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Rationality Quotes December 2012

Truth comes out of error more easily than out of confusion.

-Francis Bacon

5Jayson_Virissimo9yThis is a duplicate [] from 2009.
Rationality Quotes September 2012

Unfortunately, I can't help you with that, as you have your own models and feelings. You'll have to collect data on your own about which works better in what situation. You can probably start by going over past experiences to see if there are any apparent trends, and then just be mindful of any opportunity you might have to confirm or disconfirm any hypothesis you might generate. Watch out for unfalsifiables!

Rationality Quotes September 2012

chaosmosis said it already :)

You don't have to treat your feelings and your models differently. Just use whichever one the evidence suggests is more likely to be correct in whichever situation you find you find yourself in. See?

0roland9ySounds good, but you still have to decide which one is more likely to be correct, so it doesn't seem to solve the fundamental question at hand.
Rationality Quotes September 2012

Almost. It boils down to: when do you know that your models are correct and when do you know your feelings are correct. Well, how do you settle that question?

0roland9yI don't know, but I have the impression that you have an answer in mind, care to share?
Rationality Quotes September 2012

I agree, but that does not answer the question. How do you decide which to use? What do you need in order to decide?

0chaosmosis9yEmpiricism and logic? Just treat your emotions like a model, and judge them like you would any other. Even though you can't see the inside of your emotions, neither can you see the inside of the thought processes that produce the model. I don't see why there would be any difference between the two.
1roland9yThis boils down to: when do you know that your models are correct? And the answer is, you almost never know, unless it is already settled by science and even then there is room for error and further correction down the road(years away). But you need to make decisions now, every day.
Rationality Quotes September 2012

There are situations where your feelings are more reliable than your models. Are there situations where it is the other way around? How do you decide which to use?

0roland9yI don't intended the original quote to be an admonition against all use of models/reasoning. My point was more or less along the lines of "listen to your feelings, they might be telling you something important. Don't disregard them just because you have some neat model, your model could be wrong."
Rationality Quotes September 2012

To what extent can you expect evolution to have prepared you for your day-to-day experience?

2roland9yIs this a serious question? While the modern world might have changed in a lot of aspects a big factor remains constant: people, social interactions. What use is it to choose the logically correct decision if it still makes us feel miserable?
Rationality Quotes September 2012

Do you have good evidence that your feelings are more often correct than your models?

0roland9yFeelings honed by millions of years of evolution.
Rationality Quotes September 2012

But that's the entire point of the quote! That mathematicians cannot afford the use of irony!

0DanArmak9yYes. My goal wasn't to argue with the quote but to improve its argument. The quote said: And I said, it's not just superficially similar, it's exactly the same and there's no relevant difference between the two that would guide us to use irony in one case and not in the other (or as readers, to perceive irony in one case and serious proof by contradiction in the other).
Rationality Quotes September 2012

The paragraph, of course, was talking about integer powers of 2 that divide p. As in, the largest number 2^k such that 2^k divides p and k is an integer.

The largest real power of 2 that divides p is, of course, p itself, as 2^log_2(p) = p.

0CCC9yLooking over my post again, after a good night's sleep, I see that it wasn't as coherent as it appeared to me yesterday. Let me see if I can put my point a little more clearly. The paragraph centers its claim of the irrationality of √2 on the idea that p² contains exactly twice as many powers of 2 as p does. But that is only true because √2 is irrational, making the demonstration a circular proof. Consider. If √2 were rational, in the form of z/y for some coprime integers z and y, then it would be easy to find an integer that is not itself an integer power of 2, but whose square is an integer power of 2; z would be such a number.
Rationality Quotes September 2012

The view, I think, is that anything you can prove immediately off the top of your head is trivial. No matter how much you have to know. So, sometimes you get conditional trivialities, like "this is trivial if you know this and that, but I don't know how to get this and that from somesuch...".

4GDC39yRelatedly, a mathematician friend said that he uses "obvious" to mean "there exists a very short proof of it." He has been sometimes known to say things like "I think this is obvious but I'm not sure why yet."
Rationality Quotes September 2012

After I spoke at the 2005 "Mathematics and Narrative" conference in Mykonos, a suggestion was made that proofs by contradiction are the mathematician's version of irony. I'm not sure I agree with that: when we give a proof by contradiction, we make it very clear that we are discussing a counterfactual, so our words are intended to be taken at face value. But perhaps this is not necessary. Consider the following passage.

There are those who would believe that every polynomial equation with integer coefficients has a rational solution, a view tha

... (read more)
5DanArmak9yThe two examples are not contradictory, but analogous to one another. The correct conclusion in both is the same, and both are equally serious or ironic. 1. Suppose x² -2=0 has a solution that is rational. That leads to a contradiction. So any solution must be irrational. 2. Suppose x² +1=0 has a solution that is a number. That leads to a contradiction. So any solution must not be a number. Now what is a "number" in this context? From the text, something that is either positive, negative, or zero; i.e. something with a total ordering. And indeed we know (ETA: this is wrong, see below) that such solutions, the complex numbers, have no total ordering. I see no relevant difference between the two cases.
Rationality Quotes September 2012

The quote, phrased in a less tortuous way, says that mathematics contains true statements that cannot be proven, and is unique in being able to demonstrate that it does. So far, so good, although the uniqueness part can be debated.

But the quote also states that mathematics therefore contains an element of faith, that is, that there exist statements that have to be assumed to be true. This is not the case.

Mathematics only compels you to believe that certain things follow from certain axioms. That is all. While these axioms sometimes imply that there exist s... (read more)

Rationality Quotes September 2012

... we tend to be caught up in thinking and the models about the world we create in our minds, actually science is about this. But those models have limitations and are often wrong as the history of science shows time and again.

Now that you have noticed this, what are you going to do with it?

-2roland9yRealize that your mental models might be wrong and don't put too much weight on them, instead put more weight on your feelings.
Rationality Quotes August 2012

impossibilities such as ... tiling a corridor in pentagons

Huh. And here I thought that space was just negatively curved in there, with the corridor shaped in such a way that it looks normal (not that hard to imagine), and just used this to tile the floor. Such disappointment...

This was part of a thing, too, in my head, where Harry (or, I guess, the reader) slowly realizes that Hogwarts, rather than having no geometry, has a highly local geometry. I was even starting to look for that as a thematic thing, perhaps an echo of some moral lesson, somehow.

And ... (read more)

Rationality Quotes August 2012

I don't know that you can really classify people as X or ¬X. I mean, have you not seen individuals be X in certain situations and ¬X in other situations?


Rationality Quotes August 2012

I never meant to say that I could give you an exact description of my own brain and itself ε ago, just that you could deduce one from looking at mine.

Rationality Quotes August 2012

Certainly. I am suggesting that over sufficiently short timescales, though, you can deduce the previous structure from the current one. Maybe I should have said "epsilon" instead of "two words".

Surely there's been at least a little degradation in the space of two words, or we'd never forget anything.

Why would you expect the degradation to be completely uniform? It seems more reasonable to suspect that, given a sufficiently small timescale, the brain will sometimes be forgetting things and sometimes not, in a way that probably isn't ... (read more)

-2Eugine_Nier9ySee the pigeon-hole argument in the original quote.
Rationality Quotes August 2012

I argue that my brain right now contains a lossless copy of itself and itself two words ago!

Getting 1000 brains in here would take some creativity, but I'm sure I can figure something out...

But this is all rather facetious. Breaking the quote's point would require me to be able to compute the (legitimate) results of the computations of an arbitrary number of arbitrarily different brains, at the same speed as them.

Which I can't.

For now.

4maia9yBut our memories discard huge amounts of information all the time. Surely there's been at least a little degradation in the space of two words, or we'd never forget anything.
5RichardKennaway9yI'd argue that your brain doesn't even contain a lossless copy of itself. It is a lossless copy of itself, but your knowledge of yourself is limited. So I think that Nick Szabo's point about the limits of being able to model other people applies just as strongly to modelling oneself. I don't, and cannot, know all about myself -- past, current, or future, and that must have substantial implications about something or other that this lunch hour is too small to contain. How much knowledge of itself can an artificial system have? There is probably some interesting mathematics to be done -- for example, it is possible to write a program that prints out an exact copy of itself (without having access to the file that contains it), the proof of Gödel's theorem involves constructing a proposition that talks about itself, and TDT depends on agents being able to reason about their own and other agents' source codes. Are there mathematical limits to this?
Rationality Quotes August 2012

You'll probably have more success losslessly compressing two brains than losslessly compressing one.

0[anonymous]9yStill, I don't think you could compress the content of 1000 brains into one. (And I'm not sure about two brains, either. Maybe the brains of two six-year-olds into that of a 25-year-old.)
The scourge of perverse-mindedness

If people react badly to having somebody explain how their love works, what makes you think that things will go better with wonder?

And, in a different mental thread, I'm going to posit that really, what you talk about matters much less than how you talk about it, in this context. You can (hopefully) get the point across by demonstrating by example that wonder can survive (and even thrive) after some science. At least if, as I suspect, people can perceive wonder through empathy. So, if you feel wonder, feel it obviously and try to get them to do so also. An... (read more)

The scourge of perverse-mindedness

Eh, both phenomena are things we can reasonably get excited about. I don't see that there's much point in trying to declare one inherently cooler than the other. Different people get excited by different things.

I do see, though, that so long as they think that learning about either the cause of their wonder or the cause of the rainbows will steal the beauty from them, no progress will be made on any front. What I'm trying to say is that once that barrier is down, once they stop seeing science as the death of all magic (so to speak), then progress is much easier. Arguably, only then should you be asking yourself whether to explain to them how rainbows work or why one feels wonder when one looks at them.

0EphemeralNight10yOkay, maybe we need to taboo "excited". This right here is at the crux of my point. I am predicting that, for your average neurotypical, explaining their wonder produces significantly less feeling of stolen beauty than explaining the rainbow. Because, in the former case, you're explaining something mental, whereas in the latter case, you're explaining something mental away. The rainbow may still be there [], but it's status as a Mentally-Caused Thing is not.
The scourge of perverse-mindedness

It may be true that saying these things may not get everybody to see the beauty we see in the mechanics of those various phenomena. But perhaps saying "Rainbows are a wonderful refraction phenomena" can help get across that even if you know that the rainbows are refraction phenomena, you can still see feel wonder at them in the same way as before. The wonder at their true nature can come later.

I guess what I'm getting at is the difference between "Love is wonderful biochemistry" and "Love is a wonderful consequence of biochemistry". The second, everybody can perceive. The first, less so.

0EphemeralNight10yThis kind of touches my point You're talking about two separate physical processes here, and I hold that the latter is the only one worth getting excited about. Or, at least the only one worth trying to get laypeople excited about.
Rationality Quotes June 2012

We have a word for "morality-lessness", and it is amorality, which coincidentally works more naturally in your analogy: If morality is analogous to theism, then a-morality is analogous to a-theism.

I hope you understand my trouble with the use of an idiom that implicitly equates morality with theism. (Well, amorality with atheism, which is more the problem.)

(sorry about all the edits, this was written horribly.)

Rationality Quotes June 2012

So, having values is moral theism? The choice of words seems suspect.

-2Gastogh10yI'd say "moral atheism" is being used as an idiomatic expression; a set of more than one word with a meaning that's gestalt to its individual components. One of the synonyms for "atheism" is "godlessness", so by analogy "moral atheism" would just mean "morality-lessness".
Rationality Quotes June 2012

I am reminded of a commentary on logic puzzles of a certain kind; it was perhaps in a letter to Martin Gardner, reprinted in one of his books. The puzzles are those about getting about on an island where each native either always tells the truth or always lies. You reach a fork in the road, for example, and a native is standing there, and you want to learn from him, with one question, which way leads to the village. The “correct” question is “If I asked you if the left way led to the village, would you say yes?” But why should the native’s concept of lyin

... (read more)
4Fyrius10yIt seems to make the same point as the Parable of the Dagger []. (I.e.: logic games are fun and all, but don't expect things to work that way in the real world. Or: it's valuable to know the difference between intelligent thinking and smart-assery.)
Rationality Quotes June 2012

Duplicate of this. (Well, close enough that the monicker should apply.)

Rationality Quotes May 2012

That is entirely ok -- I am badly in need of sleep and may have failed to optimise my messages for legibility.

Rationality Quotes May 2012

The island of knowledge is composed of atoms? The shoreline of wonder is not a fractal?

7Bugmaster10yPerhaps it's composed of atomic memes ?
Rationality Quotes May 2012

right, well, it's just that 3^^^3 = 3^3^3^3^3...3^3^3 = 3^(3^3^3^3...3^3^3), for a certain number of threes. So, 3^^^3 is 3^(some odd power of three).

2Zack_M_Davis10yYes, thanks; I apologize for having misunderstood you earlier.
Rationality Quotes May 2012

and 3^19683 = 150 ... 859227, which ends in 7.

( The full number is 9392 digits long, which messes up the spacing in these comments. )

Rationality Quotes May 2012

3^odd = 3 mod 4

so it ends in 7.

(but I repeat myself)

0Zack_M_Davis10yI think you're mistaken. Counterexample: 3^9 = 19683.
Rationality Quotes May 2012

no, 7

(see other comment)

0dlthomas10yI would guess that Randaly meant to cheekily respond to in place of my actual question.
1dlthomas10yWhat's the last digit (base 10) of 3^^^3, anyway?
Welcome to Less Wrong! (2012)

As dlthomas says, Cat is the category of all (small) categories. (The small is there in certain (common (?)) axiomatizations only, in which CAT is the quasi-category of all categories.) In abjectly terrible metaphor, a category can be taken as a mathematical structure which represents a particular field of mathematics. So you have things like Grp, the category of groups and group homomorphisms, for group theory, Top, which contains topological spaces and continuous transformations for topology, Set for set theory, etc, etc... This is why they are called ca... (read more)

0Normal_Anomaly10yThank you, that helps.
Timeless Decision Theory: Problems I Can't Solve

Further elaboration on the cake problem's discrete case:

Suppose there are two slices of cake, and three people who can chose how these will be distributed, by majority vote. Nobody votes so that they alone get both slices, since they can't get a majority that way. So everybody just votes to get one slice for themselves, and randomly decides who gets the other slice. There can be ties, but you're getting an expected 2/3 of a slice whenever a vote is finally not a tie.

To get the continuous case:

It's tricky, but find a way to extend the previous reasoning to ... (read more)

Timeless Decision Theory: Problems I Can't Solve

In an undergraduate seminar on game theory I attended, it was mentioned in an answer to a question posed to the presenter that, when computing a payoff matrix, the headings in the rows and columns aren't individual actions, but are rather entire strategies; in other words it's as if you pretty much decide what you do in all circumstances at the beginning of the game. This is because when evaluating strategies nobody cares when you decide, so might as well act as if you had them all planned out in advance. So in that spirit, I'm going to use the following p... (read more)

0VKS10yFurther elaboration on the cake problem's discrete case: Suppose there are two slices of cake, and three people who can chose how these will be distributed, by majority vote. Nobody votes so that they alone get both slices, since they can't get a majority that way. So everybody just votes to get one slice for themselves, and randomly decides who gets the other slice. There can be ties, but you're getting an expected 2/3 of a slice whenever a vote is finally not a tie. To get the continuous case: It's tricky, but find a way to extend the previous reasoning to n slices and m players, and then take the limit as n goes to infinity. The voting sessions do get longer and longer before consensus is reached, but even when consensus is forever away, you should be able to calculate your expectation of each outcome...
Welcome to Less Wrong! (2012)


I should have read this post before I started posting.

I'm here because figuring out how thinking works is something I am interested in doing. I'm a freshman student in mathematics somewhere on planet Earth, but I know an unpredictable amount of mathematics beyond what I am supposed to. Particularly category theory. <3 Cat. Terrible at it for now though.

I hope I can say things which are mostly interesting and mostly not wrong, but my posting record already contains a certain number of errors in reasoning...

0Normal_Anomaly10y(Slightly belated) welcome! Can you explain this bit?
[LINK] Freeman Dyson reviews "Physics on the Fringe: Smoke Rings, Circlons, and Alternative Theories of Everything"

Essentially, yes. They just happened to have had a string of sixes when they threw the dice, culminating in prominence. If you suppose that the crank-susceptible scientists significantly outnumber the crank-immune, you get predictions which resemble our observations that many prominent scientists are susceptible to crank.

Where by crank-susceptible I mean, approximately, susceptible to infection by crank...

Rationality Quotes April 2012

As natural as QFT seems today, my understanding is that in 1960, before many of the classic texts in the domain were published, the ideas still seemed quite strange. We would do well to remember that when we set out to search for other truths which we do not yet grasp.


Rationality Quotes April 2012

Well then the term reptile is somewhat deceptive in evolutionary biology, and based more on some consensus about appearance. Fine. Whatever. The point is that the word metaphysics isn't evocative in that way or any way, except in the context of its historical usage. As such, it cannot inform us in any way about any subject that isn't the phenomenon of its acceptance as a field, and is not even a useful subject heading, being a hodgepodge. We can choose whether to continue to use it, and I don't see why we should.

2J_Taylor10yWithin the field of philosophy, the usage is a fairly normal term, much like 'reptile' or 'sex' are normal terms for most people. Much of my vocabulary comes from that field and I am most comfortable using its terms. 'Metaphysics' is one of many problematic terms which are evocative to me, because I understand how these terms are used. Asking someone who studies philosophy to stop using 'metaphysics' is like asking someone who studies biology to stop using 'species'. However, it is your prerogative to use whatever terms you prefer. I am sure that we are both trying to be pragmatic.
Rationality Quotes April 2012

"X is a metaphysic" becomes "X is somehow a model (of something), but I'm not sure how". "Y is metaphysical" becomes "Y is about or related to a model (somehow)". I assume my understanding is correct, since you didn't correct it. "sloppily-general" is then indeed kind of far from the intended meaning, but that's just because it's a terrible coinage.

Elsewhere, somebody posted a link to the Stanford Encyclopedia of Philosophy's definition of metaphysics. They say right in the intro that they haven't found a g... (read more)

-2Will_Newsome10ySorry, I was just too lazy to correct it. Still too lazy.
Rationality Quotes April 2012

My claim was not about the general lack of utility of buckets. Briefly, the reptile bucket is useful because reptiles are similar to one another, and thus having a way to refer to them all is handy. There is apparently no such justification for "metaphysics", except in the sense that its contents are related by history. But this clearly isn't the use you want to make of this bucket.

0J_Taylor10yThe word 'similar' is often frustratingly vague. However, crocodiles and birds share a more recent common ancestor than crocodiles and turtles. The word is nonetheless used. I do agree with you that it is frustrating that the word's usage is historically determined.
Rationality Quotes April 2012

Correct me if I'm wrong, but "They are probably making some implicit metaphysical claims about what it means for some object(A) to be a simulation of some other object(B)." and "They are probably making some implicit claims about what it means for some object(A) to be a simulation of some other object(B)" mean exactly the same thing.

0J_Taylor10yThey do happen to mean the same thing. This is because the question "What does it mean for some y to be an x?" is a metaphysical question. "They are probably making some aesthetic claim about why object(A) is more beautiful than object(B)" and "They are probably making some claim about why object(A) is more beautiful than object(B)" also mean the same thing.
0TheOtherDave10yCome to that, they both probably mean the same thing as "They are probably making some implicit claims about how some object(B) differs from some other object (A) it simulates," which eliminates the reference to meaning as well.
Rationality Quotes April 2012

Why would generality be opposed to falsifiability? Wouldn't having a model be more general lead to easier falsifiability, given that the model should apply more broadly?

In order to tell whether something is performing a computation, you try to find some way to get the object to exhibit the computation it is (allegedly) making. So -- if I understand correctly -- then a model is metaphysical, in the things you write, if applying it to a particular phenomenon requires an interpretation step which may or may not be known to be possible. How does this differ fr... (read more)

-1Will_Newsome10yI could replace all my uses of the word "metaphysical" with "sloppily-general", I guess, but I'm not sure it has quite the right connotations, and "metaphysical" is already the standard terminology. "Metaphysical" is vague in a somewhat precise way that "sloppily-general" isn't. I appreciate the general need for down-to-earth language, but I also don't want to consent to the norm of encouraging people to take pains to write in such a way as to be understood by the greatest common factor of readers.
Rationality Quotes April 2012

Well that at least makes some sense. I was noticing that Wiki's definition and the definition implied by its examples were in conflict. I don't particularly see why the metaphysics bucket is convenient, though.

Is there any point in discussing metaphysics as anything other than a cultural phenomenon among philosophers?

0J_Taylor10yUnless you are a cladist, 'reptile' is a bucket which contains crocodiles, lizards, and turtles, but does not contain birds and mammals. The word is still sometimes useful for communication. It depends on your goals. I do not generally recommend it, however.
Rationality Quotes April 2012

If you would be so kind as to try and tell me what you mean by "metaphysic", I would be much less confused.

0Will_Newsome10yBy "metaphysic" I mean a high-level model for phenomena or concepts that you can't immediately falsify because, though the model explains all of the phenomena you are aware of, the model is also very general. E.g., if you look at a computer processor you can say "ah, it is performing a computation", and this constrains your anticipations quite a bit; but if you look at a desk or a chair and say "ah, it is performing a computation", then you've gotten into metaphysical territory: you can abstract away the concept of computation and apply it to basically everything, but it's unclear whether or not doing so means that computation is very fundamental, or if you're just overapplying a contingent model. Sometimes when theorizing it's necessary to choose a certain metaphysic: e.g., I will say that I am an instance of a computation, and thus that a computer could make an exact simulation of me and I would exist twice as much, thus making me less surprised to find myself as me rather than someone else. Now, such a line of reasoning requires quite a few metaphysical assumptions—assumptions about the generalizability of certain models that we're not sure do or don't break down—but metaphysical speculation is the best we can do because we don't have a way of simulating people or switching conscious experience flows with other people. That's one possible explanation of "metaphysic"/"metaphysics", but honestly I should look into the relevant metaphilosophy—it's very possible that my explanation is essentially wrong or misleading in some way.
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