[HN Gopher] PHYS771 Lecture 17: Fun with the Anthropic Principle...
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PHYS771 Lecture 17: Fun with the Anthropic Principle (2006)
Author : Tomte
Score : 53 points
Date : 2024-05-15 06:39 UTC (1 days ago)
(HTM) web link (www.scottaaronson.com)
(TXT) w3m dump (www.scottaaronson.com)
| mjburgess wrote:
| The problem here arises in thinking this has anything to do with
| bayes rule, probability or any formalism of this kind.
|
| The rule `P(B|A) = P(A|B)P(B)/P(A)` is only a model of ratios the
| follow a certain sort of set logic (and measure to [0, 1]).
|
| It says nothing about what this model refers to. Does `B` refer
| to a proposition? A belief? An event? Bayesians say "belief", but
| then what do these beliefs model?
|
| Do I believe "the sky is blue" ? What would it mean to have this
| as a belief? Do I have some model of the sky, of blue? etc. Why
| should we suppose that _beliefs_ should operate according to
| bayes rule?
|
| Yes, for any given class of beliefs, _relative to some model of
| the world_ , you can construct an argument that bayes rule must
| apply. But these arent beliefs, they're truth-apt propositions
| which model a world. Beliefs are just mental states, and little
| constrains their consistency.
|
| Since we do not know what the world is like. We do not know that
| believing, "frozen water could fall in a glass of water in
| ordinary conditions" contradicts, "water is largely comprised of
| h2o" -- so we can believe both at the same time.
|
| So what's the issue here? The issue is that the formalism is
| useless for generating descriptions of the world (events,
| beliefs, propositions, ... whatever you like). And it's only when
| we have a set of such descriptions which _actually_ model
| features of reality, and which therefore have some consistency
| between them... that we can actually construct any kind of formal
| model of reasoning. At this point, most of the work is done.
|
| Thus much of the suppose normative force, and epistemic weight,
| of all this machinery is an illusion. Since we have no idea what
| beliefs affect the probabilities of what others; of what beliefs
| correspond to features of the world; and so on... no problems are
| resolved.
|
| I'm always irritated by professors who will stand in front of a
| room and demonstrate people's irrationality against some
| experiment they perform, _asserting_ that the model of the
| experiment people have in their heads is "the one on the slide",
| and then conclude that they are wrong. The issue is, in my
| experience without exception, that the audience is not so dumb as
| the professor. And has not made the very bizarre assumptions
| scrawled on the board; and hence the entire formal model is
| invalid.
| winwang wrote:
| I have a hard time grokking your wording, but I'd like to point
| out that Bayes' Rule is typically "typed" to events (i.e. B is
| of type "event").
|
| That being said, I don't think this _needs_ to be the case. The
| syntax could "compile" differently depending on context.
|
| From my understanding, Bayes' Rule is more about updates to
| pre-existing probabilities, which we label with the suggestive
| name 'beliefs', which aren't necessarily tied to a human's
| mental state.
|
| I do agree with your last paragraph, but I also accept that
| those profs likely do so because some majority or plurality of
| students _do_ hols that belief. That being said, there 's
| definitely room for different wording.
| mjburgess wrote:
| in Bayesian epistemology, the arguments to probability
| "functions" are beliefs.
|
| To simplify my phrasing: to model any aspect of reality
| requires inventing a formalism; that formalism itself largely
| fails to correspond to reality. insofar as it does, the
| formalism is useless.
|
| Bayesian epistemology pretends to greater insights than it
| has, because it assumes that the modelling relation is
| simple; whereas, really its where the whole part of
| epistemology lies.
| j7ake wrote:
| The issue of Bayes rule (it's not really theorem) is that you
| have to concretely define your set of possible hypotheses
| beforehand.
|
| In the real world, there are unknown unknowns, and those can't be
| put into the Bayes rule calculation.
| rthnbgrredf wrote:
| Reality is not a chess board. Thing is, we don't know what we
| don't know and we can't put a probability on that.
|
| We don't even know how much we don't know, but I would
| intuitively say very much.
| andsoitis wrote:
| > We don't even know how much we don't know, but I would
| intuitively say very much.
|
| I choose to believe that there is, and always will be, much
| more that we do not know than what we know. That is truly
| exciting because it means our curiosity can never be satiated.
| stareatgoats wrote:
| > I would intuitively say very much
|
| Potential knowledge is probably infinite. How much is a finite
| fraction of infinite? Likely not much.
|
| To be fair, when we say "we know much" we don't compare with
| all that potential knowledge, but with the knowledge of the
| generations that preceded us, or compared to the uneducated
| goat herder on some steppe, or some such thing. But this is
| also tricky, because they knew/know thing that we don't and so
| we find ourselves in a muddy morass, even when guessing how
| much we know (compared to someone else), let alone trying to
| accurately assess this. Unless we are very specific of course,
| like narrowing it down to maths or nuclear science.
|
| Come to think of it, that's probably what you meant.
|
| OK, scratch this.
| winwang wrote:
| You're describing games of incomplete information (i.e. as
| opposed to a perfect game like chess). Interestingly, when I
| look this up, the first thing that pops up is "Bayesian Game".
| rthnbgrredf wrote:
| A Bayesian game is a strategic decision-making model that
| assumes players have incomplete information. In such games,
| players are aware of the rules and the mechanics governing
| the game, but they lack full knowledge about certain aspects,
| like the strategies or payoffs of other players. Poker is a
| classic example where the game rules are clear to everyone,
| but players do not know each other's hands.
|
| This contrasts with the real world, where we do not fully
| understand the "rules" of reality. While we have well-
| established theories like Newtonian mechanics, quantum
| mechanics, and general relativity, these frameworks do not
| provide a complete explanation of everything. In reality, we
| are continually searching for new rules and understandings.
|
| Imagine playing a game with three known rules while being
| told there are additional unknown rules. Calculating the odds
| of these unknown rules based on the existing ones is simply
| not possible from my perspective.
|
| Then we have concepts like the anthropic principle, which
| states that "conditions observed in the universe must allow
| the observer to exist." This statement is a tautology,
| meaning it is self-evidently true. It's similar to saying, "a
| game that is played must have conditions that support
| playing." While tautologies are logically true, they do not
| offer new information and thus don't allow for substantive
| new conclusions to be drawn. They simply restate the obvious
| without providing additional insights.
| kromem wrote:
| The argument of "we can't say because of all we don't know"
| needs constant updating.
|
| Early on, you have Elihu in _Job_ arguing that we can 't
| understand creation because why it rains and where snow comes
| from is _beyond human understanding_.
|
| Now we learn it as a nursery rhyme.
|
| Maybe we should entertain the idea that we do have adequate
| information to assess our overall situation and see what we
| find.
| hbrav wrote:
| The dice room puzzle described here is a little frustrating,
| because no-one seems to get it right. In the finite population
| case the anthropic argument for "I'm likely to be the in the last
| round" is wrong. In the countably infinite case it can't be
| applied (no discrete uniform distribution on a countably infinite
| set). I wrote some ramblings about it here, though I'm not sure
| it's super-clear:
| https://harrybraviner.github.io/posts/2024-01-28-anthropic_d...
| nicklecompte wrote:
| I thought the writeup was convincing and addresses the heart of
| the paradox. The only nitpick: you can have uniform probability
| distributions on infinite sets, like [0,1]:
| https://en.wikipedia.org/wiki/Continuous_uniform_distributio...
| There p(x) = 0 for any x, but for fixed e, p(x +/- e) is the
| same for all x.
|
| But you can't have such a distribution on an _unbounded_ set,
| which is where the paradox fails. If we had a uniform
| distribution on an unbounded set, p(x + /- e) has to be the
| same for all x and therefore nonzero, but p(1
| +/- e) + p(2 +/-e) + ...
|
| has to sum to <= 1. It is an infinite sum of nonzero terms so
| this is a contradiction. (The same argument works if you drop
| the epsilon for thinking of a distribution on the integers).
|
| I think your writeup was basically clear on this in terms of
| the math, just some of the language was a bit confused.
| hbrav wrote:
| Yeh, U[0, 1] is different because it assigns non-zero
| probabilities to intervals, not points. In this case we're
| assuming that we live in an uncountable population (each real
| in [0, 1] is a person), so you can't do things like assign a
| unique number to each person. There, even if the maniac goes
| on kidnapping forever, he will only kidnap a countable subset
| of the population. Thinking about this honestly makes my
| brain hurt a little.
| stygiansonic wrote:
| Thanks for writing this.
|
| Is this concept (dice room puzzle, doomsday argument) at all
| related to the st Petersburg paradox?
| https://en.m.wikipedia.org/wiki/St._Petersburg_paradox
| hbrav wrote:
| I think it's a little different. It's like asking "what is
| the probability that a given coin is in the round that the
| player wins?" But the St Petersburg paradox isn't about that,
| it's purely about how many coins the player wins. I suppose
| it runs into similar problems when you ask about prizes that
| are so large that the bank runs out of coins, but I think it
| remains interesting even if you cap it at some finite number
| of coin flips. It still has the small-probability-of-huge-
| payout property.
|
| If you've ever looked at the Kelly Criterion, that seems
| related (and in fact is one of the articles linked to from
| that Wikipedia page). There you maximise expected log return
| at each round, and I think that tames the infinity in this
| case (though I have _not_ checked that).
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