Kindly

Based on our rational approach we are at a disadvantage for discovering these truths.

Is that a bad thing?

Because lotteries cost more to play than the chance of winning is worth, someone who understands basic probability will not buy lottery tickets. That puts them at a disadvantage for winning the lottery. But it gives than an overall advantage in having more money, so I don't see it as a problem.

The situation you're describing is similar. If you dismiss beliefs that have no evidence from a reference class of mostly-false beliefs, you're at a disadvant... (read more)

When lacking evidence, the testing process is difficult, weird and lengthy - and in light of the 'saturation' mentioned in [5.1] - I claim that, in most cases, the cost-benefit analysis will result in the decision to ignore the claim.

And I think that this inarguably the correct thing to do, unless you have some way of filtering out the false claims.

From the point of view of someone who has a true claim but doesn't have evidence for it and can't easily convince someone else, you're right that this approach is frustrating. But if I were to relax my stand... (read more)

Rational assessment can be misleading when dealing with experiential knowledge that is not yet scientifically proven, has no obvious external function but is, nevertheless, experientially accessible.

So, uh, is the typical claim that has an equal lack of scientific evidence true, or false? (Maybe if we condition on how difficult it is to prove.)

If true - then the rational assessment would be to believe such claims, and not wait for them to be scientifically proven.

If false - then the rational assessment would be to disbelieve such claims. But for most su... (read more)

I think that in the interests of being fair to the creators of the video, you should link to http://www.nottingham.ac.uk/~ppzap4/response.html, the explanation written by (at least one of) the creators of the video, which addresses some of the complaints.

In particular, let me quote the final paragraph:

There is an enduring debate about how far we should deviate from the rigorous academic approach in order to engage the wider public. From what I can tell, our video has engaged huge numbers of people, with and without mathematical backgrounds, and got them

No, I think I meant what I said. I think that this song lyric can in fact only make a difference given a large pre-existing weight, and I think the distribution of being weirded out by Solstices is bimodal: there are not people that are moderately weirded out but not enough to leave.

Extremely unlikely that people exist that aren't weirded out by Solstices in general but one song lyric is the straw that breaks the camel's back.

Not quite. I outlined the things that have to be going on for me to be making a decision.

In the classic problem, Omega cannot influence my decision; it can only figure out what it is before I do. It is as though I am solving a math problem, and Omega solves it first; the only confusing bit is that the problem in question is self-referential.

If there is a gene that determines what my decision is, then I am not making the decision at all. Any true attempt to figure out what to do is going to depend on my understanding of logic, my familiarity with common mistakes in similar problems, my experience with all the arguments made about Newcomb's prob... (read more)

Let's assume that every test has the same probability of returning the correct result, regardless of what it is (e.g., if + is correct, then Pr[A returns +] = 12/20, and if - is correct, then Pr[A returns +] = 8/20).

The key statistic for each test is the ratio Pr[X is positive|disease] : Pr[X is positive|healthy]. This ratio is 3:2 for test A, 4:1 for test B, and 5:3 for test C. If we assume independence, we can multiply these together, getting a ratio of 10:1.

If your prior is Pr[disease]=1/20, then Pr[disease] : Pr[healthy] = 1:19, so your posterior odds ... (read more)

If you're looking for high-risk activities that pay well, why are you limiting yourself to legal options?

On the subject of Arimaa, I've noted a general feeling of "This game is hard for computers to play -- and that makes it a much better game!"

Progress of AI research aside, why should I care if I choose a game in which the top computer beats the top human, or one in which the top human beats the top computer? (Presumably both the top human and the top computer can beat me, in either case.)

Is it that in go, you can aspire (unrealistically, perhaps) to be the top player in the world, while in chess, the highest you can ever go is a top human that wi... (read more)

This ought to be verified by someone to whom the ideas are genuinely unfamiliar.

I know that's what you're trying to say because I would like to be able to say that, too. But here's the problems we run into.

1. Try writing down "For all x, some number of subtract 1's cause it to equal 0". We can write the "∀x. ∃y. F(x,y) = 0" but in place of F(x,y) we want "y iterations of subtract 1's from x". This is not something we could write down in first-order logic.

2. We could write down sub(x,y,0) (in your notation) in place of F(x,y)=0 on the grounds that it ought to mean the same thing as "y iterations of su

Repeating S n times is not addition: addition is the thing defined by those axioms, no more, and no less. You can prove the statements:

∀x. plus(x, 1, S(x))

∀x. plus(x, 2, S(S(x)))

∀x. plus(x, 3, S(S(S(x))))

and so on, but you can't write "∀x. plus(x, n, S(S(...n...S(x))))" because that doesn't make any sense. Neither can you prove "For every x, x+n is reached from x by applying S to x some number of times" because we don't have a way to say that formally.

From outside the Peano Axioms, where we have our own notion of "number", we ... (read more)

What makes you think that decision making in our brains is free of "regular certainty in physics"? Deterministic systems such as weather patterns can be unpredictable enough.

To be fair, if there's some butterfly-effect nonsense going on where the exact position of a single neuron ends up determining your decision, that's not too different from randomness in the mechanics of physics. But I hope that when I make important decisions, the outcome is stable enough that it wouldn't be influenced by either of those.

I´d say this is not needed, when people say "Snow is white" we know that it really means "Snow seems white to me", so saying it as "Snow seems white to me" adds length without adding information.

Ah, but imagine we're all-powerful reformists that can change absolutely anything! In that case, we can add a really simple verb that means "seems-to-me" (let's say "smee" for short) and then ask people to say "Snow smee white".

Of course, this doesn't make sense unless we provide alternatives. For inst... (read more)

Insurance makes a profit in expectation, but an insurance salesman does have some tiny chance of bankruptcy, though I agree that this is not important. What is important, however, is that an insurance buyer is not guaranteed a loss, which is what distinguishes it from other Dutch books for me.

Prospect theory and similar ideas are close to an explanation of why the Allais Paradox occurs. (That is, why humans pick gambles 1A and 2B, even though this is inconsistent.) But, to my knowledge, while utility theory is both a (bad) model of humans and a guide to ho... (read more)

Yyyyes and no. Our utility functions are nonlinear, especially with respect to infinitesimal risk, but this is not inherently bad. There's no reason for our utility to be everywhere linear with wealth: in fact, it would be very strange for someone to equally value "Having $1 million" and "Having $2 million with 50% probability, and having no money at all (and starving on the street) otherwise".

Insurance does take advantage of this, and it's weird in that both the insurance salesman and the buyers of insurance end up better off in expec... (read more)

When it comes to neutral geometry, nobody's ever defined "parallel lines" in any way other than "lines that don't intersect". You can talk about slopes in the context of the Cartesian model, but the assumptions you're making to get there are far too strong.

As a consequence, no mathematicians ever tried to "prove that parallel lines don't intersect". Instead, mathematicians tried to prove the parallel postulate in one of its equivalent forms, of which some of the more compelling or simple are:

• The sum of the angles in a trian