All of Simetrical's Comments + Replies

In that case Warrigal would have said "rational" rather than "real". Numbers such as 17π would presumably be fine too, not just fractions. "No funny business" presumably means "I'd better be able to figure out whether it's the closest easily". For instance, the number "S(12)/2^n, where S is the max shifts function and n is the smallest integer such that my number is less than 100" is technically well-defined, in a mathematical sense. But if you can actually figure out what it is, you could publish a paper about it in any journal of computer science you liked.

1Liron
That's right, some real numbers can be easily defined while being arbitrarily difficult to calculate the game result with. But there is another reason why we want to tighten the restriction for a submission beyond the standard of being able to "figure out whether it's the closest easily". The point of the game is for people to try to submit 2/3 the average guess. In order to calculate 2/3 the average guess, you need two operations: addition and division with nonzero divisors. The rational numbers form a dense set (for all a<b there exists c such that a<c<b) that is closed under these two operations. It is the natural playing field for this game. The real numbers are constructed in a way that is unrelated to the structure of this game. (I think one typically invokes the concept of sets of rational numbers to construct the reals.) If you want to see why allowing all real numbers adds nothing to the game play, just note that every real number is equal to a terminating decimal plus a real number smaller than Epsilon, where epsilon is made to be much smaller than the difference between any two submitters' numbers. This is the only type of scenario when submitting an irrational number could help you: You are playing against the submissions π, 2π, 7π. If you submit 2π, you tie for the win, while if you submit a rational number very close to 2π then the 2π submitter wins. The scenario can happen with any irrational number, not just π. The irrational numbers just serve to add pointless additional elements to our already well-structured rationals. I hope I have clarified my previous comment.

The question required us to provide real numbers, and infinitesimals are not real numbers. Even if you allowed infinitesimals, though, 0 would still be the Nash equilibrium. After all, if 1/∞ is a valid guess, so is (1/∞)*(2/3), etc., so the exact same logic applies: any number larger than 0 is too large. The only value where everyone could know everyone else's choice and still not want to change is 0.

Doing this with server side scripting is crazy. You'd have to submit a zillion forms and take a second to get the answer for each try. This is precisely the sort of thing client-side scripting is meant for.

Of course, the page would explain that it needed JavaScript, if you had JavaScript disabled, not just show a blank page.

1JGWeissman
Porting the exact behavior of a command line application to a GUI environment like a web page is crazy. Reorganizing the content into a form that fits a new environment makes more sense. For example, the questions to test understanding of awesome sequences can all be part of one form, like in my javascript implementation. By "a zillion", do you mean "tens of"? And a second for the form is a lot shorter than the infinite time it takes on a browser that does not support scripting. No, this is precisely the sort of thing client-side scripting is meant to do better on browsers that support it, without interfering with the good enough implementation on browsers that don't. It most definitely is not meant for the sole means of delivering content that is intended for a wide audience. I know I get annoyed quickly when I am asked to enable JavaScript for a purpose that should not need it. It would be better if we could explain that the page will be more responsive with JavaScript.

I got the wrong rule, but it said I was right because I made only one mistake. I thought the rule was that a sequence was awesome if it was an increasing arithmetic progression. The only one of your examples at the end that contradicted this was 2, 9, 15. All the other awesome ones were, in fact, increasing arithmetic progressions: five out of the six awesome sequences you gave at the end. You should probably cut that down to two or three, so I'd have lost.

That clears things up a lot. I hadn't really thought about the multiple-models take on it (despite having read the "prior probabilities as mathematical objects" post). Thanks.

Even accepting the premise that voting for the proposition was clearly wrong, that's a single anecdote. It does nothing to demonstrate that Mormons are overall worse people than atheists. It is only a single point in the atheists' favor. I could respond with examples of atheists doing terrible things, e.g., the amount of suffering caused by communists.

Anecdotes are not reliable evidence; you need a careful, thorough, and systematic analysis to be able to make confident statements. It's really surprised me how commonly people supply purely anecdotal evi... (read more)

7badger
I think these two sentences are contradictory. If it is a point in favor of the proposition that atheists are better in some regard than Mormons, then it does something to demonstrate the general case, if only weakly. Rationality is not about reserving judgment until ideal evidence is available. Rationality is incorporating all the evidence at your disposal. I agree that most of the evidence available is mixed and weak, so it shouldn't be overweighted, but it is still relevant.

I think this post could have been more formally worded. It draws a distinction between two types of probability assignment, but the only practical difference given is that you'd be surprised if you're wrong in one case but not the other. My initial thought was just that surprise is an irrational thing that should be disregarded ― there's no term for "how surprised I was" in Bayes' Theorem.

But let's rephrase the problem a bit. You've made your probability assignments based on Omega's question: say 1/12 for each color. Now consider another situ... (read more)

6saturn
Not quite. The intuitive notion of "how surprised you were" maps closely to bayesian likelihood ratios. Regarding your die/beads scenarios: In your die scenario, you have one highly favored model that assigns equal probability to each possible number. In the beads scenario you have many possible models, all with low probability; averaging their predictions gives equal probability to each possible color. To simplify things, let's say our only models are M, which predicts the outcomes are random and equally likely (i.e. a fair die or jar filled with an even ratio of 12 colors of beads), and not-M (i.e. a weighted die or jar filled with all the same color beads). In the beads scenario we might guess that P(M)=.1; in the die scenario P(M)=.99. In both cases, our probability of red/one is 1/12, because neither of our models tell us which color/number to expect. But our probability of winning the bet is different -- we only win if M is correct.
0[anonymous]
The justification given in the original post was spectacularly wrong. The assignments themselves may not be. One could just as easily be using the shorthand for "slightly more than 1/12 because I now know that red is a color Omega considers 'color-worthy', he can see that I've got red receptive cones in my eyes and this influences my probability a little more than the possibility that he has obscure color beads. And screw it. Lilac is freaking purple anyway. And he asked for my probability, not that of some pedantic ponce!"
2SarahNibs
No. As another (yours is one) simple counterexample, if I flip a fair coin 100 times you expect around 50 heads, but if I either choose a double-head or double-tail coin and flip that 100 times, you expect either 100 heads or 100 tails - and yet the probability of the first flip is still 50/50. A distribution over models solves this problem. IIRC you don't have to regress further, but I don't remember where (or even if) I saw that result.

I see this conclusion as a mistake: being surprised is a way of translating between intuition and explicit probability estimates. If you are not surprised, you should assign high enough probability, and otherwise if you assign tiny probability, you should be surprised (modulo known mistakes in either representation).

That's not true at all. Before I'm dealt a bridge hand, my probability assignment for getting the hand J♠, 8♣, 6♠, Q♡, 5♣, Q♢, Q♣, 5♡, 3♡, J♣, J♡, 2♡, 7♢ in that order would be one in 3,954,242,643,911,239,680,000. But I wouldn't be the le... (read more)

3Vladimir_Nesov
Thank you, my mistake. I don't understand 'surprise'. Let's see... It looks like 'surprise' is something about promoting a new theory about the structure of environment that was previously dormant, forcing you to drop many cached assumptions. For example, if (surprise, surprise...) you win a lottery, you may promote a previously dormant theory that you are on a holodeck. If you are surprised by observing 1000 equal quantum coinflips (replicated under some conditions, with apparatus not to blame), you may need to reconsider the theory of physics. If you experience surprising luck in a game of dice, you start considering the possibility that dice are weighted.

Huh. Do you need me to post a few dozen links to articles detailing incidents where Mormons did evil acts because of their religious beliefs? I mean, Mormonism isn't as inherently destructive as Islam, but it's not Buddhism either.

Do you have empirical evidence that Mormons are more likely to cause harm than atheists? (Let's say in the clear-cut sense of stabbing people instead of in the sense of spreading irrationality.) Mormons might do more bad things because their god requires it, but atheists might do more bad things because they don't have a god... (read more)

6CronoDAS
Do you have empirical evidence that Mormons are more likely to cause harm than atheists? (Let's say in the clear-cut sense of stabbing people instead of in the sense of spreading irrationality.) I'll claim that, yes, I do have such evidence. The Mormon Church funded many advertisements in favor of California Proposition 8 which denies civil rights to homosexuals.

If the question is "Should Wednesday, while not exactly choosing to believe religion, avoid thinking about it too hard because she thinks doing so will make her an atheist?," then she's already an atheist on some level because she thinks knowing more will make her more atheist, which implies atheism is true. This reduces to the case of deception, which you seem to be against unconditionally.

That's not necessarily true. Perhaps she believes Mormonism is almost certainly right, but acknowledges that she's not fully rational and might be misled ... (read more)

[anonymous]120

I used to think this way. "I won't read Mein Kampf because I might turn out a Nazi." This is actually a very insidiously bad mindset. You should believe any argument that can convince you (in fair conditions -- reading Mein Kampf in a calm frame of mind in your own living room, as opposed to under conditions of intimidation in Nazi Germany.) If Nazism is awful, it will still be awful even when you know more about it. And, indeed, most of us don't turn into neo-Nazis when we read Mein Kampf.

Sure, we have bounded rationality. But I don't see ... (read more)

For what it's worth, if you're using MediaWiki -- I'm a MediaWiki developer and would be happy to help out if anyone wants to know "how do I do X" or otherwise get assistance of some kind setting up or configuring the wiki.

Like Mark Twain's definition of a classic: "Something that everybody wants to have read and nobody wants to read."

Well, everyone sharing the exact same opinion would be stable.

The question "Where did people come from?" is one that you'd expect to be answerable, and therefore a reasonable question to ask. We might, in principle, be able to do research in the physical world to figure out where we came from, since physical events (such as the appearance of a new species) leave traces in the physical world that we might be able to detect long after the fact. Likewise, intuition suggests that everything in the physical world comes from somewhere, and so an answer of "We were always here" seems intuitively unlike... (read more)

8Paul Crowley
No, it's still just a curiosity-stopper. Deferring a philosophical question to God is no more than shoving it underneath His great philosophical carpet of confusion.

Yes it did and does, though you're left having to handwave away the question of "how did God arise?"

Yup, but those seem less troubling if anything than the questions atheism would be unable to answer at the time.

All I ask is that laws have 1) a clearly defined goal of solving a problem that society wants to solve, and 2) empirical evidence (gathered after the fact, if needed) that they are doing what they were intended to do with acceptable side-effects.

How can you gather the evidence after the fact without experimentation? You have to try out alternative copyright schemes, for instance, to test whether it's actually working well. Otherwise I don't know what you'd consider empirical evidence for success.

Marijuana criminalization seems to badly fail at least

... (read more)
7NancyLebovitz
As mentioned previously, decriminalization in Portugal serves as a pretty good experiment, and the outcome was much less harm.

In the Middle Ages, I'm not sure atheism would be too much more rational than theism, in any sense. To the average European in the year 1000, being an atheist would probably be about as rational as being a heliocentrist, i.e., not at all. We know all the arguments in favor of atheism and heliocentrism, but they didn't. No amount of rationalism is going to let you judge things based on evidence you don't know about.

The average person back then could probably have given you plenty of evidence for God's existence. The evidence would be weak by modern stan... (read more)

7Paul Crowley
Theism has never provided answers to these questions, only curiosity-stoppers.
2AllanCrossman
Yes it did and does, though you're left having to handwave away the question of "how did God arise?"

Well, if you're altruistic in the sense you describe, you don't have the utility function I gave in my scenario, so your result will vary. If you don't really mind going to hell too much, comparatively, then the argument doesn't work well.

0Vladimir_Nesov
Of course.

For what it's worth, I've recently started reading this site and am an Orthodox Jew. I have no particular plans to stop reading the site for the time being, because it's often rather interesting.

It may be worth considering that while rationalists may feel they don't need religion, almost all religious people would acknowledge the need for rationality of some kind. If rationality is about achieving your goals as effectively as possible (as some here think), then does it suddenly not work if your goals are "obey the Bible"? No -- your actions wi... (read more)

4Vladimir_Nesov
This is a preference over rituals of cognition, choosing not just decisions, but the algorithms with which you arrive at those decisions. It is usually assumed that only the decisions matter, not the thought process. If you did live in such a world, I agree, you should avoid getting into a doubt-state, although it might be the case that you'd benefit from building an external reasoning device that would resolve the problem for you, not being hindered by limitations on the allowed cognitive algorithms. Also, I guess that an altruistic person should still undergo a conversion to rationality, on the chance that the evidence points out that the inborn priors are incorrect, thus sparing his fellow people living under such limitations on thought.
2steven0461
This is a deep and important topic -- if I lived in the middle ages then if there exists any rationality principle that in practice would have allowed me to deconvert from medieval christianity despite hell threats, I'm not sure what exactly that principle is, though it seems like there should be one.

Can you name any evidence supporting the necessity of, to pick a moderately troublesome example off the top of my head, copyright? I'm not aware of any alternatives being tried (successfully or otherwise) in modern countries, so there's no actual evidence for its necessity. Shall we abolish governmental protection of intellectual property? That's a somewhat tenable position (donation-based profit, etc.), but I'm guessing most people here don't hold it.

I suspect that if your suggestion's consequences were carefully inspected, it would turn out to be more... (read more)

2SoullessAutomaton
You seem to be expecting a much higher standard of evidence than I had in mind. Perhaps necessity was too strong of a word. Utility? Benefit? Something like that. All I ask is that laws have 1) a clearly defined goal of solving a problem that society wants to solve, and 2) empirical evidence (gathered after the fact, if needed) that they are doing what they were intended to do with acceptable side-effects. Marijuana criminalization seems to badly fail at least the latter, and the former depending on what problem you think it's solving. The examples you use both have straightforward utility (compensating positive externalities, reducing death rates), and mixed evidence of effectiveness (lots of art created but copyright terms of infinity minus epsilon inhibit building shared culture, misuse of legal firearms suggests more powerful weapons would also get misused for greater potential damage but firearm crime correlates poorly to ownership rates). Prohibiting by default strikes me as untenable on practical grounds, as well as being morally dubious in the extreme. As an aside, however, I actually would support abolishing intellectual property as weakly superior to the current scheme, but I doubt either is optimal.