Scott Aaronson over at Shtetl-Optimized asks whether mathematics or theory of computer science are actually “science.” My gut reaction to a question like this is just to avoid it: who cares whether math and TCS is science, what is important is that (some) math and (some) computer science are either (1) important to the progress of science and (2) important for practical reasons which we don’t classify as science (for example, as relating to technology.) But I guess this just explains why I’m not a pure mathematician (beside the fact that I don’t have the brains!): a connection to experiment or a connection to technology are important prerequisites for what I find important (note that this is different from what I find interesting.) Of course, I put mathematicians who do their work solely for the beauty of the work into the same category I put other, more traditional, artists, so what do I know?
Constructors, Automata, and Evolution, Oh My!
Find of the day: an online version of John von Neumann’s “Theory of Self-Reproducing Automata.”
Performance Enhanced Theorems
Among sports fans there is a lot of controversy about the use of performance enhancing drugs by athletes. Of course what exactly an performance enhancing drug is, is often left pretty vague. But most sports fans argue against the use of such drugs because they are, in some form, cheating.
So what do we do, for example, with Erdos. Paul Erdos was, for those who don’t know, one of the twentieth centuries great mathematicians. He was the author, amazingly, of over 1,500 different papers. It was well known, also, that Erdos used amphetamines. There is a famous story that his friends were so worried about his amphetamine use that they bet him that he couldn’t stay off the drugs for a month. Of course Erdos took the bet and successfully stayed off the drugs for the required amount of time. When he went to collect the bet, he reportedly said “You set Mathematics back one month!” (OK, this story is off the top of my head, the details may or may not be correct!) So, in a real sense, Erdos’ productivity was increased in large part by his use of a performance enhancing drug. So, was Erdos cheating? Should we think of his “records” his “theorems” as somehow being “less proved by Erdos” because of his use of amphetamines? Well I certainly would argue against this.
At FOCS this year I was having this conversation, and it came up that perhaps we shouldn’t penalize the result, because the outcome, i.e. the mathematical proofs isn’t really a competitive sport. But what about those who are competing for tenure? Now of course I’m disregarding the legality of the performance enhancing drugs. But disregarding this issue (which may just invalidate the whole argument, but bear with me) should there be drug testing of tenure track professors to make sure they aren’t using amphetamines to increase their productivity?
Lies, Damn Lies, and Chemistry
Geoknitting points to a very interesting site which I can highly recommend visiting: The re-Discovery Institute.
A New Kind of Disclaimer
Cosma Shalizi has posted a review of Stephen Wolfram’s “A New Kind of Science.” It’s not often that you find a review which begins
Attention conservation notice: Once, I was one of the authors of a paper on cellular automata. Lawyers for Wolfram Research Inc. threatened to sue me, my co-authors and our employer, because one of our citations referred to a certain mathematical proof, and they claimed the existence of this proof was a trade secret of Wolfram Research. I am sorry to say that our employer knuckled under, and so did we, and we replaced that version of the paper with another, without the offending citation. I think my judgments on Wolfram and his works are accurate, but they’re not disinterested.
or a review that ends (well almost) with
This brings me to the core of what I dislike about Wolfram’s book. It is going to set the field back by years. On the one hand, scientists in other fields are going to think we’re all crackpots like him. On the other hand, we’re going to be deluged, again, with people who fall for this kind of nonsense. I expect to have to waste a lot of time in the next few years de-programming students who’ll have read A New Kind of Science before knowing any better.
s, p, d, f
From Nature Physics, f-wave Superconductors?:
NaxCoO2yH2O must be hydrated to superconduct1, and its triangular CoO2 layers provide an intriguing contrast with the square CuO2 layers of the high-temperature superconductors. Its superconductivity is often assumed to be unconventional in that the Cooper pairs are not in a spin singlet state with s-wave symmetry, as with conventional superconductors. According to the Pauli exclusion principle, pairs with a singlet (triplet) spin part have a corresponding even (odd) spatial part, designated as s-, p-, d- or f-wave pairing in accordance with the pair angular momentum. However, in NaxCoO2yH2O, experimental reports are often contradictory2, 3, 4, 5, 6 and solid evidence for any particular pairing state remains lacking. This has led to an unprecedented number of proposals2, 3, 5, 7, 8, 9, 10, 11, 12, 13 for the pairing symmetry (perhaps the greatest number ever for a single compound), each in agreement with some subset of the available data. Here we test each of the 25 symmetry-allowed pairing states14 against firmly established properties of the compound. Surprisingly, this eliminates most possible pairings. The two remaining states both have f-wave symmetry, suggesting that NaxCoO2yH2O may be the most exotic superconductor discovered so far. We discuss expected features of these states and suggest experiments to distinguish between them.
The Publishing Divide
A new LA Times article about the controversy over the discovery of a possible tenth planet. As those of you who read the original article know, the controversy arose when Michael Brown from Caltech was scooped in the discovery of this object and then later noticed that the “scoop”ers, led by Professor Jose Luis Ortiz, had visited a website which contained information about where Brown and coworkers were pointing their telescope. Interestingly, here is what Professor Ortiz had to say:
Ortiz argues he has done nothing wrong, and the data he found using the Google search engine should be considered public and thus free to use.
“If … somebody uses Google to find publicly available information on the Internet and Google directs to a public Web page, that is perfectly legitimate,” Ortiz wrote in an e-mail to The Times. “That is no hacking or spying or anything similar.”
Interesting line of reasoning. Of course the real problem is not that someone accessed the public information but that no acknowledgement of this access to this information was made in Professor Ortiz and coworkers communications. One thought I had (yeah sometimes I have those things!) was whether the fact that this information was publicly accessible mean that this information was “published” in the same way that preprints are “published” or information submitted to a database is “published?” Well probably not, but it seems we could probably construct an instance which is even closer to this “published” line. Consider that a challenge 😉
Math Doh!
A biophysicalchemist sends me the following link from the San Francisco Chronicle Cal math lecture to feature binge-eating cartoon dad detailing a math program this Sunday at 2 p.m. at the MSRI in Berkeley on the Simpsons and math (I lived almost level with the MSRI in the Berkeley hills while I was a graduate student. Oh what a view!) Sounds like fun.
What is really funny, however, is what we find as examples of math and the Simpson’s being used together from the article:
Homer, in a dream, wrote that 1,782 to the 12th power plus 1,841 to the 12th power equals 1,922 to the 12th power. (It does.)
First of all, it wasn’t a dream. Homer had slipped into….the third dimension (which we define as that place where frinkahedrons exist, of course.) And second, well if what the author states is true, then Princeton mathematician Andrew Wiles would have quite a bit of egg in his face. Because the above statement would be a counterexample to Fermat’s Last Theorem (not to be confused with the other important FLT: Fermat’s Little Theorem.) which Andrew Wiles famously proved (well proved, and then they found an error, and then he fixed the error. Genius!) The statement of Fermat’s Last Theorem is that there are no positive integers, x, y, and z, such that x^n+y^n=z^n for n an integer greater than two. What is funny is that if you evaluate the two sides of this equation, they do agree in the first nine most significant digits:
1782^12+1841^12=25412102586…
1922^12=25412102593…
So if you type this equation into a caculator which only keeps ten digits of precision, it will fail (rounding that last digit to the same number, I think. For the actual program used to find this violation see here.) So it seems as if this joke, a “calculator significant digit” violation of Fermats Last Theorem, has caught its first victim. I’ll bet the journalist involved did exactly that: he just plugged it into his handy calculator! Well, maybe not, but still it’s pretty funny to think that this might have occured.
Math and Science Erosion
The New York Times has an article today entitled “Top Advisory Panel Warns of an Erosion of the U.S. Competitive Edge in Science” discussing a report issued by the National Academies concerning the scientific competitiveness of the United States. Here is an interesting fact
Last year, more than 600,000 engineers graduated from institutions of higher education in China, compared to 350,000 in India and 70,000 in the United States.
Funny, when I read this, the first thought which comes to my mind is that the competitiveness for engineering jobs in China must be huge!
I always have a big mixed bag of emotions when I read articles like this. On the one hand, like most scientist, I tend to think that science and research are underfunded. Funding as a percent of GDP is about half what it was in the 60s. On the other hand, I tend to see the increase in funding by other countries in a postive light: that other governments are realizing they need to spend more on science and research is good for the researchers in those country and also good for the world (of course global inequities mean this good is diluted as a function of distance down the first to second to third world ladder.)
What has certainly been true over the last fifty years is that the U.S. has built up an incredible system of higher education (seventy percent of Nobel prize winners work in U.S. universities, as one silly example. We spend about twice as much as western Europe on higher education per student, as another example.) But do I begrudge the rest of the world similar top universities? That doesn’t seem right. On the other hand, when I see destructive factors at work in the U.S. university system (as for example is occuring because of perceived (and actual 🙁 ) hostility towards foreign graduate students) this doesn’t make me happy.
So sometimes it’s hard to keep up a gloomy face: behind all of the rhetoric, I see the world progressing at an increasing rate, which, I believe is a good thing. I guess I just won’t be good for producing a report like this one, because I’d focus almost exclusively on the negatives of the U.S. system and little on the postives of the other nations progress (except as an example.)
Ig Nobel Prizes 2005
The 2005 Ig Nobel Prizes are out! The physics prize goes went to the University of Queensland:
PHYSICS: John Mainstone and the late Thomas Parnell of the University of Queensland, Australia, for patiently conducting an experiment that began in the year 1927 — in which a glob of congealed black tar has been slowly, slowly dripping through a funnel, at a rate of approximately one drop every nine years.
I’ve actually seen this glob of black tar. Little did I know I was looking at an experiment of Nobel proportions! Makes me wish I’d taken a picture of it.