Rationality Quotes April 2013

Another monthly installment of the rationality quotes thread. The usual rules apply:

  • Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
  • Do not quote yourself.
  • Do not quote from Less Wrong itself, Overcoming Bias, or HPMoR.
  • No more than 5 quotes per person per monthly thread, please.
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In a class I taught at Berkeley, I did an experiment where I wrote a simple little program that would let people type either "f" or "d" and would predict which key they were going to push next. It's actually very easy to write a program that will make the right prediction about 70% of the time. Most people don't really know how to type randomly. They'll have too many alternations and so on. There will be all sorts of patterns, so you just have to build some sort of probabilistic model. Even a very crude one will do well. I couldn't even beat my own program, knowing exactly how it worked. I challenged people to try this and the program was getting between 70% and 80% prediction rates. Then, we found one student that the program predicted exactly 50% of the time. We asked him what his secret was and he responded that he "just used his free will."

-- Scott Aaronson

Holy Belldandy, it sounds like someone located the player character. Everyone get your quests ready!

Woah, I'd better implement Phase One of my evil plan if it's going to be ready in time for the hero to encounter it.

My bet is that the student had many digits of pi memorised and just used their parity.

I would have easily won that game (and maybe made a quip about free will when asked how...). All you need is some memorized secret randomness. For example, a randomly generated password that you've memorized, but you'd have to figure out how to convert it to bits on the fly.

Personally I'd recommend going to random.org, generating a few hexadecimal bytes (which are pretty easy to convert to both bits and numbers in any desired range), memorizing them, and keeping them secret. Then you'll always be able to act unpredictably.

Well, unpredictably to a computer program. If you want to be able to be unpredictable to someone who's good at reading your next move from your face, you would need some way to not know your next move before making it. One way would be to run something like an algorithm that generates the binary expansion of pi in your head, and delaying calculating the next bit until the best moment. Of course, you wouldn't actually choose pi, but something less well-known and preferably easier to calculate. I don't know any such algorithms, and I guess if anyone knows a good one, they're not likely to share. But if it was something like a pseudorandom bitstream generator that takes a seed, it could be shared, as long as you didn't share your seed. If anyone's thought about this in more depth and is willing to share, I'm interested.

When I need this I just look at the nearest object. If the first letter is between a and m, that's a 0. If it's between n and z, that's a 1. For larger strings of random bits, take a piece of memorized text (like a song you like) and do this with the first letter of each word.

There's an easier way: look at the time.

Seconds are even? Type 'f'. Odd? Type 'd'. (Or vice-versa. Or use minutes, if you don't have to do this very often.)

A while ago there was an article (in NYTimes online, I think) about a program that could beat anyone in Rock-Paper-Scissors. That is, it would take a few iterations, and learn your pattern, and do better than chance against you.

It never got any better than chance against me, because I just used the current time as a PRNG.

Edit: Found it. http://www.nytimes.com/interactive/science/rock-paper-scissors.html?_r=0

Edit2: Over 25 rounds, 12-6-7 (win-loss-tie) vs. the "veteran" computer. Try it and post your results! :)

Over 12 rounds against the veteran computer, I managed 5-4-3, just trying to play "counterintuitively" and play differently from how I expected the players whose information it aggregated would play.

Not enough repetitions to be highly confident that I could beat the computer in the long term, but I stopped because trying to be that counterintuitive is a pain.

Got 7-6-7 with the same tactic. Apparently the computer only looks at the last 4 throws, so as long as you're playing against Veteran (where your own rounds will be lost in the noise), it should be possible for a human to learn "anti-anti-patterns" and do better than chance.

19-18-13 over 50 rounds against the veteran, without using any external RNG, by looking away and thinking of something else so that I couldn't remember the results of previous rounds. (My after-lunch drowsiness probably helped.)

14-11-14 over 39 rounds using gwern's linked prng (p=69, m=6, seed=minutes+seconds). Yet another cool trick to impress psychology professors!

I got 8-9-7 over 25 rounds (which seems approximately as good as chance) while trying to be smart (and not using any source of randomness).

Edit: I guess this was actually 24 rounds.

10-5-10 against veteran by trying to predict the computer and occasionally changing levels of recursion.

Second try: 14-16-15 by trying to act randomly (without conciously using an algorithm).

9-6-10 here out of 25 rounds, using current time. :(

I remember doing way better than this a few months ago, just by playing naturally. Gonna blame sample size...

Somehow managed 16-8-5 versus the veteran computer, by using the articles own text as a seed "Computers mimic human reasoning by building on simple rules..." and applying a-h = rock, i-p = paper, q-z = scissors, I think this is the technique I will use against humans (I know a few people I would love to see flail against pseudo-randomness).

That should fail in the long run because it's unlikely that the frequency of letters in English divides so evenly that those rules make each choice converge to happening exactly 1/3 of the time.

I'd just generate the random numbers in my head. A useful thing to do is to pick a couple of numbers from thin air (which doesn't work by itself because the human mind isn't good at picking 'random' numbers from thin air), then adding them together and then taking the last digit (or if you wantt 3 choices, taking them mod 3).

That'll be almost independent but not unbiased: I think that a-m will be more frequent than n-z. However, you could do the von Neumann trick: if you have an unfair coin and want a fair sequence of bits, take the first and second flips. HT is 0, TH is 1, and if you get HH or TT, check the third and fourth flips. Etc.

I just looked up the letter frequencies and it's 52% for a-m and 48% for n-z (for the initial letters of English words). Using 'l' instead of 'm' gives a 47/53 split, so 'm' is at least the best letter to use.

[Aside] When do you need to generate random numbers in your head? I can think of literally no time when I've needed to.

If you have to make a close decision and don't have a coin to flip. Or at a poker tournament if you don't trust your own ability to be unpredictable.

There once was some site that let you enter a sequence of “H” and “T” and test it for non-randomness (e.g. the distribution of the length of runs, the number of alternations, etc.), and after a couple attempts I managed to pass all or almost all the tests a few times in a row.

There once was a hare who mocked a passing tortoise for being slow. The erudite tortoise responded by challenging the hare to a race.

Built for speed, and with his pride on the line, the hare easily won - I mean, it wasn't even close - and resumed his mocking anew.

Winston Rowntree, Non-Bullshit Fables

I've always thought there should be a version where the hare gets eaten by a fox halfway through the race, while the tortoise plods along safely inside its armored mobile home.

On the meta-level, I'm not sure "quickness beats persistence" is a helpful lesson to teach. At the scale of things many LessWrongers would hope to help accomplish, both qualities are prerequisites, and it would be a mistake to believe that you don't have to worry about the latter just because you're one of the millions of people who are 99.9th percentile at the former.

On the base level, a non-bullshit version of this fable would look more like "There once was a hare being passed by a tortoise. Neither of them could talk. The end."

Now that you mention it, a fable, by definition, requires bullshit.

"Moral: life is inarguably a depressingly unfair endeavor."

FTFY:

"Moral: life is inarguably a depressingly fair endeavor."

What's unfair about that quote? The faster one did win. This would exemplify your moral.

"Fairness" depends entirely on what you condition on. Conditional on the hare being better at racing, you could say it's fair that the hare wins. But why does the hare get to be better at racing in the first place?

Debates about what is and isn't fair are best framed as debates over what to condition on, because that's where most of the disagreement lies. (As is the case here, I suppose).

Jack Sparrow: [after Will draws his sword] Put it away, son. It's not worth you getting beat again.

Will Turner: You didn't beat me. You ignored the rules of engagement. In a fair fight, I'd kill you.

Jack Sparrow: Then that's not much incentive for me to fight fair, then, is it? [Jack turns the ship, hitting Will with the boom]

Jack Sparrow: Now as long as you're just hanging there, pay attention. The only rules that really matter are these: what a man can do and what a man can't do. For instance, you can accept that your father was a pirate and a good man or you can't. But pirate is in your blood, boy, so you'll have to square with that some day. And me, for example, I can let you drown, but I can't bring this ship into Tortuga all by me onesies, savvy? So, can you sail under the command of a pirate, or can you not?

--Pirates of the Caribbean

The pirate-specific stuff is a bit extraneous, but I've always thought this scene neatly captured the virtue of cold, calculating practicality. Not that "fairness" is never important to worry about, but when you're faced with a problem, do you care more about solving it, or arguing that your situation isn't fair? What can you do, and what can't you do? Reminds me of What do I want? What do I have? How can I best use the latter to get the former?

That said, if I recognize that I'm in a group that values "fairness" as an abstract virtue, then arguing that my situation isn't fair is often a useful way of solving my problem by recruiting alliances.

If you're in a group where "that's not fair" is frequently a winning argument, you may already be in trouble.

I am in many groups where, when choosing between two strategies A and B, fairness is one of the things we take into account. I'm not sure that's a problem.

If it's a frequently-occurring observation within the group then yes, there seems to be something wrong. Possibly because things are regularly proposed and acted on without considering fairness until someone has to point it out.

If it hardly ever has to be said, but when pointed out, it is often persuasive, you're probably OK.

The pirate-specific stuff is a bit extraneous

Jack Sparrow: The only rules that really matter are these: what a [person] can do and what a [person] can't do. For instance, you can accept that [different customs from yours are traditional and commonly accepted in the world] or you can't. But [this thing you dislike] is [an inevitable feature of your human existence], boy, so you'll have to square with that some day ... So, can you [ally with somebody you find distasteful], or can you not?

Even more generally it can be taken as a paraphraasing of the Litany of Gendlin

Jack Sparrow: The only rules that really matter are these: what a [person] can do and what a [person] can't do. For instance, you can accept [reality] or you can't. But [reality] is [true whether or not you believe it], boy, so you'll have to square with that some day ... So, can you [accept it], or can you not?

Frankly this is precisely the kind of ruthless pragmatism that gives utilitarians such a horrible reputation.

Well, it certainly didn't stop Jack Sparrow from being a beloved character.

You can be ruthless and popular, if you're sufficiently charismatic about it.

It also helps to be fictional, or at least sufficiently removed from the target audience that they perceive you in far mode.

I'd say that it's possible to be ruthless and popular even among people who're familiar with you, as long as you keep your ruthlessness in far mode for the people you're attempting to cultivate popularity amongst. Business executives come to mind, and the more cutthroat strains of social maneuverers.

Dunno mate, I could name a few US Presidents and non-US leaders.

Mmm, that's a good point.

Potentially - If people know you're going to play according to a higher rule or purpose, rather than following feelings, then how much are they going to trust that you're really going to exercise that rule on their behalf?

It'd be like the old argument that people should be allowed to kidnap people off the streets and take their organs - because when you average it out any individual is more likely to need an organ than be the one kidnapped so it's the better gamble for everyone to make. But we don't really imagine it that way, we all see ourselves being the ones dragged off the street and cut up, or that people with unpopular political opinions would be the ones... You can't trust someone who'd come up with that sort of system not to be playing a different game because they've already shown you can't trust their compassionate feelings to work as bounds on their actions. Maybe any friendship they express means as little to them as the poor guy they just butchered.

I wonder how much of it is a trust problem though, and how you'd resolve that. It seems to me that if you knew someone really well, or they didn't seem to be grasping power, they could get away with being ruthless. People seem almost to gloat about how ruthless specops folks and the like are.

My impression is that whistle-blowers tend not to be trusted. It's not as though other businesses line up to hire them.

I think the problem is having moral systems which impose high local costs.

A remarkable aspect of your mental life is that you are rarely stumped. True, you occasionally face a question such as 17 × 24 = ? to which no answer comes immediately to mind, but these dumbfounded moments are rare. The normal state of your mind is that you have intuitive feelings and opinions about almost everything that comes your way. You like or dislike people long before you know much about them; you trust or distrust strangers without knowing why; you feel that an enterprise is bound to succeed without analyzing it. Whether you state them or not, you often have answers to questions that you do not completely understand, relying on evidence that you can neither explain nor defend.

Daniel Kahneman,Thinking, Fast and Slow

As far as I can tell this doesn't agree with my experience; a good chunk of every day is spent in groping uncertainty and confusion.

True, you occasionally face a question such as 17 × 24 = ? to which no answer comes immediately to mind, but these dumbfounded moments are rare.

Unless you took John Leslie's advice and Ankified the multiplication table up to 25.

I've read your link to John Leslie with both curiosity and bafflement.

17 x 24 is not perhaps the best example of a question for which no answer comes immediately to mind. Seventeen has the curious property that 17 x 6 = 102. (The recurring decimal 1/6 = 0.166666... hints to us that 17 x 6 = 102 is just the first of a series of near misses on a round number, 167 x 6 = 1002, 1667 x 6 = 10002, etc). So multiplying 17 by any small multiple of 6 is no harder than the two times table. In particular 17 x 24 = 17 x (6 x 4) = (17 x 6) x 4 = 102 x 4 = 408.

17 x 23 might have served better, were it not for the curious symmetry around the number 20, with 17 = 20 - 3 while 23 = 20 + 3. One is reminded of the identity (x + y)(x - y) = x^2 - y^2 which is often useful in arithmetic and tells us at once that 17 x 23 = 20 x 20 - 3 x 3 = 400 - 9 = 391.

17 x 25 has a different defect as an example, because one can hardly avoid apprehending 25 as one quarter of 100, which stimulates the observation that 17 = 16 + 1 and 16 is full of yummy fourness. 17 x 25 = (16 + 1) x 25 = (4 x 4 + 1) x 25 = 4 x 4 x 25 + 1 x 25 = 4 x 100 + 25 = 425.

17 x 26 is a better example. Nature has its little jokes. 7 x 3 = 21 therefore 17 x 13 = (1 + 7) x (1 + 3) = (1 + 1) + 7 x 3 = 2 + 21 = 221. We get the correct answer by outrageously bogus reasoning. And we are surely puzzled. Why does 21 show up in 17 x 13? Aren't larger products always messed up and nasty? (This is connected to 7 + 3 = 10). Any-one who is in on the joke will immediately say 17 x 26 = 17 x (13 x 2) = (17 x 13) x 2 = 221 x 2 = 442. But few people are.

Some people advocate cultivating a friendship with the integers. Learning the multiplication table, up to 25 times 25, by the means exemplified above, is part of what they mean by this.

Others, full of sullen resentment at the practical usefulness of arithmetic, advocate memorizing ones times tables by the grimly efficient deployment of general purpose techniques of rote memorization such as the Anki deck. But who in this second camp sees any need to go beyond ten times ten?

Does John Leslie have a foot in both camps? Does he set the twenty-five times table as the goal and also indicate rote memorization as the means?

I'm not sure exactly what he had in mind, but learning the multiplication tables using Anki isn't exactly rote.

Now, this may not be the case for others, but when I see a new problem like 17 x 24, I don't just keep reading off the answer until I remember it when the note comes back around. Instead, I try to answer it using mental arithmetic, no matter how long it takes. I do this by breaking the problem into easier problems (perhaps by multiplying 17 x 20 and then adding that to 17 x 4). Sooner or later my brain will simply present the answers to the intermediate steps for me to add together and only much later do those steps fade away completely and the final answer is immediately retrievable.

Doing things this way, simply as a matter of course, you develop somewhat of a feel for how certain numbers multiply and develop a kind of "friendship with the integers." Er, at least, that's what it feels like from the inside.

That's not the important point. Even if you have, you will still face the same problem when facing a question like, for example, say 34 × 57 = ?. The quote was using that particular problem as an example. If that example does not apply to you because you Ankified the multiplication table up to 25 or for any other reason, it is trivial to find another problem that gives the desired mental response. (As I just did with the 34 × 57 problem.)

Agreed. I'm not so much disagreeing with the thrust of the quote as nitpicking in order to engage in propaganda for my favorite SRS.

Of course, even if I have no complete answer to 34 × 57, I still have "intuitive feelings and opinions" about it, and so do you. For example, I know it's between 100 and 10000 just by counting the digits, and although I've just now gone and formalized this intuition, it was there before the math: if I claimed that 34 × 57 = 218508 then I'm sure most people here would call me out long before doing the calculation.

What has this got to do with the original quote? The quote was claiming, truthfully or not, that when one is first presented with a certain type of problem, one is dumbfounded for a period of time. And of course the problem is solvable, and of course even without calculating it you can get a rough picture of the range the answer is in, and with a certain amount of practice one can avoid the dumbfoundedness altogether and move on to solving the problem, and that is a fine response to give to the original quote, but it has no relevance to what I was saying.

All I was saying is that it is an invalid objection to object to the quote based on the fact that with a certain technique the specific example given by the quote can be avoided, as that example could have easily been replaced by a similar example which that technique does not solve. I was talking about that specific objection I was not saying the quote is perfect, or even that it is entirely right. You may raise these other objections to it. But the specific objection that Jayson_Virissimo raised happens to be entirely invalid.

I wasn't trying to contradict you. Try reading my comment again without the "No, you're wrong, and here's why" you seem to have imagined attached to the beginning.

I'm a little perplexed that I haven't got the multiplication table up to 25 memorized, given the number of times I've multiplied any two numbers under 25.

I'm curious - what advantage do you get from this?

So far, mostly the ability to perform entertaining parlor tricks (via mental arithmetic and a large body of facts about the countries of the world). I admit, it is not very impressive, but not useless either. In other words, nothing you couldn't do in a few minutes with a smartphone (although, I imagine, that would tend to ruin the "trick").

Those moments send me into panic attacks. (At least when they're on significant topics not on maths).

*Topics where my inability to work out the answer immediately implies a lack of ability or puts me at risk.

More specifically, one thing I learned from Terry that I was not taught in school is the importance of bad proofs. I would say "I think this is true", work on it, see that there was no nice proof, and give up. Terry would say "Here's a criterion that eliminates most of the problem. Then in what's left, here's a worse one that handles most of the detritus. One or two more epicycles. At that point it comes down to fourteen cases, and I checked them." Yuck. But we would know it was true, and we would move on. (Usually these would get cleaned up a fair bit before publication.)

-Allen Knutson on collaborating with Terence Tao

At that point I'd start wondering why there doesn't appear to be a simple proof. For example, maybe some kind of generalization of the result is false and you need the complexity to "break the correspondence" with the generalization.

(meta)

Saith the linked site: “You must sign in to read answers past the first one.”

Well, that's obnoxious.

If it's any consolation, none of the answers past the first one on this question are very good.

Or else I would say "I wonder if this is true" and Terry would say "Oh, it is for a while, but it starts to fail in six dimensions" where I hadn't hardly exhausted the 3-dim

-Same place

Don’t settle. Don’t finish crappy books. If you don’t like the menu, leave the restaurant. If you’re not on the right path, get off it.

--Chris Brogan on the Sunk Cost Fallacy

If you don’t like the menu, leave the restaurant.

If there is another one next door, maybe. If it is much farther than that the menu would have to be fairly bad.

Don’t settle.

... if there is a sufficiently convenient alternative and the difference is significant.

I think you are using settle in its more precise meaning (i.e. release a legal claim), which is not consistent with the colloquial usage. Colloquially, "settle" is often used as the antonym of "take reasonable risks."

Similarly, I think the difference between "don't like the menu" and "fairly bad" is hairsplitting for someone who would find this level and type of advice useful. In just about any city, the BATNA is "travel to another place to eat, getting no further from your home than you were at the first place." And that's a pretty good alternative. I think the quote correctly asserts that the alternative is underrated.

I think the quote correctly asserts that the alternative is underrated.

While I assert that the quote advocates premature optimization. It distracts from actual cases of the sunk cost fallacy by warning against things that are often just are not worth fixing.

"The peril of arguing with you is forgetting to argue with myself. Don’t make me convince you: I don’t want to believe that much."

  • Even More Aphorisms and Ten-Second Essays from Vectors 3.0, James Richardson

The others are quite nice too: http://www.theliteraryreview.org/WordPress/tlr-poetry/

If knowledge can create problems, it is not through ignorance we can solve them.

-- Isaac Asimov

This may not be strictly true. Consider the basilisk.

-2 points