[HN Gopher] Fitting an elephant with four non-zero parameters
___________________________________________________________________
Fitting an elephant with four non-zero parameters
Author : belter
Score : 294 points
Date : 2024-07-14 14:27 UTC (1 days ago)
(HTM) web link (arxiv.org)
(TXT) w3m dump (arxiv.org)
| EdwardCoffin wrote:
| Freeman Dyson recounts the episode [1] that inspired this paper
| in his web of life interviews (prepositioned to the fitting an
| elephant bit) [2]
|
| [1] https://youtu.be/hV41QEKiMlM
|
| [2] https://youtu.be/hV41QEKiMlM?t=118
| parker-3461 wrote:
| Thanks for linking these, I was not very familiar of these
| works/discussions taking place in the past, but these really
| helped establish the context. Very grateful that these videos
| are readily available.
| EdwardCoffin wrote:
| I listened to the whole series with Dyson some time in the
| past year. It was well worth it. I also listened to the
| series with Murray Gell-Mann [1] and Hans Bethe [2]. All time
| well worth spending, and I've been thinking of downloading
| all the bits, concatenating them into audio files, and
| putting them on my phone for listening to when out on walks
| (I'm pretty sure the videos do not add anything essential:
| it's just a video of the interviewee talking - no visual
| aids).
|
| [1] https://www.youtube.com/playlist?list=PLVV0r6CmEsFxKFx-0l
| sQD...
|
| [2] https://www.youtube.com/watch?v=LvgLyzTEmJk&list=PLVV0r6C
| mEs...
| lazamar wrote:
| Lol. Loved it.
|
| This was a lovely passage from Dyson's Web of Stories interview,
| and it struck a chord with me, like it clearly did with the
| authors too.
|
| It happened when Dyson took the preliminary results of his work
| on the Pseudoscalar theory of Pions to Fermi and Fermi very
| quickly dismissed the whole thing. It was a shock to Dyson but
| freed him from wasting more time on it.
|
| Fermi: When one does a theoretical calculation, either you have a
| clear physical module in mind or a rigorous mathematical basis.
| You have neither. How many free parameters did you use for your
| fitting?
|
| Dyson: 4
|
| Fermi: You know, Johnny Von Neumann always used to say 'with four
| parameters I can fit an elephant; and with five I can make him
| wiggle his trunk'.
| dheera wrote:
| I wish there was more humor on arXiv.
|
| If I could make a discovery in my own time without using company
| resources I would absolutely publish it in the most humorous way
| possible.
| btown wrote:
| There's plenty of humor on arXiv, and that's part of why it's
| so incredible!
|
| Some lists:
|
| https://academia.stackexchange.com/questions/86346/is-it-ok-...
|
| https://www.ellipsix.net/arxiv-joke-papers.html
| azeemba wrote:
| Consider posting this as a new post! It seems like a fun list
| to read through
| mananaysiempre wrote:
| Joke titles and/or author lists are also quite popular, e.g.
| the Greenberg, Greenberger, Greenbergest paper[1], a paper
| with a cat coauthor whose title I can't seem to recall (but
| I'm sure there's more than one I've encountered), or even the
| venerable, unfortunate in its joke but foundational in its
| substance Alpher, Bethe, Gamow paper[2]. Somewhat closer to
| home, I think computer scientist Conor McBride[3] is the
| champion of paper titles (entries include "Elimination with a
| motive", "The gentle art of levitation", "I am not a number:
| I am a free variable", "Clowns to the left of me, jokers to
| the right", and "Doo bee doo bee doo") and sometimes code in
| papers: letmeB this (F you) | you == me = B
| this | otherwise = F you
| letmeB this (B that) = B that letmeB this
| (App fun arg) = letmeB this fun `App` letmeB this arg
|
| (Yes, this is working code; yes, it's crystal clear in the
| context of the paper.)
|
| [1] https://arxiv.org/abs/hep-ph/9306225
|
| [2] https://en.wikipedia.org/wiki/Alpher%E2%80%93Bethe%E2%80%
| 93G...
|
| [3] http://strictlypositive.org/
| gjm11 wrote:
| > paper with a cat coauthor whose title I can't seem to
| recall
|
| You probably have in mind
| https://en.wikipedia.org/wiki/F._D._C._Willard (coauthor of
| multiple papers, sole author of at least one).
| msp26 wrote:
| Pretraining on the Test Set Is All You Need
|
| https://arxiv.org/abs/2309.08632
| paulpauper wrote:
| There is . it is called the General Math section. what is more
| funny than a 2 page proof of the Reiman Hypothesis?
| boywitharupee wrote:
| what's the purpose of this? is it one of those 'fun' problems to
| solve?
| jfoutz wrote:
| This quote might help -
| https://en.wikipedia.org/wiki/Von_Neumann%27s_elephant#Histo...
|
| yes, a fun problem, but also a criticism of using to many
| parameters.
| Steuard wrote:
| Sadly, the constant term (the average r_0) is never specified in
| the paper (it seems to be something in the neighborhood of 180?):
| getting that right is necessary to produce the image, and I can't
| see any way _not_ to consider it a fifth necessary parameter. So
| I don 't think they've genuinely accomplished their goal.
|
| (Seriously, though, this was a lot of fun!)
| rsfern wrote:
| They say in the text that it's the average value of the data
| points they fit to. I think whether to count it as a parameter
| depends on whether you consider standardization to be part of
| the model or not
| Steuard wrote:
| I see your point, that it's really just an overall
| normalization for the size rather than anything to do with
| the _shape_. I can accept that, and I 'll grant them the
| "four non-zero parameters" claim.
|
| Though in that case, I would have liked for them to make it
| explicit. Maybe normalize it to "1", and scale the other
| parameters appropriately. (Because as it stands, I don't
| think you can reproduce their figure from their paper.)
| lupire wrote:
| IIUC:
|
| A real-parameter (r(theta) = sum(r_k cos(k theta))) Fourier
| series can only draw a "wiggly circle" figure with one point on
| each radial ray from the origin.
|
| A compex parameter (z(theta) = sum(e^(z_ theta))) can draw more
| squiggly figures (epicycles) -- the pen can backtrack as the
| drawing arm rotates, as each parameter can move a point somewhere
| on a small circle around the point computed from the previous
| parameter (and recursively).
|
| Obligatory 3B1B https://m.youtube.com/watch?v=r6sGWTCMz2k
|
| Since a complex parameter is 2 real parameters, we should compare
| the best 4-cosine curve to the best 2-complex-exponential curve.
| elijahbenizzy wrote:
| This is humorous (and well-written), but I think its more than
| that.
|
| I'm always making the joke (observation) that ML (AI) is just
| curve-fitting. Whether "just curve-fitting" is enough to produce
| something "intelligent" is, IMO, currently unanswered, largely
| due to differing viewpoints on the meaning of "intelligent".
|
| In this case they're demonstrating some very clean, easy-to-
| understand curve-fitting, but it's really the same process --
| come up with a target, optimize over a loss function, and hope
| that it generalizes, (this one, obviously, does not. But the
| elephant is cute.)
|
| This raises the question Neumann was asking -- why have so many
| parameters? Ironically (or maybe just interestingly), we've done
| a _lot_ with a ton of parameters recently, answering it with
| "well, with a lot of parameters you can do cool things".
| visarga wrote:
| > Whether "just curve fitting" is enough to produce something
| "intelligent" is, IMO, currently unanswered
|
| Continual "curve fitting" to the real world can create
| intelligence. What is missing is not something inside the
| model. It's missing a mechanism to explore, search and expand
| its experience.
|
| Our current crop of LLMs ride on human experience, they have
| not largely participated in creating their own experiences.
| That's why people call it imitation learning or parroting. But
| once models become more agentic they can start creating useful
| experiences on their own. AlphaZero did it.
| soist wrote:
| AlphaZero did not create any experiences. AlphaZero was
| software written by people to play board games and that's all
| it ever did.
| visarga wrote:
| AZ trained in self-play mode for millions of games, over
| multiple generations of a player pool.
| soist wrote:
| I am familiar with the literature on reinforcement
| learning.
| pharrington wrote:
| They're saying the board games AlphaZero played with
| itself _are_ experiences.
| soist wrote:
| And I am saying they are confused because they are
| attributing personal characteristics to computers and
| software. By spelling out what computers are doing it
| becomes very obvious that there is nothing that can be
| aware of any experiences in computers as it is all simply
| a sequence of arithmetic operations. If you can explain
| which sequence of arithmetic operations corresponds to
| "experiences" in computers then you might be less
| confused than all the people who keep claiming computers
| can think and feel.
| nyssos wrote:
| > By spelling out what computers are doing it becomes
| very obvious that there is nothing that can be aware of
| any experiences in computers as it is all simply a
| sequence of arithmetic operations.
|
| By spelling out what brains are doing it becomes very
| obvious that it's all simply a sequence of chemical
| reactions - and yet here we are, having experiences.
| Software will never have a _human_ experience - but
| neither will a chimp, or an octopus, or a Zeta-Reticulan.
|
| Mammalian neurons are not the only possible substrate for
| intelligence; if they're the only possible substrate for
| consciousness, then the fact that we're conscious is an
| inexplicable miracle.
| soist wrote:
| This is a common retort. You can read my other comments
| if you want to understand why you're not really
| addressing my points because I have already addressed how
| reductionism does not apply to living organisms but it
| does apply to computers.
| Dylan16807 wrote:
| The comments where you demand an instruction set for the
| brain, or else you'll dismiss any argument saying its
| actions can be computed? Even after people explained that
| lots of computers don't even have instruction sets?
|
| And where you decide to assume that non-computable
| physics happens in the brain based on no evidence?
|
| What a waste of time. You "addressed" it in a completely
| meaningless way.
| godelski wrote:
| If an algorithmic process is an experience and a
| collection of experiences is intelligence then we get
| some pretty wild conclusions that I don't think most
| people would be attempting to claim as it'd make them
| sound like a lunatic (or a hippy).
|
| Consider the (algorithmic) mechanical process of screwing
| in a screw into a board. This screw has an "experience"
| and therefore intelligence. So... The screw is
| intelligent? Very low intelligence, but intelligent
| according to this definition.
|
| But we have an even bigger problem. There's the metaset
| of experiences, that's the collection of several screws
| (or the screw, board, and screwdriver together). So we
| now have a meta intelligence! And we have several because
| there's the different operations on these sets to
| perform.
|
| You might be okay with this or maybe you're saying it
| needs memory. If the later you hopefully quickly realize
| this means a classic computer is intelligent but due to
| the many ways information can be stored it does not solve
| our above conundrum.
|
| So we must then come to the conclusion that all things
| AND any set of things have intelligence. Which kinda
| makes the whole discussion meaningless. Or, we must need
| a more refined definition of intelligence which more
| closely reflects what people actually are trying to
| convey when they use this word.
| nyssos wrote:
| > If an algorithmic process is an experience and a
| collection of experiences is intelligence
|
| Neither, what I'm saying is that the observable
| correlates of experience are the observable correlates of
| intelligence - saying that "humans are X therefore humans
| are Y, software is X but software is not Y" is special
| pleading. The most defensible positions here are
| illusionism about consciousness altogether (humans _aren
| 't_ Y) or a sort of soft panpsychism (X really does imply
| Y). Personally I favor the latter. Some sort of threshold
| model where the lights turn on at a certain point seems
| pretty sketchy to me, but I guess isn't ruled out. But
| GP, as I understand them, is claiming that biology
| doesn't even supervene on physics, which is a _wild_
| claim.
|
| > Or, we must need a more refined definition of
| intelligence which more closely reflects what people
| actually are trying to convey when they use this word.
|
| Well that's the thing, I don't think people are trying to
| convey any particular thing. I think they're trying to
| find some line - any line - which allows them to write
| off non-animal complex systems as philsophically
| uninteresting. Same deal as people a hundred years ago
| trying to find a way to strictly separate humans from
| nonhuman animals.
| gowld wrote:
| Continuing this reductio ad abusrdum, you might reach the
| fallactious conclusion, as some famous cranks in the past
| did, that intelligence is even found in plants, animals,
| women, and even the uncivilized savages of the new
| continent.
|
| Intelligence appears in gradients, not a simple binary.
| rocqua wrote:
| Are you launching into a semantic argument about the word
| 'experience'? If so, it might help to state what essential
| properties alphago was missing that makes it 'not having an
| experience'.
|
| Otherwise this can quickly devolve into the common useless
| semantic discussion.
| soist wrote:
| Just making sure no one is confused by common
| computationalist sophistry and how they attribute
| personal characteristics to computers and software.
| People can have and can create experiences, computers can
| only execute their programmed instructions.
| HeatrayEnjoyer wrote:
| On what priors are you making that statement?
| soist wrote:
| Rephrase your question. I don't know what you're asking.
| nertirs wrote:
| I think he meant to ask, what is the difference between
| an experience and a predefined instruction?
| gowld wrote:
| Username `soist is an abbreviation for `solipsist, then?
| elijahbenizzy wrote:
| There are a whole bunch of assumptions here. But sure, if you
| view the world as a closed system, then you have a decision
| as a function of inputs:
|
| 1. The world around you 2. The experiences within your
| (really, the past view of the world around you) 3. Innateness
| of you (sure, this could be 2 but I think it's also something
| else) 4. The experience you find + the way you change
| yourself to impact (1), (2), and (3)
|
| If you think of intelligence as all of these, then you're
| making the assumption that all that's required for (2), (3),
| and (4) is "agentic systems", which I think skips a few steps
| (as the author of an agent framework myself...). All this is
| to say that "what makes intelligence" is largely unsolved,
| and nobody really knows, because we actually don't understand
| this ourselves.
| godelski wrote:
| > Continual "curve fitting" to the real world can create
| intelligence.
|
| I'm going to need a citation on this bold claim. And by that
| I mean in the same vein as what Carl Sagan would say
| Extraordinary claims require extraordinary evidence
| Grimblewald wrote:
| I'd simply argue what we do is precisley that, so either we
| are intelligent, or we are not, however we might define
| that intelligence.
| kgeist wrote:
| >It's missing a mechanism to explore, search and expand its
| experience.
|
| Can't we create an agent system which can search the internet
| and choose what data to train itself with?
| Xcode23 wrote:
| you need to define what the utility function of the agent
| is so it can know what to actually use to train itself. If
| we knew that this whole debate about human intelligence in
| computers would either be solved already or well on its way
| to being solved.
| luplex wrote:
| I mean the devil is in the details. In Reinforcement Learning,
| the target moves! In deep learning, you often do things like
| early stopping to prevent too much optimization.
| soist wrote:
| There is no such thing as too much optimization. Early
| stopping is to prevent overfitting to the training set. It's
| a trick just like most advances in deep learning because the
| underlying mathematics is fundamentally not suited for
| creating intelligent agents.
| rocqua wrote:
| Is over fitting different from 'too much optimization'?
| Optimization still needs a value that is optimized. Over
| fitting is the result of too much optimization for not
| quite the right value (i.e. training error when you want to
| reduce prediction error)
| soist wrote:
| What value is being optimized and how do you know it is
| too much or not enough?
| godelski wrote:
| I think the miscommunication is due to the proxy nature
| of our modeling. From one perspective, yes you're right
| because it's just on your optimization function and
| objectives. But if we're in the context where we
| recognize the practical usage of our model replies on it
| being an inexact representation (proxy) then certainly
| there is too much optimization. I mean most of what we
| try to model in ML is intractable.
|
| In fact, that entire notion of early stopping is due to
| this. We use a validation set as a pseudo test set to
| inject information into our optimization products without
| leaking information from the test set (why you shouldn't
| choose parameters based on test results. That is
| spoilage. Doesn't matter if it's status quo, it's
| spoilage)
|
| But we also need to consider that a lack of divergence
| between train/val does not mean there isn't overfittng.
| Divergence implies overfittng but the inverse statement
| is not true. I state this because it's both relevant here
| and an extremely common mistake.
| soist wrote:
| Most practitioners seem to understand that what they are
| doing is creating executable models and they don't
| confuse the model based on numeric observations with the
| actual reality. This is why I very much do not like all
| the AI hype and how statistical models were rebranded as
| artificial "intelligence" because the people who are not
| aware of what the words mean get very confused and start
| thinking they are nothing more than computers executing
| algorithms to fit numerical data to some unspecified
| cognitive model.
| godelski wrote:
| > Most practitioners seem to understand that what they
| are doing is creating executable models and they don't
| confuse the model based on numeric observations with the
| actual reality.
|
| I think you're being too optimistic, and I'm a pretty
| optimistic person. Maybe it is because I work in ML, but
| I've had to explain to a large number of people this
| concept. This doesn't matter if it is academia or
| industry. It is true for both management and coworkers.
| As far as I can tell, people seem very happy to operate
| under the assumption that benchmark results are strong
| indicators of real world performance __without__ the need
| to consider assumptions of your metrics or data. I've
| even proven this to a team at a trillion dollar company
| where I showed a model with lower test set performance
| had more than double the performance on actual customer
| data. Response was "cool, but we're training a much
| larger model on more data, so we're going to use that
| because it is a bit better than yours." My point was that
| the problem still exists in that bigger model with more
| data, but that increased params and data do a better job
| at hiding the underlying (and solvable!) issues.
|
| In other words, in my experience people are happy to be
| Freeman Dyson in the conversation Calavar linked[0] and
| very upset to hear Fermi's critique: being able to fit
| data doesn't mean shit without either a clear model or a
| rigorous mathematical basis. Much of data science is
| happy to just curve fit. But why shouldn't they? You
| advance your career in the same way, by bureaucrats who
| understand the context of metrics even less.
|
| I've just experienced too many people who cannot
| distinguish empirical results from causal models. And a
| lot of people who passionately insist there is no
| difference.
|
| [0] https://news.ycombinator.com/item?id=40964328
| maitola wrote:
| In the case of AI, the more parameters, the better! In Physics
| is the opposite.
| elijahbenizzy wrote:
| One of the hardest parts of training models is avoiding
| overfitting, so "more parameters are better" should be more
| like "more parameters are better given you're using those
| parameters in the right way, which can get hard and
| complicated".
|
| Also LLMs just straight up _do_ overfit, which makes them
| function as a database, but a really bad one. So while more
| parameters might just be better, that feels like a cop-out to
| the real problem. TBD what scaling issues we hit in the
| future.
| will1am wrote:
| A dichotomy between these fields
| will1am wrote:
| Your humorous observation captures a fundamental truth to some
| extent
| maitola wrote:
| I love the ironic side of the article. Perhaps they should add
| the reason for it, from Fermi's and Neumann's. When you are
| building a model of reality in Physics, If something doesn't fit
| the experiments, you can't just add a parameter (or more) variate
| it and fit the data. The model should have zero parameters,
| ideally, or the least possible, or, even at a more deeper level,
| the parameters should emerge naturally from some simple
| assumptions. With 4 parameters you don't know whether you are
| really capturing a true aspect of reality of just fitting the
| data of some experiment.
| jampekka wrote:
| This was mentioned in the first paragraph of the paper. The
| paper is mostly humoristic.
|
| That said, the wisdom of the quip has been widely lost in many
| fields. In many fields data is "modeled" with huge regression
| models with dozens of parameters or even neural networks with
| billions of parameters.
|
| > In 1953, Enrico Fermi criticized Dyson's model by quoting
| Johnny von Neumann: "With four parameters I can fit an
| elephant, and with five I can make him wiggle his trunk."[1].
| This quote is intended to tell Dyson that while his model may
| appear complex and precise, merely increasing the number of
| parameters to fit the data does not necessarily imply that the
| model has real physical significance.
| karmakaze wrote:
| That's how I feel about dark matter. Oh this galaxy is slower
| than this other similar one. The first one must have less
| dark matter then.
|
| What can't be fit by declaring the amount of dark matter that
| _must be present_ fits the data? It 's unfalsifiable, just
| because we haven't found it, doesn't mean it doesn't exist.
| Even worse than string/M-theory which at least has math.
| edflsafoiewq wrote:
| It's easy to say "Epicycles! Epicycles!", but people are
| going to continue using their epicycles until a Copernicus
| comes along.
| jampekka wrote:
| There will be no Copernicus if everybody just studies
| epicycles. E.g. there are massive resources put into the
| desperate WIMP hunt that could be used for finding new
| theories.
| Dylan16807 wrote:
| I don't see how those resources are fungible with each
| other.
| jampekka wrote:
| Research funding is very competitive and scarce.
| Dylan16807 wrote:
| Building a physics machine, and thinking about how the
| equations might work, are so very different.
|
| Does the latter even _get_ funding?
| jampekka wrote:
| Of course. It's called theoretical physics.
| fiddlerwoaroof wrote:
| Well, the funny thing is Copernicus posits just about as
| many epicycles in his theory as previous geocentric
| theories. Only Kepler's discovery of the equal area law
| and elliptical orbits successfully banishes epicycles.
| aeneasmackenzie wrote:
| The history of these discoveries is fascinating and shows
| that Kuhn's scientific revolutions idea is wrong but it's
| always rounded off to "Copernicus and Galileo" and
| doesn't even get them right
| rocqua wrote:
| I used to think this, but dark matter does make useful
| predictions, that are hard to explain otherwise.
|
| This is partially because there are two ways to detect
| dark-matter. The first is gravitational lensing. The second
| is the rotatinal speed of galaxies. There are some galaxies
| that need less Dark Matter to explain their rotational
| speed. We can then cross check whether those galaxies cause
| less gravitational lensing.
|
| Besides that, the gravitational lensing of galaxies being
| stronger than the bright matter in the galaxies can justify
| is hard to explain without dark matter.
| jampekka wrote:
| The problem with dark matter is that there's no (working)
| theory on how the dark matter is distributed. It's really
| easy to "explain" gravitational effects if you can
| postulate extra mass ad-hoc to fit the observations.
| rocqua wrote:
| If there are two different types of observations, and one
| parameter can explain both, that is pretty strong
| evidence. Put differently, dark matter is falsifyable,
| and experiments have tried to falsify it without success.
|
| Besides the idea 'not all mass can be seen optically' is
| not that surprising. The many theories on what that mass
| might be are all speculation, but they are treated as
| such.
| XorNot wrote:
| It's worth noting that one dark matter explanation is
| just: it's cold matter we just can't see through
| telescopes. Or black holes without accretion disks.
|
| Both of these are pretty much ruled out though: you can't
| plausibly add enough brown dwarfs, and if it's black
| holes then you should see more lensing events towards
| nearby stars given how many you'd need.
|
| But they're both concrete predictions which are
| falsifiable (or boundable such that they can't be the
| dominant contributors).
| kaibee wrote:
| I dunno if this is the correct way of thinking about it,
| but I just imagine it as a particle that has mass but
| does not interact with other particles (except at big-
| bang like energy levels?). So essentially a galaxy would
| be full of these particles zipping around never colliding
| with anything. And over time, some/most of these
| particles would have stable orbits (as the ones in
| unstable orbits would have flown off by now) around the
| galactic core. And to an observer, it would look like a
| gravitational tractor ahead of the rest of the physical
| mass of the galaxy (which is slower because it is
| affected by things like friction and collisions?). And so
| you'd see galaxies where the arms are spinning faster
| than they should be?
| nyssos wrote:
| > I dunno if this is the correct way of thinking about
| it, but I just imagine it as a particle that has mass but
| does not interact with other particles (except at big-
| bang like energy levels?).
|
| Not even anything that extreme. What's ruled out is
| interaction via electromagnetism (or if you want to get
| really nit-picky, electromagnetic interaction with a
| strength above some extremely low threshold).
| GuB-42 wrote:
| The dark matter theory is falsifiable. Sure we can't see
| dark matter (it doesn't interact electromagnetically), but
| we can see its effects, and it has to follow the laws of
| physics as we understand them today.
|
| It is actually a satisfying theory with regard to the Occam
| razor. We don't have to change our laws of physics to
| explain the abnormal rotations of galaxy, we just need
| "stuff" that we can't see and yet interact gravitationally.
| When we have stuff like neutrinos, it is not that far
| fetched. In fact, though unlikely given our current
| understanding of physics, dark matter could be neutrinos.
|
| If, as it turn out, the invisible stuff we call dark matter
| doesn't follow the laws of physics as we know them, then
| the dark matter theory is falsified and we need a new one
| (or at least some tweaks). And it may actually be the case
| as a recent paper claims that gravitational lensing doesn't
| match the predictions of the dark matter theory.
|
| The main competitor to dark matter is modified gravity,
| which calls for no new stuff, but changes the equations for
| gravity. For the Occam razor, adding some random term to an
| equation is not really better than adding some invisible
| but well characterized stuff, especially when we consider
| that the equation in question is extremely well tested. It
| is, of course, also falsifiable.
|
| The problem right now is not that these theories are
| unfalsifiable, it is that they are already pretty much
| falsified in their current form (dark matter less than
| modified gravity), and some rework is needed.
| nyssos wrote:
| > Sure we can't see dark matter (it doesn't interact
| electromagnetically), but we can see its effects
|
| Even this is granting too much: "seeing it" and "seeing
| its effects" are _the same thing_. No one has ever
| "directly seen", in the sense that internet DM skepticism
| demands, anything other than a photon.
| adrian_b wrote:
| "Seeing" is indeed a poorly chosen word.
|
| The problem with dark matter is that there does not exist
| any second relationship from which to verify its
| existence, like in the case of normal matter, which takes
| part in a variety of interactions that lead to measurable
| effects, which can be compared.
|
| The amount and the location of dark matter is computed
| from the gravitational forces that explain the observed
| movements of the bodies, but there are no additional
| relationships with any other data, which could
| corroborate the computed distribution of dark matter.
| That is what some people mean by "seeing".
| nyssos wrote:
| All major DM candidates also have multiple interactions:
| that's the WI in WIMP, for instance. In fact I don't know
| that anyone is seriously proposing that dark matter is
| just bare mass with no other properties - aside from the
| practical problems, that would be a pretty radical
| departure from the last century of particle physics.
| jampekka wrote:
| No interactions have been found, despite a lot of
| resources put into the search. So currently all dark
| matter particle theories apart from "non-interacting"
| have been falsified. And non-interacting theories are
| probably unfalsifiable.
|
| Radical departure may well be needed, for other reasons
| too.
| karmakaze wrote:
| > The problem with dark matter is that there does not
| exist any second relationship from which to verify its
| existence.
|
| This is exactly it! Dark matter is strictly defined by
| its effects. The only 'theory' part is a belief that it's
| caused by yet to be found particle that's distributed to
| fit observations. Take all the gravitational anomalies
| that we can't explain with ordinary matter, then
| arbitrarily distribute an imaginary 'particle' that
| solves them: that's DM.
|
| The problem is that the language used to talk about DM is
| wrong. It's not that DM doesn't interact with EM, or the
| presence of DM is causing the galaxies to rotate faster
| than by observed mass. These are all putting the cart
| before the horse. What we have is unexplained
| gravitational effects being attributed to a hypothetical
| particle. If we discovered a new unexplained
| gravitational property, we would merely add that to the
| list of DM's attributes rather than say "oh then it can't
| be DM".
| nyssos wrote:
| > Dark matter is strictly defined by its effects
|
| All physical entities are defined by their effects!
| Suppose we found axions and they had the right mass to be
| dark matter. Would that mean we now "really knew" what
| dark matter was, in your sense? No, it would just push
| the defining effects further back - because all an axion
| is is a quantum of the (strong CP-violation term promoted
| to a field).
|
| Just like the electromagnetic field is the one that acts
| on charged particles in such and such a way, and a
| particle is charged if the electromagnetic field acts on
| it in that way. There's no deeper essence, no intuitive
| "substance" with some sort of intrinsic nature. _All_
| physical properties are relational.
| andrewflnr wrote:
| > For the Occam razor, adding some random term to an
| equation is not really better than adding some invisible
| but well characterized stuff...
|
| You're being too kind. It's worse. Especially when (in my
| understanding anyway) that added term doesn't even
| explain all the things dark matter does.
| adrian_b wrote:
| Adding any finite number of parameters is strictly better
| than adding an infinity of parameters (i.e. an arbitrary
| distribution of dark matter chosen to match the
| observations).
| Dylan16807 wrote:
| The distribution has to be consistent forward and
| backwards in time. It's a lot less arbitrary than you're
| implying, and adding a hundred parameters (or similar
| finite number) to gravity is not better.
| adrian_b wrote:
| If we add an arbitrary amount of dark matter everywhere,
| to match the observed motions of the celestial bodies,
| that adds an infinity of parameters, and not even a
| enumerable one.
|
| This obviously can match almost anything and it has
| extremely low predictive power (many future observations
| may differ from predictions, which can be accounted by
| some dark matter whose distribution was previously
| unknown), so it is a much worse explanation than a
| modified theory of gravity that would have only a finite
| number of additional parameters.
| smallnamespace wrote:
| > to match the observed motions of the celestial bodies
|
| The point is that even with current observational data
| there's no reasonable distribution of dark matter that
| correctly explains all evidence that we have.
|
| Your intuition that "if I have an infinite number of
| degrees of freedom anything at all can be fit" is leading
| you astray here.
| adgjlsfhk1 wrote:
| the reason this isn't true is that by the hypothesis of
| dark matter, it follows gravity but not electromagnetism.
| as such it only fits distributions recoverable from
| evolving gravity. e.g. if we require a certain
| distribution today, it fixes the distribution at all
| other points in time, and we can use light speed delay to
| look into the past to verify whether the distributions
| have evolved according to gravity.
| Retric wrote:
| All observations of individual galaxies occur at a
| specific point in time. We can't use light speed delay to
| see the evolution of individual galaxies only completely
| different galaxies at some other point in time. As such
| each galaxy gets its own value for the amount of dark
| matter.
|
| At minimum this is a ~200 billion parameter model, and
| more if you're looking at smaller structures.
| beeforpork wrote:
| 'dark matter' is not a theory, it is the name of an
| observational problem.
|
| There are many theories to explain dark matter
| observations. MOND is not a competitor with 'dark
| matter', because MOND is a theory and it tries to explain
| some aspects (spiral galaxy rotation) of what is observed
| as the dark matter problem, which consists of many more
| observations. There is no competition here. There are
| other theories to explain dark matter, like dark matter
| particle theories involving neutrinos or whatever, and
| these may be called competitors, but dark matter itself
| is not a theory, but a problem statement.
| XorNot wrote:
| Yes and no...MOND's core proposition is that dark matter
| doesn't exist, and instead modified gravity does.
|
| Whereas you can have many proposals for what dark matter
| is, provided it is capable of being almost entirely only
| gravitationally interacting, and there's enough of it.
|
| MOND has had the problem that depending which MOND you're
| talking about, it still doesn't explain _all_ the dark
| matter (so now you 're pulling free parameters on top of
| free parameters).
| wavemode wrote:
| I've seen this opinion before, but can't seem to square
| it with any reliable source.
|
| Wikipedia has: "dark matter is a hypothetical form of
| matter that appears not to interact with light or the
| electromagnetic field ... Although the astrophysics
| community generally accepts dark matter's existence, a
| minority of astrophysicists, intrigued by specific
| observations that are not well-explained by ordinary dark
| matter, argue for various modifications of the standard
| laws of general relativity. These include modified
| Newtonian dynamics, tensor-vector-scalar gravity, or
| entropic gravity."
|
| Even its name, "dark matter", sort of strongly implies
| this. If someone were just trying to refer to the
| observations, rather than a specific explanation for the
| observations, wouldn't they just say "abnormal galaxy
| rotation curves" rather than "dark matter"?
|
| I'm not saying Wikipedia is an end-all-be-all source on
| this, I'm just asking where you're getting this alternate
| definition. If it is somewhere reliable then perhaps the
| article needs to be rephrased.
| nyssos wrote:
| > What can't be fit by declaring the amount of dark matter
| that must be present fits the data?
|
| Tons of things - just like there are tons of things that
| can't be fit by declaring the amount of
| electromagnetically-interacting matter that must be present
| fits the data.
|
| You can fit anything you like by positing new and more
| complicated laws of physics, but that's not what's going on
| here. Dark matter is ordinary mass gravitating in an
| ordinary way: the observed gravitational lensing needs to
| match up with the rotation curves needs to match up with
| the velocity distributions of galaxies in clusters; you
| don't strictly _need_ large scale homogeneity and isotropy
| but you really really want it, etc. Lambda-CDM doesn 't
| handle everything perfectly (which in itself demonstrates
| that it's not mindless overfitting) but neither does
| anything else.
| XorNot wrote:
| You also have to do other things like not break General
| Relativity.
|
| Which MOND does: it creates huge problems fitting into
| GR.
|
| Whereas dark matter as just regular mass that interacts
| poorly by other means does not.
| jampekka wrote:
| There are modified gravity theories that are
| compatible/extensions to GR, e.g the f(R) gravity
| theories.
|
| Nobody probably believes MOND as such is some fundamental
| theory, rather as a "theory" it's sort of a stepping
| stone. Also MOND is used often interchangeably (and
| confusingly) with modified gravity theories in general.
| karmakaze wrote:
| > Dark matter is ordinary mass gravitating in an ordinary
| way: the observed gravitational lensing needs to match up
| with the rotation curves needs to match up with the
| velocity distributions of galaxies in clusters
|
| Those are all the same thing, the shape of spacetime. The
| only thing DM adds is a backstory that this shaping comes
| from hypothetical undiscovered particles with properties
| that match observations.
| andrewflnr wrote:
| Dark matter is constrained by, among other things,
| dynamical simulations. For instance, here's an example of
| reproducing real world observations, that previously didn't
| have great explanations, using simulations with dark
| matter:
| https://www.youtube.com/live/8rok8E_tz8k?si=Q7vmQYpZr_6K7--
| m. And that's not even getting into the cosmology that has
| to (and mostly does) fit together.
| karmakaze wrote:
| Interesting that you should link that video. Its title
| card says "Angela Collier". Here's a more recent video by
| the physicist[0].
|
| Re: where it says "using simulations with dark matter",
| we can't _simulate_ DM because it doesn 't _have_ any
| properties beyond our observations. All we do is
| distribute amounts of _it_ to match observations. _It_
| could be "Dyson spheres with EM shields" and the results
| would be the same.
|
| [0] https://www.youtube.com/watch?v=PbmJkMhmrVI
| andrewflnr wrote:
| Yes, and I think that video is stupid. She doesn't use
| the term that way in her own talk, and neither does any
| scientist I've ever heard. I think she's trying to make
| some abstract point about science in general and muddying
| the water in the process. Her takes on terminology are
| often bad IMO.
|
| That doesn't take away the fact that when you work with
| the slightly more specific theory of "particle dark
| matter" it produces real results. And I believe there's a
| lot more work over the years in similar areas. It doesn't
| get talked about because it's not sexy, so people who
| only follow cosmology when there's drama don't hear about
| it. That was just the example at the top of my mind
| because I'd seen it recently, and the result is really
| quite spectacular. Did you watch it through?
| Calavar wrote:
| > > In 1953, Enrico Fermi criticized Dyson's model by quoting
| Johnny von Neumann: "With four parameters I can fit an
| elephant, and with five I can make him wiggle his trunk."
|
| For those who are interested, you can watch Freeman Dyson
| recount this conversation in his own words in an interview:
| https://youtu.be/hV41QEKiMlM
| dilawar wrote:
| Hmm..
|
| Hodgin and Huxley did ground-breaking work on squid's giant
| axon and modelled neural activity. They had multiple parameters
| extracted from 'curve fitting' of recorded potential and
| injected currents which were much later mapped to sodium
| channels. Similarly, another process to potassium channels.
|
| I woudnt worry too much having multiple parameters -- even four
| when 3 can't just explain the model.
| nyssos wrote:
| Neuron anatomy is the product of hundreds of millions of
| years of brute contingency. There are reasons why it can't be
| certain ways (organisms that were that way [would have] died
| or failed to reproduce) but no reason whatsoever why it had
| to be exactly _this_ way. It didn 't, there are plenty of
| other ways that nerves _could_ have worked, this is just the
| way they actually do.
|
| The physics equivalent is something like eternal inflation as
| an explanation for apparent fine-tuning - except that even if
| it's correct it's still absolutely nowhere near as complex or
| as contingent as biology.
| will1am wrote:
| The balance between empirical data fitting and genuine
| understanding of the underlying reality
| edflsafoiewq wrote:
| Isn't the form of an equation really just another sort of
| parameter?
| qarl wrote:
| Yes, it is.
|
| Which makes the only truly zero parameter system the
| collection of all systems, in all forms.
| tobias2014 wrote:
| This is why I think that modeling elementary physics is
| nothing else than fitting data. We might end up with
| something that we perceive as "simple", or not. But in any
| case all the fitting has been hidden in the process of ruling
| out models. It's just that a lot of the fitting process is
| (implicitly) being done by theorists; we come up with new
| models and that are then being falsified.
|
| For example, how many parameters does the Standard Model
| have? It's not clear what you count as a parameter. Do you
| count the group structure, the other mathematical structure
| that has been "fitted" through decades of comparisons with
| experiments?
| slashdave wrote:
| You are using the word "fitting" rather loosely. We usually
| "fit" models of fixed function form and fixed number of
| parameters.
|
| You are also glossing over centuries of precedent that
| predate high-energy physics, namely quantum field theory,
| special relativity, and foundational principles such as
| conservation of energy and momentum.
| rocqua wrote:
| It tends to be a parameter that can be derived from rrasoning
| and assumptions. This contrasts to free parameters where you
| say "and we have no idea what this value should be, so we'll
| measure it"
| olalonde wrote:
| Kolmogorov complexity[0] solves this loophole :)
|
| [0] https://en.wikipedia.org/wiki/Kolmogorov_complexity
| gowld wrote:
| Kolmogorov complexity is an effort to wrangle it. It's
| impossible to fully solve.
|
| You can change measured complexity by altering the baseline
| assumptions.
| ahazred8ta wrote:
| Notably done for the first time irl in "Least square fitting of
| an elephant", James Wei (1975) Chemtech
| Pamar wrote:
| https://demonstrations.wolfram.com/FittingAnElephant/
| bee_rider wrote:
| Ya know, in academic writing I tend to struggle with making it
| sound nice and formal. I try not to use the super-stilted
| academic style, but it is still always a struggle to walk the
| line between too loose and too jargony.
|
| Maybe this sort of thing would be a really good tradition.
| Everyone must write a very silly article with some mathematical
| arguments in it. Then, we can all go forward with the comfort of
| knowing that we aren't really at risk of breaking new grounds in
| appearing unserious.
|
| It is well written and very understandable!
| xpe wrote:
| One take away: Don't count parameters. Count bits.
| Scene_Cast2 wrote:
| Better yet, count entropy.
| xpe wrote:
| Why "better"? Entropy in the information theoretic sense is
| usually quantified in bits.
| xpe wrote:
| Another take away (not directly stated in the article but
| implied): Counting the information content of a model is more
| than just the parameters; the structure of the model itself
| conveys information.
| will1am wrote:
| I think often underappreciated insight
| pharmacy7766 wrote:
| One parameter is enough:
| https://aip.scitation.org/doi/10.1063/1.5031956
| dweinus wrote:
| "This single parameter model provides a large improvement over
| the prior state of the art in fitting an elephant"
|
| Lol
| Nition wrote:
| Nice. This is like how you can achieve unlimited compression by
| storing your data in a filename instead of in the file.
| redox99 wrote:
| That's like saying your entire hard drive is a single number.
| comex wrote:
| https://en.wikipedia.org/wiki/Illegal_number
| gowld wrote:
| https://github.com/philipl/pifs
|
| > pfs: Never worry about data again!
|
| > pfs is a revolutionary new file system that, instead of
| wasting space storing your data on your hard drive, stores
| your data in p! You'll never run out of space again - p holds
| every file that could possibly exist! They said 100%
| compression was impossible? You're looking at it!
| danbruc wrote:
| The number of parameters is just the wrong metric, it should be
| the amount of information contained in the parameter values,
| their entropy, Kolmogorov complexity or something along that
| line.
| zellyn wrote:
| From the paper:
|
| > Paintadosi [4] argues that one parameter is always enough. He
| constructed a function that, through a single parameter, can
| depict any shape. However, in essence, this work is a form of
| encoding, mapping the shape into a real number with precision
| extending to hundreds or even thousands of decimal places. For
| our problem, this is meaningless, although the paper's theme is
| that "parameter counting" fails as a measure of model
| complexity
| aqme28 wrote:
| > It only satisfies a weaker condition, i.e., using four non-zero
| parameters instead of four parameters.
|
| Why would that be a harder problem? In the case that you get a
| zero parameter, you could inflate it by some epsilon and the
| solution would basically be the same.
| Sesse__ wrote:
| They also, effectively, fit information in the indexes of the
| parameters. I.e., _which_ of the parameters are nonzero carries
| real information.
|
| In a sense, they have done their fitting using nine parameters,
| of which five are zero.
| aqme28 wrote:
| I didn't read enough to catch that. How the heck did they
| justify that?
| nyssos wrote:
| > In the case that you get a zero parameter, you could inflate
| it by some epsilon and the solution would basically be the
| same.
|
| Not everything is continuous. Add an epsilon worth of torsion
| to GR and you don't get almost-GR, you get a qualitatively
| different theory in which potentially arbitrarily large
| violations of the equivalence principle are possible.
| aqme28 wrote:
| That's not relevant here though, because their function _is_
| continuous and they 're fitting to an arbitrary shape. It's
| not a "perfect science," so there would be wiggle room.
| ggm wrote:
| No love for D'Arcy Thompson on growth and form? His parametric
| models for organisms were quite nice (if very simplistic)
|
| https://en.wikipedia.org/wiki/On_Growth_and_Form
| classified wrote:
| What is that horizontal bar above r0 in the last equation?
| pietroppeter wrote:
| Love how they misspelled Piantadosi as Paintadosi :)
| foobarian wrote:
| Reminds me of an old joke: "What is the difference between an
| elephant and an aspirin?" - "There isn't any, except the elephant
| is large, wrinkly and grey."
| tagami wrote:
| ATCG
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