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CCC comments on Rationality Quotes Thread September 2015 - Less Wrong
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Well, I suppose in principle there might. But would you really want to bet that way?
Yes, I completely agree.
Almost, but not exactly. It makes a difference how wrong, and in which direction.
One in a billion is only about 30 bits. I don't think it's at all impossible for the complexity-based calculation, if one could do it, to give a much bigger odds ratio than that. The question then is what to do about the possibility of having got the complexity-based calculation (or actually one's estimate of it) badly wrong. I'm inclined to agree that when one takes that into account it's not reasonable to use an odds ratio as large as 10^9:1.
But it's not as if this complexity argument is the only reason anyone has for not believing in God. (Some people consider it the strongest reason, but "strongest" is not the same as "only".)
Incidentally, I offer the following (not entirely serious) argument for pressing the boom-if-God button rather than the boom-with-small-probability button: the chances of the world being undestroyed afterwards are presumably better if God exists.
Insufficient information to bet either way.
Yes, that's what I meant by "capped" - if I did that calculation (somehow working out the complexities) and it told me that there was a one-in-a-billion chance, then there would be a far, far better than a one-in-a-billion chance that the calculation was wrong.
Noted.
If I assume that the second-strongest reason is (say) 80% as strong as the strongest reason (by which I mean, 80% as many bits of persuasiveness), the third-strongest reason is 80% as strong as that, and so on; if the strength of all this (potentially infinite) series of reasons is added together, it would come to five times as strong as the strongest reason.
Thus, for a thirty-bit strength from all the reasons, the strongest reason would need a six-bit strength - it would need to be worth one in sixty-four (approximately).
Of course, there's a whole lot of vague assumptions and hand-waving in here (particularly that 80% figure, which I just pulled out of nowhere) but, well, I haven't seen any reason to think it at all likely that the complexity argument is worth even three bits, never mind six.
(Mind you, I can see how a reasonable and intelligent person might disagree on me about that).
...serious or not, that is a point worth considering. I'm not sure that it's true, but it could be interesting to debate.
I would expect heavier tails than that. (For other questions besides that of gods, too.) I'd expect that there might be dozens of reasons providing half a bit or so.
For what it's worth, I might rate it at maybe 7 bits. Whether I'm a reasonable and intelligent person isn't for me to say :-).
Fair enough. That 80% figure was kindof pulled out of nowhere, really.
You think the theistic explanation might be as much as a hundred times more complex?
...there may be some element of my current position biasing my estimate, but that does seem a little excessive.
So far as this debate goes, my impression is that you either are both reasonable and intelligent or you're really good at faking it.
No, as much as seven bits more complex. (More precisely, I think it's probably a lot more more-complex than that, but I'm quite uncertain about my estimates.)
Damn, you caught me. (Seriously: I'm pretty sure that being really good at faking intelligence requires intelligence. I'm not so sure about reasonable-ness.)
One bit is twice as likely.
Seven bits are two-to-the-seven times as likely, which is 128 times.
...surely?
I can think of a few ways to fake greater intelligence then you have. Most of them require a more intelligent accomplice, in one way or another. But yes, reasonableness is probably easier to fake.
128x more unlikely but not 128x more complex; for me, at least, complexity is measured in bits rather than in number-of-possibilities.
[EDITED to add: If anyone has a clue why this was downvoted, I'd be very interested. It seems so obviously innocuous that I suspect it's VoiceOfRa doing his thing again, but maybe I'm being stupid in some way I'm unable to see.]
...I thought that the ratio of likeliness due to the complexity argument would be the inverse of the ratio of complexity. Thus, something twice as complex would be half as likely. Is this somehow incorrect?
(I have no idea why it was downvoted)
All else being equal, something that takes n bits to specify has probability proportional to 2^-n. So if hypothesis A takes 110 bits and hypothesis B takes 100, then A is about 1000x less probable.
Exactly what "all else being equal" means is somewhat negotiable.
Anyway, the point is that the natural way to measure complexity is in bits, and probability varies exponentially, not linearly, with number of bits.
Yes, and hypothesis A is also 1024x as complex - since it takes ten more bits to specify.
...it seems that our disagreement here is in the measure of complexity, and not the measure of probability. My measure of complexity is pretty much the inverse of probability, while you're working on a log scale by measuring it in terms of a number of bits.