Politics vs. climate science

Mostly just a pointer here. Chris C. Mooney reports:

House Energy and Commerce Committee chair Joe Barton has sent a threatening letter to the heads of the Intergovernmental Panel on Climate Change and the National Science Foundation, as well as to the three climate scientists who produced the original "hockey stick" study. Barton isn't simply humoring questionable contrarian attacks on the "hockey stick" graph; he's using his power as a member of Congress to intimidate the scientists involved in producing it.

Subsequent posts on Mooney's site provide further information and reactions.

Deltoid presents additional reaction, and comments:

It is probably just a coincidence that Joe Barton has received $574,000 in campaign contributions from the oil and gas industry, more than any other congressman.

Finally (for now), Prometheus assesses both reasonable and unreasonable aspects of the Congressional action, but especially on the unreasonable side notes that

Congressional meddling in science research has been happening science Senator Proxmire (D-WI) began giving away Golden Fleece Awards in 1975. By ridiculing specific NSF awards (among myriad other federal expeditures, see this link), Sen. Proxmire was essentially putting pressure on the scientific community to fund more "relevant" work. Senator Inhofe's proclamations of hoaxes and other comments on climate change are in a similar vein. However, this is congressional meddling taken to a whole new level and has the potential to set a bad precedent for the future, when the topic and stakes are different and the parties in power have switched. Furthermore, while some Sens and Reps have spoken vociferously against climate change, expressing their opinions of the research, none have yet used the dais to harass climate researchers.

The Woodstock of Evolution

Michael Shermer (Skeptic Magazine) has written an excellent set of notes on talks given at the recent World Summit on Evolution held in the Galapagos June 9-12. (The notes are also available here in a more readable, but possibly less permanent, form.)

Most of the participants were heavy-duty experts on evolution, of whom the most notable include William Calvin, Daniel Dennett, Niles Eldredge, Douglas Futuyma, Peter and Rosemary Grant, Antonio Lazcano, Lynn Margulis, William Provine, William Schopf, Frank Sulloway, and Timothy White. Shermer would be the first to admit that he's an outsider and definitely not in that league. So the substantial value of his notes lies in the impressionistic picture they offer of a significant event rather than an authoritative evaluation of the present state of evolutionary theory.

Nevertheless, one can glean from the notes echoes of most of the important open questions in evolutionary theory today, such as:

• What we know about the existing conditions and sequence of events that led to the origins of life on Earth.
• Whether cells (or cell-like structures) appeared before or after genetic material (RNA).
• The nature of the different "levels of selection" that occur in the process of evolution (genes, chromosomes, organelles, and cells below the level of the individual, and social groups, demes, species, and multispecies communities above).
• What exactly happened in the "Cambrian explosion", and why did it take so long after the origins of life to occur.
• Whether the neo-Darwinian idea of "selection" needs revision to something more like a scenario of random genetic drift, and whether Darwin's idea of sexual selection does or does not have merit.
• How far Lynn Margulis' ideas of symbiogenesis apply more widely in evolution, not just in the emergence of eukaryotic cells.

Yes, there is still vigorous debate about many fundamental questions of evolutionary theory. But this hardly means that the basic ideas of evolution are wrong. Instead, it means that the theory is robust enough to allow us to ask very detailed questions about processes that mostly happened far outside our ability to observe directly -- but questions that can in principle be answered by enough further rigorous scientific research.

As Shermer concludes

Herein lies science’s greatest strength: not only the ability to withstand such buffeting, but to actually grow from it. Creationists and other outsiders contend that science is a cozy and insular club in which meetings are held to enforce agreement with the party line, to circle the wagons against any and all would-be challengers, and to achieve consensus on the most contentious issues. This conclusion is so wrong that it cannot have been made by anyone who has ever attended a scientific conference. The World Summit on Evolution, like most scientific conferences, revealed a science rich in history and tradition, data and theory, as well as controversy and debate.

Mahlburg's result on partitions

It irks me that popular science publications have almost nothing to say when important developments occur in mathematics. So I feel disposed to go out of my way to make up for that.

My starting point is a nice feature article in the June 18, 2005 issue of Science News: Pieces of Numbers. But since the article, unfortunately, eschews any mathematical notation, it may not be as clear as it should be. (The editors may be to blame for hostility towards mathematical notation.)

I'll try to remedy this problem. Define a function p(n) on the positive integers as follows. Let p(n) be the number of different ways (not counting order) that n can be expressed as a sum of positive integers. For instance, p(3) is 3 because we can write 3 as 1+1+1, 1+2, or simply 3. The values that p(n) takes on (the "range" of the function) are called "partition numbers". We can then refer to p(n) as the n^th partition number.

The remarkable Indian mathematician Srinivasa Ramanujan made the first interesting observations about partition numbers, among his very numerous other curious results. He found that starting with p(4), every value of the form p(4+5k) is divisible by 5 for nonnegative integers k. If we use another common mathematical symbolism for divisibility, we can express this fact as p(4+5k) ≡ 0 (mod 5). (In such an expression, we shall assume this means for all integers k ≥ 0.) Ramanujan also found that p(5+7k) ≡ 0 (mod 7), and p(6+11k) ≡ 0 (mod 11). But that's as far as he could go. It doesn't seem to be true that there is any prime q such that p(7+q⋅k) ≡ 0 (mod q).

However, starting in 1968, some other relationships of this sort were found, begining with p(237+17303k) ≡ 0 (mod 13). Note that the starting partition number p(237) skips over a large number of intervening partition numbers, and that the interval between partition numbers (17303) is not the same as the prime divisor. But in 2000 Ken Ono proved, remarkably, that some such relationship does exist for every prime number other than 2 and 3. A little later Ono and Scott Ahlgren proved such relationships exist for all positive powers of primes other than 2 and 3. In other words, for any prime p other than 2 or 3, and any n ≥ 1, there exist integers l and m (that depend on p and n) such that p(l+m⋅k) ≡ 0 (mod pⁿ). There can even be different numbers l and m that work for a given prime. For instance, p(111247+157525693k) ≡ 0 (mod 13).

What is remarkable in all of this is that partition numbers represent additive properties of integers, yet they have striking multiplicative properties in terms of divisibility by prime powers.

The proofs that Ono created used sophisticated number theoretic techniques. But long before 2000 the mathematician-turned-physicist Freeman Dyson conjectured that there might be characteristic numbers of specific partitions of a given number which could be used to explain Ramanujan's results. Dyson suggested that the set of partitions of a given number could be divided into subsets of partitions that have the same characteristic number. If all subsets had the same size and the number of subsets was divisible by the prime number in questions, the result would follow.

It was shown in the 1950s that this is true for the primes 5 and 7, using a characteristic number that Dyson called the "rank" of a partition. In this case, there were 5 and 7 subsets of partitions (respectively) for 4+5k and 5+7k where the subsets were of equal size. Unfortunately, this technique didn't work for 11. Dyson guessed that there might be a different characteristic number which he called the "crank" that might do the trick, but neither he nor anyone else, including Ono, could devise a plausible candidate.

But then this year, Ono's graduate student Karl Mahlburg succeeded where others had failed. This made the proofs of all known results much simpler. However, there was a curious wrinkle. The "crank" that Mahlburg came up with divided the set of partitions of a given number into many subsets, but (except for primes 5, 7, 11), the subsets were not of equal size. Yet, surprisingly, the number of partitions in each subset were divisible be the prime or prime power involved. And so the total number of partitions, which is the sum of the sizes of all the subsets, must also be divisible by the same prime power.

Here are a couple of short articles on Mahlburg's result:

Mathematician Untangles Legendary Problem
Classic maths puzzle cracked at last

Scientific truth is what the politicians in power say it is...

And I don't have any further comments at present about how the current administration rewrites science any way it feels like...

Pentaquarks, RIP

Not all scientific hypotheses pan out. In fact, most don't. This is disappointing to researchers eager to learn some new truth about Nature. But it is what makes science reliable and valuable. As attractive as it might seem to have the freedom to spin out a web of scientific theory to match one's imagination, it is even more worthwhile to build theoretical edifices that can be relied upon. This is actually much better for speculative theorists. It means that there is a trustworthy foundation one can build upon, without running too much risk of wasting one's time, or even a whole career, on developing theories that become worthless when the foundations that others laid turn out to be incapable of supporting further construction.

The way that science avoids such disasters is by requiring new ideas and hypotheses to meet as many strict tests against experimental data as possible. A recent article by Frank Close, as summarized in this piece On the Nonexistence of Pentaquarks, provides a good case study of this process in action.

Most of us would be better off in our personal lives as well if we'd learn to test our bright new ideas and cherished beliefs against known facts and data -- even if it takes some effort to acquire the relevant facts and data. And especially even though it means we sometimes have to give up on those ideas and beliefs when they don't pass a conscientious reality check.

Political science, H. L. Mencken

One little known fact about me is that I have an M. A. degree in political science. I didn't pursue it farther than that, as I realized that I was simply studying a branch of psychopathology. But that's a story for another time....

What I really wanted to talk about is H. L. Mencken, as I came across this really wonderful H. L. Mencken page. It shows, I think, that Mencken's understanding of political science was as astute as that of anyone in the halls of academe today.

I've accumulated many good quotes from Mencken myself, but I haven't organized them, so I'll just offer a few political science gems right now, and leave the rest for other occasions.

A Galileo could no more be elected president of the United States than he could be elected Pope of Rome. Both high posts are reserved for men favored by God with an extraordinary genius for swathing the bitter facts of life in bandages of self-illusion.

For every difficult question there is a simple answer -- and it's wrong.

The whole aim of practical politics is to keep the populace alarmed (and hence clamorous to be led to safety) by menacing it with anendless series of hobgoblins, all of them imaginary.

The men that American people admire most extravagantly are the most daring liars; the men they detest the most violently are those who tryto tell them the truth.

Democracy is the theory that the common people know what they want, and deserve to get it good and hard.

A good politician, under democracy, is quite as unthinkable as an honest burglar.

Democracy is the art of running the circus from the monkey cage.

I do not believe in democracy, but I am perfectly willing to admit that it provides the only really amusing form of government ever endured by mankind.

Small gaps between primes

The usual sources of online science news seldom deal with important stories in mathematics. This is especially annoying when one considers the kind of trivia often reported in other scientific fields. So things are proceding true to form with respect to the news that Dan Goldston and colleagues appear to finally have a valid proof of their "prime gaps" theorem.

But the information is out there if you know to look for it and you look hard enough. The basics are in this note on MathForge. There's an interview with Dan Goldston in his hometown paper. And you can read the technical paper on Small gaps between primes or almost primes at ArXiv.org.

So what does the theorem actually say? It isn't that hard to explain. The prime number theorem states that the average gap between two consecutive primes p_n and p_n+1 is about log(p_n), where "log" is the natural logarithm. But that is a very rough estimate. It is suspected that the gap can be as small as possible (two) infinitely often -- a proposition known as the twin prime conjecture. This is one of the most famous (to mathematicians) unsolved problems in number theory, right up there with the Riemann Hypothesis and Goldbach's conjecture.

The result that Goldston and colleagues have sought to prove is a little weaker. Symbolically it is that

lim inf_n→∞ (p_n+1 - p_n)/log(p_n) = 0

What this says is that the ratio of the difference between the n+first prime and the n^th prime to the natural logarithm of the n^th prime is smaller than any positive number ε for infinitely many n, no matter how small ε is. Using the same notation, one could express the twin prime conjecture as

lim inf_n→∞ (p_n+1 - p_n) = 2

Exciting stuff, no? Well, it is to number theorists, anyhow.

NASA plans for cosmology

A June 2 news story from New Scientist describes recommendations from a NASA advisory panel.

Four key research areas were listed for the next 3 decades.

The first key area is searching for evidence of cosmic inflation. From now to 2015 this is to be done by analysis of the cosmic microwave background. From 2015 to 2025 gravitational wave astronomy will be employed. Around 2025 the Big Bang Observer will continue by providing the next generation of gravitational wave astronomy.

The second issue is gaining a better understanding of black holes and related relativistic effects. From now to 2015 the Gamma-Ray Large Area Telescope will study the relativistic jets associated with black holes. The James Webb Space Telescope (JWST) will search for evidence of black hole growth and mergers in the early universe. Around 2015 gravitational wave astronomy will be used along with a new X-ray telescope (Constellation-X) to study black hole properties. After 2025 there will be an attempt to image matter falling into black holes.

The third issue is the investigation of dark energy. Up to 2025 this is to be done by studies of the distribution of visible and dark matter. After 2025 the Big Bang Observer will enable measurements of distances to binary systems consisting of neutron stars and black holes in order to better determine the geometry of the universe.

The fourth issue is the study of how galaxies, stars, and stellar planetary systems evolve. From now to 2015 the HST and the JWST will study stars in the earliest galaxies. From 2015 to 2025 Constellation-X will study the dispersal of heavy elements. After 2025 later instruments will study the evolution of nuclei, atoms and molecules.

All this depends, of course, on appropriate priorities being given to these objectives, so that solid science is not crowded out of the budget by ostentatious displays of national vanity in the form of manned junkets to the moon and Mars.

More information on NASA roadmaps is here and here.

Related documents include a report on Science in NASA's Vision for Space Exploration and the details about proposed cosmology research in Universe Exploration: From the Big Bang to Life.