A friend of mine has a rather precocious daughter with poor impulse control, and asked if I knew any behavior games that encourage children to think out the consequences of actions before they do them.

I'm familiar with the Good Behavior Game and the like, but standard conditioning hasn't been very effective with this child in the past. She's quite clever about subverting rules when possible, and shutting down entirely when subversion fails.

Please, one suggestion per thread so that the karma thing can do its thing.

Link to ACM press release.

In addition to their impact on probabilistic reasoning, Bayesian networks completely changed the way causality is treated in the empirical sciences, which are based on experiment and observation. Pearl's work on causality is crucial to the understanding of both daily activity and scientific discovery. It has enabled scientists across many disciplines to articulate causal statements formally, combine them with data, and evaluate them rigorously. His 2000 book Causality: Models, Reasoning, and Inference is among the single most influential works in shaping the theory and practice of knowledge-based systems. His contributions to causal reasoning have had a major impact on the way causality is understood and measured in many scientific disciplines, most notably philosophy, psychology, statistics, econometrics, epidemiology and social science.

While that "major impact" still seems to me to be in the early stages of propagating through the various sciences, hopefully this award will inspire more people to study causality and Bayesian statistics in general.

Yes, this a repost from Hacker News, but I want to point out some books that are of LW-related interest.

The Hacker Shelf is a repository of freely available textbooks. Most of them are about computer programming or the business of computer programming, but there are a few that are perhaps interesting to the LW community. All of these were publicly available beforehand, but I'm linking to the aggregator in hopes that people can think of other freely available textbooks to submit there.

The site is in its beginning explosion phase; in the time it took to write this post, it doubled in size. If previous sites are any indication, it will crest in a month or so. People will probably lose interest after three months, and after a year the site will probably silently close shop.

MacKay, Information Theory, Inference, and Learning Algorithms

I really wish I had an older version of this book; the newer one has been marred by a Cambridge UP ad on the upper margin of every page. Publishers ruin everything.

The book covers reasonably concisely the basics of information theory and Bayesian methods, with some game theory and coding theory (in the sense of data compression) thrown in on the side. The style takes after Knuth, but refrains from the latter's more encyclopedic tendencies. It's also the type of book that gives a lot of extra content in the exercises. It unfortunately assumes a decent amount of mathematical knowledge — linear algebra and calculus, but nothing you wouldn't find on the Khan Academy.

Hacker Shelf review, book website.

Easley and Kleinberg, Networks, Crowds, and Markets

There's just a lot of stuff in this book, most of it of independent interest. The thread that ties the book together is graph theory, and with it they cover a great deal of game theory, voting theory, and economics. There are lots of graphs and pictures, and the writing style is pretty deliberate and slow-paced. The math is not very intense; all their probability spaces are discrete, so there's no calculus, and only a few touches of linear algebra.

Hacker Shelf review, book website.

Gabriel, Patterns of Software

This is a more fluffy book about the practice of software engineering. It's rather old, but I'm linking to it anyway because I agree with the author's feeling that the software engineering discipline has more or less misunderstood Christopher Alexander's work on pattern languages. The author tends to ramble on. I think there's some good wisdom about programming practices and organizational management in general that one could abstract away from this book.

Hacker Shelf link, book website (scroll down).

Nisan et. al., Algorithmic Game Theory

I hesitate to link this because the math level is exceptionally high, perhaps high enough that anyone who can read the book probably knows the better part of its contents already. But game/decision theory is near and dear to LW's heart, so perhaps someone will gather some utility from this book. There's an awful lot going on in it. A brief selection: a section on the relationship between game theory and cryptography, a section on computation in prediction markets, and a section analyzing the incentives of information security.

Hacker Shelf review, book.

I'm a bit at a loss as to where to put this. I know the inferential gap is too great for it to go anywhere but here, and I know that the number of people on LW interested in this subject could be counted on one hand. The prerequisites would almost certainly be Timeless Causality and more mathematics than anyone is really interested in learning.

So, I apologize in advance if you read this and discover at the end it was a waste of your time. But at the same time, I need people who know about these things to talk about them with me, to ensure that I haven't gone crazy... yet. And most importantly, I need to know the people who have done this before, so that I don't have to do it. Google can't find them.

Introduction

There are currently some efforts to generalize the causal models of Pearl to continuous-time situations. Most of these attempts involve replacing some causal discrete variables X_i with time-dependent random variables X_i(t). Possibly due to memetic infection from Yudkowsky, I don't think this is necessarily the correct approach. The philosophical power of Pearl's theory comes from the fact that it is timeless, that ba'o vimcu ty bu.

In order to motivate my working definitions for where such a timeless continuous-time theory will go, I need to go back to classical causality and decide what a timeless formulation actually means, formally. Spoiler: it means replacing time-dependent evolution with a global flow on the phase space of the system. This is more or less in line with what is said in Timeless Physics with regard to the glimpse of "quantum mist" illustrated there.

The role of phase space

What is "timelessness"? The first thing I thought of after reading the timeless subsequence was, "What does a timeless formulation of the wave equation look like?" First of all, this was the right thought, because the wave equation is what I'll call (after the fact) "classically causal" in a sense to be described soon. I wouldn't have seen the timelessness in a different mathematical model, because not all mathematical models of reality preserve the underlying phenomena's causal structure. On the other hand, this was the wrong thought, because the wave equation is not the simplest continuous-time system that would have led me to this formalization of timelessness. Unfortunately the one that is easier for me to see (Lagrangian mechanics) is harder for me to explain, so you're stuck with a suboptimal explanation.

The wave equation models all sorts of wave-like phenomena: light, acoustic waves, earthquakes, and so on. If we take the speed of sound to be one (as physicists are wont to do), the dispersion relation is ω² = k². Such a dispersion relation satisfies the Kramers-Kronig relation. As it turns out, equations whose dispersion relation satisfies this condition satisfy what I'm calling "classical causality", but what is more commonly known as finite speed of propagation — or, more physically speaking, the fact that signals stay within their light cone.

The most common problem associated with the wave equation is the Cauchy problem. At time zero, we specify the state of the system: its initial position and velocity at every point. Then the solution of the wave equation describes how that initial state evolves with time. From a more abstract point of view, this evolution is a curve in the space of all possible initial states. This space is commonly referred to in the specific case of the wave equation as "energy space", which further illustrates why this example is a bit bad for pedagogical purposes. From now on, we're only going to talk about phase space.

Here is where we can remove time from the equation. Instead of thinking of the wave equation as associating to every state in phase space a time-dependent curve issuing forth from it, we're going to think of the wave equation as specifying a global flow on the whole of phase space, all at once. In summary, I am led to believe that timeless formulations amount to abstracting away the time-dependence of the system's evolution as a flow on the phase space of the system. And to think, this insight only took three years to internalize, provided I've gotten it correct.

Causal flow

The situation for a causal model is harder. In part, because stochastic things have shoddy excuses for derivatives. For the moment, we're going to take the easiest possible continuous-time system: our causal N variables of interest, X_i, take only real values. The space of all the possible states of the system is N-dimensional Euclidean space, which is easy enough to work with. I'm going to implicitly assume that causal variables evolve continuously; that is, the sidewalk doesn't go from being completely dry to completely wet instantaneously. Things like light switches and push buttons can still be modeled practically by bump functions and the like, so I don't see this as a real limitation.

The somewhat harder bullet to swallow is the assumption that the random variables are Markovian; that is, they are "memoryless" in the sense that only the present state determines the future. Pearl spends some time in Causality defending this assumption from criticism that it doesn't apply to quantum systems — I believe this defense is reasonable. I believe that causal models are necessarily refinements of our beliefs about what is still for the most part a classical world, and so the Markov assumption is not necessarily unnatural.

The phase space of N-dimensional Euclidean space is known as the tangent bundle, which amounts to having an additional copy of N-space at every point. Morally speaking, the tangent bundle represents all the directions and speeds in which the system can evolve from any given state.

We need some data about how the system is supposed to evolve: what I will call the causal flow. As best as I can currently conjecture, this data should take the form of a "bundle" of probability measures P, one for each point in N-space, such that each probability measure P(x) is defined over the tangent copy of N-space attached to that point.

By analogy with the previous section, the time-evolution of the system is given by Lipschitz-continuous curves in N-space. (Lipschitz-continuous, because if we assume they are differentiable curves, the Markov assumption goes out the window.) In contrast with the discrete theory of causality, and as mentioned above, we don't allow causal variables to "jump" spontaneously, and there is a limit to how sharply they can "turn".

A useful thing to have around would be the probability that the system will evolve from one state to another via a specific choice of one of these curves. Lipschitz-continuous curves are rectifiable, and so one can recapitulate a sort of Riemann sum — if you're interested, I have it formally written down in a .pdf, but the current format is unfriendly to maths. So for now, you'll just have to take my word for it when I say I can define the probability of the flow following a specific path. From there, it's just a path integral to defining the probability of getting from one state to another.

Where to go from here?

Given this causal flow, d-separation should arise as a geometrical condition — but perhaps only a local one, for the causal structure of the system can also evolve with time. To intervene in this system is to project it onto a certain hyperplane, presumably, in some yet-to-be-determined way. And finally, there ought to be some way to define counterfactuals, but my limited mathematical foresight has already run too thin.

BONUS: If you've made it this far and can't think of anything else to say, I'm willing to Crocker-entertain probabilities that I'm insane and/or a crackpot.

It's been a couple days since the funding plea, so I thought I'd like to take this chance to compare self-reported donations to short-term karma gains. Naturally, I voted on none of these comments. Note that after posting this, the karma on these posts will almost definitely change; the values here are for 27/8/11 at around 9:00 GMT.

So, the data:

• Kaj_Sotala ~172USD, 5 karma
• Rain 12000USD, 25 karma
• Nisan 100USD, 16 karma
• pengvado 10000USD, 36 karma
• JGWeissman 2000USD, 24 karma
• Benquo 1000USD, 18 karma
• AlexMennen 285USD, 7 karma; and 30USD, 2 karma
• wmorgan 1000USD, 13 karma

Note: two people (Kaj_Sotala and Rain) reported monthly commitments, but as far as I understand only the yearly pledge is matched, so for the purposes of this informal study I treat them as reporting X*12 USD donations, instead of X/month.

There's not enough data for an honest causal analysis (I tried), but there are a few observations one can make. Intuitively one expects karma to be determined by the donation amount, the duration of time since the posting, and some unknown error.

First observation: the users with the best USD/karma exchange rate made modest contributions early. Nisan came out best, with $6.25/karma — though some of this karma may be due also to the fantastic signal, on their part, that they overcame a rational hazard to make this donation. (Also, EY responded afterward, confounding the karmic flow with his wake.)

In this spirit, we now name "doing the least restrictive, obviously acceptable thing, instead of doing nothing while contemplating alternatives" Nisan's razor, (ニサンの剃刀, perhaps) unless it happens to have a better, previously-existing name.

Second observation: Hyperbolic discounting is alive and well. Those reporting monthly donations have karma below comparable one-shot donations, though both monthly data points did come slightly later than their one-shot counterparts.

Third observation: Large donations are really inefficient at netting karma. pengvado paid $277.48/karma; no one above 1000USD paid less than $50/karma.

Naturally, there's little point to this analysis. If anyone is trying to maximize net karma by donating to SIAI, something is probably wrong with their priorities.

In this comment thread, I stated that

I have read the Book of Mormon in the past, but I hereby precommit to reading it again and "searching in my heart" (I have a copy on my bookshelf) if you can demonstrate that my skepticism regarding your evidence is unwarranted.

In the resulting thread five evidences were given, and some back-and-forth occurred. Being myself somewhat biased, I feel unfit to judge if Arandur actually showed that a non-Mormon's skepticism is unwarranted.

So you, who wish to become stronger, I ask: please comment below whether or not you believe the proposition was satisfied.

Remember! This is not a vote on whether the evidence is factually correct or not!

Remember! This is not a chance to anonymously signal your agreement or disagreement with the LW hive mind!

Remember! If the sky is green, wish to believe that the sky is green!

I don't know what else I can say to forestall thread hijacking.