Monday, December 19, 2011

Viva la verite!

 Notre Dame, Paris

Instead of singing hymns of the glory of God of Israel in Notre Dame, the revolutionaries brought to the altar a beautiful woman all dressed her in white and thus worshipped Reason.
(It is said that this woman died in a mental asylum)

Indeed, French Revolution and the Age of Enlightenment is alive!

The worship of human brilliance was brought to focus during the Revolution. Down with the ancien regime! Down with the superstitions of religion and the inequalities brought by the Church of Christ and the King of France!

The people were on the move after hundreds of years of oppression and the hated symbol of Bastille fell July 14th 1789.

Head of King Louis XVI was severed by guillotine 21 January 1793 and many of those hated nobles and many scientists, too, shared his faith. Does revolution need scientists?

"Off with the Christian God and the religious stupidity so well described by Voltaire!"

(Introduce USA constitution and freedom of religion, separation of the regimes.)

(Introduce the scientific atheism of Josef Stalin and his destruction of the Moscow Cathedral. Well, instead of reason he made the proud new world and worker's paradise sing Te Deum to himself.)

God, Bose and Einstein

In my ears I already hear some reader's comments objecting to the potpourri:

"Nice blog, Mikko, even though we do notice how superficial your understanding is about the subjects you are talking about. At least you know how to quote those who really are familiar with the subject.

What on earth has religion and God to do with the Bose-Einstein statistics described by those two brilliant scientists?

How you dare to mix mythology, faith based on authority of some holy book and on feeble human imagination with the most exact of sciences, Mathematics?

What has God to do in the purest Temple of Reason, mathematical science?"

Dear Madam, Sir
you who strongly disagree with my talking about God, Einstein and Bose in the same blog.

Your dislike of the mix of religious thought and exact mathematical science rises from a sad history of religious authority suppressing the search for truth by Galileo and others. You worry that such combinations, for example calling Higgs particle the God particle, is misleading to the general public and is thus not only annoying to the pure scientific mind but actually a bit dangerous.

Dear Madam, Sir, the question is not what God has to do with the brilliant theories of Bose and Einstein.

It is the opposite.

What have Bose and Einstein to do with God's works.

For, excuse my frankness, it was not Satyendra Nath Bose who made bosons.

It was not Albert Einstein who set up the relative time-space continuum.

These respected fellows got some insight in their brains of what the God of Israel has created.

With the help of Bose and Einstein, human race has achieved a little more understanding of God's deep thinking.

There is still a lot to be learned.

For God, Thy thoughts are VERY deep.

Bose-Einstein statistics

Increasing disorder

In statistical mechanics, Bose–Einstein statistics ... determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium. Fermi–Dirac and Bose–Einstein statistics apply when quantum effects are important and the particles are "indistinguishable"... Fermi–Dirac statistics apply to fermions... and Bose–Einstein statistics apply to bosons...

As the quantum concentration depends on temperature; most systems at high temperatures obey the classical (Maxwell–Boltzmann) limit unless they have a very high density, as for a white dwarf. Both Fermi–Dirac and Bose–Einstein become Maxwell–Boltzmann statistics at high temperature or at low concentration.

Bosons, unlike fermions, are not subject to the Pauli exclusion principle: an unlimited number of particles may occupy the same state at the same time. This explains why, at low temperatures, bosons can behave very differently from fermions; all the particles will tend to congregate at the same lowest-energy state, forming what is known as a Bose–Einstein condensate.

B–E statistics was introduced for photons in 1924 by Bose and generalized to atoms by Einstein in 1924-25.

Errare humanum est
After Satyendra Nath Bose surprised himself by getting unexpected results during that famed lecture at the University of Dhaka he carefully went over his "error". Repeated calculations proved to his own great amazement that, in fact, it was not an error but rather a discovery of something quite important - a truth that had not been previously known by the entire human race.

Erring is human, as the Romans said.

But not recognizing the truth is also a very human characteristic.

When there is a commonly accepted scientific truth and some Bengali fellow comes with a short article to the publisher claiming it is not true - the editor in chief has a dilemma. Should he or she allow the publication of a possibly embarrassing article by some nobody in the distinguished scientific journal?

The answer to that question depends on the ability of the editors to distinguish truth from error - not an easy task when someone nobody presents a paper that challenges the common knowledge and accepted scientific traditions and theory.

Satyendra Bose was not the first to have his paper on a new discovery, observation, theory turned down by almost all respected scientific journals. Charles Darwin had his problems in the 19th century. Just now, in 2011, we have been told the story of the Israeli Nobel Prize Winner in Physics, Dan Shechtman, how his discovery of chemical structures called quasicrystals was shunned by the scientific community and his papers left unpublished.

Scientific research fixes itself as knowledge increases. But the process is painful and possibly even fatal to those thrown into the dynamics where human vanity and glory produce dislike of anything challenging the peace of mind of the best and brightest.

Einstein to the help
Physics journals refused to publish Bose's paper. Various editors ignored his findings, contending that he had presented them with a simple mistake. Discouraged, he wrote to Albert Einstein, who immediately agreed with him. His theory finally achieved respect when Einstein sent his own paper in support of Bose's to Zeitschrift für Physik, asking that they be published together. This was done in 1924.

There you have it.

Respected editors of Physics journals refuse to publish a controversial paper talking about some "error". These people know a lot - but not enough.

That former patent office worker in Bern with sometimes funny hairstyle immediately understood that this paper is true. Science does not like authority faith - for good reasons! - but the authority of Albert Einstein was already in 1924 strong enough to give Bose's paper a chance. He not only understood the Bengali guy's math but applied the brilliant idea from photons to the more general level of atoms.

Not that Einstein had not experienced himself how it is to get letters of rejection from respected scientific publishers.

Simple way to look at it
A much simpler way to think of Bose–Einstein distribution function is to consider that n particles are denoted by identical balls and g shells are marked by g-1 line partitions. It is clear that the permutations of these n balls and g-1 partitions will give different ways of arranging bosons in different energy levels.

Say, for 3(=n) particles and 3(=g) shells, therefore (g-1)=2, the arrangement may be like |..|. or ||... or |.|.. etc.

Hence the number of distinct permutations of n + (g-1) objects which have n identical items and (g-1) identical items will be:


How simple can you get!

So what?
Bose-Einstein statistics have a truly significant dimension in interdisciplinary applications.

Here is where theoretical mathematical thinking meats not only Physics but also other branches of science involving various types of networks. For example in Economics, in understanding growth patterns of computer networks or - and here is for me the most surprising point - even in Evolutionary Biology.

The evolution of many complex systems, including the World Wide Web, business, and citation networks, is encoded in the dynamic web describing the interactions between the system’s constituents. Despite their irreversible and nonequilibrium nature these networks follow Bose statistics and can undergo Bose–Einstein condensation. Addressing the dynamical properties of these nonequilibrium systems within the framework of equilibrium quantum gases predicts that the “first-mover-advantage,” “fit-get-rich(FGR),” and “winner-takes-all” phenomena observed in competitive systems are thermodynamically distinct phases of the underlying evolving networks.

Sunday, December 18, 2011

Bose's mistake

Satyendra Nath Bose in 1925

It happens even to the best among us - we make mistakes.

This one was rather embarrassing, though.

Satyenda Nath Bose (1894-1974) should have known better, a naturally gifted mathematician as he was, one who in his youth had already learned many foreign languages and who even knew how to play the esraj.

Errare humanum est, as they say (or as I wrote in my Latin test errarum humane est amusing my teacher and the class).

Bose was born in Calcutta, British India, the eldest of seven children. His father, Surendranath Bose, worked in the Engineering Department of the East Indian Railway Company. Bose attended Hindu School in Calcutta, and later attended Presidency College, also in Calcutta, earning the highest marks at each institution. He came in contact with teachers such as Jagadish Chandra Bose and Prafulla Chandra Roy who provided inspiration to aim high in life. From 1916 to 1921 he was a lecturer in the physics department of the University of Calcutta. In 1921, he joined the department of Physics of the then recently founded Dacca University (now in Bangladesh and called University of Dhaka).

While presenting a lecture at the University of Dhaka on the theory of radiation and the ultraviolet catastrophe, Bose intended to show his students that the contemporary theory was inadequate, because it predicted results not in accordance with experimental results. During this lecture, Bose committed an error in applying the theory, which unexpectedly gave a prediction that agreed with the experiment (he later adapted this lecture into a short article called Planck's Law and the Hypothesis of Light Quanta).

The error was a simple mistake—similar to arguing that flipping two fair coins will produce two heads one-third of the time—that would appear obviously wrong to anyone with a basic understanding of statistics. However, the results it predicted agreed with experiment, and Bose realized it might not be a mistake at all. He for the first time took the position that the Maxwell–Boltzmann distribution would not be true for microscopic particles where fluctuations due to Heisenberg's uncertainty principle will be significant. Thus he stressed the probability of finding particles in the phase space, each state having volume h³, and discarding the distinct position and momentum of the particles.

Physics journals refused to publish Bose's paper. Various editors ignored his findings, contending that he had presented them with a simple mistake. Discouraged, he wrote to Albert Einstein, who immediately agreed with him. His theory finally achieved respect when Einstein sent his own paper in support of Bose's to Zeitschrift für Physik, asking that they be published together. This was done in 1924. Bose had earlier translated Einstein's theory of General Relativity from German to English.

So a rather trivial mistake Bose made during his lecture (depending, of course, who is talking).

The rest is history and the guy would definitely have deserved Nobel Price for his achievements.

Never got one.

But bosons are called in his honor!

Psalm 92

It is a good thing to give thanks unto the LORD, and to sing praises unto Thy name, O Most High,
to show forth Thy loving kindness in the morning, and Thy faithfulness every night,
upon an instrument of ten strings and upon the psaltery, upon the harp with a solemn sound.
For Thou, LORD, hast made me glad through Thy work; I will triumph in the works of Thy hands.
O LORD, how great are Thy works! And Thy thoughts are very deep.
A brutish man knoweth not, neither doth a fool understand this: when the wicked spring up as the grass, and when all the workers of iniquity do flourish, it is that they shall be destroyed for ever; but Thou, LORD, art Most High for evermore.

For lo, Thine enemies, O LORD, for lo, Thine enemies shall perish; all the workers of iniquity shall be scattered.
But my horn shalt Thou exalt like the horn of a unicorn; I shall be anointed with fresh oil.
Mine eye also shall see what I desire on mine enemies, and mine ears shall hear what I desire upon the wicked that rise up against me.
The righteous shall flourish like the palm tree; he shall grow like a cedar in Lebanon.
Those that are planted in the house of the LORD shall flourish in the courts of our God.
They shall still bring forth fruit in old age; they shall be fat and flourishing to show that the LORD is upright.

He is my rock, and there is no unrighteousness in Him.

Psalm 92 KJ21