Enigma

Enigma was a secret coding machine used by the Germans to encrypt messages during World War II.
In appearance the Enigma machine was no more than wooden box that contained a typewriter but it proved to be much more, as the Allies found out. It was made from numerous components including a light board, a plugboard, a keyboard, a reflector and finally a set of rotors.
The Germans had an operating manual that told the operators how to configure the Enigma machine every day. This was to reduce the risk of the encrypted messages being deciphered. They would daily change the plugboard connection, the starting positions of the rotors and the order they were in. The Germans under Hitler were extremely confident that nobody can break the code.

For the message to be deciphered the set up of the Enigma machine for the day is to be known. Otherwise one had to try million, million possible combinations.



The settings of the Enigma machine would be according to those printed in the manual for that particular day. The message would then be typed out in its existing form onto the keyboard. As the operator typed the message alternative letters would light up on the light board, the message was now in code. This would be written down to make the encrypted message. Finally by wireless the coded version of the message could now be sent in the form of Morse code. Thus preventing the Enemy from being able to understand what was being sent.

Fortunately for the British, Polish scientists had been quietly working behind the scenes and learned much about the Enigma in late 1930s. They pooled their information with the British when Poland was invaded by the Nazis. Two gentlemen, Alan Turing and Alfred Knox, were instrumental in the final breakdown of the Enigma. They created a gigantic machine called Colossus, which helped decipher complex intercepted Enigma messages. Colossus performed thousands of mathematical calculations at unheard-of-speed, at least for that time. The "computer" could read and check about 5,000 characters per second !

The British Army, Navy, Mathematicians and Scientists were all involved in this Code breaking process. British Commanders devised wild tricks : they would crash land a captured German plane into the English channel and then wait for the German Patrol boats to come for rescuing any survivors, whereupon they would capture the patrol boat and with it the code-book. This helped them know the enigma settings for that month and sometimes for the next month as well. The messages decrypted from the enigma were called Ultra and were kept a top secret, even if the information was not a valuble one (ex: weather forecase related) for fear of Germans coming to know that the Enigma code has been broken. It is said that even when they knew of possible attacks, the British soldiers weren't on alert fearing that this would lead to Germans getting suspicious.

This technique payed off for a while until the Germans came to know about it and in 1942, they promptly added a fifth rotor to the enigma machines. But it was too late for them. Though this increased the number of combinations and pushed the allies back to square one, the British had by now become experienced and they could still decipher many important information by using a combination of human guess work and the computers. Finally the allies were able to gain an upperhand in the battle of atlantic against the Germans. Though it would be an exaggeration to say that the Germans would have won the battle if the enigma codes had not been deciphered, it is believed that it could have easily taken another 4 to 5 years for the war to end.

Richie rich

His name is Hassanal and he has 10 children.
He plays professional polo.
He owns a big Automotive Empire.
He is the Ruler, Prime Minister, Defence Minister, Finance Minister and Religious head of his country.
He remained the richest man on the planet for longer than any of us can remember.

Yes. The Sultan of Brunei. Sultan Haji Hassanal Bolkiah Mu'izzaddin Waddaulah.
Not a big name in comparison to the neighbouring Malaysia's rulers.

A small flash back :
Long long ago, in 2002, when compsci Bals and I saw a news clipping regarding the death of the Malaysian King, we were so impressed by his name that we decided to "memorise" it. We also had a competition on who would recite the name first. He won. I doubt if he still remembers the name, but let me recollect : Sultan Salahuddin Abdul Aziz Shah Al Haj Ibni Al'Marhoum Sultan Hisamuddin Alam Shah Al Haj.

So how did the Sultan get so much money?
From his father, he inherited a personal fortune estimated at $40 billion! Thats too much money. If he wanted to spend the whole thing in 100 years, imagine how much he would have to spend per day.
Vinayaga.. we are depending on you for exact numbers. For those who didn't know, our Vinayagamoorthy (eee : novell) is an expert in such calculations.

Well recent reports however suggest that his treasure has dwindled to a mere $10 billion - relatively peanuts.
It's not so easy to blow $30 billion, which is roughly equivalent to the entire annual income of all 125 million people living in Bangladesh
A sizeable chunk of it went on the Sultan's palace, a monstority that boasts 1,788 rooms and is larger than the Vatican. When the sultan's daughter turned 18 he bought her an Airbus. For himself he prefers his own Jumbo jet, originally designed to carry over 400 people.
Great skill in extravagance has also been acquired by his brother Jefri. He buys and plays super-cars like toys, gets bored very soon, buys new ones and store the old ones in any of the 4 huge garages forever along with tens of thousands of other cars.

So many cars that they are the top customers for Rolls-Royce and the likes.

Why did they buy so many McLaren and Dauer? Perhaps they like to share with their relatives. Perhaps their wives like to drive them for shopping. Perhaps they want to have a few spare cars when the normally used one is under servicing. Most likely, perhaps because money is nothing to his majesty (or should i say money was).

Diophantus

Something is always better than nothing.
Well, i tried to solve Koushik's Quest..., concluded pretty soon that it was not going to be that easy and then decided to "ask-my-friend".(i.e. google search)
My search was not up to the mark this time, but i ended up going through a lot of material on Diophantine equations.

Here is koushik's question :

Can you solve this problem ?
For given prime number p, solve the equation in set of integers Z:
xyz=p(x+y+z)

Koushik, did you manage to solve this ?

Back to Diophantus.
Greek Mathematician. Lived from about 200 - 284 A.D in Alexandria, Egypt. Historians could find his age only from one of his puzzles. (a classic - if my father's age is twice that of blah..blah..).
He wrote Arithmetica a collection of over 130 problems and their solutions. The class of equations that he dealt with most came to be known as Diophantine equations. A Diophantine equation is a polynomial equation with integral coefficients to which only integral solutions are sought. The study of Diophantine equations is one of the central areas of number theory. Fermat's Last Theorem is one such equation.



That's the front page of his book. (ofcourse printed, republished,

Diophantus may not be, as he is often called, the father of Algebra. Nevertheless, his remarkable, if unsystematic, collection of indeterminate problems is a singular achievement that was not fully appreciated and further developed until much later.
This considering the fact that symbolism (usage of short notations) was not prevalent those days.

Instead of "x+y" he would say "the first unknown added to the second unknown".
For "(12+6n)/(n^2-3)" he says "a sixfold number increased by twelve, which is divided by the difference by which the square of the number exceeds three".
SK's chemistry book was far better.

We should be able to appreciate the advantage of symbolism, and also take pride in the fact that Indians were the first to employ a lot of such techniques. ( ahh.. think short-cuts think Indian ! )
The Arithmetica remained the authority in Algebra for many more years to come. It is on one of the margins of the pages on one of these that Fermat made the famous (some call it sadistical) remark : " I have a truly marvelous proof of this (his last theorem) which this margin is too small to contain".

One Joke for today :

A physicist, an Astronomer and a Mathematician are travelling on a train in Scotland.
Suddenly the Astronomer peeps out of the window and exclaims
"Look at the sheep out there ! Looks like sheep in Scotland are black !"
The Physicist says "Correction.. Some sheep in Scotland are black"
The Mathematician finally says "This only means.."
"..that in scotland there exists atleast one field with atleast one sheep, atleast one side of which is black".

The Manhattan project

In 1938 many people feared that Hitler would build an atomic bomb after word spread that German scientist Otto Hahn and others had split the uranium atom (fission). However, one of Hitlers mistakes was his persecution of Jewish scientists. This persecution resulted in numerous scientists seeking asylum in the United States. One such scientist was Albert Einstein. Einstein and a few others, abandoning their belief in pacifism, urged the then president Franklin Roosevelt to develop an atomic bomb before Hitler did. Eventually Roosevelt agreed and the United States attempt at building the atomic bomb was codenamed The Manhattan Project.

The Manhattan Project was carried out in extreme secrecy. By 1945, the project had nearly 40 labratories and factories which empolyed approximately 200,000 people. Among these employees were some of the greatest scientists that have ever lived. Included in this lot were Albert Einstein, Enrico Fermi, Richard Feynman, J. Robert Openheimer, Harold Urey, Niels Bohr and james chadwick among others.

In 1945 the United States covert operation known as The Manhattan Project achieved its goal - to create the first atomic bomb. Since its inception in 1939, scientist had struggled to find a way to harness the power of fission. Through the combined efforts of many, a test bomb known as "Fat Boy" was finally created. On July 16, 1945 in a desert in New In 1945 the United States covert operation known as The Manhattan Project achieved its goal - to create the first atomic bomb. Since its inception in 1939, scientist had struggled to find a way to harness the power of fission. Through the combined efforts of many, a test bomb known as "Fat Boy" was finally created. On July 16, 1945 in a desert in New Mexico the worlds first nuclear test, codenamed Trinity, was conducted and ushered in the Atomic Age. The Trinity test success led to the creation of two more atomic bombs that would be used in WWII.

Trinity Test :

On August 6, 1945 an American B-29 bomber released the first atomic bomb to be used in warfare. The 9,000 pound bomb nicknamed "Little Boy" detonated in Hiroshima, Japan. "Little Boy's" explosion was catastrophic and resulted in 66 thousand instantanous deaths. Total vaporization from the blast measured one half a mile in diameter. Total destruction ranged one mile in diameter and serious blazes extended as far as three miles in diameter.

Little Boy & Hiroshima blast :

Three days after the release of "Little Boy" a second bomb named "Fat Man" was released on the town of Nagasaki. "Fat Man" weighed 10,000 pounds and annihilated nearly half of the city. In one split-second, the population of Nagasaki dropped from 422,000 to 383,000. As astonishing as this seems, scientist estimate that both "Little Boy" and "Fat Man" only utilized 1/10th of 1 percent of their explosive capabilities.Mexico the worlds first nuclear test, codenamed Trinity, was conducted and ushered in the Atomic Age. The Trinity test success led to the creation of two more atomic bombs that would be used in WWII.

Fat Man & Nagasaki blast :


The initial explosion of an atomic bomb is devastating but its destructive capabilities do not end there. Rain that follows an atomic bomb is heavily contaminated with radioactive particles. Many survivors of the initial blast eventually died due to radiation poison. Those survivors that did not die suffured severe burns, nausea, vomitting, fatigue, diarrhea, and hair loss. Other effects are still being discovered to date. One such discovery is the passing on of Leukemia to offspring.

Not all by-products of the atomic bomb have been negative. Through the atom bomb, scientist have discovered how to harness the power of nuclear energy. Nuclear power plants are far more efficient than traditional power plants. The medical field has also taken advantage of the atomic bomb. Technology used in the atomic bomb is also used for CAT scans and chemotherapy.

The Asian Brains - part II

Some more skills of asians :




--

The Asian Brains - part I

1) Yes sir, yes sir 9 bags full



2) We salute you !!



3) Ring-a-Ring-a-Broomsticks !

pic humour

No.1

No.2

King of kings

A poem for today:

I met a traveler from an antique land
Who said: Two vast and trunkless legs of stone
Stand in the desert. Near them, on the sand,
Half sunk, a shattered visage lies, whose frown,
And wrinkled lip, and sneer of cold command,
Tell that its sculptor well those passions read,
Which yet survive, stamped on these lifeless things,
The hand that mocked them, and the heart that fed,
And on the pedestal these words appear:
"My name is Ozymandias, King of Kings:
Look upon my works, ye Mighty, and despair!"
Nothing beside remains. Round the decay
Of that colossal wreck, boundless and bare
The lone and level sands stretch far away
- Percy Bysshe Shelley


Well, Ozymandias was actually Ramesses II, a pharaoh who ruled for 67 years from 1279 to 1212 B.C. He built more temples, monuments, obelisks than any other pharoah in history. And he presided over an empire that stretched from present day Libya to Iraq in the east and as far north as Turkey and southward into Sudan.
This Shelley's poem "Ozymandias", inspired by the fallen statues at his mortuary temple at Thebes, takes its title from the Greek version of one of the ruler's alternate names : User-maat-re.

An inscription on one of the statues reads :
I am Ozymandias, King of kings.
If anyone would know how great I am and where I lie,
let him surpass any of my works.

Though Ramses II thought of himself to be immortally great, the poem goes to show how we think of things that are seemingly a pinnacle of greatness today, not realizing that for all our boasts and thoughts of self importance soon will only be a faded memory, if that. Greatness today, sad broken down statuary 2000 years down the road.
Nothing would stay on forever.

The Bernoulli family

One of the most distinguished families in the history of mathematics and science is the Bernoulli family of Switzerland, which from the late seventeenth century on, produced an unusual number of capable mathematicians and scientists. The family record starts with the two brothers, Jakob Bernoulli and Johann Bernoulli.
They were among the first mathematicians to realize the surprising power of calculus and to apply the tool to a great diversity of problems.

Several things in mathematics now bear Jakob Bernoulli's name. Among these are the Bernoulli distribution and Bernoulli theorem of statistics and probability theory; the Bernoulli equation , met by every student of a first course in differential equations;the Bernoulli numbers, and Bernoulli polynomials first course in the calculus. In jakob Bernoulli's soulution to the problem of the isochrone curve, which was published in the Acta eruditorum, in 1690, we meet for the first time the word integral in a caculus sense. Leibniz had called the integral calculus calculus summatorius; in 1696, Leibniz and Johann Bernoulli agreed to call it calculus calculus integralis.

Johann Bernoulli was an even more prolific contributor to mathematics than was his brother Jakob, Though he was a jealous and cantankerous man, he was one of the most successful teachers of his time (Leonhard Euler was his pupil). He greatly enriched the calculus and was very influential in making the power of the new subject appreciated in continental Europe. It was his material that the Marquis de L'Hospital (1661-1704), under a curious financial agreement with Johann, assembled in 1696 into the first calculus textbook. In this way, the familiar method of evaluating the indeterminate form 0/0 became incorrectly known in later calculus texts as L'Hospital's rule.

The Bernoulli family tree :
Jakob BernoulliJohann Bernoulli
Jacob HermannNicolaus II
Daniel BernoulliJohann II
Johann Bernoulli IIIJacob II

Johann Bernoulli had three sons, Nicolaus (1695-1726), Daniel(1700- 1782), and Johann II (1710-1790), all of whom won renown as eighteenthcentury mathematicians and scientists. Nicolaus, who showed great promise in the field of mathematics, was called to the St.Petersburg Academy, where he unfortunately died by drowining, only eight months later. He wrote on curves, differential equations, and probability. A problem in probability, which he proposed from St. Peresburg, later became known as the Petersburg paradox. The problem is:If A receives a penny when a head appears on the first toss of a coin, two pennies if a head does not appear until second toss, four pennies if a head does not appear until the third toss, and so on, what is A's expectation? Mathematical theory shows that A's expectation is infinite, which seems a paradoxical result. The problem was investigated by Nicolaus' brother Daniel, who succeeded Nicolaus at St. Petersburg. Daniel returned to Basel seven years later. He was the most famous of Johann's three sons, and devoted most of his energies to probability, astronmy, physics and hydrodynamics. In probability he devised the concept of moral expectation, and in his Hydrodynamica, of 1738, appears the principle of hydrodynamics that bears his name ( Bernoulli's principle) in all present-day elementary physics texts.

Johann II, the youngest of the three sons, studied law but spent his later years as a professor of mathematics at the University of Basel. He was particularly interested in the mathematical theory of heat and light.
There was another eighteenth-century Nicolaus Bernoulli (1687-1759), a nephew of Jakob and Johann, who achieved some fame in mathematics. This Nicoiaus held, for a time, the chair of mathematics at Padua once filled by Galileo. He wrote extensively on geometry and differential equations. Later in life, he taught logic and law.
Johann Bernoulli II had a son Johann III (1744-1807) who, like his father, studied law but then turned to mathematics. When barely nineteen years old, he was called as a professor of mathematics to the Berlin Academy. He wrote on astonomy, the doctrine of chance, recurring decimals, and indeterminate equations.

Vinland map

In the early 1960s, something called the "Vinland map" was uncovered. It became famous because it proved that Vikings came to America before Columbus. It seemed to be a map of the North Atlantic as drawn from Scandinavian discoveries between 800 and 1100 CE, well before western Europe's great Age of Exploration that began in 1400. It was announced by Yale University in the early 1960s, receiving much fanfare, and much skepticism.

Ever since it surfaced in 1957, the Vinland Map has been controversial. Some experts purport that it was drawn in the 15th century and that it chronicles the Vikings' travels to the New World, prior to Christopher Columbus's 1492 journey. Others argue that it is instead the work of a 20th-century counterfeiter. Now the results of two new studies are adding further fuel to the debate. A report published recently in the journal Analytical Chemistry concludes that the map's ink has modern roots; researchers writing in the August issue of the journal Radiocarbon, on the other hand, say that the parchment dates back to 1434.

Katherine L. Brown and Robin J. H. Clark of University College London used a technique known as Raman microphone spectroscopy to examine the ink on the map. The drawing contains both yellowish lines that adhere strongly to the parchment and overlaid black lines that have begun to flake off. The researchers detected anatase, a rare form of titanium dioxide, solely in the yellow lines. Because anatase could not be synthesized until the 1920s, detection of the compound has sparked forgery accusations in the past. Brown and Clark also found that the black ink contains carbon, which would not produce the telltale yellow lines that mark medieval inks made of iron gallotannate. As a result, the scientists suggest that a forger actually applied the two components separately on the parchment to give the appearance of antiquity. According to Clark, "the Raman results provide the first definitive proof that the map itself was drawn after 1923."

If the map is indeed genuine, its value is estimated to be almost $20 million. Whatever its origin, it is an impressive piece of handiwork. "If it is, in fact, a forgery," Harbottle says, "then the forger was surely one of the most skillful criminals ever to pursue that line of work."

Reality TV

A prototype digital video system producing images of such high quality that the human eye struggles to distinguish them from reality has been developed by Japanese engineers.
The system, called ultra high definition video (UHDV), achieves image resolution 16 times greater than even the most advanced video broadcasting technologies now available.
Its developers at the Japan Broadcasting Corporation (NHK) said the system could be used to provide an ultra realistic 'immersive' viewing experience when, for example, showing sporting events.

UHDV displays images with 4,000 horizontal scanning lines, compared to the 1,000 offered by the current state-of-the-art high definition television (HDTV) technology and just 625 for standard TV broadcasts. When horizontal and vertical scanning are both taken into account a UHDV picture contains 16 times the number of pixels of HDTV.
NHK, which unveiled details of UHDV for the first time at broadcast technology conference IBC in Amsterdam, said its engineers had to custom-design a video camera, data-storage device and projection system, as no standard broadcasting equipment could cope with their extreme demands.

NHK researcher Dr. Kohji Mitani said the project team had shot a three-minute demonstration video by attaching the camera to the front of a vehicle and driving it around the streets.
The footage was then shown to members of the public on a 4x7m wide-angle screen provoking, according to Mitani, gasps of astonishment. Some viewers even experienced nausea because of the ultra realistic visual effect of speed without the usual physical sensation of movement.
Mitani said the system was still at a basic stage of development, but he claimed it had proved that image qualities so realistic that they approximated to actually being at the recorded event were possible.

The untold sardarji joke :

A man enters a Bar in Jalandhar, INDIA. He finds his way to a bar stool and orders a drink.
After sitting there for a while, he yells to the gathering, " Hey, you want to hear a Sardarji joke?"
The whole bar immediately falls absolutely silent.

In a very deep, husky voice, the man next to him says, "Before you tell that joke,you should know five things.....
1 -- The bartender is a Sardarji.
2 -- The Security man outside is a Sardarji.
3 -- I'm a 6 feet tall, 200-pound Sardarji with a black belt in karate.
4 -- The man sitting next to me is Sardarji and is a professional weight lifter.
5 -- The man to your right is a Sardarji and is a professional wrestler.

Now think about it seriously, Mister. Do you still want to tell that joke?"

The man thinks for a second, shakes his head, and declares, "Nah...Not if I am having to explain it five times..."

Erdos number

Paul Erdos (1913-1996) was a prolific hungarian mathematician of the highest calibre. He wrote more than 1500 papers, more than any mathematician who has ever lived !! He had collaborated with over 500 mathematicians in the process. This gave rise to a concept called Erdos number.

Paul Erdos has an Erdos number of 0. Anyone who has co-authored a paper with Erdos has an Erdos number of 1. If you have co-authored a paper with a person whose Erdos number is 1, then your Erdos number is 2, and so on. If you are never in the link, then your Erdos number is infinity.
More : http://www.loni.ucla.edu/~thompson/ERDOS/erdo.htm

Joke :

A mathematician, a biologist and a physicist are sitting in a street cafe watching people going in and coming out of the house on the other side of the street.
First they see two people going into the house. Time passes. After a while they notice three people coming out of the house.

The physicist: "The measurement wasn't accurate."
The biologist: "They have reproduced".
The mathematician: "If now exactly one person enters the house then it will be empty again."