Two most useful papers of this week :-)

(1) D. Kobak, S. Shpilkin, M. S. Pshenichnikov, "Statistical anomalies in 2011-2012 Russian elections revealed by 2D correlation analysis", arXiv:1205.0741

A solid scientific base for what basically everyone knows already :-) Also, unlike previous analyses appearing on the internet, this one is in English, so everyone can understand it and spread the word.

(2) H. C. Mayer, R. Krechetnikov, "Walking with coffee: Why does it spill?", Phys. Rev. E 85, 046117 (2012). There is also a popular synopsis about it.

I was used to think that spilling coffee while walking (and then making innocent eyes and speeding up) was my own problem, because I basically break everything I touch. This article made me feel normal, just as everyone else. Finally, there is a scientific base for spilling coffee!

Take care,

Misha

Some links for 25.03.12

(1) Picture-hanging puzzles by Demaine and coauthors

(2) What the referee reports on some citation classics might have looked like? (computer science)

(3) Why do physicists need a salary raise?


Take care,

Misha

How long does it take for an article to be accepted?

I posted it on facebook at some point, but it certainly deserves a wider audience :-)

Take care,

Misha

The 1917 in mathematics

You probably know that in 1917 the October Revolution happened in Russia: the bolsheviks got power and created the Soviet Union five years later. The revolution split many lives into the "before" and "after" the 1917.

Here is how famous Russian mathematician Dmitrii Menshov tells about those times:

"...In 1915 we studied function series, in 1916 - orthogonal series. And then the 1917 happened. That was a very memorable year in our lives, this year there happened an event that had drastically affected our future lives: we started looking at trigonometric series."

source (in Russian)

I wish I could care that little about anything that's not science :-D

Take care,

Misha

Fibonacci salad

Bad food in the university cantine can be described by simple math. Every day they feed us with Fibonacci Salad - it's when you mix a yesterday salad with a salad from two days ago to get the salad for today.

(via Valera Yundin)

Take care,

Misha

What's Special About This Number?

A webpage, explaining why every single number is special. Nice.

Misha

A nice title

It's an art to write a title in such a way that no one even needs to read an article:

"In general, the less degeneracy the less transition. A principle for time‐dependent Hamiltonian systems in quantum mechanics", H. Gingold, J. Math. Phys. 28, 2400 (1987).

Misha

A Million Random Digits Book

Back to Russia I had two favorite books: one was called "The history of the USSR in IX-XIII centuries" (yes, of the USSR!), and the second one was "Tables of prime numbers from 2 to [some 10-digit prime number I don't remember]"

Actually, there exist something more weird than that: a book called "A Million Random Digits with 100,000 Normal Deviates" published by the RAND corporation. Only $81 on amazon.com.

Don't ask me how I found it. :-)

Misha

Benford's law

In 1881 the American astronomer Simon Newcomb noticed that in books of logarithm tables first pages (logarithms of numbers starting with 1) are much more worn than others. This means that  people look up numbers starting with 1 more often than higher ones, which is a pretty weird result.

This effect was rediscovered in 1938 by Frank Benford, who checked it for different real data sets, and it's called Benford's law since then.

The thing is that such a distribution of numbers arises if their logarithms are distributed uniformly, like it's equally probable to find a value between 10 and 100 and between 100 and 1000. This is the case for most of real world statistics, such as distributions of salaries or building heights.

Well, I'm writing about all that because in 1972 the law was proposed to detect fraud in statistics, because people who make up their data tend to distribute numbers pretty much uniformly. For instance, Benford's law was used as an evidence of falsifications in the 2009 Iranian elections.

Be careful if you're making up your experimental data :-)

Misha

Hitler about the P=NP problem

Math is like love

There is a famous quote by R. Drabek:

"Math is like love - a simple idea but it can get complicated."

Does anyone know who this guy Drabek was (or is)? It looks like wiki has no idea about him, I cannot figure out even his first name.

Thanks for collaborating :-)

Misha

von Neumann's words come true

Everyone heard a famous quote of John von Neumann: "with four parameters I can fit an elephant, and with five I can make him wiggle his trunk".

A friend of mine Valera Yundin sent me a link to an awesome article:

Jürgen Mayer, Khaled Khairy, Jonathon Howard, "Drawing an elephant with four complex parameters", Am. J. Phys. 78, 648 (2010)

And it works!


That is definitely something to highlight in the Max Planck Research magazine :-)


Take care,

Misha

Nice quote from the past

"Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry... if mathematical analysis should ever hold a prominent place in chemistry – an aberration which is happily almost impossible – it would occasion a rapid and widespread degeneration of that science."

Auguste Comte, Cours de philosophie positive, 1830

History of science: Gulio Racah kicks ass

As many other branches of atomic, molecular, and chemical physics, the field of chemical stereodynamics emerged from nuclear physics. Basically all this business about how molecules rotate after a chemical reaction, or how to boost the reaction efficiency controlling the reagents – it was already there, in nuclear reactions and spectroscopy.

In 30's some people were involved in studying double gamma decays, when a nucleus goes from some excited state A to state B and then to the ground state C, emitting two gamma-quanta. Already in 1940 Dunworth proposed that there might be some correlations between the directions of emission of these two quanta. Here "correlations" mean that, for instance, if we detect the first gamma-ray from the upper side of the nucleus, the second one most likely will be emitted to the left, less likely to the bottom, and never to the right.

Dunworth was not able to check this experimentally, but induced Donald Hamilton to theoretically prove that there should be some correlations. A few years later Edward Brady and Martin Deutsch from MIT found an experimental evidence of gamma-gamma correlations in the decay of Co(60) and Sc(46) nuclei.

In the meantime theorists published lots of papers, step by step trying to improve approximations and thoroughly elaborate the problem. This lasted for more then a decade, from 1940 to 1951, when a brilliant article by Gulio Racah was published.

He starts it literally as: "Hey guys, last ten years I was interested in something else, but I just bumped into you and I see that you are really stuck. Well, the problem becomes very easy if you use the tensor operator algebra that I developed about a decade ago..."

And, of course, the problem turned out to be solvable in a very natural and straightforward manner. Now tensor operators is an important tool, not only in nuclear physics, but anywhere in physics in general. We all use it and like it.

Take care,

Misha


UPD: By the way, I never knew that Gulio Racah was a cousin of Ugo Fano...

In fifty words or less

In his book “Indiscrete thoughts” famous Italian-born American mathematician Gian-Carlo Rota mentions that Stan Ulam was used to say “Whatever is worth saying can be stated in fifty words or less”.

Well, these days he would probably adjust it a bit:

“Whatever is worth saying can be stated in 140 symbols or less”

)

A bug in Mathematica: Clebsch-Gordan coefficients

A technical issue for those of you using Wolfram Mathematica. Apparently there is a bug in the function furnishing Clebsch-Gordan coefficients, check it out:


These two inputs are equivalent, but the outputs are different somehow. Actually, this Clebsch-Gordan coefficient is zero, because the angular momentum j=9/2 cannot give a projection of m=0. In general, for a coefficient to be nonzero all the (j+m)'s should be nonnegative integer numbers.

The ClebschGordan[] function in Mathematica is used to test all the conditions of existence, such as the triangle rule, but as we see it fails when it comes to substitutions of parameters.

I dropped a message to the Wolfram support team, and they promised to do their best to figure out where the problem comes from. I hope to hear from them soon and I'll keep you posted about it.

Take care,

Misha

Mathematical Tools for Physics

Yesterday I came across a wonderful lecture notes of math methods in physics for undergrads, namely "Mathematical Tools for Physics" by James Nearing. There is a lot of simple math in there, but with really good explanations where in physics this may be of use. Also James gives a lot of funny math tricks.

I wish I had such a lecture course while studying in university.

Things I don't like in Mathematica. Part II: A writing tool.

Here is what I think about writing in Mathematica. For quite a long time I thought that Mathematica can be used for nothing else but calculations. Later I came across a post of Terry Tao "Write professionally", where (among other good things) he states:

"The standard format for mathematical papers is TeX, AMS-TeX, LaTeX, or AMS-LaTeX; other formats such as Word or Mathematica can cause technical difficulties (and will ultimately need to be converted to a TeX format), and so should be avoided."

The first thing I thought was "No way, I do not believe that somebody uses Mathematica for writing papers." I know a few experimentalists who submit articles in .doc format and are happy with it, due to lack of equations. But, as far as I know, using something but TeX is considered as kind of "mauvais ton" in math community (please tell me if I'm not right).

This post is not really about some disadvantages of Mathematica interface. But such useless options of notebook formatting as e.g. "Journal Article", "Preprint", "Report", "Book" and "Monograph" can inculcate a bad taste of writing papers in students, who may postpone learning TeX. 

Nevertheless, as mentioned by Philip, Mathematica notebooks can be used to write up some daily results with the following data analysis. For a final draft it is better to use something else, though.

Things I don't like in Mathematica. Part I: License.

In my daily work I use Mathematica, and I like it very much. About 7-8 years ago, during first years of university, we were mainly using Maple for analytical derivations. Mathematica was considered to be better for numerics, since it was impossible for Maple to do them more or less fast. But nowadays (on my opinion), Mathematica is the best instrument to work with analytical stuff.

However, it is absolutely useless to write about "what I like", so I better describe things which I don't like, and which I hope will be changed soon. First I thought that it will be a little post with a list of disadvantages, but it looks like there is no way to make it short. So, there will be a few posts, and here is the first part - about the license.

In our relatively small and, in general, experimental institute we have about 20 online Mathematica licenses. In other words, twenty people can connect the server and perform calculations in the same time. 

One of my roommates was doing quite extensive computations, often lasting several days. Sometimes his calculations were stopped during the night, because Mathematica suddenly decided to check the online license, and simply interrupted the ongoing evaluation before doing this. 

Why are guys from Wolfram so agitated about the copyright? I guess I know the reason. For instance, in Russia one can buy a DVD with the last versions of Mathematica, Matlab, Mathcad, Origin Pro and other stuff (of total cost more than 10k Euro) for about 5 (yes, five) Euro. And people usually do. Furthermore, the illegal software is widely used for teaching in high schools and universities even nowadays. Hopefully, in Germany this is not the case.

Piracy is a problem. But do you really think that interrupting computations is the best way to attract new users?

The described above was actually the reason for my boss to buy me two home-licenses. But even activating home licenses is usually a pain in the neck, as mentioned in comment of BiophysicsMonkey to Chad's post, and I agree with it. Even updating licenses on both of my computers once a year is some kind of a problem I have to waste my time on, not to mention if you have a lot of machines as Chad does.

I'm completely ignorant in commercial software development, but I do not believe that there is no easier way to preserve the copyright.

The greatest math problem ever

This is a problem, which can be easily solved by children before entering elementary school. If you want to give it a try, please forget everything you have ever studied. Here it comes:

8809 = 6
7111 = 0
2172 = 0
6666 = 4
1111 = 0
3213 = 0
7662 = 2
9312 = 1
0000 = 4
2222 = 0
3333 = 0
5555 = 0
8193 = 3
8096 = 5
7777 = 0
9999 = 4
7756 = 1
6855 = 3
9881 = 5
5531 = 0

2581 = ?

I took it from here (Russian)