Kindly

Karma: 3,097

Kindly 25 Jan 2017 22:02 UTC
1 point
in reply to: Erfeyah’s comment on: Too Much Effort | Too Little Evidence

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 disadvantage in knowing about unlikely-but-true facts that have yet to become mainstream. But you’re also not paying the opportunity cost of trying out many unlikely ideas, most of which don’t pan out. Overall, you’re better off, because you have more time to pursue more promising ways to satisfy your goals.

(And if you’re not better off overall, there’s a different problem. Are you consistently underestimating how useful unlikely fringe beliefs that take lots of effort to test might be, if they were true? Then yes, that’s a problem that can be solved by trying out more fringe beliefs that take lots of effort to test. But it’s a separate problem from the problem of “you don’t try things that look like they aren’t worth the opportunity cost.”)

Kindly 25 Jan 2017 17:40 UTC
1 point
in reply to: Erfeyah’s comment on: Too Much Effort | Too Little Evidence

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 standards, the odds are that I wouldn’t start with your true claim, but start working my way through a bunch of other false claims instead.

Evidence, in the general sense of “some way of filtering out the false claims”, can take on many forms. For example, I can choose to try out lucid dreaming, not because I’ve found scientific evidence that it works, but because it’s presented to me by someone from a community with a good track record of finding weird things that work. Or maybe the person explaining lucid dreaming to me is scrupulously honest and knows me very well, so that when they tell me “this is a real effect and has effects you’ll find worth the cost of trying it out”, I believe them.

Kindly 25 Jan 2017 5:35 UTC
3 points
on: Too Much Effort | Too Little Evidence

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 such claims, this is the right thing to do! It’s true that person A has actually got hold of a true claim that there’s no evidence for. But there’s many more people making false claims with equal evidence; why should B believe A, and not believe those other people?

(More precisely, we’d want to do a cost-benefit analysis of believing/disbelieving a true claim vs. a comparably difficult-to-test false claim.)

Kindly 23 Jan 2017 4:31 UTC
1 point
on: Infinite Summations: A Rationality Litmus Test
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 debating divergent sums in internet forums and in the office. That cannot be a bad thing and I’m sure the simplicity of the presentation contributed enormously to that. In fact, if I may return to the original question, “what do we get if we sum the natural numbers?”, I think another answer might be the following: we get people talking about Mathematics.

In light of this paragraph, I think a cynical answer to the litmus test is this. Faced with such a ridiculous claim, it’s wrong to engage with it only on the subject level, where your options are “Yes, I will accept this mathematical fact, even though I don’t understand it” or “No, I will not accept this fact, because it flies in the face of everything I know.” Instead, you have to at least consider the goals of the person making the claim. Why are they saying something that seems obviously false? What reaction are they hoping to get?

Kindly 7 Jan 2017 16:49 UTC
3 points
in reply to: itaibn0’s comment on: A quick note on weirdness points and Solstices [And also random other Solstice discussion]
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.

Kindly 22 Dec 2016 2:33 UTC
13 points
on: A quick note on weirdness points and Solstices [And also random other Solstice discussion]
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.

Kindly 30 Jun 2015 5:08 UTC
0 points
in reply to: Unknowns’s comment on: Two-boxing, smoking and chewing gum in Medical Newcomb problems
Not quite. I outlined the things that have to be going on for me to be making a decision.

Kindly 29 Jun 2015 19:21 UTC
0 points
on: Two-boxing, smoking and chewing gum in Medical Newcomb problems
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 problem, and so on; if, despite all that, the box I choose has been determined since my birth, then none of these things (none of the things that make up me!) are a factor at all. Either my reasoning process is overridden in one specific case, or it is irreparably flawed to begin with.

Kindly 12 Jun 2015 23:53 UTC
4 points
in reply to: Bound_up’s comment on: Open Thread, Jun. 8 - Jun. 14, 2015
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 are 10:19. This means that Pr[disease|+++] = ¹⁰⁄₂₉, just over ¹⁄₃.

You may have obtained ¹⁄₂ by a double confusion between odds and probabilities. If your prior had been Pr[disease]=1/21, then we’d have prior odds of 1:20 and posterior odds of 1:2 (which is a probability of ¹⁄₃, not of ¹⁄₂).

Kindly 20 May 2015 4:11 UTC
4 points
in reply to: Ishaan’s comment on: What Would You Do If You Only Had Six Months To Live?
If you’re looking for high-risk activities that pay well, why are you limiting yourself to legal options?

Kindly 12 May 2015 15:21 UTC
2 points
in reply to: Toggle’s comment on: Open Thread, May 11 - May 17, 2015
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 will still be defeated by computers?

Or is it that chess, which computers are good at, feels like a solved problem, while go still feels mysterious and exciting? Not that we’ve solved either game in the sense of having solved tic-tac-toe or checkers. And I don’t think we should care too much about having solved checkers either, for the purposes of actually playing the game.

Kindly 11 May 2015 23:37 UTC
8 points
in reply to: John_Maxwell’s comment on: Open Thread, May 11 - May 17, 2015
This ought to be verified by someone to whom the ideas are genuinely unfamiliar.

Kindly 7 May 2015 14:53 UTC
0 points
in reply to: Houshalter’s comment on: Logical Pinpointing
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 subtract 1′s from x cause it to equal 0”. Unfortunately, it doesn’t actually mean that because even in the model where pi is a number, the resulting axiom “∀x. ∃y. sub(x,y,0)” is true. If x=pi, we just set y=pi as well.
The best you can do is to add an infinitely long axiom “x=0 or x = S(0) or x = S(S(0)) or x = S(S(S(0))) or …”

Kindly 5 May 2015 14:40 UTC
0 points
in reply to: Houshalter’s comment on: Logical Pinpointing
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 can say that “Adding N to x is the same as taking the successor of x N times”, where N is a real-honest-to-god-natural-number. But even from the outside of the Peano Axioms, we cannot convince the Peano Axioms that there is no number called “pi”. If pi happens to exist in our model, then all the values …, pi-2, pi-1, pi, pi+1, pi+2, … exist, and together they can be used to satisfy any theorem about the natural numbers you concoct. (For instance, sub(pi, pi, 0) is a true statement about subtraction, so the statement “∀x. sub(x, x, 0)” can be proven but does not rule out pi.)

Kindly 5 May 2015 5:51 UTC
3 points
in reply to: [deleted]’s comment on: Is Determinism A Special Case Of Randomness?
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.

Kindly 3 May 2015 16:49 UTC
3 points
in reply to: PetjaY’s comment on: Disputing Definitions

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 instance, “er” for “I have heard that”, as in “Snow er white, though I haven’t seen it myself” or “The dress er gold, but smee blue.”

Kindly 2 May 2015 20:18 UTC
2 points
in reply to: Xachariah’s comment on: Stupid Questions May 2015
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 how decisions should be made, prospect theory is a better model of humans but often describes errors in reasoning.

(That is, I’m sure it prevents people from doing really stupid things in some cases. But for small bets, it’s probably a bad idea; Kahneman suggests teaching yourself out of it by making yourself think ahead to how many such bets you’ll make over a lifetime. This is a frame of mind in which the risk thing is less of a factor.)

Kindly 2 May 2015 19:36 UTC
7 points
in reply to: Xachariah’s comment on: Stupid Questions May 2015
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 expected utility, but it’s not a Dutch Book in the usual sense: it doesn’t guarantee either side a profit.

The Allais paradox points out that people are not only averse to risk, but also inconsistent about how they are averse about it. The utility function U(X cents) = X is not risk-averse, and it picks gambles 1A and 2A (in Wikipedia’s notation). The utility function U(X cents) = log X is extremely risk-averse, and it picks gambles 1B and 2B. Picking gambles 1A and 2B, on the other hand, cannot be described by any utility function.

There’s a Dutch book for the Allais paradox in this post reading after “money pump”.

Kindly 1 May 2015 3:45 UTC
1 point
in reply to: Epictetus’s comment on: Mental Context for Model Theory
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 triangle is 180 degrees. (Defined to equal two right angles.)
- There exists a quadrilateral with four right angles.
- If two lines are parallel to the same line, they are parallel to each other.
It’s also somewhat misleading to say that mathematicians were mainly motivated by the inelegance of the parallel postulate. Though this was true for some mathematicians, it’s hard to say that the third form of the parallel postulate which I gave is any less elegant, as an axiom, than “If two line segments are congruent to the same line segment, then they are congruent to each other”. Some form of the latter was assumed both by Euclid (his first Common Notion) and by all of his successors.

A stronger motivation for avoiding the parallel postulate is that so much can be done without it that one begins to suspect it might be unnecessary.

Kindly 30 Apr 2015 23:50 UTC
0 points
in reply to: dxu’s comment on: Mental Context for Model Theory
Understandable; perhaps. In mathematics, it is very easy to say understandable things that are simply false. In this case, those false things become nonsense when you realize that the meaning of “parallel lines” is “lines that do not intersect”.

You might say that an explanation gets these facts completely wrong, then it is still a good explanation if it makes you think the right things. I say that such an explanation goes against the spirit of all mathematics. It is not enough that your argument is understandable, for many understandable arguments have later turned out to be incoherent. It is not enough that your argument is believable, for many believable arguments have later turned out to be false.

If you want to do good mathematics, the statements you make must be true.