The tables of contents for Science magazine are online. Looking through these might jog your memory. But there are quite a lot of issues.
garethrees
Karma: 213
Recently in another topic I mentioned the “two bishops against two knights” chess endgame problem. I claimed it was investigated over two decades ago by a computer program and established that it is a win situation for the two bishops’ side. Then I was unable to Google a solid reference for my claim.
I believe that subject to the ambiguity in what is meant by “a win situation for the two bishops”, your recollection is correct.
The 6-piece pawnless endgames were were first analyzed systematically by Lewis Stiller starting in the late 1980s and reported in his papers in 1991 and 1992. The storage technologies available at this time meant that only summarized results could be saved, such as the longest win, and the total number of wins, draws and losses. I can’t find these papers online, but the results also appear in Stiller (1995) and there’s a summary of the state of the art in Thompson (1996).
For the KBBKNN ending Stiller only analyzed positions with the two bishops on opposite coloured squares (and I think with white to move), and reported that the longest win for white was 37 moves and the percentage of wins for white was 63%.You probably also want to note Stiller’s caveat:
The percent-win can be misleading because of the advantage of the first move in a random position—White can often capture a piece in one move—and because it includes positions in which Black is in check.
So I think if you said “mostly a win for the two bishops from a random position with bishops on opposite-coloured squares, with the player with the bishops to move” that would be a fair summary of the facts.
Modern tablebases usually also include positions with the two bishops on the same colour square, so that analyses of these databases will give different results to Stiller. For example, according to Kirill Kryukov, the KBBKNN positions split like this:
With white (bishops) to move: 28429 losses, 885809752 draws (76%), 282912378 wins (24%)
With black (knights) to move: 54327970 losses (4%), 1247006005 draws (96%), 154105 wins
How could you have found this using Google? Well, it always helps to know of specialized databases to search (because the results tend to be of higher quality). I used Google Scholar to search for academic papers relevant to the keywords “6-piece chess endgame” and that returned Thompson (1996) as the first hit, and reading Thompson’s summary of the state of the art led me to the Stiller papers. Of course, domain expertise is a big help too: I realised after discovering Stiller (1995) in the course of this search that I have a copy of this on my bookshelves.
References
Lewis Stiller (1991), “Some results from a massively parallel retrograde analysis”, ICCA Journal 14:3, pp. 129–134.
Lewis Stiller (1992). “KQNKRR”. ICCA Journal 15:1, pp. 16–18.
Lewis Stiller (1995). “Multilinear algebra and chess endgames”, in Games of No Chance edited by Richard J. Nowakowski, MSRI Publications Volume 29.
Ken Thompson (1996). “6-piece endgames”, ICCA Journal 19:4 pp. 215–226.
Spelling Latin with u has always been there (but as a tiny minority of texts). Here are some occurrences of omnia uincit amor over the years: 1603, 1743, 1894, 1974.
If you compare the frequencies of vincit and uincit on Google Ngram viewer, you’ll see that the u spelling has always been present at a low frequency. There doesn’t seem to be any noticeable recent trend (other than the general decline of Latin as a proportion of printed material). I tried a few other Latin words and got similar results.
The earliest reference I can track down is from 1952. In Roger Sessions: a biography (2008), Andrea Olmstead writes:
[In 1952] Sessions published “Some notes on Schoenberg and the ‘method of composing with twelve tones’.” At the head of the article he quoted from one of Schoenberg’s letters to him: “A Chinese philosopher speaks, of course, Chinese; the question is, what does he say?” Sessions [had performed] the role of a Chinese philosopher in Cleveland.
(The work that Sessions had performed this role in appears to have been Man who ate the popermack in the mid-1920s.)
Sessions’ essay (originally published in The Score and then collected in Roger Sessions on Music) begins:
Arnold Schönberg sometimes said ‘A Chinese philosopher speaks, of course, Chinese; the question is, what does he say?’ The application of this to Schönberg’s music is quite clear. The notoriety which has, for decades, surrounded what he persisted in calling his ‘method of composing with twelve tones’, has not only obscured his real significance, but, by focusing attention on the means rather than on the music itself, has often seemed a barrier impeding a direct approach to the latter.
An entertaining later reference to this quotation appears in Dialogues and a diary by Igor Stravinsky and Robert Craft (1963), where Stravinsky tabulates the differences between himself and Schoenberg, culminating in this comparison:
Stravinsky: ‘What the Chinese philosopher says cannot be separated from the fact that he says it in Chinese.’ (Preoccupation with manner and style.)
Schoenberg: ‘A Chinese philosopher speaks Chinese, but what does he say?’ (‘What is style?’)
It’s hardly fair to call EY Egan’s ‘biggest fan’
I based this description on Yudkowsky’s comments here, where he says of Permutation City, “This is simply the best science-fiction book ever written [...] It is, in short, my all-time favorite.”
I don’t see how those novels could have been an inspiration?
Yudkowsky describes Egan’s work as an important influence in Creating Friendly AI, where he comments that a quote from Diaspora “affected my entire train of thought about the Singularity”.
The Wikipedia page explains how a frequentist can get the answer ⅓, but it doesn’t explain how a Bayesian can get that answer. That’s what’s missing.
I’m still hoping for a reference for “the Bayesian rules of forgetting”. If these rules exist, then we can check to see if they give the answer ⅓ in the Sleeping Beauty case. That would go a long way to convincing a naive Bayesian.
I think this kind of proposal isn’t going to work unless people understand why they disagree.
You’re not obliged to give a lecture. A reference would be ideal.
Appealing to “forgetting” only gives an argument that our reasoning methods are incomplete: it doesn’t argue against ½ or in favour of ⅓. We need to see the rules and the calculation to decide if it settles the matter.
If I understand rightly, you’re happy with my values for p(H), p(D) and p(D|H), but you’re not happy with the result. So you’re claiming that a Bayesian reasoner has to abandon Bayes’ Law in order to get the right answer to this problem. (Which is what I pointed out above.)
Is your argument the same as the one made by Bradley Monton? In his paper Sleeping Beauty and the forgetful Bayesian, Monton argues convincingly that a Bayesian reasoner needs to update upon forgetting, but he doesn’t give a rule explaining how to do it.
Naively, I can imagine doing this by putting the reasoner back in the situation before they learned the information they forgot, and then updating forwards again, but omitting the forgotten information. (Monton gives an example on pp. 51–52 where this works.) But I can’t see how to make this work in the Sleeping Beauty case: how do I put Sleeping Beauty back in the state before she learned what day it is?
So I think the onus remains with you to explain the rules for Bayesian forgetting, and how they lead to the answer ⅓ in this case. (If you can do this convincingly, then we can explain the hardness of the Sleeping Beauty problem by pointing out how little-known the rules for Bayesian forgetting are.)
D is the observation that Sleeping Beauty makes in the problem, something like “I’m awake, it’s during the experiment, I don’t know what day it is, and I can’t remember being awoken before”. p(D) is the prior probability of making this observation during the experiment. p(D|H) is the likelihood of making this observation if the coin lands heads.
As I said, if your intuition tells you that p(H|D) = ⅓, then something else has to change to make the calculation work. Either you abandon or modify Bayes’ Law (in this case, at least) or you need to disagree with me on one or more of p(D), p(D|H), and p(H).
Bayes’ Law says, p(H|D) = p(D|H) p(H) / p(D) where H is the hypothesis of interest and D is the observed data. In the Sleeping Beauty problem H is “the coin lands heads” and D is “Sleeping Beauty is awake”. p(H) = ½, and p(D|H) = p(D) = 1. So if your intuition tells you that p(H|D) = ⅓, then you have to either abandon Bayes’ Law, or else change one or more of the values of p(D|H), p(H) and p(D) in order to make it come out.
(We can come back to the intuition about bets once we’ve dealt with this point.)
That’s interesting. But then you have to either abandon Bayes’ Law, or else adopt very bizarre interpretations of p(D|H), p(H) and p(D) in order to make it come out. Both of these seem like very heavy prices to pay. I’d rather admit that my intuition was wrong.
Is the motivating intuition beyond your comment, the idea that your subjective probability should be the same as the odds you’d take in a (fair) bet?
I did check both threads, and as far as I could see, nobody was making exactly this point. I’m sorry that I missed the comment in question: the threads were very long. If you can point me at it, and the rebuttal, then I can try to address it (or admit I’m wrong).
(Even if I’m wrong about why the problem is hard, I think the rest of my comment stands: it’s a problem that’s been selected for discussion because it’s hard, so it might be productive to try to understand why it’s hard. Just as it helps to understand our biases, it helps to understand our errors.)
The Sleeping Beauty problem and the other “paradoxes” of probability are problems that have been selected (in the evolutionary sense) because they contain psychological features that cause people’s reasoning to go wrong. People come up with puzzles and problems all the time, but the ones that gain prominence and endure are the ones that are discussed over and over again without resolution: Sleeping Beauty, Newcomb’s Box, the two-envelope problem.
So I think there’s something valuable to be learned from the fact that these problems are hard. Here are my own guesses about what makes the Sleeping Beauty problem so hard.
First, there’s ambiguity in the problem statement. It usually asks about your “credence”. What’s that? Well, if you’re a Bayesian reasoner, then “credence” probably means something like “subjective probability (of a hypothesis H given data D), defined by p(H|D) = p(D|H) p(H) / p(D)”. But some other reasoners take “credence” to mean something like “expected proportion of observations consistent with data D in which the hypothesis H was confirmed”.
In most problems these definitions give the same answer, so there’s normally no need to worry about the exact definition. But the Sleeping Beauty problem pushes a wedge between them: the Bayesians should answer ½ and the others ⅓. This can lead to endless argument between the factions if the underlying difference in definitions goes unnoticed.
Second, there’s a psychological feature that makes some Bayesian reasoners doubt their own calculation. (You can try saying “shut up and calculate” to these baffled reasoners but while that might get them the right answer, it won’t help them resolve their bafflement.) The problem somehow persuades some people to imagine themselves as an instance of Sleeping Beauty selected uniformly from the three instances {(heads,Monday), (tails,Monday), (tails,Tuesday)}. This appears to be a natural assumption that some reasoners are prepared to make, even though there’s no justification for it in the problem description.
Maybe it’s the principle of indifference gone wrong: the three instances are indistinguishable (to you) but that doesn’t mean the one you are experiencing was drawn from a uniform distribution.
I think it’s both. “Brave New World” portrays a dystopia (Huxley called it a “negative utopia”) but it’s also post-utopian because it displays skepticism towards utopian ideals (Huxley wrote it in reaction to H. G. Wells’ “Men Like Gods”).
I don’t claim any expertise on this subject: in fact, I hadn’t heard of post-utopianism at all until I read the word in this article. It just seemed to me to be overstating the case to claim that a term like this is meaningless. Vague, certainly. Not very profound, yes. But meaningless, no.
The meaning is easily deducible: in the history of ideas “post-” is often used to mean “after; in consequence of; in reaction to” (and “utopian” is straightforward). I checked my understanding by searching Google Scholar and Books: there seems to be only one book on the subject (The post-utopian imagination: American culture in the long 1950s by M. Keith Booker) but from reading the preview it seems to be using the word in the way that I described above.
The fact that the literature on the subject is small makes post-utopianism an easier target for this kind of attack: few people are likely to be familiar with the idea, or motivated to defend it, and it’s harder to establish what the consensus on the subject is. By contrast, imagine trying to claim that “hard science fiction” was a meaningless term.
Stanislaw Lem, “The Twenty-First Voyage of Ijon Tichy”, collected in “The Star Diaries”.
You write, “suppose your postmodern English professor teaches you that the famous writer Wulky Wilkinsen is actually a ‘post-utopian’. What does this mean you should expect from his books? Nothing.”
I’m sympathetic to your general argument in this article, but this particular jibe is overstating your case.
There may be nothing particularly profound in the idea of ‘post-utopianism’, but it’s not meaningless. Let me see if I can persuade you.
Utopianism is the belief that an ideal society (or at least one that’s much better than ours) can be constructed, for example by the application of a particular political ideology. It’s an idea that has been considered and criticized here on LessWrong. Utopian fiction explores this belief, often by portraying such an ideal society, or the process that leads to one. In utopian fiction one expects to see characters who are perfectible, conflicts resolved successfully or peacefully, and some kind of argument in favour of utopianism. Post-utopian fiction is written in reaction to this, from a skeptical or critical viewpoint about the perfectibility of people and the possibility of improving society. One expects to see irretrievably flawed characters, idealistic projects turn to failure, conflicts that are destructive and unresolved, portrayals of dystopian societies and argument against utopianism (not necessarily all of these at once, of course, but much more often than chance).
Literary categories are vague, of course, and one can argue about their boundaries, but they do make sense. H. G. Wells’ “A Modern Utopia” is a utopian novel, and Aldous Huxley’s “Brave New World” is post-utopian.
Front page: missing author
The front page for Facing the Singularity needs at the very least to name the author. When you write, “my attempt to answer these questions”, a reader may well ask, “who are you? and why should I pay attention to your answer?” There ought to be a brief summary here: we shouldn’t have to scroll down to the bottom and click on “About” to discover who you are.