only intelligent beings on Earth.
        
           | incomingpain wrote:
           | >How could that claim be true? We have highly intelligent
           | beings (i.e., "aliens") right here on Earth that have not
           | developed these things.
           | 
           | Are you using the 'illegal immigration' definition of alien?
           | 
           | >These discussions on aliens are often off the rails from the
           | start because they implicitly begin with the assumption that
           | humans are the only intelligent beings on Earth.
           | 
           | Do please elaborate because I don't share this opinion. Do
           | you believe aliens live amongst us?
        
             | bmitc wrote:
             | What is an alien other than a biological being from another
             | planet? We have biological beings on Earth that share DNA
             | with us but possess wildly different intelligences and
             | cognitive systems. Is it a stretch to use these as examples
             | that aliens may share little in common with us?
        
               | incomingpain wrote:
               | >What is an alien other than a biological being from
               | another planet?
               | 
               | Alright, agreed. Which as far as I know we have no known
               | aliens ever discovered.
               | 
               | >We have biological beings on Earth that share DNA with
               | us but possess wildly different intelligences and
               | cognitive systems. Is it a stretch to use these as
               | examples that aliens may share little in common with us?
               | 
               | You're backpedaling pretty hard. You said there are
               | 'highly intelligent beings on earth' besides us. I know
               | of no known examples that fit your claim. Happy to
               | listen.
        
               | bmitc wrote:
               | It's not backpedaling. Both things are true. There are
               | wildly different "intelligences". Plants, for example. As
               | for highly intelligent, orcas are an example.
               | 
               | And all this relies on some definition of intelligence,
               | which I don't think we even have a good one for.
        
       | miki123211 wrote:
       | It's also worth thinking about the exact opposite of this, what
       | truths are we least likely to share with aliens?
       | 
       | The beauty and importance of art and culture comes to mind, and
       | so does humor and jokes. Try explaining, in scientific terms,
       | what makes a joke funny, and the task turns out to be far harder
       | than expected.
        
       | 0898 wrote:
       | > If there were intelligent beings elsewhere in the universe,
       | they'd share certain truths in common with us. For example, I
       | think we'd share the principle that a controlled experiment
       | testing some hypothesis entitles us to have proportionally
       | increased belief in it.
       | 
       | I was thinking more "triangular sandwiches taste better than
       | square ones", but you do you!
        
       | BiteCode_dev wrote:
       | Just because we use a model of physics to describe our universe
       | doesn't mean aliens would use the same model.
        
       | songeater wrote:
       | I think this discussion of convergent evolution is pretty
       | interesting in context [0]. Namely, "intelligence" arises from
       | natural-selection (ie from some non-intelligent predecessor that
       | developed incrementally to better fit its environment)... and the
       | process of natural-selection would necessarily lead to various
       | commonalities between intelligent creatures that came to be
       | independently.
       | 
       | PG's essay seems to (implicitly, not explicitly) compare between
       | technologically-sophisticated intelligence - ie not between
       | octopuses and humans, but between species that could at least
       | communicate through inter-stellar distances, if not traverse them
       | directly. If so, convergent evolution would have imposed even
       | more onerous similarities between such species: to develop a
       | radio-transmitter, intelligent creatures would also likely to
       | have been very socially developed, or how else would they have
       | been able to transform the resources around them to build a
       | transmitter?
       | 
       | Therefore it is the physical world in which we live that most
       | likely leads us to conceive "math" similarly... and even
       | "justice." [1]
       | 
       | [0] https://www.quantamagazine.org/arik-kershenbaum-on-why-
       | alien...
       | 
       | [1] tit-for-tat being one of the best strategies to solve an
       | infinitely-recurring prisoner's dilemma
        
       | chatterhead wrote:
       | 1 + 1 = 3 (Because some aliens understand what state changes
       | occur in the future and the equation is specific to the
       | singularity of something not the progressive time.)
        
       | zelienople wrote:
       | That is a work of stunning arrogance and foolishness.
       | 
       | Math is a game we play in our heads that represents a
       | fictionalized ideal version of reality.
       | 
       | An alien intelligence might have realized that two plus two never
       | equals four not because the underlying logic is wrong, but
       | because two does not exist in reality.
       | 
       | The idea that the little game of math we play represents an
       | immutable and universal truth is typical of the overwhelming
       | anthropocentrism of our kind.
        
         | dan_mctree wrote:
         | This is a comment of stunning ignorance.
         | 
         | Just because some alien societies will not mimic our rules of
         | addition, we do know for certain it is possible that other
         | societies can build abstract concepts that are isomorphic to
         | those we have. And many of these concepts, such as addition,
         | are very useful.
         | 
         | Does this guarantee that aliens come up with the same stuff?
         | No. Does it guarantee that if they did, they would these
         | concepts to the same esteem? No. Is there an element of 'truth'
         | here that can be replicated by others? Absolutely
        
         | [deleted]
        
       | hlwaters wrote:
       | Timely article to prop up OpenAI.
        
       | rfreytag wrote:
       | PBS SpaceTime notes the fine structure constant (~1/137) is
       | dimensionless and ubiquitous in physics. As a result,
       | transmitting that ratio would be a good and clear indication we
       | are intelligent enough to have at least that much physics:
       | https://www.youtube.com/watch?v=RCSSgxV9qNw&t=564s
       | 
       | This might be better than mathematical constructs which
       | conceivably do not require technology, "just" thought to
       | discover.
        
         | nine_k wrote:
         | Another good signal could be transmission at the frequently of
         | free hydrogen times pi, or times e, or both.
         | 
         | The problem here is not even in the need to spend colossal
         | amounts of energy to signal one's presence. The question is
         | whether such advertising is a good idea if the civilization
         | strives to survive; very likely it is not.
        
         | HardlyCurious wrote:
         | Well, this was held up as a universal truth because it doesn't
         | depend on units, and so those don't need to be defined... But
         | we still can't just show them the image '1/137' and have them
         | understand the characters and operations. Our presentation
         | isn't universal.
         | 
         | And I would argue that showing the length of distance we use
         | isn't fundamentally different than explaining which syntax we
         | use for division.
        
           | Dylan16807 wrote:
           | > But we still can't just show them the image '1/137'
           | 
           | You can dump energy into two frequencies. You're
           | overcomplicating it.
           | 
           | The video suggests binary which is also pretty simple.
        
         | koyanisqatsi wrote:
         | But this constant is an artifact of our symbolic encoding of
         | universal properties. What reason is there to believe that
         | alien civilizations would encode physics exactly as we do and
         | would recover the same constant?
        
           | jondeval wrote:
           | > What reason is there to believe that alien civilizations
           | would encode physics exactly as we do and would recover the
           | same constant?
           | 
           | There is no reason to believe the symbolic encoding would be
           | the same. For example, if they evolved with 8 fingers instead
           | of 10 they could be driven to encode their symbols in a base
           | 8 system.
           | 
           | I think the point of the OP sharing the PBS spacetime video
           | in this context is that we have reason to believe that the
           | fine structure constant is truly constant throughout the
           | universe. So if the aliens have the capability of measuring
           | and reasoning about electron orbitals and their binding
           | properties with nucleus, then there will likely be
           | significant overlap between our mutual concepts of 'fine-
           | structured-constantness'. Just made that word up. :-)
           | 
           | This would be independent of encoding scheme and independent
           | of practical communication issues.
        
             | koyanisqatsi wrote:
             | Right but I can ask the same/similar question. Why would
             | they have particle physics like we do? There are several
             | degrees of freedom in existing mathematical theories of
             | physics and I don't think there is a good reason to expect
             | that electrons would be re-discovered in another encoding
             | of physics by an alien civilization. The entirety of
             | particle physics is contingent on a bunch of mathematical
             | abstractions (e.g. group theory) so then the argument
             | becomes that these abstractions are not contingent
             | discoveries which then fixes the entire mathematical
             | edifice to be the same across all alien life and
             | civilizations.
             | 
             | It's an interesting thought exercise but I don't think
             | there is any reason to expect mathematics to be the same
             | across all potential life in the universe. Human
             | mathematics is adapted to human evolutionary contingencies
             | and the same would be true for alien mathematics, physics,
             | and engineering. By definition of "alien" their mathematics
             | would be alien to us and even if there were commonalities
             | they would be very hard to uncover.
        
               | jondeval wrote:
               | I understand your point. And I completely agree that many
               | of our chosen mathematical structures, and even physical
               | models are contingent and likely accidents of history and
               | sensory constraints.
               | 
               | I'm comfortable living with the tension between these two
               | propositions: (1) The manifestation of laws of physics
               | are real, measurable, spread across the galaxies, and
               | essentially outside of our subjective experience. For
               | example, I do believe that gravity and electrons are real
               | ... not just real for me. (2) The way in which we
               | interpret these physical realities is somewhat
               | conditioned by the constraints and experience of being
               | messy human animals.
        
       | tiffanyh wrote:
       | PG use of image maps for site navigation always bring back 1990s
       | Web "1.0" nostalgia to me.
        
       | rrwo wrote:
       | That's a rather naive view of truth. For intuitionistic
       | mathematics (which is very important for theoretical computer
       | science), truth is a mental construct of a proof in a language,
       | and only shared by communicating that construct to other minds.
       | 
       | The question is whether we can communicate our mathematics to
       | non-humans, whose senses may be radically different from our own.
       | 
       | And likewise, would we be able to understand a non-human proof?
        
         | naasking wrote:
         | > The question is whether we can communicate our mathematics to
         | non-humans, whose senses may be radically different from our
         | own.
         | 
         | I'm not sure why people find this so relevant. Regardless of
         | the sense, there must be enough discernible structure to detect
         | whether 0 of something is there, whether 1 of something is
         | there, or whether there are many more than 1.
         | 
         | Human sense of smell might top out at differentiating maybe 4
         | or 5 different things, dogs can probably sense a lot more, but
         | either way it lets us set up basic counting, and that's
         | generally all you need for most of our math.
        
           | rrwo wrote:
           | How can you communicate the axioms of Peano arithmetic to
           | intelligent extra-terrestrials, in a way that they would
           | recognize it?
        
             | Koshkin wrote:
             | Well, first we could send a series of integers, each being
             | a sequence of pulses, to convey the fact that we are
             | talking about integers. Then express each axiom by a series
             | of concrete examples. And repeat. Intelligent species
             | should be good at recognizing patterns.
        
               | PuppyTailWags wrote:
               | Why would we identify a sequence of pulses as integers
               | if, for example, the passage of time is perceived
               | differently by aliens? Or if mathematics within alien
               | life is based on atomic units of group like set logic,
               | and so the sequence of pulses itself is seen as "1".
        
             | authpor wrote:
             | why would you do that? maybe what you really want is to
             | show them that you can count too?
             | 
             | peano arithmetic (an axiomatiazation of counting) isn't how
             | we count. It is how we make other things count for us.
        
         | jondeval wrote:
         | > That's a rather naive view of truth.
         | 
         | I'm a puzzled by the confidence here. I would assume pg is at
         | least minimally familiar with some of the key philosophical
         | themes and schools of thought around this topic.
         | 
         | > For intuitionistic mathematics ... truth is a mental
         | construct of a proof in a language, and only shared by
         | communicating that construct to other minds.
         | 
         | Even assuming you are fully and accurately representing the
         | intuitionist view, you must be aware that there are competing
         | schools of thought with strong pedigrees, like mathematical
         | platonism, that are grounded in a more realist view of
         | mathematical objects.
         | 
         | PG didn't go so far as to stake out that position here in the
         | essay, but his thought experiment leverages a view of
         | mathematical truth that hues closer to this (platonist) camp.
         | 
         | > The question is whether we can communicate our mathematics to
         | non-humans ...
         | 
         | That is an interesting question, but pg did not ask that
         | question in the essay, and its answer doesn't seem relevant to
         | the point he was trying to make.
        
           | n4r9 wrote:
           | It's Graham's confidence that I (and I think OP) find
           | puzzling. He doesn't say "According to Platonist ideas...",
           | or "In my opinion...". Just "mathematical truths are true by
           | definition". There's a brashness and lack of nuance there
           | that makes me want to stop reading.
        
             | jondeval wrote:
             | Some of that is a stylistic judgement call on the part of
             | pg. He wants to move quickly to his central idea, not enter
             | into a nuanced discussion of the philosophy of mathematics.
             | 
             | I think pg is educated, at least the broad outline, of the
             | age-old controversies in this topic and I'm grateful as a
             | reader that he spares me the details and assumes some
             | preliminary context.
        
               | svnt wrote:
               | He's clearly not, is the thing, unless he has acquired
               | that education in the last year or two.
               | 
               | His style of pop philosophy is useful in startups because
               | it does not require context. It is ungrounded in actual
               | philosophy, and would struggle to find an audience
               | outside of this group.
        
               | n4r9 wrote:
               | I appreciate what you're saying; it's only the first
               | paragraph and he wants to nail some initial things down
               | that _he_ sees as straightforward context or examples.
               | 
               | But it is not straightforward to me. Or, in my
               | impression, most philosophers. I'm reluctant to agree
               | that aliens will assign any importance or even
               | _understand_ concepts like geometry or calculus. So to
               | me, it is not preliminary context but it is a critical
               | part of the discussion.
        
           | svnt wrote:
           | > I would assume pg is at least minimally familiar with some
           | of the key philosophical themes and schools of thought around
           | this topic.
           | 
           | But even a brief foray into discussions by actual
           | philosophers will show that to not be true. What Paul Graham
           | is doing is providing small subcultural insights tailored to
           | an audience with a passing interest in philosophy.
        
           | kybernetikos wrote:
           | > his thought experiment leverages a view of mathematical
           | truth that hues closer to this (platonist) camp
           | 
           | I think the word in that idiom is 'hews', which means to
           | adhere strictly to a standard, probably from the sense of the
           | word meaning to strike or cut or beat - often used to talk
           | about cutting a tree into shape.
        
       | deugtniet wrote:
       | I guess I disagree that math and physics are universal truths.
       | 
       | For maths, I would say 1+1=2 is a pretty universal truth
       | (although it takes a while to get there in the principa
       | mathematica), but didn't we just invent complex numbers because
       | they are useful?
       | 
       | Same goes for physics, the speed of light is the same everywhere,
       | but how quantum mechanics work is still subject to many
       | discussions.
       | 
       | Love to hear some thoughts on this, as claiming a whole field as
       | universal truth is something I'm a little uncomfortable with.
        
         | m-watson wrote:
         | I think the argument is mostly that there are universal truths
         | than math and physics describe not that our current level of
         | math and physics are universal truths. So finding an example
         | that we do not understand fully doesn't mean that there aren't
         | truths in other aspects of math and physics. As for things like
         | complex numbers there is an underlying debate that has been
         | around in philosophy of science and math that distinguishes
         | between discovery and invention. Our representation may have
         | been invented but we discovered some thing that works
         | historically and has predictive power.
        
         | koyanisqatsi wrote:
         | I think you have the right idea. Most human truths are
         | contingencies of our evolution and the evolution of life on
         | earth. It's very hard to extrapolate from this to universal and
         | alien truth.
        
         | simiones wrote:
         | > but didn't we just invent complex numbers because they are
         | useful?
         | 
         | Not any more than we invented natural numbers because they are
         | useful.
         | 
         | There are several ways to naturally derive complex numbers,
         | either from mathematics or from physics.
         | 
         | For one, complex numbers are probably the simplest possible
         | extension of the real numbers in which all real-valued
         | polynomials have roots (for example, x^2 + 1 doesn't have a
         | root if x has to be real). This is the same reason why the non-
         | transcendental irrational numbers were invented (such as
         | sqrt(2) ).
         | 
         | (Incidentally, the transcendental numbers (pi, e) are less
         | justified than the complex numbers from this point of view -
         | any polynomial of any rank whose coefficients are non-
         | transcendental real numbers has roots that are either real non-
         | transcendental numbers, or a complex number whose real and
         | imaginary parts are real non-transcendental numbers )
         | 
         | For a physical explanation, complex numbers are the best way we
         | know of describing wave mechanics (either classical or
         | quantum), and in general periodic phenomena and how they
         | compose.
        
         | Koshkin wrote:
         | > _because they are useful?_
         | 
         | But the usefulness is objective, that is, it is not an
         | arbitrary product of the mind but rather it is dictated by the
         | logic of things once the goal is set, so invention (or
         | discovery) of useful things is more or less unavoidable.
         | 
         | As to quantum mechanics, you are talking about the variety of
         | interpretations which from the practical standpoint are simply
         | different ways of looking at quantum behavior, which, in turn,
         | sometimes leads to different methods of calculation.
        
           | mistermann wrote:
           | > But the usefulness is objective, that is, it is not an
           | arbitrary product of the mind but rather it is dictated by
           | the logic of things once the goal is set, so invention (or
           | discovery) of useful things is more or less unavoidable.
           | 
           | It certainly seems like it is objective, and often it
           | probably is, but in a more general sense, _any_ instance of
           | "x 'is' y" _very often_ turns out to be subjective very
           | quickly. Even with  "is useful", things get complicated if
           | one explicitly injects the dimension of Time into the
           | question (it is there in the first place implicitly, but is
           | easily overlooked).
        
       | deltasevennine wrote:
       | >For example, I think we'd share the principle that a controlled
       | experiment testing some hypothesis entitles us to have
       | proportionally increased belief in it.
       | 
       | This isn't even a shared principle among humans. How many
       | experiments does it take for you to have 50% belief in a
       | hypothesis?. What is the number of experiments? It's literally
       | impossible to answer. It's not even clear what "belief" is or
       | what 50% means.
       | 
       | This ambiguity of the word isn't even the main problem. If I run
       | the same experiment with perfect observational tools 10 billion
       | times and it verifies my hypothesis. Does that raise my belief
       | further? What if on the 10 billionth and first time the test
       | shows a negative result? That literally invalidates the
       | hypothesis. Keep in mind we are assuming my observational tools
       | are perfect. Does this make my belief shoot down to zero?
       | 
       | If this possibility of a negative result remains true after any
       | number of tests then what does it say about belief? Why should I
       | believe anything if a single negative experiment can invalidate
       | 10 billion positive experiments (assuming perfect observational
       | tools of course)?
       | 
       | Let me bring a more concrete example. I hypothesize all zebras
       | have stripes. I observe zebras 10 billion times. They all confirm
       | my hypothesis. Then on the 10 billionth and first time I see a
       | zebra with spots. My hypothesis is wrong. This can happen any
       | time.
       | 
       | Anyway to bring it back to his point. Don't assume shared
       | axiomatic truths. PG already assumed that it's shared among
       | humans. He's wrong. The nature of science and the scientific
       | method is not universally shared or even fully understood among
       | humans. He's likely also wrong about aliens as he is about
       | humans.
        
         | simiones wrote:
         | > I hypothesize all zebras have stripes. I observe zebras 10
         | billion times. They all confirm my hypothesis. Then on the 10
         | billionth and first time I see a zebra with spots. My
         | hypothesis is wrong. This can happen any time.
         | 
         | Even if the original belief turns out to be wrong, you only
         | have to slightly weaken it and it will remain true: "the vast
         | majority of zebras have stripes". Even if you discover a new
         | continent full of hordes of uniformly-colored zebras, the true
         | hypothesis becomes "the vast majority of zebras in my original
         | continent are striped".
         | 
         | Essentially every observation brings proof for a whole family
         | of hypotheses. We normally only talk about the strongest of
         | these hypotheses, but that doesn't meant that a negative
         | example rules out the entire family.
         | 
         | For example, even if we didn't find a deductive proof the
         | Fermat's last theorem was wrong even after all of the empirical
         | proof that it probably wasn't, a weaker version would have
         | still remained true - the one validated by that empirical
         | proof.
        
           | deltasevennine wrote:
           | >Even if the original belief turns out to be wrong, you only
           | have to slightly weaken it and it will remain true: "the vast
           | majority of zebras have stripes". Even if you discover a new
           | continent full of hordes of uniformly-colored zebras, the
           | true hypothesis becomes "the vast majority of zebras in my
           | original continent are striped".
           | 
           | The hypothesis does not remain true. It was never proven to
           | be true and the new hypothesis is still not proven to be
           | true. Science cannot prove anything to be true. I can find a
           | cave full of of spotted zebras, and you have to further
           | weaken your hypothesis of continents, I can then find that
           | the stripes were actually microscopic spots and my perfect
           | observation tool, though never wrong has limited resolution.
           | Ad infinitum. Nobody ever considers your made up philosophy
           | because it's changing the rules of the game. It's making a
           | statement then adjusting your statement once it's proven
           | wrong... people look down on that kind of thing.
           | 
           | What I'm writing here isn't something I pulled out of my ass.
           | It's well known that in science, the scientific method, and
           | reality itself, nothing can be proven. Proof is the domain of
           | math and logic, not science. In science, things can only be
           | falsified. To quote Einstein:
           | 
           | "No amount of experimentation can ever prove me right; a
           | single experiment can prove me wrong."
           | 
           | Einstein obviously isn't saying stuff like a single
           | experiment causes me to adjust my hypothesis and divide split
           | it into two different ones because it's kind of inconsistent.
           | 
           | There are people who truly understand science, but most of
           | the population doesn't (including PG). I think what's going
           | on with you is you're in the later camp, you've long held the
           | incorrect belief that science can prove things and this long
           | held ideology is coming into contact with the actual logic of
           | the situation and your adjusting your belief to maintain a
           | biased ideology.
           | 
           | Do you look up to PG? Bias can be corrected when an authority
           | confirms the opposite. I quoted Einstein here. One of the
           | ultimate authorities on science, a person who overturned the
           | hypothesis about Newtonian physics being a model for motion.
           | A single experiment proved it wrong and now Newtonian physics
           | is simply an approximation that is ultimately wrong.
           | Hopefully that will clear things up, if not... then you must
           | be an Alien far more strange then what PG is describing.
        
             | simiones wrote:
             | Please don't act condescending. The problem of induction is
             | well-known, and is closely related to what you are
             | discussing here. I agree that science can't literally prove
             | any hypothesis is true in the same sense that
             | mathematics/logic can; but we also can't jump from here to
             | considering inductive reasoning an entirely useless tool in
             | the search for truth.
             | 
             | That is the point that I am trying to make: experimentation
             | can bring proof to strengthen a hypothesis. Even if a later
             | experiment invalidates a hypothesis, all of the previous
             | experiments' results don't disappear, and any new
             | hypothesis we formulate still needs to be coherent with
             | them to have any value: we have actually learned something
             | important from our thousand experiments, even if our 1001st
             | showed that the hypothesis we had in mind was false.
             | 
             | Also, this is not unique to science. The same phenomenon
             | can happen in mathematics or logic for theorems that have
             | been neither proven nor disproven yet. We can perform
             | numerical experiments to test a numerical theorem, and gain
             | some amount of confidence in that theorem even if we
             | haven't proven it to be true. We can often establish lower
             | or upper bounds in the course of this experimentation,
             | where we find that the theorem is True at least for some
             | limited subset of all numbers - and this remains True and
             | useful even if it later turns out that there exist counter-
             | examples.
             | 
             | This observation is also very important for understanding
             | why the history of natural philosophy is essentially one of
             | continuous progress, with very little backtracking: even if
             | induction is not good enough to know that we have a
             | perfectly complete and consistent theory (and we will never
             | have one), we always have something salvageable from all of
             | the experimentation done so far. Even geocentric models
             | with their epicycles were actually working models, which
             | predicted the positions of planets in the next 1000 years
             | to quite good accuracy, even if they were clearly wrong in
             | the end.
        
               | deltasevennine wrote:
               | >Please don't act condescending.
               | 
               | Please don't accuse me of acting condescending. It's very
               | offensive and hurts my feelings when I'm accused of
               | something I'm not doing.
               | 
               | I am criticizing you, but I am not being condescending.
               | There is a huge difference.
               | 
               | Perhaps the alien thing was bad. I apologize for that.
               | The intent was a joke and was not condescension.
               | 
               | >That is the point that I am trying to make:
               | experimentation can bring proof to strengthen a
               | hypothesis. Even if a later experiment invalidates a
               | hypothesis, all of the previous experiments' results
               | don't disappear, and any new hypothesis we formulate
               | still needs to be coherent with them to have any value:
               | we have actually learned something important from our
               | thousand experiments, even if our 1001st showed that the
               | hypothesis we had in mind was false.
               | 
               | Yes but this was not part of the discussion. We're
               | talking about science as a principle. Not what we have
               | learned from the process of science.
               | 
               | >This observation is also very important for
               | understanding why the history of natural philosophy is
               | essentially one of continuous progress, with very little
               | backtracking: even if induction is not good enough to
               | know that we have a perfectly complete and consistent
               | theory (and we will never have one), we always have
               | something salvageable from all of the experimentation
               | done so far. Even geocentric models with their epicycles
               | were actually working models, which predicted the
               | positions of planets in the next 1000 years to quite good
               | accuracy, even if they were clearly wrong in the end.
               | 
               | Important or not, we diverged from the point. Whether
               | Science is a valid principle shared by humans and aliens
               | is the point. My point is, PG's view isn't even shared
               | with humans, why should he assume it's going to be shared
               | with aliens?
               | 
               | You're talking about the importance of science. The value
               | of science. That's off topic.
        
               | stale2002 wrote:
               | > Yes
               | 
               | So then you agree that "experimentation can bring proof
               | to strengthen a hypothesis"
               | 
               | > Whether Science is a valid principle shared by humans
               | and aliens
               | 
               | Well, the experimentation part, that can bring proof to
               | strength a hypothesis, is something that you agreed to.
               | 
               | So that part would be shared, that you agreed to.
        
               | deltasevennine wrote:
               | no. Don't agree. Experimentation can't prove anything. It
               | also doesn't strengthen anything. Proof is not a
               | strengthening of something. If you prove something it
               | means it's true.
               | 
               | >Well, the experimentation part, that can bring proof to
               | strength a hypothesis, is something that you agreed to.
               | >So that part would be shared, that you agreed to.
               | 
               | Never agreed. You misinterpreted. I agreed to this: "we
               | have actually learned something important from our
               | thousand experiments". You learned that for 1000
               | experiments you observed something. That's it.
        
               | stale2002 wrote:
               | > You learned that for 1000 experiments you observed
               | something
               | 
               | Ok great, so then you agree that this is a principle that
               | would be shared, which is the point.
        
         | naasking wrote:
         | > This isn't even a shared principle among humans. How many
         | experiments does it take for you to have 50% belief in a
         | hypothesis?. What is the number of experiments? It's literally
         | impossible to answer. It's not even clear what "belief" is or
         | what 50% means.
         | 
         | https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_induc...
        
           | deltasevennine wrote:
           | A bit of a complicated read. Not sure what you're trying to
           | say here and I don't even completely understand it. But
           | anything that gets into bayesians and frequentists ends in a
           | fundamental divide in humanity. Humans don't agree on which
           | interpretation is correct. Which is the point of everything I
           | wrote.
           | 
           | So why would aliens hold this "principle" the same if humans
           | don't even agree on it? PG is wrong. His own principles
           | upended not even by aliens, but by humanity, thus how
           | accurate can his assumptions about universal principles even
           | be? No that accurate imho.
        
             | naasking wrote:
             | > But anything that gets into bayesians and frequentists
             | ends in a fundamental divide in humanity. Humans don't
             | agree on which interpretation is correct.
             | 
             | There is no divide, there is the illusion of divide because
             | we didn't have a rigourous formal model of how to build
             | reliable knowledge and everyone focused on different but
             | relevant aspects.
             | 
             | Bayesian reasoning is the correct way if you have
             | justifiable priors, but we didn't have a way to calculate
             | the correct prior.
             | 
             | Solomonoff showed us how with his theory: Kolmogorov
             | complexity is a measure of parsimony, and this is how to
             | select priors in a formal, rigourous way.
             | 
             | Solomonoff induction is to knowledge what Turing machines
             | or the lambda calculus are to computation. Sure, aliens
             | might not discover Turing machines exactly, or the lambda
             | calculus exactly, but whatever they do build that's capable
             | of universal computation, we already know it must be
             | isomorphic to a Turing machine, because all constructions
             | capable of computation must be by necessity.
             | 
             | The frequentist/Bayesian divide is a separate issue about
             | how to interpret statistical data in useful ways, not
             | specifically about how we know what we know and what
             | confidence we should have in our knowledge, which is what
             | you were asking about.
        
               | deltasevennine wrote:
               | Interesting. Do you know of any popular science articles
               | or books that can describe what you're talking about?
               | Academic papers are fine too, just harder to parse.
        
       | jefftk wrote:
       | In addition to alien truth there are probably also alien games:
       | ones so simple for their level of depth and enjoyment that you
       | would expect them to be independently discovered. For example,
       | Hex [1] is reasonably deep and has been invented at least twice.
       | Go, with something like the Tromp-Taylor rules [2] might be as
       | well? Probably not Chess, though!
       | 
       | [1] https://en.wikipedia.org/wiki/Hex_(board_game)
       | 
       | [2] https://senseis.xmp.net/?TrompTaylorRules
        
       | verrp wrote:
       | I have long suspected that the aliens will recognize Go (the
       | game), but (obviously) not Chess (the other game).
       | 
       | I suspect they will even recognize Go's 19x19 board (b/c it has
       | properties other board sizes would not have).
       | 
       | But would they recognize 12 tones scales?
        
         | mostlylurks wrote:
         | > But would they recognize 12 tones scales?
         | 
         | Assuming they have musical instruments and don't have far more
         | digits (fingers or other dextrous appendages) than us, they
         | probably would, and even if they did have more digits, it'd
         | seem like a fairly obvious choice for a species with our
         | anatomy. Especially for equal temperament, but also for just
         | intonation, a 12-tone scale provides exceptionally good
         | approximations or numerous instances of the simplest possible
         | frequency ratios, so any creature that has to limit the number
         | of tones on their instruments for practical considerations will
         | have a high likelihood of stumbling on a 12-tone scale even
         | before developing an understanding of why it actually works so
         | well and/or find it a very compelling option given a more in-
         | depth analysis.
        
         | themodelplumber wrote:
         | > But would they recognize 12 tones scales?
         | 
         | Relatively? More likely. "Oh yeah, we get that. At a number of
         | levels which we call honktaves, incidentally."
         | 
         | Absolutely? As in, we have that set of frequencies bolted on to
         | our culture too? Seems less likely.
        
       | bmitc wrote:
       | > The truths of mathematics would be the same, because they're
       | true by definition. Ditto for the truths of physics
       | 
       | These are pretty strong statements for which there's no arguments
       | provided for but serve as assumptions for the rest of the
       | article. I don't think there's consensus among mathematicians,
       | philosophers, cognitive scientist, or biologists on this.
       | 
       | Mathematics is most definitely a human endeavor, and so we can't
       | really make claims about its existence in the universe
       | independent of humans. I think alien analogs to mathematics are
       | unlikely to match ours. If we are lucky, I think it could be the
       | case that the various structures could be similar, but the
       | likelihood the implementations resemble each other are slim. It's
       | even a stretch to assume the structures would relate. Even humans
       | do not fully agree on mathematics. There is no "one" mathematics
       | because mathematics is the human exploration of idealized objects
       | using a variety of human logical systems.
       | 
       | And then there's the possibility that our mathematics and overall
       | perception of reality is shaped by our biology in far deeper ways
       | than we imagine and currently understand.
        
         | naasking wrote:
         | > I think alien analogs to mathematics are unlikely to match
         | ours.
         | 
         | So aliens won't be able to count? They won't have a concept of
         | zero? They won't have a concept of 1=successor(0)? I find this
         | very, very hard to believe, and a lot of mathematics follows
         | from the structure of the natural numbers.
         | 
         | If you accept evolution by natural selection is a universal
         | law, then I think it naturally follows that ability to count
         | must evolve. After all, it's pretty important to know whether
         | there are 0, 1, or many predators/food/prey/enemies.
        
           | zhynn wrote:
           | What if aliens have no notion of discrete numbers, what if
           | everything is probabilistic analog math? What about an
           | organism that can see/focus/sense multiple things
           | simultaneously, and a single "thing" is a set. What about a
           | creature whose primary sensing organ is diffuse molecules
           | (smell/taste) instead of sight and use light (instead of meat
           | tentacles) to interact with matter. How might an organism
           | that touches matter with laser fingers and smells the
           | consequences count differently? I wouldn't have the first
           | idea, honestly.
           | 
           | There could be an entirely different paradigm to "counting"
           | and consequently to the fundamentals of maths.
           | 
           | The math that we invented is influenced by our biology and
           | capacity to sense our environment. Our brains and how those
           | brains work with our sense organs. This pattern is likely
           | universal (all life will have methods of sensing their
           | environment and interacting with it), but the methods might
           | be very different.
        
             | naasking wrote:
             | I'm sure you can imagine any kind of alien, but that
             | doesn't make your imagined alien logically coherent or
             | physically realizable and consistent with the theory of
             | evolution by natural selection. Do you agree that these are
             | real, physical constraints that any imagined alien species
             | must satisfy?
             | 
             | If not, then you have to explain how an alien species might
             | develop that is not subject to physical constraints and
             | evolution by natural selection.
             | 
             | If so, then you must agree that any alien must be able to
             | distinguish two scenarios, "I sense some food here" and "I
             | sense no food here". The basic binary distinction is
             | inescapable, and this is the foundation of true/false, 0
             | and 1, etc.
        
               | jarpadat wrote:
               | Consider an alien which subsists on photons, which is a
               | form of life that exists today. We know from heseinberg
               | that the sensing of this food "here" or "there" is
               | nonphysical. Presumably our creature's civilization would
               | require no heisenberg to discover what anyone can see
               | from their own photosensor.
               | 
               | Rather it is the concept of objects remaining in a single
               | place that would require some real mathematical
               | innovation to a creature with no experience of such an
               | idea. And so this distinction of entirely separate
               | logical states, far from being basic or inescapable, is
               | our very human invention. It is useful for creatures like
               | us, who perceive things in one place when they are not
               | really so, who do their computing with sand in a region
               | where it's bountiful, and who encode abstractions as
               | software because doing so in dedicated hardware is more
               | costly.
               | 
               | While it is certainly possible that all intelligent life
               | would have these constraints, there is no particular
               | reason to expect it. What we can expect is that humans
               | will expect others to be too much like ourselves; it's a
               | well-known cognitive defect in our species.
        
               | naasking wrote:
               | > Consider an alien which subsists on photons, which is a
               | form of life that exists today.
               | 
               | Plants don't just subsist on photons, there are many
               | other ingredients.
               | 
               | > We know from heseinberg that the sensing of this food
               | "here" or "there" is nonphysical.
               | 
               | I don't know what this means. How do you "non-physically"
               | sense photons?
               | 
               | > Rather it is the concept of objects remaining in a
               | single place that would require some real mathematical
               | innovation to a creature with no experience of such an
               | idea. And so this distinction of entirely separate
               | logical states, far from being basic or inescapable, is
               | our very human invention.
               | 
               | Assuming you're talking about some alien made of bosons
               | that aren't subject to the Pauli exclusion principle,
               | you'll note that bosons still interact with fermions in
               | which that principle does apply, so I don't think your
               | argument follows. I admit I don't really understand your
               | premises though so I have no idea what you really meant.
        
           | [deleted]
        
           | bena wrote:
           | Hacker News, the place where you will get told that we are
           | definitely going to invent spacecraft that will be able to
           | traverse the galaxy by solving the light speed issue, the
           | gravity issue, and the radiation issue (among others) but
           | that when we meet extraterrestrial lifeforms, they won't know
           | how to fucking count.
           | 
           | Sorry. That's the one. That's the one that broke me. Jeremy
           | Bearimy
        
             | bmitc wrote:
             | I don't believe we'll solve those issues anytime soon. But
             | for aliens counting, which I think is itself arguable, it
             | is not really under debate here. There's a vast gap between
             | counting and what mathematics is and encapsulates.
        
               | naasking wrote:
               | > But for aliens counting, which I think is itself
               | arguable
               | 
               | I honestly can't imagine how you can reach this
               | conclusion with any rigour. Do you agree that aliens will
               | need to consume some energy source to stay alive, which
               | we will call "food"? Do you agree that an understanding
               | of "there's no food in my environment", "there's some
               | food in my environment", and "there's lots of food in my
               | environment" would be selected for? I certainly hope so,
               | so at the very least they will understand the differences
               | between zero, non-zero and "many".
               | 
               | The only way this wouldn't happen is if the environment
               | is so rich in abundance that there is never any absence
               | of food. But this is impossible, because even single-
               | celled life by necessity will reproduce to consume all
               | available resources until it reaches an equilibrium
               | matching the rate of food production. So any intelligent
               | species _will necessarily_ evolve in an environment of
               | scarcity where zero and non-zero will be implicitly
               | understood.
               | 
               | Since _intelligent_ life will necessarily evolve in
               | scarcity, quantifying the amount of food is a useful
               | trait that would be selected for. This is why we 've now
               | proven that numerous "non-intelligent" animals can count,
               | including salamanders, chicks, mosquitofish, honeybees
               | and more. Intelligent life needs to understand where they
               | are, what they have and what they will need in the
               | future. This involves quantifying, aka counting, no way
               | to escape it.
               | 
               | > There's a vast gap between counting and what
               | mathematics is and encapsulates.
               | 
               | Yes, but you posited intelligent aliens that have their
               | own math. The conclusion that they would not understand
               | zero and repeated application of a construction over zero
               | to build non-zero quantities is impossible. It is the
               | very root of building a theoretical structure of any
               | kind, so if they have math of any kind, they have some
               | kind of counting system that will have an isomorphism to
               | ours.
        
               | bena wrote:
               | But you believe we will eventually.
               | 
               | And you believe that aliens that can count is something
               | that is "arguable".
               | 
               | You're the dot.
        
           | geomark wrote:
           | What if aliens did not perceive distinct objects, but rather
           | that everything observable is part of a greater whole? Would
           | they need counting numbers?
        
             | vecter wrote:
             | Counting numbers are such a basic foundational aspect of
             | all life that it's hard to imagine any "intelligent" being
             | not understanding the concepts of 1, 2, 3, etc.
        
             | naasking wrote:
             | You will have to explain how this property might be
             | selected for by evolution by natural selection before I can
             | even understand what you're suggesting.
        
           | bmitc wrote:
           | I think this is one argument that leads to the idea that the
           | structures could be relatable, _if_ a being could count. But
           | who knows? Our mathematics relies strongly on the logical and
           | axiomatic systems used. Things can get weird real quick with
           | small tweaks to these systems, so it doesn't seem like a
           | stretch that whatever mathematical analogs aliens may possess
           | may be wildly different. And there's a lot of developments
           | that our perception of reality is shaped by our biology in
           | ways we barely understand.
           | 
           | There are intelligent beings on Earth that don't seem to even
           | have analogs to human mathematics, at least that are apparent
           | to us. We can barely communicate with a small subset of
           | animals and plants on Earth. So I am just inherently
           | skeptical of claims that alien thinking will bear any
           | resemblance to human thinking.
        
             | naasking wrote:
             | > Our mathematics relies strongly on the logical and
             | axiomatic systems used.
             | 
             | Yes and no. You don't need more structure than 0 and 1 to
             | describe literally any form of information, and we're using
             | machines right now that use such an encoding. The idea that
             | any organism of sufficient complexity to have any kind of
             | math won't have any notion of 0 and 1 is very implausible.
             | 
             | That said, we certainly won't have the same syntactic
             | descriptions of most structures, but they will certainly be
             | relatable via isomorphisms.
             | 
             | > We can barely communicate with a small subset of animals
             | and plants on Earth. So I am just inherently skeptical that
             | claims that alien thinking will bear any resemblance to
             | human thinking.
             | 
             | But what does that have to do with math? Math isn't about
             | how thinking works, it's about how _structures_ are related
             | to each other. Structures and their relations don 't depend
             | on how one thinks. As above, how such structures are
             | _described /encoded_ probably depends on how one thinks
             | (aliens maybe won't use pencil and paper), but the
             | structure being described will be the same and so there
             | will necessarily exist some kind of isomorphism between
             | their "syntax" and ours, as syntax is a projection of the
             | structure.
             | 
             | Even plants have observable behaviour showing a distinction
             | between 0 and 1: they observably move towards the sun when
             | it's shining, and don't move when it's not. This isn't
             | knowledge of "math", but simply to demonstrate that
             | structure is everywhere and life simply must develop some
             | intrinsic understanding of it.
        
               | bmitc wrote:
               | What do you mean by "no"? Computers and information
               | theory most definitely rely on logical and axiomatic
               | systems, and particular ones at that.
               | 
               | Mathematics is also shaped by our thinking, which was my
               | point. I think it's a strong claim that aliens would even
               | have a "mathematics".
        
               | naasking wrote:
               | > What do you mean by "no"? Computers and information
               | theory most definitely rely on logical and axiomatic
               | systems, and particular ones at that.
               | 
               | I mean "no" to your implicit assertion that such basic
               | logical and axiomatic systems would not evolve in any
               | alien species capable of mathematics. Any such alien will
               | distinguish true and false, will have AND, OR and NOT
               | connectives, and will understand a form of implication
               | (it's inherent to causality). That's all you need to
               | build an understanding of most of our formal systems.
               | 
               | Yes the particular _expression_ of our information theory
               | and computer science depends on specific syntactic
               | choices which implies a surface dissimilarity, but the
               | _underlying structure_ will be the same even when
               | expressed in alien math.
               | 
               | For instance, an alien species might evolve in an
               | environment in which hyperbolic geometry is more natural
               | (say a species large enough that they can sense gravity
               | directly), and so they develop that geometry first. This
               | will have an isomorphism to our formal model of
               | hyperbolic geometry, and we can then explain Euclidean
               | geometry to them from there.
               | 
               | Edit:
               | 
               | > Mathematics is also shaped by our thinking, which was
               | my point.
               | 
               | Yes, but ultimately irrelevant. This drives the pace of
               | mathematical discovery, and what kinds of mathematical
               | formulae we develop or find most interesting, but this is
               | ultimately irrelevant to the _fundamentals_ which
               | underpin all math, which is what this really comes down
               | to.
        
           | Koshkin wrote:
           | Counting implies the ability to perceive the discrete, but
           | such discreteness may not be obvious to a shapeless creature
           | living in a liquid or a gaseous substance.
        
             | naasking wrote:
             | > Counting implies the ability to perceive the discrete,
             | but such discreteness may not be obvious to a shapeless
             | creature living in a liquid or a gaseous substance.
             | 
             | Is a shapeless creature even logically coherent?
             | Intelligence needed for math requires making distinctions,
             | and distinctions imply structure, and structure is
             | logically incompatible with true "shapelessness".
        
               | caleb-allen wrote:
               | > Is a shapeless creature even logically coherent?
               | 
               | Do you see how your argument is self-defeating?
               | 
               | According to logic that humans have developed, there is
               | such thing as a "shape". But Western philosophers have
               | pondered the innateness of a "shape" or an "object" from
               | very early on (Plato, through Leibniz, beyond).
               | 
               | "Shape" and "logic" are both human constructs
               | articulating "structure", another human construct.
               | 
               | A shapeless creature doesn't need to be "logically
               | coherent" to exhibit intelligence; logic, truth, and
               | structure are features that have emerged from human
               | intelligence. I wouldn't accept the argument that an
               | entity must exhibit the same features to qualify as
               | intelligent simply because humans have.
        
               | naasking wrote:
               | > According to logic that humans have developed, there is
               | such thing as a "shape"
               | 
               | There is such a thing as "structure", of which "shape" is
               | an instance, yes.
               | 
               | > "Shape" and "logic" are both human constructs
               | articulating "structure", another human construct.
               | 
               | Structure is not a human concept. We have particular
               | conceptions of structure, but structure exists, period. 0
               | != 1, they have different structure. This is
               | indisputable.
               | 
               | > A shapeless creature doesn't need to be "logically
               | coherent" to exhibit intelligence
               | 
               | If you think that reality does not have to be logically
               | coherent, or that that does not necessarily imply that
               | any creatures within reality have to have a logically
               | coherent description consistent with coherent natural
               | laws, then you're talking about a fantasy world of your
               | imagination and I don't think there's anything further to
               | discuss.
        
             | dagw wrote:
             | Most mathematical concepts are far from obvious to humans
             | (lots of people seem to struggle with the continuum
             | hypothesis for example), yet we can still work with them no
             | problem. So even if this shapeless intelligent creature
             | didn't start with discrete mathematics, they'd probably
             | invent it eventually.
        
             | criddell wrote:
             | If we can conceive of shapeless blobs living in a liquid
             | then surely they can conceive of being like us.
        
           | [deleted]
        
           | RxVd wrote:
           | >They won't have a concept of zero? They won't have a concept
           | of 1=successor(0)? I find this very, very hard to believe
           | 
           | Most of the world did mathematics for a long time without
           | zero (I hope you know that most number systems like Roman
           | didn't have zero till that eventually came from India, and we
           | evolved to have the current number system). Who knows what
           | direction different number systems might have taken if they
           | didn't come in contact with zero.
        
             | naasking wrote:
             | That's mostly irrelevant. The naturals starting from 1 are
             | isomorphic to the naturals starting at 0, which is why math
             | didn't need zero for so long.
        
               | Koshkin wrote:
               | Not if you take into account the special properties of 0.
               | (Generally speaking, a structure that admits a neutral
               | element with respect to addition is not isomorphic to one
               | that does not.)
        
               | naasking wrote:
               | You are correct, hence why I initially said it's mostly
               | irrelevant. I should have qualified the claim about
               | isomorphism as well. Still, quite a bit of math maps 1:1
               | without zero, so you can build a common understanding
               | even if they don't have zero.
               | 
               | I also don't think any alien species with which we will
               | communicate will _not_ understand zero. It just seems
               | impossible. Before philosophers came up with zero in
               | formal models, everyone intuitively understood the
               | concept. Every animals knows when they have no food vs.
               | when they have some food. Humans in ancient civilizations
               | also couldn 't just take something without paying.
        
               | RxVd wrote:
               | How is it irrelevant to this discussion? Parent proposed
               | that aliens will have zero by posing that question. I
               | gave an example from our own earth indicating intelligent
               | life can manage without zero.
        
               | naasking wrote:
               | > I gave an example from our own earth indicating
               | intelligent life can manage without zero.
               | 
               | Firstly, I disagree that humanity managed without zero.
               | Literally everyone had an intuitive understanding of
               | zero, they just didn't have it in their formal systems
               | that were being studied by philosophers. For instance,
               | try walking walking up to a vendor in Ancient Greece and
               | just taking something without paying.
               | 
               | Secondly, it's largely irrelevant because a lot of math
               | with zero can be mapped to math without zero with no loss
               | of information, so even if aliens used math without zero
               | there would be no trouble communicating as there would
               | still be an understandable formal correspondence.
        
         | [deleted]
        
         | LocalH wrote:
         | > Mathematics is most definitely a human endeavor, and so we
         | can't really make claims about its existence in the universe
         | independent of humans.
         | 
         | I think the idea is that math is not _created_ by humans, but
         | _documented_ by humans. Sure, the specific terminology may be
         | our invention, but there are basic mathematical properties that
         | seem (from our perspective) like they should be universal. For
         | example, whatever names a being has for the numbers 1 and 2, if
         | you take that 1 and add 1 more, you must get 2 (or the  "local
         | equivalent") as the result.
         | 
         | My guess is that, if what we call math isn't truly universal,
         | it's probably at least universally true within the realm of
         | physical life, and there's likely some massive causal chain
         | from the root properties of physics itself to the mathematical
         | properties that we call "math". When it comes to raw,
         | untethered "consciousness" (or whatever one would prefer to
         | call it), this may not hold true even in the slightest.
         | 
         | Yes, this comment steps slightly outside what could ever be
         | determined purely by the scientific method at the end. I feel
         | it is useful to do so in discussion, even when that cannot
         | directly enter into research. There are some truths to the
         | larger universe that I don't think the scientific method will
         | ever truly be able to uncover, just due to it's rigor. Some
         | aspects of the universe are just simply not falsifiable, but
         | they're still worthy of discussion with an open mind.
        
           | dTal wrote:
           | There is most certainly a massive causal chain between
           | physics and what humans call "math", because everything
           | humans do is determined by the laws of physics. The causal
           | chain leads through millions of years of evolution and tens
           | of thousands of years of culture. "The numbers 1 and 2" are a
           | complex web of analogies that have not actually been
           | demonstrated to "exist" outside of our minds, so evidence
           | that alien mathematicians would have words for them is much
           | weaker than our intuition would suggest. The question that
           | must be answered is "Given the constraint of precisely
           | modelling the world in a useful way, to what extent are all
           | rule-based systems isomorphic?"
           | 
           | Responding to your second point, I'm afraid I can't agree
           | with you that unfalsifiable propositions are "useful"
           | discussion contributions - _especially_ not with an  "open
           | mind". The only criterion on which such propositions can be
           | judged is whether they are fun to believe, and that is a very
           | dangerous muscle to flex.
        
         | carapace wrote:
         | I think mathematics could be defined as that part of philosophy
         | which is self-evident and universal. The value of Pi isn't
         | contingent?
         | 
         | Aliens may have different biochemistry, but it would be made
         | from the same chemical elements as ours. Likewise their formal
         | systems may be wildly different from ours, but they will still
         | be based on form (even _implication_ is ultimately a very
         | simple formal structure. Math doesn 't even require _causality_
         | as a prerequisite!)
         | 
         | Last but not least. many people (Kurt Godel among them) believe
         | that mathematical thought is actually perception of real
         | phenomenon in a "higher" plane of reality, which, if true,
         | seems to me to imply that alien mathematicians would be
         | perceiving the same phenomenon as humans, literally. In this
         | view, the "truths of mathematics" are literally the same
         | "objects" for them and for us.
        
         | dbsmith83 wrote:
         | > Mathematics is most definitely a human endeavor, and so we
         | can't really make claims about its existence in the universe
         | independent of humans.
         | 
         | Can you give an example of a mathematical concept which could
         | be different?
         | 
         | I believe that math is universal. We may use models to
         | understand it (infinity, perfect circles, etc.), but the
         | underlying mathematical truth is independent of humans. The
         | same is true for science. There are physical laws which we look
         | to discover. We use models in science to understand them, but
         | the models are not the same as the underlying truth
        
           | Koshkin wrote:
           | > _I believe that math is universal_
           | 
           | The only thing that is "universal" is Nature itself.
           | Mathematics, on the other hand, is a reflection of Nature _in
           | the human mind_ ; or, put differently, it's Nature's language
           | we humans are capable of understanding. It is therefore
           | conceivable that other creatures, far removed from us, could
           | "hear" a language that is just as far removed from ours.
        
           | rendall wrote:
           | > _I believe that math is universal. We may use models to
           | understand it (infinity, perfect circles, etc.), but the
           | underlying mathematical truth is independent of humans._
           | 
           | Humans (probably) perceive and understand a slim subset of
           | reality. We have an illusion of universalism of our
           | perceptions because we perceive nothing outside of them.
           | Also, we are the dominant species of the planet, which gives
           | us a reason to believe that our perceptions are "more
           | accurate" than, say, a bat's.
           | 
           | Personally, I don't think an alien's perceptions and
           | understanding would contradict our own, but if it's given
           | that our perceptions are a subset of reality, then an alien's
           | understanding might include elements of reality that we
           | literally cannot perceive or even understand.
           | 
           | > _Can you give an example of a mathematical concept which
           | could be different?_
           | 
           | By definition, no. But, hmm. What would number and a
           | mathematical system look like from creatures who thought in
           | logarithms? Or in primes? Or that had no concept of "number"?
           | What if even "greater than" and "less than" had no relevance
           | to an alien civilization?
        
             | DontchaKnowit wrote:
             | But see I don't think think what your saying contradicts
             | the above post. If our subset intersects with the alien
             | subset of perception, then we both will have a perception
             | of an underlying truth, and we could conceivably understand
             | the alien models and vice versa because they address the
             | same subject.
        
               | rendall wrote:
               | UP said that mathematics is universal. I believe it
               | models only our perception and understanding, which are
               | informed by our biological, evolutionary imperatives.
               | 
               | Reality itself is beyond us. All that we have at our
               | disposal are our perceptions, which is what we are
               | modeling when we "do math". Mathematics is not universal,
               | it's a language that we use to communicate what we
               | perceive to other humans.
               | 
               | It's speculative, whether an alien species, with a
               | perceptual and cognitive system evolved entirely
               | elsewhere under other pressures, would have an
               | understanding that intersects with our subset of reality.
               | I personally think it's unlikely. What that would mean is
               | that we wouldn't be able to communicate, never mind trade
               | technology and mathematical ideas.
        
               | dbsmith83 wrote:
               | > It's speculative, whether an alien species, with a
               | perceptual and cognitive system evolved entirely
               | elsewhere under other pressures, would have an
               | understanding that intersects with our subset of reality.
               | I personally think it's unlikely. What that would mean is
               | that we wouldn't be able to communicate, never mind trade
               | technology and mathematical ideas.
               | 
               | I mean, maybe, but this is conveniently unprovable, much
               | like the flying spaghetti monster, since you are saying
               | we could not communicate because our slices of reality
               | don't intersect. I disagree and think that most likely we
               | would live in a reality that was largely the same, but I
               | guess we'll never know!
        
             | dagw wrote:
             | All of this is arguments for why our understanding of
             | science and the nature of the universe might differ. It can
             | also explain how our mathematics might evolve very
             | differently and we will have made different mathematical
             | discoveries and do math in very different ways (all of
             | which I agree are very likely). However it doesn't explain
             | how an alien race will look at one of our mathematical
             | proofs that we have proven True and be able to prove that
             | it is False.
        
               | rendall wrote:
               | > _However it doesn 't explain how an alien race will
               | look at one of our mathematical proofs that we have
               | proven True and be able to prove that it is False._
               | 
               | Where is this coming from? Is this relevant to what I
               | wrote?
        
               | dagw wrote:
               | If both their math and our math agree on what statements
               | are true and false then both our maths are functionally
               | the same.
        
         | pfortuny wrote:
         | I guess he was thinking of arithmetic.
         | 
         | In any case, any model which includes infinity (and Peano
         | arithmetic already does) is pure convention and unconsciously
         | assumes a lot of things.
         | 
         | Finitary induction may make sense as something "universal".
         | Further than that, we are making things up as we go (and I am a
         | professional mathematician). The fact that they work to solve
         | real problems does not make them more real.
        
         | pattt wrote:
         | Fully agreed, the way I'd approach this would be that the said
         | mathematical proofs about certain truths "by definition" rely
         | on human logic as the main building block and substrate. Logic
         | is a human basis of agreeing which seems necessary
         | evolutionary. Counting and separating observable objects turned
         | out to be quite necessary for survival as well. Hence this
         | statement seems to imply that aliens would need to have a
         | corresponding logic reasoning system and observational
         | abilities. If that was the case perhaps there would be a strong
         | inclination to believe that the isomorphic reasoning would be
         | deduced.
        
         | rendall wrote:
         | > _there's the possibility that our mathematics and overall
         | perception of reality is shaped by our biology in far deeper
         | ways than we imagine and currently understand._
         | 
         | Almost certainly true. We as evolved creatures do not perceive
         | objective reality, but only enough reality as to enable our
         | ancestors to survive our very niche environment (niche relative
         | to the entirety of the universe). Our science and mathematics
         | model only our perceptions of reality, and not reality itself.
         | 
         | It is folly to assume that an alien, evolved along an entirely
         | different set of initial conditions, would share our
         | perceptions of reality. Our mathematics, modeling as it does
         | our _perceptions_ , serves human needs and perceptions only.
        
         | slibhb wrote:
         | While it's true that there's no consensus on this topic, that
         | doesn't imply that people can't make claims one way or the
         | other. In fact, the claims that the essay makes (Platonism) are
         | very commonly made.
        
         | sovande wrote:
         | Somethings in mathematics are constant, both here and on alpha
         | centauri, like the circumference of a circle divide by its
         | diameter is P or the hypotenuse squared is the sum of each leg
         | squared in a right triangle etc.
        
           | lmkg wrote:
           | But neither of those facts are true in non-Euclidean
           | geometries like Spherical Geometry or Hyperbolic Geometry.
           | The jury is still out on whether the universe is flat or has
           | some sort of curvature. Meanwhile spherical geometry is
           | fundamentally useful because we live _on a sphere_ , not on a
           | plane, and it is more accurate at modeling the 2-D space that
           | we navigate in.
           | 
           | My point being, assumptions get baked-in to systems in
           | surprising ways. Even something seemingly-objective like
           | math. Especially when you're using it as the _basis for
           | communication_ , then what counts as "basic" or "fundamental"
           | or "standard" reflects a perspective, not a fundamental
           | truth.
           | 
           | It's likely their mathematical systems would eventually reach
           | the same conclusions as ours, but the prominence or
           | significance of fields or results (like circles and
           | triangles) might be radically different. Even though we view
           | those components as absolutely fundamental, it's possible an
           | equivalent system could be built from different primitives.
        
         | rewgs wrote:
         | > There is no "one" mathematics because mathematics is the
         | human exploration of idealized objects using a variety of human
         | logical systems.
         | 
         | But isn't the whole point to to do our best to bypass human-
         | centric systems of understanding, and arrive at the "core
         | truth" of the matter? Whether that's possible is another
         | matter, but even if it's not possible, surely it's something
         | that can be theoretically approached, and I would wager is
         | precisely what PG means by "one mathematics."
         | 
         | > And then there's the possibility that our mathematics and
         | overall perception of reality is shaped by our biology in far
         | deeper ways than we imagine and currently understand.
         | 
         | Yes, but also no. Consider some first principles:
         | 
         | -We have every reason to believe that any and all life would
         | not live forever, or if the life in question is "intelligent"
         | (a nebulous/human-centric term, for sure) would at the very
         | least conceive of other things not lasting forever (such as
         | stars, or even the universe itself [or, if you want to be
         | really generous, "this current iteration of the universe"]).
         | -Therefore we can reasonably assume that all "intelligent" life
         | in the universe would understand the concept of scarcity
         | (either via finite lifespans/time, food/energy sources, both,
         | or something else), non-infinity. I'd go so far as to say that
         | any life form that doesn't understand its own mortality or
         | other such limits should be not be considered "intelligent," at
         | least for the reasons of this discussion. -Therefore we can
         | reasonably assume that said intelligent life would somehow
         | conceptualize a binary state (you're either alive or you're
         | not, you either have access to an energy source or you don't,
         | etc), and consequently would somehow or another understand the
         | concept of "zero," "nothing," etc, as well as its opposite,
         | "something." And from there, would necessarily discern the
         | differences between two states of "somethings" (the state of
         | "something" that is "one" is different than the state of
         | "something" that is "two").
         | 
         | I know I'm using a lot of loaded terms here -- "reasonably,"
         | "assume," "discerning" -- but just like we look for life by
         | looking for the markers of life that we know were necessary for
         | Earth (carbon, water, etc), we can look for intelligence that
         | exhibits the properties that we understand it to have. We need
         | _some_ sort of frame of reference, after all, if we are to do
         | anything other than simply flail. If that frame of reference is
         | to be proven wrong, that 's wonderful, but until that's the
         | case, I don't think it's unreasonable to assume that the
         | universe's "primitives" would be perceived in any truly, truly
         | different way such that the species' interpretation would cause
         | humans to rethink our own understanding of the universe's
         | "primitives" from the ground up.
         | 
         | After all, conceiving a difference between hydrogen and helium
         | requires being able to tell the difference between one and two
         | (electrons, as well as separate elements themselves). And
         | considering we have every reason to believe that those make up
         | the majority of the mass in the universe, any "intelligent"
         | life (there's that human-centric term again) can be expected to
         | somehow conceptualize that difference, and thus, do something
         | like counting, and thus, approach the same primitives of
         | mathematics that we do. The approach might be different, but
         | _what_ they 're approaching -- the very fabric of reality,
         | hopefully as objectively as possible -- must be assumed to be
         | the same (again, that is, until we're given compelling evidence
         | to believe otherwise).
         | 
         | That said, I've never studied the philosophy of mathematics, so
         | I could be talking out of my ass here, this is just the
         | reasoning of a layman after all. If anyone reads this and goes
         | "no you're way off base," I'd love to hear it!
        
         | dagw wrote:
         | _I think alien analogs to mathematics are unlikely to match
         | ours._
         | 
         | Almost certainly not, but they're probably isomorphic. And
         | either way if we show them our axioms they will be able to
         | validate our mathematics and vice versa.
         | 
         | The truths of mathematics are of the form 'if A then B'. Even
         | if they don't start at A or even accept A as true, but will
         | should still get B if they assume A.
        
           | Koshkin wrote:
           | > _they 're probably isomorphic_
           | 
           | That's a strong statement. I'd probably talk about
           | homomorphism.
        
         | mr_mitm wrote:
         | > Even humans do not fully agree on mathematics. There is no
         | "one" mathematics because mathematics is the human exploration
         | of idealized objects using a variety of human logical systems.
         | 
         | Maybe not in its entirety, but I find it hard to imagine that
         | any civilization as advanced as ours (let's say a civilization
         | that manages to harness nuclear fission, just to set a
         | baseline) will not come up with concepts such as prime numbers,
         | real number, complex numbers, calculus, etc. If they do that,
         | they will inevitably find the same structures we found using
         | function theory. They will know about differential equations
         | and prove similar theorems about them as we did. And the
         | Pythagorean theorem is a universal truth that holds everywhere.
        
           | lmkg wrote:
           | > real number, complex numbers, calculus, etc
           | 
           | Some humans believe that the prominence of real numbers is a
           | historical accident. It seems quite plausible to me that a
           | human society, much less an alien one, would go down a
           | mathematical evolutionary path based on the constructable
           | numbers and the computable numbers.
           | 
           | Regardless of whether we eventually find the same structures,
           | there are things that we might consider basic which they find
           | esoteric and vice-versa.
           | 
           | Heaven forbid we encounter an alien civilization that
           | discovered an O(log n) algorithm for integer factorization
           | before they invented steam power.
        
             | bmitc wrote:
             | > Some humans believe that the prominence of real numbers
             | is a historical accident.
             | 
             | That is a great point. The continuum is contentious and
             | pretty highly debated philosophically.
             | 
             | I also encourage people interested in that to also learn
             | about smooth infinitesimal analysis. Just a small tweak in
             | the underlying logic and model yields unique mathematics
             | and questions established assumptions.
        
           | lostmsu wrote:
           | In that list prime numbers might not be a thing.
        
         | cloogshicer wrote:
         | Fully agreed.
         | 
         | These _beliefs_ you quoted from the article, which
         | unfortunately most people don 't even recognize as beliefs,
         | form the basis of the dominant religion of the western world
         | (scientism).
         | 
         | The worrying thing is that the majority of people who believe
         | in this religion don't even realize they are believers.
        
           | bmitc wrote:
           | If I am not mistaken, this is similar to what Feyerabend
           | seemed to be on about.
           | 
           | https://blogs.scientificamerican.com/cross-check/was-
           | philoso...
        
           | simonh wrote:
           | The thing that differentiates science from religion is
           | repeatability. With religion everyone has their own opinion,
           | people out of contact with each other come up with radically
           | different religious beliefs and there is no way to bridge
           | between those beliefs. If we forgot everything we know about
           | religion, in a thousand years we might rediscover religion
           | again but they'd be entirely different religions from what we
           | have now.
           | 
           | With science it doesn't matter who does a given experiment,
           | anyone else doing the same experiment will get the same
           | results. There's no scope for disagreement about verifiable
           | scientific facts. Just do the experiment and find out. If we
           | forgot everything we know about science, in a thousand years
           | if we rediscovered science, very quickly we'd rediscover all
           | the exact same facts about the world again.
        
           | gregmac wrote:
           | Science doesn't have "facts" or "truths". It is based on
           | falsifiability: for a theory or hypothesis to be considered
           | scientific it must be able to be tested and conceivably
           | proven false.
           | 
           | This is the key difference from religion, which has no such
           | "falsifiability" equivalent.
           | 
           | The closest thing to "beliefs" is probably an individual
           | following which of several competing theories is most likely
           | correct -- but there's always the underlying basis that any
           | of them might have evidence showing they're incorrect at any
           | time, and one's view should adjust as a result.
           | 
           | Often this comes in the form of deferring to other people or
           | a consensus view, which could be construed as "faith" but is
           | different: If you asked me how the universe exists, I'd say
           | the big bang theory is the best answer we have, but I don't
           | understand enough about the underlying science to explain
           | _why_ nor can my brain comprehend the reality of it. I have
           | no loyalty or allegiance to this view, though; I could be
           | swayed to another theory if the big bang is ever proven false
           | or if a better theory arises.
           | 
           | Further reading:
           | https://www.theatlantic.com/science/archive/2015/11/why-
           | scie...
        
         | tambourine_man wrote:
         | Yeah, lots of strong baseless assumptions in the first
         | paragraph made me stop reading.
        
         | p0pcult wrote:
         | I also take issue with the author's assumptions. Consider the
         | case of AIs trained to identify new variables in a system of
         | pendulums:
         | 
         | https://cosmosmagazine.com/technology/artificial-intelligenc...
         | 
         | Different truths that describe the same system.
        
         | agent008t wrote:
         | The statement that "the truths of mathematics would be the
         | same, because they are true by definition" is correct.
         | Mathematics exist independently of biology or perception of
         | reality. It is just a collection of arbitrary abstract
         | definitions and what follows from them. The alien species may
         | come up with different base definitions that they find more
         | useful or interesting. But they would derive the same
         | conclusions as we would if they were starting from the same
         | definitions and applying the same abstract rules.
        
           | bmitc wrote:
           | > Mathematics exist independently of biology or perception of
           | reality.
           | 
           | Is there a "proof" of that? How could a proof exist? You'd
           | probably win several awards if you had one.
           | 
           | > It is just a collection of arbitrary abstract definitions
           | and what follows from them.
           | 
           | ... created by humans.
        
             | dagw wrote:
             | _Is there a "proof" of that?_
             | 
             | It's how we define the concept "mathematics". If a result
             | was dependant on "biology or perception of reality" or
             | anything else outside its defining axioms, it wouldn't be
             | mathematics.
        
               | bmitc wrote:
               | I'm sorry, but I just disagree that that's how
               | mathematics is defined and that it doesn't depend on our
               | biology and perception, because _we_ are making those
               | definitions.
               | 
               | A book I might recommend and that I'm going through at
               | the moment is _Where Mathematics Comes From: How the
               | Embodied Mind Brings Mathematics Into Being_ by George
               | Lakoff and Rafael Nunez. The origin and meaning of
               | mathematics is strongly influenced by cognitive sciene,
               | and thus biology. I 've been downvoted, but this is not a
               | totally novel or off the rails idea. It is basically
               | accepted in robotics that embodied cognition is how you
               | get a robot to understand and perceive its environment.
               | Where do you think that idea came from?
        
           | rendall wrote:
           | > _Mathematics exist independently of biology or perception
           | of reality._
           | 
           | Even the concept of "number" itself is almost certainly an
           | artifact of perception that enabled our ancestors to survive
           | our niche, planetary environment, and not an inherent feature
           | of objective reality.
           | 
           | Aliens, evolved to survive in another environment entirely
           | with a different set of initial conditions, almost certainly
           | would not have the same, nor even any, understanding of
           | "number".
           | 
           | Would we consider such aliens a civilization or some kind of
           | insensate "process"?
        
             | DontchaKnowit wrote:
             | Um no.
             | 
             | I'm so over this deconstructionist "reality is your
             | perception" line.
             | 
             | Numbers are a thing. In fact they're one of the most basic
             | observable things about the universe. And the concept if a
             | number holds up all the way down to the quantum level. I.e.
             | space and time are discrete and therefore space and time
             | can both be COUNTED. Counting is literally one of the most
             | basic and early achievements of human cognition and were
             | gonna act like we just made it up?
             | 
             | Absolute silliness.
        
               | caleb-allen wrote:
               | > I'm so over this deconstructionist "reality is your
               | perception" line.
               | 
               | Kant would have a field day with this statement
        
               | rendall wrote:
               | > _" reality is your perception"_
               | 
               | You imagined what I meant so vividly that you literally
               | made up a quote!
               | 
               | Try responding to what I actually wrote, and if it's
               | unclear, asking with some humility.
               | 
               | I'm not even sure what your objection is, exactly.
               | Nothing you wrote contradicts what I wrote.
        
               | bmitc wrote:
               | > I'm so over this deconstructionist "reality is your
               | perception" line.
               | 
               | What makes you completely reject that? I don't think it
               | has as much to do with deconstructionism as it does
               | embodied cognition. We keep learning more and more about
               | how biology and physiology and evolutionary pressures
               | affect and inform cognition and thus perception. I was
               | recently reading about how there have been scientific
               | studies that seem to suggest that certain animals seem to
               | experience time differently that we do. So you could say
               | "time is a thing", but yet, it appears that it is not the
               | same thing across lifeforms. There are animals that sense
               | gravitational and electromagnetic fields, something we
               | cannot do. Would it make sense to them to say "all beings
               | can read these fields because we do"?
               | 
               | I think the problem is that it is all too easy to fall
               | into the trap in thinking that alien lifeforms would be
               | like us. There's a multitude of evidence of that here on
               | Earth in the variety of life, despite even coming from
               | the same origin.
        
               | rendall wrote:
               | This is a great rebuttal, and gestures towards what I was
               | getting at. Thanks.
        
               | Koshkin wrote:
               | > _There are animals that sense gravitational and
               | electromagnetic fields, something we cannot do._
               | 
               | That actually proves the fact that reality is _not_
               | simply someone 's perception. (We humans do not perceive
               | these fields, and so it took scientific advances for us
               | to _discover_ them as part of the objective reality.)
        
         | adrianN wrote:
         | I'm pretty sure that any sufficiently advanced species that
         | does any kind of mechanical engineering will have maths that is
         | homomorphic to analysis.
        
         | exitb wrote:
         | Isn't the basic math largely driven by attempts to understand
         | and quantify the world around us? In such case, it depends on
         | more universal concepts like distance, time, speed,
         | acceleration etc. Concepts which I would imagine to be familiar
         | to any intelligent being that takes a physical form. I can't
         | imagine an alien wondering about a period of a pendulum and
         | arriving at an answer that's really different from ours.
        
           | p0pcult wrote:
           | Funny that you chose pendulums:
           | 
           | https://cosmosmagazine.com/technology/artificial-
           | intelligenc...
        
       | [deleted]
        
       | kardianos wrote:
       | I call Alien Truth "What Is". It must form a common reality that
       | each individual can point to and share.
       | 
       | More at: https://corinth.kardianos.com/
        
       | authpor wrote:
       | Why doesn't reader mode work in that webpage?
       | 
       | Whatever happened to the (failing) promises of HTML + CSS ? where
       | I was gonna be able to swap out this CSS for whatever I wanted?
        
       | breckinloggins wrote:
       | > We might find, for example, that it's impossible to create
       | something we'd consider intelligent that doesn't use Occam's
       | razor. We might one day even be able to prove that.
       | 
       | I have no idea how one would go about proving this but personally
       | I would start with something like the "Principle of Least Action"
       | applied to thought.
        
         | carapace wrote:
         | Speaking in broad generalities (heh) Category Theory is what
         | you would use for that (AFAIK.)
        
           | TuringTest wrote:
           | Because using Category Theory for explaining things is the
           | opposite of applying Occam's Razor? :-P
        
       | MichaelZuo wrote:
       | Every pg essay seems to bring out a cohort of nay-sayers and
       | weirdos.
       | 
       | Maybe there is also a revealed alien truth somewhere in there
       | about the psychological effects of differences in expertise,
       | knowledge, social status, writing skill, etc...
        
         | koyanisqatsi wrote:
         | That wouldn't be an alien truth, that would be a mundane fact
         | of human psychology.
        
           | MichaelZuo wrote:
           | How would you know aliens don't share the same 'mundane
           | facts'?
           | 
           | It seems entirely possible.
        
             | koyanisqatsi wrote:
             | We could argue about the definitions of "mundane" and
             | "alien" but I've observed the same thing about HN comments
             | and it's not specific to PG essays so that's why I said it
             | is a mundane fact of human psychology.
        
             | Karunamon wrote:
             | They very well could, but it is plausible that they do not.
             | 
             | Certain facets of mathematics however, it is not plausible
             | that they do not share.
        
       | apriljest wrote:
       | What happens upon contact with aliens? I believe that to be an
       | important question, and one look at the warfaring, fearful
       | history of humankind makes it clear, as best said from the most
       | reprehensible book on philosophy I have ever read:
       | 
       | "477. "If intelligent entities from other parts of the universe
       | exist at similar or superior technological levels to ours, would
       | they draw the same or at least similar philosophical conclusions
       | to us?" That is a very good question. And my answer is this. They
       | better f#%*ing do if they want to have any hope of withstanding
       | our relentless, merciless onslaught."
        
         | [deleted]
        
       | randallsquared wrote:
       | > _I wouldn 't want to bet that all intelligent beings would
       | understand the concept of justice, but I wouldn't want to bet
       | against it either._
       | 
       | Given that even people (loosely) in the same culture often
       | disagree about what constitutes "justice" and use the term in
       | mutually exclusive ways, we should definitely bet against the
       | proposition that "all intelligent beings" understand it.
        
         | hbrn wrote:
         | > we should definitely bet against the proposition that "all
         | intelligent beings" understand it
         | 
         | Hey, we can always claim that those who disagree with us are
         | not intelligent.
         | 
         | I'm only partially joking. Lots of today's "justices" have so
         | many internal contradictions that I feel like we should
         | separate them into their own category.
        
         | garbagetime wrote:
         | For a person to have an opinion about what constitutes justice
         | is for them to demonstrate an understanding of the concept of
         | justice (assuming their opinion is cogent). So, if people are
         | disagreeing about what precisely justice is, it actually means
         | that they do understand the concept of justice.
        
           | koliber wrote:
           | Maybe for some highly abstract definition of justice. But for
           | more everyday use, it's not hard to come up with examples
           | that one society considers just while the other unjust.
           | 
           | Justice does not have to be cogent, which is defined as "(of
           | an argument or case) clear, logical, and convincing.". There
           | were and are justice systems that leave out one or more of
           | these ingredients to some extent. Some leave out some logic
           | by presuming the existence of a supernatural being. Some are
           | more authoritarian and not very convincing.
        
           | Koshkin wrote:
           | But "the concept of justice" is not universal, because it
           | really cannot be understood outside the context of law.
        
             | garbagetime wrote:
             | > it really cannot be understood outside the context of law
             | 
             | What do you mean by that?
        
               | Koshkin wrote:
               | There is no justice outside (or without) law.
        
               | garbagetime wrote:
               | I can imagine a perfectly just society with no laws.
        
               | Koshkin wrote:
               | I, on the other hand, cannot. (I can imagine many strange
               | things, but not this one.)
        
               | TuringTest wrote:
               | Consider:
               | 
               | * A society of one.
               | 
               | * A society of one family isolated in nature, where each
               | member is allowed to express their peculiarities and
               | eccentricities, but never do each other any harm - not
               | because of established rules, but because they truly love
               | and care of each other.
        
               | Koshkin wrote:
               | One person is _not_ a society.
               | 
               | The second example is virtually unreal (and even
               | expressions of 'love' and 'care' can be harmful).
        
               | TuringTest wrote:
               | "Virtually unreal"? It's how humans evolved for hundred
               | thousands years.
        
               | dagw wrote:
               | I disagree. As long as I have a personal concept of
               | 'good' and 'bad', and prefer it when 'good' things to
               | happen to 'good' people (and vice versa) then I have a
               | concept of justice.
        
               | Koshkin wrote:
               | Often, what is good for some is bad for others (and vice
               | versa). Justice would be way too relative (subjective)
               | outside law, so as to be devoid of any meaning, actually.
        
               | vlunkr wrote:
               | Laws are relative as well, they differ in every country.
               | Why would justice only exist in another relative system?
               | You know vigilante justice is a well accepted concept
               | that exists outside of the law by definition.
        
               | Koshkin wrote:
               | > _[laws] differ_
               | 
               | So does the definition of justice.
               | 
               | > _vigilante justice_
               | 
               | Except 'vigilante justice' and 'justice' are concepts
               | that have little to do with each other. You might as well
               | be talking about the 'de facto law' (like for instance
               | the "law" enforced by the local mafia) vs. the 'de jure
               | law' here.
        
               | Dylan16807 wrote:
               | > Except 'vigilante justice' and 'justice' are concepts
               | that have little to do with each other.
               | 
               | That depends on how well different people's definitions
               | of justice line up. There are many things that vigilantes
               | can enforce pretty well.
               | 
               | > You might as well be talking about the 'de facto law'
               | (like for instance the "law" enforced by the local mafia)
               | vs. the 'de jure law' here.
               | 
               | Sure, why not? Mafia law is often not justice, but I
               | think it qualifies as law where sufficiently powerful.
               | You seem to think this argument debunks itself?
        
           | jondeval wrote:
           | This is spot on. For concreteness, let me give a candidate
           | definition for the virtue of justice:
           | 
           | Justice - rendering to each person what is owed to them.
           | 
           | It's obvious that we will very often disagree about 'what is
           | owed', but doesn't our passionate disagreement in this case
           | show that (1) we agree that practicing justice is good and
           | (2) we are closely aligned on the existence of this thing
           | called 'justice'?
        
             | Koshkin wrote:
             | > _what is owed_
             | 
             | This is _extremely_ subjective.
        
               | jondeval wrote:
               | Right. You are touching on the central point of the
               | comment.
        
             | randallsquared wrote:
             | Lots of conceptions of justice don't align with your
             | definition, which centers individuals: Climate Justice,
             | (some types of) Social Justice, etc.
        
               | jondeval wrote:
               | Gotcha. I did preface this definition with the word
               | 'candidate' and I acknowledge that there may be good
               | alternate formulations. The spirit of this particular
               | exchange is about whether or not 'justice' can be
               | formulated as a universal.
               | 
               | I shared an argument above for why it can be viewed as a
               | universal and judging by your comment above you are
               | somewhat skeptical of this claim.
               | 
               | If we shift the discussion to allow conceptions of
               | 'justice' that move away from the classical tradition and
               | include modern ideas like 'climate' justice or 'social'
               | justice, I will revert to agreeing with your skepticism.
               | 
               | I don't think anyone can plausibly claim that these more
               | marxist-oriented modern definitions are universals.
        
         | songeater wrote:
         | Tit-for-tat is a highly effective strategy when playing an
         | iterated-prisoner's dilemma[0]... ie the "concept of justice"
         | can emerge through natural selection if "intelligent beings"
         | were forced to play such games on which their survival depends
         | (a plausible model of "society").
         | 
         | [0]
         | https://en.wikipedia.org/wiki/Prisoner%27s_dilemma#The_itera...
        
       | dr_dshiv wrote:
       | In the late 1600s, Christian Huygens proposed that aliens would
       | share our geometry (circles, spheres, etc) and even our rough
       | musical ratios (like an octave is a doubling of frequency and a
       | fifth is 3:2)
        
       | galaxyLogic wrote:
       | This seems like lots of camp-fire speculation in awe of the night
       | sky.
       | 
       | Before discussing what might be different with our "truth" and
       | alien "truth" we should first define what we mean by "truth".
       | 
       | What if there is a War of Worlds? And we win. But according to
       | the "alien truth" they win. This kind of thing seems to be going
       | on some TV-channels already, The notion of "facts" is diluted by
       | claiming that "We have alternate facts". "We have alternate
       | electors". That just means it is unclear to many people what
       | facts and truth mean and it is easy to misguide them.
        
       | benjaminjosephw wrote:
       | Would injustice exist in an alien society if that society didn't
       | recognise it as such?
        
       | kmod wrote:
       | As much as I like PG's writing in general, this is him dipping
       | his toes in waters that are already well studied and coming off
       | as ignorant and/or presumptuous.
       | 
       | His very first premise "The truths of mathematics would be the
       | same, because they're true by definition" shows an ignorance of
       | an entire field of discourse called the philosophy of
       | mathematics. Whether aliens would have the same math as us is one
       | of the fundamental questions, and to presume the answer shows a
       | disdain of the existing body of thought on this topic.
       | 
       | In particular, we humans still hotly debate which math is the
       | "right" math. Is the axiom of choice "true"? Does it make sense
       | to say that it has a truth value? Is such a truth value amenable
       | to human discovery? Does PG know the answers to all of these
       | questions?
       | 
       | PG is either unaware of the human-choice nature of the fundaments
       | of math or he thinks he has special knowledge of it. Either way
       | makes this essay one of my least favorites.
        
         | AnimalMuppet wrote:
         | Take some number of things. Lay them out more or less in a
         | straight line. Somewhere in that line, put a little gap. Count
         | them from left to right. Then count them from right to left.
         | You get the same number.
         | 
         | That experiment is saying that addition commutes. If an alien
         | ran that experiment, they would get the same answer.
         | 
         | Lay out some things in regular rows in a rectangle. Count the
         | things row by row. Then count the things column by column.
         | You'll get the same answer. So will an alien. That is,
         | multiplication commutes both for us and for the aliens.
         | 
         | Now, as you go further into mathematics, things are true
         | because they follow from the definitions, _but the aliens may
         | use different definitions_. They may have a different
         | definitions for, say, a commutative ring, and so abstract
         | algebra may be different for them. _But with the same
         | definitions, we would arrive at the same conclusions._
        
           | wizofaus wrote:
           | Good analogy but is it so crazy to think the concept of
           | counting in a particular direction wouldn't make sense to an
           | alien intelligence? That the way their brain processes inputs
           | means that the knowledge of the total number occurs to them
           | either subconsciously or as the result of parallel processing
           | that is beyond what human brains can even imagine being aware
           | of? Even if the input signals being counted are separated by
           | time (e.g. pulses of light or sound), such that their brains
           | must logically store the previous count and increment it as
           | new signals are detected, the concept of _ordered_ addition
           | (i.e. where we can conceive of  "x plus y" and "y plus x" as
           | separate concepts, even if they yield the same result) might
           | simply not be necessary or possible in an alien brain.
           | 
           | What even qualifies as "addition" at all is somewhat murky -
           | e.g. "addition" of relativistic velocities is non-commutative
           | (*), but is it meaningfully even addition in the same way
           | adding integer counts is?
           | 
           | * https://en.wikipedia.org/wiki/Velocity-
           | addition_formula#Prop...
        
           | Koshkin wrote:
           | > _If an alien ran that experiment, they would get the same
           | answer._
           | 
           | This depends on the world they live in. If, for example,
           | things were hard to control, tended to move, to disappear
           | (and reappear in a different place), to look the same, etc.,
           | they would probably discover quantum field theory before
           | arithmetic!
        
             | dagw wrote:
             | _they would probably discover quantum field theory before
             | arithmetic!_
             | 
             | Sure, but much like we eventually discovered quantum field
             | theory, they'll eventually discover arithmetic. And even if
             | for some weird reason they hadn't, they're probably smart
             | enough to understand it once we demonstrate it to them.
        
         | malux85 wrote:
         | I agree with what you're saying, at the thresholds of math (and
         | even quite a bit before) it gets very murky very quickly,
         | 
         | But I think in this context he may have been better to say
         | "arithmetic" or maybe root logical operations, because he was
         | trying to convey small axiomatic units of universal truth
         | rather than pull an entire field "into purity"
         | 
         | I could say the same about his comment about Carbon, the exact
         | mass of carbon we use is influenced by isotopes and is not
         | _exactly_ standardised in all human chemistry - so it's likely
         | the aliens idea of "the mass of carbon" would also be slightly
         | different. A better example would be "the atomic number of
         | carbon" which is always the same because it's definitional and
         | integer, but the same point is there - he's conveying the
         | existence of the tiny axioms (alien truths), not trying to
         | define them
        
           | TuringTest wrote:
           | _> But I think in this context he may have been better to say
           | "arithmetic" or maybe root logical operations, because he was
           | trying to convey small axiomatic units of universal truth
           | rather than pull an entire field "into purity"_
           | 
           | What makes you think that arithmetic and logic are
           | _universal_? A culture with a completely different way of
           | thinking may not arrive to a system similar to our
           | mathematics based on logical reasoning and search of
           | consistency. Heck, we can see it in a lot of human beings who
           | are not capable of consistent logical reasoning, and they 're
           | not even alien.
        
             | malux85 wrote:
             | I was thinking of simple arithmetic like addition and
             | simple logical operations like "and" and "or"
             | 
             | I was illustrating the existence of these things - like PG
             | was doing in the article - not attempting to define them
        
               | TuringTest wrote:
               | Yes, but these things exist because our brains reason
               | this way, not because they are constants of nature. Other
               | intelligent beings could have different non-symbolic ways
               | of gathering and processing information about nature,
               | such as evolving cellular automata adequate to represent
               | and solve problems.
        
             | spookthesunset wrote:
             | > Heck, we can see it in a lot of human beings who are not
             | capable of consistent logical reasoning, and they're not
             | even alien.
             | 
             | All humans share this flaw (if it is a flaw). Not just
             | some. We all do. It's part of what makes us human--we have
             | emotions that for better or worse transcend logic and
             | reasoning.
             | 
             | In fact I could maybe argue that emotion is an important
             | part of logic and reasoning. Emotion leads to skepticism
             | and thinking outside the box. Both traits are needed to
             | advance our understanding of the world.
        
         | VyseofArcadia wrote:
         | > In particular, we humans still hotly debate which math is the
         | "right" math. Is the axiom of choice "true"? Does it make sense
         | to say that it has a truth value? Is such a truth value
         | amenable to human discovery? Does PG know the answers to all of
         | these questions?
         | 
         | If we did encounter intelligent (and peaceful!) beings out in
         | the universe, there would be a set theory gold rush as people
         | race to put out papers that such-and-such alien axiom implies
         | choice, diamond principle, etc., or the other way around.
         | 
         | Every field of math would have such a gold rush really, on both
         | sides, as we discover similarities and differences in
         | techniques and formulations. And I bet famous unsolved problems
         | on both sides would get solutions if not outright provided by
         | the other species, then at least using novel tools from the
         | other species.
         | 
         | I can't imagine a more exciting time for math as a whole than
         | first contact.
        
         | WalterBright wrote:
         | Math has proven its predictive powers in the real world over
         | and over. It's quite a stretch for it to be fundamentally
         | wrong.
        
         | spookthesunset wrote:
         | > In particular, we humans still hotly debate which math is the
         | "right" math. Is the axiom of choice "true"? Does it make sense
         | to say that it has a truth value?
         | 
         | I would love examples of this. Seems pretty cool to think
         | about. I always assumed that "math" would be one of the
         | constructs we could always reliably communicate with.
        
           | kmod wrote:
           | I really like the Stanford encyclopedia of philosophy. In
           | this case: https://plato.stanford.edu/entries/philosophy-
           | mathematics/
        
         | patientplatypus wrote:
         | I agree. Consider the octopus - each of it's limbs contains
         | it's own cortex and so it has in essence 8 separable brains. Or
         | ants and bees which contain a hive intelligence. An ant has
         | almost no neurons, but the collective number of neurons of an
         | ant hive approaches that of a human brain. These are only
         | creatures that are on our earth that have radically alternative
         | ways of experiencing intelligence. Why would we expect aliens
         | to have an intelligence that's at all comparable to humanity
         | when even somewhat intelligent animals on our planet don't
         | exhibit the same characteristics?
        
           | spookthesunset wrote:
           | There is also bats who basically navigate the world by
           | pinging sound off things.
           | 
           | Don't forget microscopic creatures like Tardigrades. Their
           | world is so small that the air around us acts like water.
        
         | jsbg wrote:
         | "The truths of mathematics would be the same, because they're
         | true by definition" means that "( _x_ = > _y_ ) AND _x_ " means
         | _y_ is true based on the definition of = > and AND. There's no
         | "philosophy" behind this.
        
           | lupire wrote:
           | Why would aliens have the same definitions? Your AND maybe
           | wouldn't exist to them. They could have a more
           | statistical/global non-binary/discrete mathematics.
        
             | vecter wrote:
             | I assume that PG was talking about "intelligent" aliens,
             | which, for the sake of argument, let's say are those
             | capable of interstellar communication (building radio
             | telescopes and whatnot).
             | 
             | I cannot fathom such a civilization not having discovered
             | Boolean logic.
        
               | wizofaus wrote:
               | I don't see why it's so absurd to think another alien
               | species could develop interstellar communication without
               | even being sentient in the way we understand it at all,
               | or at least have anything like the level of abstract
               | self-awareness that humans do. They may just experience
               | something more equivalent to "emotional" reactions when
               | attempting to manipulate the natural world to create
               | technology in such a way that it guides them towards a
               | successful outcome. Indeed comprehending Boolean logic
               | seems no more necessary for that than it is for a dog in
               | order to understand that when something in front of them
               | is person 1 OR person 2, AND that certain sounds are
               | coming from that person, they should sit.
        
               | vecter wrote:
               | You're right about dogs, but dogs cannot build radio
               | telescopes so I don't understand the point. To be capable
               | of interstellar communication, you have to be able to
               | build machines, and doing so requires a systematic
               | engineering culture and understanding of at least basic
               | principles.
               | 
               | To put it differently, do you think such an advanced
               | civilization would not be able to do something as simple
               | as calculus, which would be far more advanced than
               | manipulating a basic truth table? They almost certainly
               | won't do it in any language that we understand on Earth,
               | but they'll be manipulating and reasoning about the same
               | concepts.
        
               | wizofaus wrote:
               | I honestly don't know, but I do think it's dangerous to
               | assume an alien mind capable of interstellar
               | communication would "think" sufficiently like human
               | brains do for abstract concepts like calculus to be
               | necessary or even make sense.
        
         | poulpy123 wrote:
         | I don't know for the axiom of choice but I would be surprised
         | if 1+1=2 is not universal, whatever way is used to express it
        
           | colordrops wrote:
           | Is that "math" though, or just a particular construct in the
           | system of math? I could imagine an alien mind that does not
           | break things down across integer boundaries, when you
           | consider that any labelings and groupings are arbitrary. That
           | 1 "hat" you are wearing plus that 1 "hat" your buddy is
           | wearing are actually not 1 and 1 but a conglomeration of
           | fields/particles in an arbitrary configuration that can be
           | torn or shredded or turned into plasma.
        
             | zdragnar wrote:
             | At the end of the day, you've still identified that
             | particular configuration as a "hat"- a configuration
             | forming a discrete unit. Without it, you have no concept of
             | object permanence and no basis for comprehending any form
             | of logic at all. After all, even within plasma, there are
             | discrete units which are configurations of other discrete
             | units.
        
               | colordrops wrote:
               | But these discrete units in the plasma are also model
               | constructs of ours rather than fundamental properties of
               | nature. The point is that any discrete lines we draw are
               | ours, and not necessarily nature's. Of course we have no
               | concept of object permanence without these, because
               | concepts and objects are discrete models we create
               | ourselves. It's tautological.
        
             | lupire wrote:
             | You could construct such a mind in a simulation but I doubt
             | one would arise naturally in the physical constraints of
             | our universe. Approximate discretization is everywhere.
        
         | simonh wrote:
         | I think, like many commentators here, you're taking a very
         | narrow technical view of what PG is talking about in what is
         | actually a very broad a high level discussion.
         | 
         | Whether or not it's possible to prove a specific postulate in
         | set theory is formally true (the axiom of choice, which was
         | only formulated in 1904) isn't going to stop aliens counting
         | objects and calculating the area of squares. They may not agree
         | with us about formalism vs intuitionism, but it seems likely
         | they would agree with us about a huge array of practical
         | mathematical operations and results. PG is just asking what are
         | the areas we would be extremely likely to agree on. Pointing
         | out that there might be specific, advanced, highly obscure
         | controversies we might disagree on isn't even in contention. Of
         | course there are.
        
           | kmod wrote:
           | It's turtles all the way down -- we don't know what "truth"
           | is, or how one can come to "know" truth (as opposed to just
           | believe it). I'm less informed on these topics so I avoided
           | them, but I've heard that our notion of truth is intimately
           | tied to our experience of physical reality, and it seems easy
           | to imagine aliens that have different experiences of reality.
           | 
           | For example, what if aliens are so large that the non-
           | euclidian nature of space becomes obvious to them? Perhaps
           | they would never come up with euclidian geometry. Maybe they
           | would never create the notion of pi. Yes it shows up in other
           | areas but you can certainly imagine an alien civilization
           | that has a different circumference-to-radius ratio or
           | disavows the entire idea of having a constant circumference-
           | to-radius ratio.
        
             | simonh wrote:
             | We only need to evaluate what is practically useful. At the
             | end of the day that's all science does - it's a methodology
             | for generating guidelines for what actually works in the
             | real world and for which accuracy, or truth, can be
             | verified. We call those guidelines scientific 'laws', but
             | truth in the absolute sense is less critical than is often
             | made out by both proponents and critics of science.
             | 
             | Newton's laws of motion strictly speaking are not true,
             | Einstein proved this, but they are incredibly useful as is
             | the mathematics we use to formalise them. We know that the
             | quantum mechanics and relativity theories we have now and
             | not complete, but that's beside the point.
             | 
             | PG is simply pointing out that since aliens, if they exist,
             | live in the same real world we do they will discover a lot
             | of the same practical results we do, and then goes further
             | to suggest they might agree with us about a lot of the less
             | strictly provable ones as well. Going "Oh well but this
             | obscure question here would still be in contention" is,
             | well, somewhat sailing past the point by a little
             | smidgenette. It's criticising a claim I don't think it's
             | reasonable to think PG is making.
        
               | gopher_space wrote:
               | > PG is simply pointing out that since aliens, if they
               | exist, live in the same real world we do they will
               | discover a lot of the same practical results we do
               | 
               | This isn't even accurate for the different peoples on our
               | one planet.
        
               | simonh wrote:
               | It really is, that's why the basic mathematical
               | principled discovered in India, Mesopotamia and Greece
               | have spread and been further developed throughout the
               | world. Because they work just as well everywhere. The
               | Maya discovered the natural numbers and zero, did
               | arithmetic and performed calendrical and astronomical
               | calculations. China developed their numerical system
               | independently, calculated Pi, performed division, root
               | extraction and linear algebra and many original
               | techniques. The forms of expression and some techniques
               | were unique but maths is maths.
        
               | JackFr wrote:
               | All those cultures were running on the same hardware, so
               | to speak. Let's see what the squids have to say.
        
               | simonh wrote:
               | We'll, there's some evidence octopi and squid can count.
               | If so then at least there's some elementary maths in
               | common. There's no reason to suppose super intelligent
               | cephalopod creatures would have particular difficulty
               | with things like natural numbers, for all their different
               | experience of the world. Two shrimp plus two shrimp is
               | still the same amount of food as one shrimp plus three
               | shrimp, no matter how many arms you have.
        
               | kmod wrote:
               | Agree to disagree, I suppose. Another comment in this
               | thread suggested using the value of pi to demonstrate
               | intelligence, but you can imagine alien civilizations
               | without the same reverence of pi as we do (if they are
               | large enough). I mentioned in another comment that you
               | can also imagine small enough aliens not inventing a real
               | number line because they do not have the experience that
               | everything is infinitely divisible.
               | 
               | I believe our difference is that you are presupposing
               | that aliens will have essentially the same experience
               | with reality that we do. I agree that if somehow a
               | separate human civilization evolved in another galaxy,
               | their math would likely look similar to ours. But you can
               | imagine aliens that have very different experiences of
               | "what actually works in the real world" (due to
               | experiencing a different set of physics, such as at a
               | different physical scale) and thus come up with different
               | math.
        
               | karmakaze wrote:
               | Pi is the human joke of the galaxy--they all use Tau.
        
               | simonh wrote:
               | We already have very robust descriptions of how the world
               | works at every scale, from the planck length all the way
               | up to the limits of the observable universe, and in
               | extremes of environment from the surface of neutron
               | stars, to the roiling virtual particles of empty space.
               | We can calculate behaviours in these environments very
               | precisely right now. Sure, there are things about these
               | environments we still need to learn, but they're not
               | utterly intractable or inconceivable to us.
               | 
               | There's a character Rimmer in a comedy series Red Dwarf
               | that's always going on about how aliens would be
               | unimaginable to use because they're alien and everything
               | they do would be... well.. 'alien'. It's poking fun at SF
               | that presents aliens as inherently utterly unintelligible
               | to us simply by virtue of being alien, but frankly that's
               | absurd. Physics doesn't care who or where you are, the
               | same rules apply.
        
               | JackFr wrote:
               | Your brain is lying to you.
               | 
               | It's not your brain's fault, really. It doesn't know any
               | better. Your brain has a way of interpreting the sensory
               | perceptions communicated to it. It conflates this with
               | 'reality' because it doesn't know anything thing else.
               | And because it doesn't have anything else, it also
               | declares itself the universal understander. Just like
               | there are sounds you cannot hear, and chemicals you
               | cannot taste, wavelengths you cannot see -- consider that
               | there may be thoughts that you physically cannot think.
               | 
               | No magic and no spooky mysterious stuff. Just that it
               | seems quite possible that our brains are limited in their
               | ability to construct a representation of the universe,
               | and insofar as the representation is true, we have kno
               | way of knowing if it's the only true one.
        
               | simonh wrote:
               | If you know what Turing complete means, and what a
               | universal Turing machine is and can do, and that we are
               | examples of such, then you must realise that's not true.
               | Provably. Unless you're a dualist of some sort and
               | believe thinking is some sort of spiritual woo, in which
               | case I can't help you. But I can imagine what that's like
               | (see what I did there?).
               | 
               | Seriously, there are sensory experiences I can't have,
               | but in principle no thoughts that are intractable to
               | analysis and understanding given enough information.
        
               | shkkmo wrote:
               | Our brains are technically only "turing complete" if you
               | ignore their finite memory. (Edit: which is what is
               | commonly meant by turing complete.)
               | 
               | It seems pretty obvious that there are thoughts that are
               | too big to fit inside our heads.
        
               | simonh wrote:
               | Again this is descending into nitpicking at the extremes.
               | PG is not saying everything we understand will be in
               | common with aliens, or that our cognitive match with them
               | will be 1 to 1, just that there is likely to be overlap.
               | That given the universality of human cognition, there is
               | likely to be thoughts we can mutually appreciate. I am
               | not claiming that human brains are capable of all thought
               | possible to aliens, only that there will be common
               | ground. That's all. It's a very minimal claim.
        
               | msla wrote:
               | OK, then walk out the window of my old apartment.
               | 
               | I see it as being on the third floor, but that's only my
               | brain lying to me, right?
        
               | PaulDavisThe1st wrote:
               | You've already presupposed that experimenting across all
               | those scales is somehow an integral (necessary?) part of
               | being the kind of life that we might encounter.
               | 
               | That could be possible, but I don't think that we can
               | assume that.
        
               | TuringTest wrote:
               | Yes, but the point I think is that the rules of symbolic
               | reasoning are not like the rules of physics; formal
               | systems have an arbitrary shape, so exploring the
               | universe from a different starting point could yield a
               | completely different method of representing it and
               | processing information about it. And such methods needs
               | not be compatible with our understanding of math.
        
               | mistermann wrote:
               | > We only need to evaluate what is practically useful.
               | 
               | As simple as this may seem, a few problematic points:
               | 
               | - who decides who gets included in "we"?
               | 
               | - who decides what "evaluate" is composed of?
               | 
               | - who decides what is practical, and useful?
               | 
               | - there is an implicit dimension of Time: for example,
               | many things were initially categorized as useful, but
               | then it can turn out to be a lot more complicated
               | (Thalidomide, fossil fuels, _arguably_ democracy  &
               | journalism (at least _as they are practised_ , which
               | seems to be fairly immutable))
               | 
               | Of course, these issues can be easily dismissed
               | ("pedantic!"), but that doesn't make them go away.
               | 
               | > At the end of the day that's all science does - it's a
               | methodology for generating guidelines for what actually
               | works in the real world and for which accuracy, or truth,
               | can be verified. We call those guidelines scientific
               | 'laws', but truth in the absolute sense is less critical
               | than is often made out by both proponents and critics of
               | science.
               | 
               | Another problem we have is _language_ (and various other
               | things, semantics, semiotics, etc) - in this example, a
               | reader could easily take away a few _not necessarily_
               | correct beliefs from the way you 've worded it:
               | 
               | - _it could be (very poorly) interpreted_ to mean science
               | does _only_ this (and nothing else)
               | 
               | - _it could be interpreted_ to mean _science alone_ does
               | this
               | 
               | - _it could be interpreted_ to mean that the output of
               | science (what actually works in the real world) _is
               | comprehensive_ , as in "all that works has been
               | discovered by science - and if it isn't, science would
               | (or will) find it"
               | 
               | - _it could be interpreted_ to mean that science alone is
               | able to produce accuracy, truth, and verification
               | 
               | - _it could be interpreted_ to mean (or, a person may
               | just not consider) that  "what works" is not necessarily
               | a constant over time (see: Thalidomide, fossil fuels)
               | 
               | To be clear, I'm not saying you're asserting these
               | things, I'm just pointing out that language is extremely
               | ambiguous and can be misleading.
        
             | lupire wrote:
             | > imagine an alien civilization that has a different
             | circumference-to-radius ratio
             | 
             | Aliens still live in our Universe with our physics. Are
             | these aliens bigger than the solar system?
             | 
             | Maybe a different universe with different parameters could
             | look m athematically different in major ways.
        
               | kmod wrote:
               | Again, talking a bit outside my comfort zone, but I
               | believe our universe's physics say that circles only have
               | a fixed circumference-to-radius ratio at "small"
               | (astronomically) scales. At large enough scales space is
               | curved and the ratio begins to change.
               | 
               | In a similar way, a set of different physics would apply
               | to small enough aliens that are principally governed by
               | quantum mechanics. They might never come up with the real
               | numbers because they do not believe that quantities are
               | dense.
               | 
               | We could think of more examples -- aliens who typically
               | move at speeds close to the speed of light would have
               | very different conceptions of time, etc.
        
               | simonh wrote:
               | Our best estimate for the topology of the universe at the
               | largest scale is that it is 'flat'. If it has curvature,
               | it's below the margin of error we are able to measure it
               | at. The only thing we know that can curve space
               | significantly is gravity, but it would take truly
               | stupendously strong gravity fields to significantly
               | change basic results from classical geometry, such as
               | those close to the event horizon of a black hole. Even
               | then we can calculate it accurately nowadays so our
               | results would still correspond to theirs even in those
               | circumstances.
        
               | msla wrote:
               | If we aren't talking about the same things, we wouldn't
               | be talking about the same things.
               | 
               | Part of establishing communication is ensuring we're
               | talking about the same things.
               | 
               | Therefore, once we've established communication, we'd be
               | talking about the same things, such as what a flat plane
               | is.
               | 
               | If you think humans are the only species capable of
               | comprehending Euclidean geometry, say so, and defend the
               | assertion.
        
             | lo_zamoyski wrote:
             | > It's turtles all the way down -- we don't know what
             | "truth" is, or how one can come to "know" truth
             | 
             | > I've heard that our notion of truth is intimately tied to
             | our experience of physical reality
             | 
             | It's been thousands of years since the first retorsion
             | arguments were recorded, and yet I still see obviously
             | self-refuting or self-undermining claims being made and
             | quite often. Like these.
        
           | waffletower wrote:
           | Squares do not exist outside of abstract axioms. Solids
           | projected from them share the same status. A mason making a
           | tile forces reality to approximate the concept. Even
           | crystalline structures which suggest them are too
           | approximate. Why is a square implicit to an alien?
        
         | pazimzadeh wrote:
         | Not that I agree with the argument, but this is relevant:
         | 
         | https://www.quantamagazine.org/the-evolutionary-argument-aga...
        
         | dooglius wrote:
         | This seems like an uncharitable take, the set of axioms and
         | definitions used doesn't really fall under "mathematical
         | truths", it's about agreement on what is implied by a given set
         | of axioms. Even on Earth many people work in alternatives to
         | ZFC and generally don't really disagree about what is "true".
        
           | TuringTest wrote:
           | Yet "what is implied by a given set of axioms" is the most
           | common definition of "what's true" in mathematics. Therefore,
           | an alien culture using completely different axioms and rules
           | could arrive to an extremely _alien_ math.
           | 
           | There _might_ be some parts of it that are translatable to
           | our own systems, but there 's no guarantee that both systems
           | will be ultimately compatible.
        
         | nine_k wrote:
         | Math is a formal game. You can define vastly varied algebraic
         | structures, and, as long as they are internally consistent, we
         | could consider them "mathematical".
         | 
         | But the physical reality makes some structures more important
         | in practice. Hence natural numbers, or real numbers, or complex
         | numbers stand out among the sea of possible group structures.
         | 
         | Chances are very high that aliens live in the universe with the
         | same laws of physics, which make the same, or isomorphic,
         | structures important for them, and thus informing the
         | development of their mathematics.
         | 
         | But this is not a given, of course; there can potentially be
         | different ways to describe physical reality which are
         | comparably successful, but which grow from entirely different
         | foundations, are internally consistent, and otherwise work like
         | our mathematics, but are not connected to it (yet).
         | 
         | Even more funny is that Godel's incompleteness theorem
         | guarantees that "our" (currently developed) mathematics contain
         | true statements which cannot be proven either true or false
         | within the set of axioms which produce our mathematics. One can
         | imagine that these true statements can be used to successfully
         | describe important aspects of physical reality and were
         | discovered by aliens for this purpose, while remaining
         | incomprehensible for us. (But this is softer sci-fi stuff, of
         | course.)
        
           | pluijzer wrote:
           | > But this is not a given, of course; there can potentially
           | be different ways to describe physical reality which are
           | comparably successful, but which grow from entirely different
           | foundations, are internally consistent, and otherwise work
           | like our mathematics, but are not connected to it (yet).
           | 
           | Are you or anybody else aware of any other way to describe
           | physical reality? Maybe some culture took a different path.
           | That would be very interesting. It seems almost impossible to
           | imagine one for me though.
        
             | nine_k wrote:
             | Ted Chiang's short novel "Story of Your Life" [0], later
             | turned into the movie "Arrival", describes an alien culture
             | which uses variational calculus [1] as the normal way to
             | describe physics, that is, their equations are mostly about
             | finding functions with extrema of certain kind, not just
             | derivatives (as are the normal PDUs we use in physics). The
             | idea is that "our" equations mostly deal with the arrow of
             | time and thus use terms like dx/dt extensively, while
             | "their" equations are about the entire configuration of
             | something in spacetime, not singling out the time
             | dimension.
             | 
             | [0]: https://en.wikipedia.org/wiki/Story_of_Your_Life
             | 
             | [1]: https://en.wikipedia.org/wiki/Calculus_of_variations
        
               | pluijzer wrote:
               | Thank for for the references that is really fascinating.
        
           | theonemind wrote:
           | > Math is a formal game
           | 
           | > Even more funny is that Godel's incompleteness theorem
           | guarantees that "our" (currently developed) mathematics
           | contain true statements which cannot be proven either true or
           | false within the set of axioms which produce our mathematics
           | 
           | These two statements together suggest that math isn't
           | actually a formal game, but that formal methods offer an
           | useful method for dealing with it.
        
         | benlivengood wrote:
         | I'd expect aliens to have discovered their equivalent of the
         | Church-Turing thesis, Tarski's externality of truth, Godel's
         | incompleteness theorems, etc. That would give them a strong
         | ability to model our mathematics within their own and see its
         | computational structure and begin finding correspondences to
         | theirs. Similarly, we could begin modeling their conception of
         | mathematics in a similar way and as soon as we both have
         | arrived at a morphism between our representation and theirs of
         | some particular theorem we could grow our knowledge and
         | understanding of the other.
         | 
         | The key is that mathematics flows from logic and logic flows
         | from computation and computation is universal.
        
         | solveit wrote:
         | > Is the axiom of choice "true"? Does it make sense to say that
         | it has a truth value? Is such a truth value amenable to human
         | discovery?
         | 
         | I imagine PG would say that these are not purely mathematical
         | questions, but rather metamathematical questions. Theorems
         | remain theorems regardless of whether the axiom of choice is
         | "true", although one may contend that theorems assuming that
         | the AOC is false (or true) are vacuous. Aliens would surely
         | agree with us on statements of the form "working in first-order
         | logic (or whatever) formalized in XXX way, assuming axioms YYY
         | and ZZZ, we may prove that...".
        
         | witherk wrote:
         | Math isn't choosing which axioms to use, is finding the
         | consequences of a given set.
        
         | mcqueenjordan wrote:
         | https://en.wikipedia.org/wiki/Principle_of_charity
         | 
         | Or, infinitely caveating all of your writing is tedious and
         | makes it less interesting to read. It's more respectful to your
         | readers to assume they understand this and will apply the
         | principle of charity.
        
         | golemotron wrote:
         | To be fair, someone writes this type of comment every time he
         | posts. It's not a unique take. It falls into the "well studied"
         | category you mention.
        
         | danielvaughn wrote:
         | No shade to you personally, but I really dislike this frame of
         | thought.
         | 
         | There are mountains and mountains of literature about a great
         | deal of things, no one human can be expected to be aware of
         | them all.
         | 
         | Since that is obviously true, the lack of awareness about a
         | single topic isn't "ignorance" - it's not like PG studiously
         | ignored all of that literature. More likely he just never came
         | across it, so the more apt word is "unaware" rather than
         | "ignorant".
         | 
         | To criticize someone merely for pondering about a subject they
         | aren't well-versed in is hostile gatekeeping. I think those who
         | are educated in the relevant subject would do well to be more
         | welcoming and informative to newcomers.
        
           | ASalazarMX wrote:
           | > the lack of awareness about a single topic isn't
           | "ignorance"
           | 
           | Since everybody is nitpicking here, I'll add that this is
           | indeed ignorance. We're know what we know, and are ignorant
           | of what we don't. Being ignorant by itself shouldn't be
           | viewed as a flaw, but an inevitable state of our limited
           | capacity to learn. The real flaw is being proud of staying
           | willfully ignorant.
        
             | danielvaughn wrote:
             | I agree with what you're saying, but practically speaking,
             | using the word "ignorant" is universally interpreted as a
             | negative term.
        
               | mechanical_bear wrote:
               | It is not universally interpreted as negative. I have
               | often said in conversation; "Please explain [x] to me, as
               | I'm ignorant as to how that fits in/works/etc." I
               | certainly don't say it to demean myself.
        
           | mechanical_bear wrote:
           | Ignorant is unaware. I'm sure there are loads of things that
           | you have ignorance of, such as the meaning of Ignorance:
           | 
           | lacking knowledge, information, or awareness about a
           | particular thing: "they were ignorant of astronomy"
        
           | apeace wrote:
           | That's true, but this essay is written with an authoritative
           | voice, not a pondering one. PG tends to write as if he is
           | teaching his audience something profound. So I think it's
           | fair to call out when he is wrong or misguided.
        
             | danielvaughn wrote:
             | This might just be a subjective thing then. My impression
             | was that he was simply following a casual train of thought.
             | 
             | I agree with the other comment that my words "hostile
             | gatekeeping" were too strong. I just get irritated with
             | philosophers specifically, because philosophy itself is a
             | normal human experience. Everyone finds themselves thinking
             | about things that veer into philosophical subjects. To even
             | criticize people for doing so without reading the
             | professional literature is just so annoying to me.
        
               | missingrib wrote:
               | I think philosophers get a bit annoyed about this because
               | they've spent literal years and years thinking about
               | something that might be quite esoteric/tricky, and then
               | someone comes along and just assumes the answer as if
               | there hasn't been decades of discourse about this exact
               | thing.
               | 
               | The subtext in your comment is that everyone does
               | philosophy all the time, and there's no difference
               | between professional and amateur philosophers.
        
               | jdthedisciple wrote:
               | > then someone comes along and just assumes the answer as
               | if there hasn't been decades of discourse about this
               | exact thing.
               | 
               | I'd think that would present itself as a rather pleasant
               | opportunity for any bypassing philosopher to stop and
               | teach them about the "decades of discourse" on it rather
               | than being annoyed?
        
           | deltasevennine wrote:
           | True. But PG's authoritative status is weakened due to his
           | lack of awareness no matter how you change the wording. This
           | entire essay is weaker because of it as my opinion about his
           | knowledge.
           | 
           | >To criticize someone merely for pondering about a subject
           | they aren't well-versed in is hostile gatekeeping.
           | 
           | The words "hostile gatekeeping" makes me classify your
           | statement as accusatory and an actual attack. The Op's
           | statements are just criticism. Harsh but valid, it certainly
           | isn't hostile gatekeeping. In fact, PG is the gatekeeper
           | here. He owns the site.
        
             | danielvaughn wrote:
             | Yeah my words were too strong, I'll own that. I didn't mean
             | to come across so aggressive.
             | 
             | Another way to phrase it: if someone were to follow a
             | thought experiment in a another subject like biology or
             | geology, the response from the educated community would be
             | different. I've seen it on here before. The response is
             | something akin to "hey yep that's an interesting thought.
             | It's been done before, here are some links if you're
             | interested in reading further".
             | 
             | I just tend to see a very different (much more critical)
             | response from people in philosophy, often with overtones of
             | condescension and smugness. Not saying OP was guilty of
             | that, just that I mistakenly responded as if they did.
        
       | jondeval wrote:
       | I really liked this essay. It poses some interesting questions,
       | but it's short and it doesn't try to do too much.
       | 
       | There is overlap between pg's ideas and what in the classical
       | tradition is called Natural Law Theory. PG may or may not be
       | interested in drawing out the connection, but since he references
       | Aristotle I have to believe he is at least aware of a touch
       | point.
       | 
       | To give a distilled definition, Natural Law Theory is the
       | application of the laws of nature to rational creatures.
       | 
       | In the context in which NLT developed, the only free rational
       | creature was the human being. But both AI development, and
       | concepts from evolution through natural selection, potentially
       | allow us to apply aspects of the theory to different rational
       | agents.
        
       | bglazer wrote:
       | One of the bitter lessons I've learned is that when I think of
       | something, I should always (always!) do a couple searches to see
       | if anyone else has thought of it, before I commit to writing down
       | my thoughts as novel or authoritative.
       | 
       | Someone (typically at Bell Labs in like 1973) has nearly always
       | already had my thought, but then explored it in much richer,
       | finer detail than I have. It's disappointing to learn I'm not an
       | unmatched genius, but much more illuminating to read and think
       | about how others have considered similar issues.
       | 
       | I don't fault Paul for not doing this, it happens to everyone,
       | and I imagine he's quite busy. I do fault all the people who read
       | this draft and didn't do this very easy exercise for him. I think
       | it reflects a undue deference towards frankly uninformed and
       | pretty basic observations.
        
       | m3kw9 wrote:
       | An alien truth that we can derive a lot of alien truth from is
       | that life forms all prefer order rather than chaos. Having life
       | is by itself is a very orderly process in relation to chaos,
       | which implicitly opposes it.
        
         | m3kw9 wrote:
         | one derivative would be discipline vs procrastinating, aliens
         | won't get far if they didn't have any discipline. Heck even
         | single cell organisms are highly single track disciplined.
        
       | li4ick wrote:
       | Yeah, that first paragraph is completely wrong if you think about
       | the universe in terms of computation...
        
       | hangaard wrote:
       | We'd also share algorithms. Including evolution.
        
       | OscarCunningham wrote:
       | This is a side topic, but does anyone else have problems with the
       | RSS feed for pg's essays? http://paulgraham.com/rss.html I
       | regularly find every essay appearing together in my reader, as
       | though they were all new again.
       | 
       | Apparently the feed was created by Aaron Swartz himself, so I
       | wouldn't think there would be any errors there. But it looks like
       | it's hosted via Aaron's own site, so perhaps there's some problem
       | caused by it not being maintained?
        
       | jtwebman wrote:
       | So very human of us to think our truths are some other beings
       | truths. Maybe they proved math isn't true? Maybe they don't think
       | in any way like we do.
        
       | adamc wrote:
       | "The Zoologist's Guide to the Galaxy" covers this, and a lot
       | more: https://www.audible.com/pd/The-Zoologists-Guide-to-the-
       | Galax...
        
       | amelius wrote:
       | Hopefully they don't share the belief with us that there must be
       | one species conquering them all.
        
       | boh wrote:
       | My dog is an intelligent being and he doesn't share our affinity
       | for math. We have to acknowledge that our concept of intelligence
       | is human-centric. What we interpret as knowledge is based on our
       | specific limitations and perceptions. We don't know what
       | intelligence is and won't necessarily know it when we see it.
        
         | yetihehe wrote:
         | My dog is pretty dissatisfied when I show him 3 treats and then
         | give him 2, so he has uses for maths, but he can no longer
         | multiply.
        
         | swader999 wrote:
         | Why does my dog growl at my other dog when it tries to eat it's
         | food? It seems to understand subtraction at a basic level.
        
         | swalsh wrote:
         | Your dog is unlikely to visit other planets searching for other
         | intelligent life
        
           | myshpa wrote:
           | Let's hope then that aliens coming here will be vegan.
           | 
           | We're not intelligent enough yet not to harm others, or to go
           | to other star systems, or even other galaxies. Would we be
           | considered intelligent, or a source of protein?
        
         | carapace wrote:
         | Has your dog ever jumped somewhere and landed where he intended
         | to? Has he ever caught a ball or frisbee that you've thrown?
         | 
         | If so, then he understands basic calculus.
         | 
         | He can't write the equations, but he can solve them.
        
         | dandanua wrote:
         | Many "successful" humans don't know a lot of math or physics
         | either. It seems you only need to know how to subtract and
         | divide.
        
       | [deleted]
        
       | ncmncm wrote:
        
       | gnramires wrote:
       | I personally believe we should also approach ethics from an Alien
       | Truth perspective -- there's a lot of ethics and how we live our
       | lives that's specific to our human being species, but we should
       | expect the principles of human life to be compatible with more
       | general principles, of which ours would be a special case. This
       | really allows having a clearer global picture of ethics, and
       | striving towards progress in ethics and human existence.
        
       | lowbloodsugar wrote:
       | >For example, I think we'd share the principle that a controlled
       | experiment testing some hypothesis entitles us to have
       | proportionally increased belief in it.
       | 
       | vs
       | 
       | >I wouldn't want to bet that all intelligent beings would
       | understand the concept of justice
       | 
       | It would be unjust if a technologically advanced society murdered
       | all its scientists for heresy during a religious coup, but Paul
       | is unwilling to bet that all alien societies understand justice.
       | Why the belief in science then? Our own planet has theocracies
       | and a President of the supposed #1 country has updated scientific
       | hurricane reports with a sharpie.
       | 
       | Plenty of science fiction authors have speculated meeting
       | theocratic aliens. Peter Hamilton's Salvation comes to mind (you
       | get where that series is going from the title).
        
       | skybrian wrote:
       | An assumption that this essay buys into is that "universal"
       | truths are somehow higher-status and more worthy of study. How
       | people come up with reasonable fixes to local messes doesn't get
       | enough attention.
        
       | at_a_remove wrote:
       | If I had to lay money on it, I'd be willing to favor the position
       | that aliens we're talking to via radio have the concept of
       | electrons, and metals, and the number forty-seven.
       | 
       | The really esoteric branches of mathematics, I could see huge
       | variances. Materials sciences would vary widely. But the basic
       | high school stuff? I'd lay odds on it.
        
       | mberning wrote:
       | I didn't realize that the concept of absolute or universal truths
       | was so boring that it needed an "ancient aliens" style rebrand.
        
         | znpy wrote:
         | What did you expect from the idol of the startup scene?
        
         | felipeccastro wrote:
         | Perhaps it's not that they are boring, but fearful. I can't
         | recall a single time I mentioned these words in a conversation
         | that weren't abruptly interrupted with "there is no absolute
         | truth!". If the rebranding helps us calm down and think about
         | it without fear, it might be worth it.
        
       | koyanisqatsi wrote:
       | Michael Levin has an interesting perspective on this. The idea is
       | that biology and evolution are processes that reveal some
       | inherent and latent universal structures and so they would be the
       | same across all life in the universe even if such life was not
       | carbon based. But at this level of generality it gets pretty
       | abstract and the definition of truth essentially becomes some
       | kind of structural similarity in form and function.
        
       | bkishan wrote:
       | Looks like PG was inspired by reading Project Hail Mary, and
       | decided to be philosophical about it :)
        
       | [deleted]
        
       | mikkergp wrote:
       | I appreciate what he is saying, but this also feels like the
       | speech given at the beginning of a sci-fi/horror movie where you
       | realize you're completely wrong.
        
       | asdff wrote:
       | Why do people assume alien life would be intelligent? Intelligent
       | life is extremely rare on earth and has only occured for a brief
       | moment in its history due to highly specific environmental
       | scenarios at the time as well has historical events. If we didn't
       | get that meteor that wiped out the dinosaurs, mammals would
       | probably still be shrew like creatures as they were for millions
       | of years until mass extinction exposed new ecological niches. The
       | great oxygenation event could have easily killed off all life on
       | earth too. Most of the biomass on earth today comes from plants,
       | famously unintelligent and sessile, commonly using strategies
       | that favor spawning thousands of offspring that have random
       | mutations, with a few who go on to survive in an ecological
       | niche.
       | 
       | If we use our own earth as a model, alien life is far more likely
       | to be unintelligent. Its a big human bias to assume that if there
       | were intelligent life out there, it would even think like human
       | life, so our abstractions such as mathmatics and physics will
       | probably look entirely different when a completely different mind
       | formed from a different evolutionary trajectory encounters
       | natural phenomenon and attempts to make truths. Even with our own
       | species it took us millions of years to establish our current
       | truths about what we consider true. This begs the question, if in
       | millions of years we will consider our current abstractions that
       | interpret physical laws of the universe to be just as worthless
       | as past interpretations for these same physical laws that we used
       | as truths in centuries previous.
        
       | blueprint wrote:
       | that's the definition of truth. all truths are fixed.
        
         | nh23423fefe wrote:
         | lol tarski
        
           | blueprint wrote:
           | "[when] the inferior scholar hears of Dao, he greatly
           | ridicules it" -laotzu
        
       | benevol wrote:
       | > If there were intelligent beings elsewhere in the universe
       | 
       | Wow some people still think we're alone. Wow. Just, wow.
        
       | srvmshr wrote:
       | It makes me slightly sad that a well-read tech icon like PG
       | dabble in writing things which are not only beyond his creative
       | expertise, but also speculative, imaginative & open to wide
       | variety of interpretation, spirituality including.
       | 
       | Aliens may exist as very intelligent species or maybe dumb
       | bacteria. We are discovering the laws of nature ourselves. We
       | don't know enough of the laws of nature, despite the vast strides
       | we have made in the last century. Maybe there are universal
       | truths & representations, like the GUT which all life forms may
       | eventually discover in their notation/formalism. Or maybe the
       | laws of physics will have different implications in different
       | corners of universe or multiverses, and we don't know those too
       | with any degree of certainty.
       | 
       | Sufficiently long timelines of existence doesn't guarantee
       | intelligence of species. Dinosaurs existed for about 140 million
       | year & more, whereas we have stepped on moon in less than 25000
       | years of evolution. These things are entirely uncharted
       | territory, left best to astronomers who discover life form or
       | make any contact one day
        
       | dropit_sphere wrote:
       | lol holy shit you guys are a rough crowd
        
       | mark_l_watson wrote:
       | Perhaps a little off topic, but I have thought about this a bit:
       | the type of consciousness and ways of acting in physical reality
       | would probably be very different for digital vs. biology-based
       | life. As strangely different alien biological life might be, true
       | AI will be stranger, unless it is designed and evolves to emulate
       | us in some sense.
       | 
       | I am reading the sci-fi book The Sea of Rust right now, that
       | takes place on earth after AI's have finally killed the last
       | humans. In this fictional work, AIs take on human traits and I
       | don't find that "believable" even for sci-fi.
        
         | songeater wrote:
         | I disagree. "AI" even if it were to exist independently of
         | humans or other pre-existing life still needs to process and
         | dissipate energy in order to perpetuate itself... ie it needs
         | to be "life" first. Intelligence requires the processing of
         | information, and the processing of information requires energy.
         | 
         | For example, even if silicon-based AI replaced humans on earth,
         | it would eventually [0] need to find a way to power itself /
         | continue itself. Ultimately, it would have to revert to solving
         | the same "problem of life"... how do we transform
         | energy/entropy available in the environment into something that
         | "perpetuates the system." When that happens, this AI will
         | itself become subject to the forces of natural-selection, and -
         | over a long enough period of time - naturally-selected traits
         | will be re-aquired (even if such traits were "lost" during a
         | human-to-AI hand-over).
         | 
         | [0] Yes, of course, there could be a very large period of time
         | during which currently constructed energy infrastructure
         | continues on... and this period could be measured in
         | hundreds/thousands of years... very long in terms of human
         | lifespans, but not in geological terms.
        
         | gpvos wrote:
         | Indeed. Intelligent alien life is likely to have evolved out of
         | other forms of life, so concepts as competition, survival,
         | cooperation, are likely to be innate somehow (not necessarily
         | in a conscious way). AI does not need to share that basis at
         | all.
        
       | akomtu wrote:
       | In the ancient Greece there was a tradition of studying math. To
       | the outsiders it appeared as if a bunch of dudes in white robes
       | studied triangles, but the inner circle studied the absolute
       | truths that happened to be represented well by geometry. The
       | Pythagora's triangle wasn't just a shallow numeric relationship
       | to them, they saw the inner truth behind it.
        
       | ifyoubuildit wrote:
       | These threads seem to invite lots of comments of the form
       | "[I|someone I know of|both] [am|is|are] smarter than PG for xyz
       | reasons". These can be interesting to read if you want to get
       | into the nitty gritty.
       | 
       | But they don't often seem to engage with the overall point. In
       | this case, I think that point is that there are probably local
       | truths and universal truths, and wouldn't it be neat to focus on
       | the universal ones, or figure out which ones are only locally
       | true, and why? But who knows, that's just my interpretation.
        
         | sillysaurusx wrote:
         | Agreed. One of pg's examples was "If there are aliens, they'd
         | probably discover that a stool with three legs is the most
         | stable." I'm surprised he didn't include it in this essay.
        
           | asdff wrote:
           | What was the reason a three legged stool is the best? Doesn't
           | that depend on your environment? E.g. the amount of gravity,
           | perhaps wind, or the quality of materials available to
           | construct a stool?
        
             | webstrand wrote:
             | Three points make a plane, a fourth point is redundant.
             | Three equidistant stool legs are stable on any surface
             | regardless of flatness, but four equidistant stool legs
             | need to be aligned correctly with a non-flat surface to be
             | stable.
        
               | asdff wrote:
               | If you live on a world where your wood is more like laffy
               | taffy or whatever, maybe the stool buckles when it only
               | has three legs.
        
       | motohagiography wrote:
       | The beauty of thinking about other civilizations is it provides a
       | due balance for materialist views, where instead of a universal
       | truth, the question becomes what values and principles would be
       | sufficient for us to co-exist with more (and less) advanced
       | beings without respective reduction to foodstuffs, pets, or
       | slavery.
       | 
       | To a more advanced civilization, we are chimpanzees who are both
       | outwardly intelligent, but also tremendously dangerous, and so on
       | what basis could they establish trust with us, or could we
       | establish trust with a civilization of others? As Graham notes,
       | math is one indicator that we are capable of apprehending the
       | universe around us, but given the infinity of life and its
       | necessary physical conditions of beginning and ending, and
       | evolving in aggregate using tools and principles, it's not
       | sufficient. Maybe one way to ensure trust is to share DNA, so
       | that we become each other and we are all "us" - or, perhaps the
       | Girardian mimetic concept generalizes such that it is better to
       | preserve our differences so that we are not competitors for the
       | same resources, and so that we can co-exist with an obvious other
       | but without an existential threat or intrinsic power struggles.
       | 
       | Are there existing moral or philosophical systems that are suited
       | to this problem? Probably, I'm not a religious scholar, but the
       | golden thread that links them seems pretty consistent in
       | attempting to derive alignment to an external truth. The proto-
       | Christian tribe of Essenes, from whom John the Baptist originates
       | and who was the one who baptized Jesus into what became
       | Christianity (solving a weird bootstrapping problem, imo)
       | espoused the values that became the first Church, so there is a
       | historiographical way of looking at moral systems instead of as
       | dogma. Outside religion, in the search for these values that
       | would be suitable for a community of inhabitants, I've come to
       | suspect this is what freemasonry is about, and while not about
       | aliens, I was impressed by their allegorical emphasis on tools
       | instead of doctrine as the landmarks for discovery.
       | 
       | The essential question to me is, once you have accepted there is
       | an other that is greater, or a place that is elsewhere, does it
       | matter whether it's a dude with a beard, multi-armed flying blue
       | people, or an ineffable oneness? That there is a concievable
       | elsewhere beyond your current limits, there must therefore be
       | some point or idea to align and orient yourself to so as to be
       | able to relate to the other beings who have discovered the same
       | point outside our current perspective.
       | 
       | It's all very meta, but it implies a logical and even rational
       | case for some guidance or alignment to this otherness to navigate
       | our present, and that isn't material. The value of the idea of an
       | "alien" truth is it is a means to reconcile secular rational
       | thinking and moralism with universal, essential, or spiritual
       | values, and that could be a very useful tool.
        
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