Comments on: Conversations on the mathematics of belief
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/
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By: kamileon
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-714
Tue, 24 Jun 2003 04:19:15 +0000http://zunger.wordpress.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-714Oh my god?
What really horrifies me is that I have taken just enough discrete math and probability for that all to make PERFECT SENSE. I’m going to go soak my head in Epsom salts for a little bit to ease the pain.
Fortunately for me, this is pretty much the argument I have been living my life by since about 10 anyways (minus the math, I had only gotten as far as geometry at that point), coupled with an ornery state of mind that indicated if god(ess)(e)(s) didn’t like me the way I like me, he/she/it could fuck off.
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By: zunger
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-713
Fri, 20 Jun 2003 04:50:46 +0000http://zunger.wordpress.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-713Well, (a) almost certainly wouldn’t, but why would it be interesting? In the wager, we’re trying to calculate the expected actual reward given a behavior, which means we need to average over possible maps from behavior to reward. Since the only thing that affects the results is the actual correct religion, the set of already-known religions doesn’t enter into it. (b) is close to the set of “contemplatable religions” described above, but as you point out, the cancellation argument applies to that set.
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By: saizai
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-712
Fri, 20 Jun 2003 04:34:34 +0000http://zunger.wordpress.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-712A somewhat more practical poke at this argument:
It is useless, for the original basis of the wager, to consider the set of all *possible* religions. They are not all accessible, and thus one cannot place bets upon them. One must consider the set of *accessible* religions, which would be a) religions that currently or previously existed on Earth, and b) religions that one could entirely conduct on one’s own from scratch (which would sum out to zero, per the previous argument). I don’t believe that (a) would, however.
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By: zunger
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-711
Thu, 19 Jun 2003 23:24:22 +0000http://zunger.wordpress.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-711Well, I think our idea was that non-contemplatables could still be expressed as functions, just not computable ones. But the argument of pairs should still apply, since for any function f, –f is still a function, whether or not it is computable.
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By: zunger
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-710
Thu, 19 Jun 2003 23:22:55 +0000http://zunger.wordpress.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-710Well, this comes down to the question of whether the model is valid at all. For the purpose of this argument, a religion has been modelled by a function from the set of behaviors onto the reals, which I believe is the correct generalization of Pascal’s original construction, and for the specific purpose of a probability calculus seems to encapsulate all of the “relevant” information.
The choice of the reals as the target space for these functions is a bit arbitrary, but I believe it is correct in that we follow the economist’s usual assumption that people can rank-order their preferences, and these are quantifiable by some sort of universal medium of exchange. (e.g., “how much money will you give me for this sack of oranges” determines the value of a sack of oranges, and “how much money do I have to pay you to let me hit you over the head” determines the value of a blunt trauma.)
So the model is that any religion R is uniquely specified by its reward-function fR(B), and the set of all such functions is isomorphic to the set of religions. So for any R, we can define the antireligion R’ by fR'(B)=-fR(B). There’s nothing novel in this definition; I’m simply observing that if f is a function, so is -f, and so the set of all functions can be broken into pairs. (They’re always pairs and not triplets or something else, since -(-f)=f) Then the sum over all functions can be broken into the sum over these pairs, and the pairs sum to zero, since both p and f(B) are real numbers and so obey the usual laws of arithmetic.
So I don’t think this is circular — simply the nature of the model.
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By: grandmoffdavid
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-709
Thu, 19 Jun 2003 22:50:38 +0000http://zunger.wordpress.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-709Another path to wander down would be to question if religions are vectors. If you follow 90% of the Catholic church and 10% Zen Buddhism, do you end up an Episcopalian?
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By: grandmoffdavid
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-708
Thu, 19 Jun 2003 22:47:30 +0000http://zunger.wordpress.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-708Yes, but that’s circular reasoning. You say you handle the the case because you defined that you can handle the case. In other words, since you’ve reduced the religion down to a function you can just multiply it by -1. However, the process of reducing a religion down to an equation is left as an excercise for the reader. This means that you haven’t established that doing so produces an ordinary equation. It is, in fact, possible that a particular religion’s equation contains unsigned numbers or other values for which simply multiplying by -1 is insufficent for negation (sadly my math skills are lacking to the point where I may be talking complete bollocks, but I’m going to soldier on regardless).
In essence, I’m pondering the case where p f(b) – p f(b) != 0. I strongly suspect that this violates at least one mathmatical law, but then again we’re pondering the divine, so anything is really possible.
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By: jrpseudonym
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-707
Thu, 19 Jun 2003 22:45:47 +0000http://zunger.wordpress.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-707Actually, I believe the triplet of anti-religions or the non-opposite anti-religion are possible, but only in the realm of the non-contemplatables. Since a non-contemplatable can’t be expressed as a function (as it cannot be formally expressed by definition), there’s no reason that occurs to me you’d need religion-antireligion pairs in that space. Thus, the non-contemplatable religions could give a non-zero term to our sum.
However, since they aren’t contemplatable, it is impossible to evaluate the value of following any given non-contemplatable, let alone the expectation value of all of them. So, we are given that there is an extra, and by definition, unknowable term in here.
I like to call this “God’s Grace”, or alternatively, the “You’re all screwed” factor.
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By: Anonymous
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-705
Thu, 19 Jun 2003 22:26:25 +0000http://zunger.wordpress.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-705Simon
This goes to prove that super intelligent human beings should never be allowed to not work. A idle mind is a very very very dangerous one. Specially Yonatan’s mind. Thank god its only idle til monday.
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By: moof
https://yonatanzunger.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-703
Thu, 19 Jun 2003 19:21:24 +0000http://zunger.wordpress.com/2003/06/19/conversations-on-the-mathematics-of-belief/#comment-703The most important Zen things you can do are not provable determinable within the system of Zen.
Mmm, g\”odel.
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