Nix and Hydra

Two additional moons of Pluto (in addition to Charon) were imaged by astronomers working with the Hubble Space Telescope on 5/15/2005. The International Astronomical Union officially named the moons Nix and Hydra. These moons orbit Pluto at approximately two and three times the distance of Charon: Nix at 48,700 kilometres and Hydra at 64,800 kilometres from the barycenter of the system.

Geeky Math Humor

Q: What's the value of a contour integral around Western Europe?
A: Zero, because all the Poles are in Eastern Europe.

Itzykson & Zuber is back in print

Dover rocks!

http://www.amazon.com/gp/product/0486445682/

Ridiculous

On today's Law & Order Criminal Intent, I learned that elementary age kids without any training in advanced mathematics or supervision by a knowledgeable mathematician nevertheless have a reasonable chance of solving the Riemann Hypothesis just because they are geniuses.

A couple of weeks ago, I learned that in theoretical physics "theories" are formulated without any appeal to mathematics, and then mathematics is used to prove those theories.

Ridiculous

Having a bad day? No wonder. According to one scientist, today, January 23, is the gloomiest day of 2006. Cliff Arnall, a health psychologist at the University of Cardiff in Wales, has devised a formula that combines personal and seasonal factors to calculate the year's emotional low point.

Caught this story in today's paper. The same story made the rounds last year. It's utterly ridiculous. According to this "scientist," the variables are weather (W), debt (D), monthly salary (S), time since Christmas (T), time since failure to quit a bad habit (Q), low motivational levels (M) and the need to take action (N). Sounds reasonable enough. But now let's look at his "formula."

Gloominess = [W + (D-S)xTxQ] / [M x N]

So we take time (since Christmas) times time (since failure) times money. So we have a quantity that is measured in $ x days squared. Then we add this to a weather variable, which is measured in . . . ?

Then we take this already meaningless concoction and further divide it by "low motivational levels" and "the need to take action." I'm unclear on how either of these can be measured well enough to allow any mathematical comparisons to be made between January 23 and January 20 or January 26 ... or July or November or any other random date I pull out of a hat. Furthermore, why do we divide by them; why not multiply?

I am appalled that some idiot can get this "research" published. What a freakin' joke.

Ridiculous

I'm watching an episode of Law & Order: Criminal Intent, and in just a five minute interval, I've learned the following:

• "After three tries, most password programs give you a hint." Funny, most password programs I've ever seen after three tries LOCK YOU OUT!
• Senior math majors take multivariable calculus. (I took it first semester of sophomore year, and I was far from the most advanced student in my cohort.)
• Seniors who have not completed multivariable calculus are given research grants by the Department of Defense.
• Random number generator programs increase your odds of winning the lottery.

2005 Nobel Prize in Physics

Roy J. Glauber
"For his contribution to the quantum theory of optical coherence."

John L. Hall
Theodor W. Hänsch
"For their contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique."

http://nobelprize.org/physics/laureates/2005/

MIT Open CourseWare

MIT has a website, Open Course Ware, where professors present a lot of the teaching materials from their various courses. When the site first started, the math and physics offerings were pretty thing. However, over the last year, many of the courses have been substantially enhanced, to the point where they are now quite useful resources, including extensive lecture notes and many solutions to homework assignments. I am also providing the link to the MIT math and physics departments, since those sites still have the home pages of professors with resources for courses being offered in the current academic years.

Physics OCW

Physics Department Website

Mathematics OCW

Mathematics Department Website

Dr. Serge Lang, R.I.P.

Serge Lang died today. Rather than create a lengthy post that would still not do this great mathematician justice, I'll just link to his wikipedia entry.

Methods of Theoretical Physics

The famous mathematical physics textbook by Morse & Feshbach has finally been republished. I've long wanted to get my hands on a copy, but not at this price ($329 for the set, up from the original price of $250).

Not sure why the price is going up or what is he thinking, but I don't think his company will never be successful at this price. It's a shame.

Thirteen things that do not make sense

New Scientist has an article on thirteen things that do not make sense in science. Historically, such paradoxes have provided the impetus for new discoveries. The most notable examples are the Michelson-Morley null experiment (leading to special relativity), the unexpected blackbody radiation spectrum (leading to the quantum hypothesis), and the anomalous precession of the perihelion of Mercury (leading to general relativity).

1. The placebo effect
2. The cosmological horizon problem
3. Ultra-energetic cosmic rays
4. Belfast homeopathy results
5. Dark matter
6. Viking's discovery methane on Mars
7. Tetraneutrons
8. The Pioneer anomaly
9. Dark energy
10. The Kuiper cliff
11. The "Wow" signal
12. Not-so-constant constants
13. Cold fusion

[Thanks to DVD for the link]

Superstrings <> Cosmic Strings

I have seen this article twice today, so I thought I'd make a quick post about it.

Could two lookalike galaxies, barely a whisker apart in the night sky, herald a revolution in our understanding of fundamental physics? Some physicists believe that the two galaxies are the same - its image has been split into two, they maintain, by a "cosmic string." If this interpretation is correct, then CSL-1 - the name of the curious double galaxy - is the first concrete evidence for "superstring theory": the best candidate for a "theory of everything", which attempts to encapsulate all the phenomena of nature in one neat set of equations.

Not sure why the author of this article switched from "cosmic strings" to "superstrings" without a word of explanation, but these two concepts are completely unrelated. Superstrings are the extension of Quantum Field Theory of point particles to one-dimensional "strings," a theory which leads to highly speculative predictions about a 10 dimensional universe and may succeed in unifying quantum field theory with classical General Relativity. Cosmic strings are astronomical objects described by the rules of classical general relativity. The two things have absolutely nothing to do with each other.

http://www.astronomycafe.net/qadir/ask/a11828.html

Astronomers find star-less (dark matter?) galaxy

Astronomers say they have discovered an object that appears to be an invisible galaxy made almost entirely of dark matter. The team, led by Cardiff University, claimed it is the first to be detected. It was found 50 million light years away using radio telescopes in Cheshire and Puerto Rico.

[Thanks to GB for the link.]

No Evidence of Life on Mars

News reports on February 16, 2005, that NASA scientists from Ames Research Center have found strong evidence that life may exist on Mars are incorrect. NASA does not have any observational data from any current Mars missions that supports this claim. The work by the scientists mentioned in the reports cannot be used to directly infer anything about life on Mars, but may help formulate the strategy for how to search for martian life. Their research concerns extreme environments on Earth as analogs of possible environments on Mars. No research paper has been submitted by them to any scientific journal asserting martian life.

Life on Mars? Never mind!

A pair of NASA scientists told a group of space officials at a private meeting Sunday that they have found strong evidence that life may exist today on Mars, hidden away in caves and sustained by pockets of water. The scientists, Carol Stoker and Larry Lemke of NASA's Ames Research Center in Silicon Valley, told the group that they have submitted their findings to the journal Nature for publication in May, and their paper currently is being peer reviewed. What Stoker and Lemke have found, according to several attendees of the private meeting, is not direct proof of life on Mars, but methane signatures and other signs of possible biological activity remarkably similar to those recently discovered in caves here on Earth.

Dr. Herbert Goldstein, R.I.P.

Herbert Goldstein, Professor Emeritus of Nuclear Science and Engineering at Columbia, died today. He was 82. Long recognized for his scholarship in classical mechanics and reactor shielding, he was the author of the classic (pun intended) graduate textbook, Classical Mechanics. The book has been a standard text since it first appeared 55 years ago and has been translated into nine languages.

Goldstein's contributions to nuclear energy were honored by the U.S. Department of Energy, which awarded him the E.O. Lawrence Memorial Award in 1962. In 1977, he was the recipient of the Distinguished Service Award from the shielding division of the American Nuclear Society. He was a professor of nuclear science and engineering at the Fu Foundation School of Engineering and Applied Science since 1961. He received the Great Teacher Award, given by the Society of Columbia Graduates, in 1976. In 1984, he was the first to hold the Thomas Alva Edison Professorship at the University. In addition to research, he devoted time to promoting scientific literacy by teaching undergraduate courses. In 1977, he taught a course he designed to increase scientific understanding of energy issues "Nuclear Energy: A Semi-technical View for the Non-scientist." He was also one of the faculty members instrumental in developing an innovative science course for non-scientists, "The Theory and Practice of Science," at the College. He was a consultant for Oak Ridge National Laboratory and Brookhaven National Laboratory.

Goldstein was a fellow of the American Physical Society, the American Nuclear Society, the New York Academy of Sciences and the American Association for the Advancement of Science. He also was a member of the American Association of Physics Teachers and was a founding member and president of the Association of Orthodox Jewish Scientists. He received a B.S. from City College of New York in 1940 and a Ph.D. from Massachusetts Institute of Technology in 1943.

Goldstein is survived by his wife, Channa; his children, Penina, Aaron Meir and Shoshanna; and 10 grandchildren.

2005

is the 100th anniversary of Einstein's miracle year (Annus Mirabilis)!

Putnam Competition

The William Lowell Putnam Mathematics Competition is today.

The Putnam Competition is a North American math contest for college students offered each year on the first Saturday in December. Over 3000 students will spend 6 hours (in two sittings) trying to solve 12 problems (at 10 points a problem, the maximum score is 120). Individual and team winners get some money and a few minutes of fame. High scorers almost invariably go on to earn their Ph.D. and generally end up as top-tier mathematicians in their particular research areas.

I took this exam once in my undergraduate career and scored either 11 or 13 (I don't remember). A most humbling experience, but also not a bad result, relatively speaking. The median score is usually 2 (yes, 2 out of 120, that's not a typo).

For past exams and their solutions see this website.

Also, the wikipedia article has a list of past winners.

Progress on Two Unsolved Problems

Some news on two of the unsolved problems previously mentioned in this blog. See Seven Mathematical Tidbits by Eric W. Weisstein and Ed Pegg Jr. for more details.

Conjecture: There are no odd perfect numbers.

It is still not known if any odd perfect numbers exist, although it is known that any such number would have to be greater than 10^300. Kevin Hare has been investigating the existence of odd perfect numbers and has proven that any odd perfect number must have at least 47 prime factors (including repetitions), and that improving this result depends upon finding factors of three large numbers. In particular, a higher bound can be computed if a certain composite 301-digit number can be factored.

References:
Odd Perfect Numbers by K. G. Hare
Some Factorizations That I Want by K. G. Hare

Riemann Hypothesis: All of the non-trivial zeros of the Zeta Function are located on the line Re(s) = ½.

On October 13, Xavier Gourdon and Patrick Demichel announced that they had used an efficient technique due to Odlyzko and Schönhage to find the first ten trillion nontrivial zeroes of the Riemann zeta function, more than ever before computed. Every single one of these zeros lies along the critical line, which is a necessary requirement for the Riemann hypothesis to hold but not sufficient.

References:
Computation of Zeros of the Zeta Function by Xavier Gourdon and Patrick Demichel
The 10^13 First Zeros of the Zeta Function, and Zeros Computation at Very Large Height by Xavier Gourdon

Second black hole found at the centre of our Galaxy

Just three years ago, astronomers confirmed that the Milky Way revolves around a supermassive black hole, called Sagittarius A*, which is about 2.6 million times more massive than the Sun. But now a much smaller black hole, just 1,300 times our Sun's mass, has been found orbiting about three light years away from its supermassive cousin.

"This is the first intermediate-mass black hole found in our Galaxy." - Jean-Pierre Maillard, an astronomer from the Institute of Astrophysics in Paris, France.

[Thanks to DVD for providing this link.]

An interesting discussion of black holes with special emphasis on the famous Cygnus X-1 black hole candidate can be found here.