by Tyler Cowen
on March 28, 2014 at 11:55 am
in Uncategorized |
1. Why computers find it hard to win at Go.
2. “The Clovis paradigm is finally buried.”
3. How has the mining boom changed Perth?
4. Did childhood obesity really decline? And NYC receives its first cupcakes ATM.
5. Propagating confusion about money creation.
6. History of European border changes (short video). Many lessons in that one.
re: #4 I liked cupcake ATMs better the first time, when they were called vending machines.
File this under The Great Stagnation.
As one of the comment pointed out, the first article is a little misleading. The computer was given a four-stone handicap, which is not a small handicap. With the four stones, you occupy all the four corners, which are the most important areas on the board. http://en.wikipedia.org/wiki/Go_handicaps
Yup. What’s more, Crazy Stone made many stupid moves (close to not making a move at all) and hyper-ultracautious moves, which a human playing at the KGS strengths they claim would never make (examples: 76, 124, 126, 132, 140, 146, 166, 202, 224). This sort of very defensive style in a handicap game makes it tough going even for a pro, but playing against a large handicap is an excercise in patience in any case. Yoshida was about 30 points behind around move 100, 15 points behind around 166, 10 points behind at 226 and probably could have won if he tried a bit harder. Pros can usually manage to lose by half a point when they play amateurs for money. It is also difficult to play against a program, especially a Monte Carlo program, because its moves make no sense like a human’s do, and this throws off the thinking of a pro playing a program for the first time. Note that computer Go teams rarely organize multiple-game matches or rematches against the same professional opponent, because once a pro gets the hang of the program’s style he can just haul it in.
I also looked at the two programs’ match (Zen vs Crazy Stone) shown alongside the Yoshida-Crazy Stone game (http://gogameguru.com/crazy-stone-computer-go-ishida-yoshio-4-stones/). Both programs’ play is simply atrocious, nowhere near even amateur 1 dan. Like two dead-drunk boxers slugging it out on a roller-coaster. I believe they only maintain 5-6 dan on KGS (equivalent to 3-4 ama-dan in Europe) by (a) playing handicap and (b) not playing the same opponent more than a couple of times, see my comment above.
All you say is true but just 20 years ago, people were saying that no computer would ever reach 1 Dan professional strength or be able to beat a professional at modest handicap. The latter is already the case, the former is probably quite close as some programs are about 6 Dan amateur on many servers. 4 stones may be a lot for pros, but Takemiya Masaki was supposedly shocked 2 years ago when he lost a 4 stone handicap game by 20 points saying “I had no idea that computer go had come this far.” I remember once hearing a pro tell me that no program would ever beat a top ranked 9 Dan pro even at a 9 stone handicap.
It’s still true that no computer has reached anything like professional 1 dan. FYI, professional 1 dan is equivalent to European amateur 8 dan (American strength levels are generally 1 dan lower than European, and KGS 2 dan lower than European). I am European amateur 3 dan. Judging from their actual play as shown at the link above, these two programs are rather weaker than amateur 1 dan. Please reread my comments above. What they unquestionably have learned is how to get good PR by hiring retired Japanese pros to play one-off handicap games against their programs. I’d like to see a 9-game match instead.
A professional player can sometimes beat a one dan amateur while giving nine stones handicap. So the computer programs are comfortably stronger than most club players.
In Japan, there is a yearly competition between the amateur and professional Honinbo (winners of a particular and prestigious tournament). Handicaps are adjusted based on the part years results, and the professionals have managed to win at up to 2 stones plus a few points Komi.
So, in short, while we don’t know when computers will equal professionals, this is a very strong performance.
#3. Good article about Perth.
#2: This means we can stop calling the guys at the slot parlors “Native Americans.”
#2: and start calling all humans East Africans
Well some people prefer the term East-est African. But unfortunately I’m just one of those Westerner East Africans, so what would I know. 😉
I think the GO New Yorker article is wrong when it says: “To say that Go is more complex than chess, though, is a little like saying that one infinity is larger than another. While technically true—and mathematically possible—it does not fully explain why computers, which can’t fully compute chess or Go, have become good at one and not the other” – it is not technically true that one infinity is larger than another infinity. I believe A. Church, the mathematician, proved this. Infinity is infinity. The game of Go I do believe will be mastered by a PC soon, which will use AI pattern recognition techniques as well as Monte Carlo simulation.
As for the Clovis model, that North America was habituated in 12k bc, it’s false of course, but keep in mind 30k bc is a limiting factor since the land bridge in Bering submerged after that. Further, keep in mind that 20k bc the ice age was in full force, to the point that glaciers were miles think in North America so much so that even animals had a hard time navigating the continent. Thus animals–and any humans–stuck to the coasts and along certain corridors. That’s why you’ll not find many fossils of humans in the middle of North America during that time.
The notion of infinity, of course, depends on the context. In most “regular” math, you would be right. But there are contexts within set theory, where partial orders within different infinities make sense. Here, again, the situation is different depending on whether you are looking at cardinal numbers, or ordinal numbers. Search for Cantor’s diagonalization argument.
Thanks, I did search, and I was right. See: http://en.wikipedia.org/wiki/Controversy_over_Cantor%27s_theory
So if you are doing a one-to-one mapping exercise, which is a finite exercise (akin to Turnings Universal Machine), then indeed Cantor’s diagonalization argument makes sense, but if you take infinite to mean uncountable, then not.
The primary well-known contemporary mathematician (Kronecker) who had objections to Cantor’s work would not even agree to the “existence” of real numbers. The thing is set theory is needed in the finer parts of analysis, and assumption of axiom of choice (which is not necessary to prove the result referred to above) does lead to results that are counter-intuitive, but is still accepted as regular part of mathematics. Go visit your local analysis department and ask what they would teach a junior mathematics major.
Plus, this is on the cardinal numbers side. You should also look at the ordinal numbers.
I do thank you for the link. I would treasure it as one of those rare exceptions that prove the rule that wiki produces superb pages on technical mathematics that are accurate, informative and not misleading.
The number of distinct Go and Chess games are both countable and therefore would have the same size — if they were infinite.
But neither game is truly infinite. Go has a finite number of stones. Chess does have some infinite games which are not draws under the official rules, but in practice they become draws at some finite point.
Alex, I didn’t understand what you said.
Ambiguous troll response. Whoosh as in “right over your flattop” (i.e. you missed the point, jughead”) or whoosh as in perfect nothing-but-net (i.e., you made the point, as in three-pointer). Shows how ambiguous English is, with the heavy use of cliches and idioms.
Correction: the Bering land bridge was open until 11k bce, but the rest of my argument is sound I believe.
Which land bridge did Columbus and the Pilgrims use to get to the Americas?
“I think the GO New Yorker article is wrong when it says: “To say that Go is more complex than chess, though, is a little like saying that one infinity is larger than another. While technically true—and mathematically possible—it does not fully explain why computers, which can’t fully compute chess or Go, have become good at one and not the other””
I also think they’re wrong, but not for your reason. Go is not a little bit more complex than Chess, it’s massively more complex. Chess is much closer to Checkers or Backgammon than it is to Go.
The article is particularly disappointing in leaving out the “Tree Search” part of Monte Carlo Tree Search, since it’s the combination of the two concepts that led to competitive programs.
I initially had the same reaction you did, but on further thought, I realize that while that sentence actually has a valid point. They do seem to be understating the problem of the huge difference in search spaces for the two games, but they are correct in pointing out that this isn’t the whole story, and that the lack of viable pruning heuristics is also a major part of the problem.
1. Neither Chess nor Go is infinite. The article was using a fancy literary technique called metaphor.
2. There are exactly two kinds of infinity known today. One kind, the uncountable infinity, is larger than the other, the countable infinity. Cantor Diagonalization is the usual way to demonstrate the difference.
3. “Controversy Over Cantor’s Theory” is hilarious: Intelligent Math Design. Teach the controversy.
4. While real numbers are abstract and not physically “real” the way algebraic numbers are, they are well defined and work fine to approximate all kinds of things. Imaginary numbers, ironically, are the most “real” thing there is, being an essential factor in projecting solutions to the wave equations of quantum mechanics onto physical measurements that define the most precise and exact results in studies of physical reality.
2. No. There are many kinds of uncountable infinity, some of them larger than others. For instance, the set of real numbers is uncountable, but strictly smaller than the set of infinite sequences of real numbers, and in certain well-defined senses (Lebesque measure, nowhere-dense-ness) ‘infinitely’ smaller. If you go to sequences of sequences etc. you can build ever larger uncountable cardinals, and in some formulations of set theory there exist still larger cardinals which are greater than any cardinal built in this manner.
Actually, this is incorrect. The set of sequences of real numbers has the same cardinality as the set of real numbers itself.
You’re right, I should have said sets not sequences. Obviously it’s time for more coffee.
Comparing “controversy” over Cantor to ID seems specious. One can conceive of infinities in ways that are not mutually compatible and this seems to be no problem for math.
most North American anthropologist and archaeologist of my acquaintance believe that the first Americans migrated by boat down the Pacific coast, the land bridge was not necessary as long as enough of Beringia existed to moderate the North Pacific’s climate.
I am in the Western US and know this is mostly a west coast opinion, but it is held by most archaeologists with any knowledge of the US west coast environment. It also explains why pre Clovis sites are non existent in North America, as most campsites would be offshore today because of rising sea level.
Serendipitously, I came across this which seems quite relevant to this small kerfuffle over infinity:
“With respect to finite collections, two uncontroversial principles hold:
Part-whole: a collection A that is strictly contained in a collection B has a strictly smaller size than B.
One-to-one: two collections for which there exists a one-to-one correspondence between their elements are of the same size.
What Galileo’s paradox shows is that, when moving to infinite cases, these two principles clash with each other, and thus that at least one of them has to go. In other words, we simply cannot transpose these two basic intuitions pertaining to counting finite collections to the case of infinite collections. As is well known, Cantor chose to keep One-to-one at the expenses of Part-whole, famously concluding that all countable infinite collections are of the same size (in his terms, have the same cardinality); this is still the reigning orthodoxy.
In recent years, an alternative approach to measuring infinite sets is being developed by the mathematicians Vieri Benci (who initiated the project) Mauro Di Nasso, and Marco Forti. It is also being further explored by a number of people – including logicians/philosophers such as Paolo Mancosu, Leon Horsten and my colleague Sylvia Wenmackers. This framework is known as the theory of numerosities, and has a number of theoretical as well as more practical interesting features.”
#6: Someone upload that in HD. WTF.
Anyone else notice that the borders seem off for the WWII years? Everything seems shifted forward by 6-7 years or so, hard to tell because it goes so fast. For example, Germany is still expanding into the late 40s and the Allies only move in in the early 50s.
Napoleon seems off too.
And funny that the Austrian empire is called “Bohemia.”
And it shows Crimea as part of Ukraine
Because it is.
There’s more of this, apparently battle of Mohács either happened way sooner than 1526 or the Turks sneakily occupied most of Hungarian Kingdom without Jagiellos’ and bishop Tomori taking notice. Also, in the 1890s , Germany seems to have annexed Luxemburg, Belgium, northern France and Russian part of Poland and Baltics; simulation is off by 2-3 decades (minor bug, I guess) and takes temporary changes of front lines as state border changes.
#6: lots of lessons from US border changes too, with all this talk of annexation. Mexicans might have a thing or two to say about that.
What would Mexico say? Since the U.S. did it in the 1800s Russia is right to do it now? That Crimea is populated by Mexicans so probably the world will be a better place once they are replaced by Russian frontiersmen?
A comparison of Perth and North Dakota would be fascinating.
Nothing involving North Dakota is fascinating.
Oh, I don’t know about that.
I certainly wouldn’t hold it against the current American Indian population, but I bet there would be some outrage and denial from certain White people if some kind of evidence turned up that the great great… granddaddies of the current Indians displaced, genocided, or subjugated a pre-existing population.
The evidence is pretty weak, at the end of the day. Much of South America is extremely remote and some regions even still retain uncontacted tribes. We’d expect to find unambiguous remnants of these early American peoples, just like we find Khoisan and Pygmies in Africa.
Right, I agree this isn’t much evidence, there could have been earlier peoples who died out all on their own, etc.
We have excellent evidence of long term inhabitation of the Australian continent but nothing conclusive has so far turned up in the much more intensely investigated North America? To me it seems very unlikely that the Americas were inhabited much more than 13,000 or so years ago.
Interesting, perhaps, but inconsequential.
You’re talking about the most remote leaf nodes though. The trunk nodes have been displaced several times. Three different times, I believe.
3. The article on Perth states, “The mining boom of the last decade has done many things for the state and for Australia, most notably being the economic factor that stopped Australia dipping into negative economic growth during the Global Financial Crisis.” I’m sorry but I’ve just got to to kill this lie that is getting pretty old now. In the immediate aftermath of the Global Financial Crisis the mining industry contracted more than the rest of the economy and so was was more responsible for dragging Australia to the brink of recession than other industries on average. Fortunately, Australia was able to avoid a recession thanks to a well planned stimulus and demand for minerals soon picked up mainly thanks to Chinese stimulus and the mining boom continued. But I can’t blame the writer too much for repeating the lie as it is the sort of thing one is likely to hear if one hangs around in Perth.
Regarding the cupcake ATM, it better support deposits.
Go: if the computer is playing in a totally new way, I think it is fair to say that its successes are in large measure due to its strangeness. I am guessing that when club players learn the ins and outs of Crazy Stone, its rating will decline precipitously.
Clovis: There is evidence that humans reached Australia by boat around 40,000 years ago. Can’t see why some of them couldn’t have reached South America the same way 20,000 years later. Could well be that it was tough going and that is probably why there are few sites of such antiquity and why their line seems to have reached a dead end.
#6 has a lot of mistakes in it. The video implies that East Germany was created in the 1960s rather than in 1949.
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