Category: Mathematics

Happy Pi Day

Source : http://byzantiumshores.blogspot.com

Source : http://byzantiumshores.blogspot.com

Peter said to me that it was Pie Day and encouraged me to blog about it. I was just too ill to jump with any form of enthusiasm to his challenge. ¬†In my condition, being only half alive ūüôĀ , the last thing in my mind is thinking about food. ¬†And enthusing about the delicacy and efficacy of apple pies, pork pies, or any other pies do not interest me in the least.

It was a few second before we both realised that we were talking in cross purposes. Peter in fact was talking about Pi (514_400x400_NoPeel), the 3.1416 Pi. ¬†Having found this out, I still can’t understand why today is Pi Day? ¬†It is not 2016! ¬†Or is it? ¬†I have been sleeping for most of the days and I might have slept for a year for all I know or even care! LOL

In my mind’s eye, I don’t understand why 3.1416 or rather 3.1415 is celebrated as Pi day afterall, Great Britain are used to dates in the order of date first, followed by the month and then the year. So today is 14 March 2015 or 14/3/2015. Another thing 3.1416 is what I have always thought as the value of Pi. It was rounded of from 3.14159265359. It cannot just be cut off as 3.1415 as the next number is 9 and this can’t just be ignored!

Anyway this is just my two cent. I do not really want to upset anyone in anyway who wants to celebrate Pi day. For me, I would probably raise a drink to Pi next year 14 March 2016!

Google Doodle: Grace Hopper

Grace the Original Hopper

grace-hoppers-107th-birthday-5447077240766464.3-hp

Today’s¬†Google Doodle is an animation of Grace Hopper sitting on her computer, using COBOL ¬†to print out her age. ¬†Google is celebrating the 107th birthday of Grace Hopper, the “mother” of the COBOL computer language.

220px-Commodore_Grace_M._Hopper,_USN_(covered)

“‘all Navy’, but when you reach inside, you find a ‘Pirate’ dying to be released”
– Jay Eliot

Just toward the end of animation a moth was seen coming out of the computer; that was a reference to Grace popularising the term “debugging”. ¬† ¬†Apparently whilst in the Navy and working on a Mark II computer, it was found that a moth was stuck in the relay, which was impending the ¬†system, quick as a flash Grace said they are debugging the system.

The remains of the moth can be seen at the Smithsonian in Washington DC.

Grace lived a full and hectic life.

At a very young age, she showed a very inquisitive mind. ¬†At the age of seven, she tried to find out how clock works and managed to disassemble seven of them much to her mother’s consternation. ¬†In the end she was only allowed to touch one clock. ¬†LOL

Grace was a Vassar girl but at 16 she was declined entry to the College because she had a low score in Latin. ¬†She got admitted the next year and went on to earn bachelor’s degree in Mathematics and Physics. ¬†She then went to Yale University and became a history maker for becoming ¬†the first woman to graduate with a doctorate in Maths in Yale’s long history.

Grace Brewster Murray, as she was, married Vincent Foster Hopper, a New York professor in 1930. ¬†The marriage ended in divorce in 1945. ¬†Grace never married again thus retaining her ex-husband’s surname. ¬†Grace Hopper has a memorable ring to it.

Grace Hopper, to me, was like a grasshopper.  She leaped from one success to another.  She leaped from one awards to the next.

Even her retirement was one of the ¬†longest hopping in history. ¬†She first retired at 60 but was recalled almost immediately and then retired again and then recalled and then retired and then recalled………

Grace ended up working until her death at 85.

What is Special about 1,729? Futurama Mystery

15 October 2013 Last updated at 00:36

Why is the number 1,729 hidden in Futurama episodes?

By Simon Singh Science writer
Bender from Futurama

The year 1913 marked the beginning of an extraordinary relationship between an impoverished Indian clerk and a Cambridge don. A century later, their remarkable friendship has left its mark in the strangest of places, namely in Futurama, the animated series from The Simpsons creator Matt Groening and physics graduate David X Cohen.

GH Hardy (1877-1947) and Srinivasa Ramanujan (1887-1920) were the archetypal odd couple. Hardy, whose parents were both teachers, grew up in a middle-class home in Surrey, England. At the age of two he was writing numbers that reached into the millions, so it was no surprise that he eventually read mathematics at Trinity College, Cambridge, where he joined an elite secret society known as the Cambridge Apostles.

Ramanujan was born in the Indian state of Tamil Nadu. At the age of two he survived a bout of smallpox, but his three younger siblings were less fortunate, each one dying in infancy. Although he was enrolled in a local school, Ramanujan’s most valuable education was thanks to a library book, A Synopsis of Elementary Results in Pure Mathematics by GS Carr, which contained thousands of theorems. He investigated these theorems one by one, relying on a chalk and slate for calculations, using his roughened elbows as erasers.

1,729 in Futurama

  • The characters travel to Universe 1729
  • Registration number of the starship Nimbus
  • The unit number of robot Bender
  • (Incidentally, Bender’s serial number is 2716057, which is also the sum of two cubes, namely 952¬≥ + -951¬≥)

Aged 21, he married Janakiammal, who was just 10 years old. Unable to afford college fees and needing to support his wife, Ramanujan got a job as a clerk. Nevertheless, he continued his interest in mathematics in his spare time, developing novel ideas and proving fresh theorems.

Curious about the value of his research, Ramanujan began to write to mathematicians in England in the hope that someone would mentor him, or at least give him feedback. Academics such as MJM Hill, HF Baker and EW Hobson largely ignored Ramanujan’s pleas for help, but Hardy was mesmerised by the two packages he received in 1913, which contained a total of 120 theorems.

Hardy’s reaction veered between “fraud” and so brilliant that it was “scarcely possible to believe”. In the end, he concluded that the theorems “must be true, because, if they were not true, no-one would have the imagination to invent them”.

GH Hardy and Srinivas Ramanujan GH Hardy photo courtesy of the Royal Society РSrinivasa Ramanujan picture from Topfoto

The British professor made arrangements for the young Indian, still only 26, to visit Cambridge. Hardy took great pride in being the man who had rescued such raw talent and would later call it “the one romantic incident in my life”.

The resulting partnership gave rise to discoveries in several areas of mathematics and Ramanujan’s genius was recognised in 1918 when he was elected as a fellow of the Royal Society.

Ask Simon a question on Twitter, using #AskSimonSingh, or use the comments form at the bottom of the page. He will answer selected questions at 16:30BST.

He has a PhD in particle physics from Cambridge University and has studied at the Cern research institute in Geneva.

The young Indian savant would later say that many of his theorems were whispered to him in his sleep by Namagiri, an avatar of the Hindu goddess Lakshmi: “While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing.”
Ramanujan’s career was brilliant, but ended prematurely when he began to suffer from tuberculosis. He returned to India in 1919 and died the following year, aged 32.

However, the life of Ramanujan continues to fascinate modern mathematicians, including Dr Ken Keeler, who swapped his job as a researcher to join the writing team behind the science fiction sitcom Futurama.

He is actually one of a number of mathematicians who write for The Simpsons and its sister series Futurama. They have retained their love for the subject and they continue to express their passion for numbers by smuggling mathematical references into both series.

For example, in order to pay homage to Ramanujan, Keeler has repeatedly inserted 1,729 into Futurama, because this particular number cropped up in a famous conversation between Hardy and Ramanujan.

According to Hardy, he visited Ramanujan in a nursing home in 1918: “I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one and that I hoped it was not an unfavourable omen. ‘No,’ he replied. ‘It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.'”
Futurama characters
Their exchange can be unpacked and expressed as follows:

1,729 = 1³ + 12³ = 9³ + 10³

It is rare that a number can be split into two cubes, and even rarer that it can be split into two positive cubes in two different ways, and 1,729 is the smallest number that exhibits this property.

It is in recognition of Ramanujan’s comment that Bender, Futurama’s cantankerous robot, has the unit number 1729.

The number also appears in an episode titled “The Farnsworth Parabox”. The plot involves Futurama characters hopping between multiple universes, and one of them is labelled “Universe 1729”.

Moreover, the starship Nimbus has the hull registration number BP-1729.

This has certainly helped keep Ramanujan’s memory alive, but it is probably not the sort of immortality that Hardy had in mind when he wrote: “Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. Immortality may be a silly word, but probably a mathematician has the best chance of whatever it may mean.”

Keeler is proud of his mathematical references in Futurama, and he is philosophical about the many years he spent as a mathematician before becoming a comedy writer: “Everything that happens to us has some effect on us, and I do suppose that the time I spent in grad school made me a better writer. I certainly don’t regret it.

“For example, I chose Bender’s serial number to be 1,729 and I think that reference alone completely justifies my doctorate.

“I don’t know if my thesis advisor sees it that way though.”

Simon Singh will be answering your questions on Twitter at 16:30BST. Tweet with #AskSimonSingh or submit your question using the form below.

We will publish a selection of questions and answers.

The Amazing Story of British Science

The British have a remarkable talent for keeping calm, even when there is no crisis.

– Franklin F. Jones

 

From the 1700s Britain, this small group of islands was and still is a leader in science and engineering. Surely Sir Isaac Newton must be regarded as the greatest scientist that ever lived. He formulated the laws or motion and gravity, proved that sun light was not pure white but made up of colour and corpuscular(tiny particles of matter)when he produced a spectrum via two prisms and isolated one colour. He invented the reflecting telescope and for mathematics he invented calculus still a valuable mathematic tool today. His discoveries about energy gravity and motion laid the ground for Einstein.

Below is an article about an excellent new BBC TV series charting the successes and discoveries made by British scientists and engineers.

The Amazing Story of British Science

Sir Isaac Newton, Isambard Kingdom Brunel, Sir Tim Berners-Lee. Pictures via Getty

Britons Sir Isaac Newton, Isambard Kingdom Brunel and Sir Tim Berners-Lee all changed the world through their discoveries and inventions

Science Britannica 
Professor Brian Cox
Scientist and presenter

The British Isles are home to just one percent of the world’s population and yet our small collection of rocks poking out of the north Atlantic has thrown up world beaters in virtually every field of human endeavour.

Nowhere is this more obvious than in science and engineering. Edward Jenner came up with vaccines, Sir Frank Whittle ushered in the jet age and Sir Tim Berners-Lee laid the foundations of the world wide web for the Internet. Sir Isaac Newton, Robert Boyle, Charles Darwin, Michael Faraday, George Stephenson, James Watt, Isambard Kingdom Brunel (engineer), Francis Crick ( co discoverer of DNA)‚Ķ the list is gloriously long. ¬†We can now add Peter Higgs,who proposed the so called ‘God particle’ Higgs Bosun a field that holds particles together, which if if did not exist , sub atomic particles would never had formed into atoms and ultilmately us! The Higgs Bosun has been tentatively discovered by the Large Hadron Collider (LHC)

What is it about Britain that allowed so many great minds to emerge and flourish?

This is a very important question to ask, because science and engineering are not only part of our past – the future of our economy depends to an ever-increasing extent on our continued excellence in scientific discovery and high-tech manufacturing and engineering.

The roots of our success can be traced back many centuries. Oxford and Cambridge Universities were formed over 800 years ago.

They paved the way for the world’s oldest scientific institution, The Royal Society, formed in 1660 by a group including Sir Christopher Wren, professor of astronomy and architect of St Paul’s Cathedral in London.

Science Heroes

¬†Robert Boyle Boyle¬†1627 ‚Äď 1691¬†is one of ¬†founders of modern chemistry¬†and one of the pioneers of modern experimental scientific method which Britain gave to the world. ¬†He is best known for Boyles Law¬†¬†which describes the inversely proportional relationship between the absolute pressure and volume¬†of a gas, if the temperature is kept constant within a closed sytem.

Sir Isaac Newton (1642-1727) was a brilliant physicist and mathematician who is considered a founding father of science.

Charles Darwin (1809 – 1882) was a naturalist and geologist who came up with the world-changing theory of evolution.

Isambard Kingdom Brunel (1806-1859) was an inventor and engineer who designed some of the UK’s most famous tunnels, bridges, railway lines and ships

Sir Frank Whittle (1907 – 1996) was a daredevil test pilot who is credited with inventing the turbo jet engine

Sir Tim Berners-Lee (1955 – ) is the inventor of the world wide web

Scientist Rosalind Franklin’s photograph’s of X Ray diffraction of DNA confirmed it’s double helix structure

Any theory or idea about the world should be tested and if it disagrees with observations, then it is wrong.

Even today, that’s radical, because it means that the opinions of important and powerful people are worthless if they conflict with reality. So central is this idea to science that it is enshrined in The Royal Society’s motto: “Take nobody’s word for it”.

Shortly after The Royal Society was formed, Sir Isaac Newton deployed this approach in his great work The Principia, which contains his law of gravity and the foundations of what we now call classical mechanics – the tools you need to work out the forces on bridges and buildings, calculate paths of artillery shells and the stresses on aircraft wings. This was arguably the first work of modern physics.

This has become known as the scientific method, and its power can be seen in some unexpected places. During the filming of Science Britannica, I met Capt Jerry Roberts who worked at Bletchley Park during the Second World War.

Bletchley intercepted enemy messages and the captain and his colleagues were given the job of decoding them. He told me the story of his colleague, Bill Tutte, who worked on the ‘Tunny” code used by the Nazi high command to send orders to generals in the field.

Bill spent most of his time staring into space, but after just a few months, with awesome mathematical acumen he cracked the code.

In an age before computers, he did it using mathematics, logic and pencil and paper, aided by a single mistake by a German telegraph operator who sent a message twice. In the opinion of many, Tutte’s achievement was the greatest single intellectual achievement of the 20th Century, shortening the war by years and saving millions of lives on both sides.

This is what happens when genius is aided by the careful, scientific approach pioneered by Newton and others at The Royal Society. Capt Roberts and his colleagues at Bletchley are, in my view, heroes in every sense of the word.

¬†Bletchley Park was Britain’s main decryption establishment during World War II.

The Buckinghamshire compound is famous as the place where wartime codebreakers cracked the German Enigma code
Codebreaking machines Colossus and Bombe were the forerunners of modern computers. Mathematician Alan Turing helped create the Bombe
Historians estimate that breakthroughs at Bletchley shortened the war by two years
Bletchley Park’s computing ¬†was so innovative
Alan Turing’s work built the foundations of computer science,programming etc. He is regarded as a true genius and founder of modern computing.

Another such genius was Nobel Prize winning phycisist Paul Dirac¬†He was regarded by his friends and colleagues as unusual in character. Albert Einstein¬†said of him “This balancing on the dizzying path between genius and madness is awful” ¬†Among other discoveries, he formulated the Dirac Equation,¬†which ¬†predicted the existence of antimatter.

Despite its tremendous success, scientists have occasionally had a difficult relationship with the wider public. Frankenstein – the ultimate ‘scientist out of control’, has become a short-hand for things we fear.

A particularly colourful example can be found in the grim tale of George Forster, convicted of the double murder of his wife and daughter in 1803 and duly hanged.

This being the 19th Century, nobody was concerned about the hanging itself but rather illogically, the fate of Forster’s corpse caused a public outcry. It was taken directly to a nearby lecture theatre and used to demonstrate the effect of electricity on the human body.

The corpse twitched and jerked and even ‘opened an eye’ as an electric current was applied. There were reports of fainting and a particularly sensitive audience member died of shock – a wonderfully Georgian thing to do. The scientist – a visiting Italian called Giovanni Aldini – was forced to leave the country, when in fact his motives were absolutely sound. He was trying to resuscitate people using electricity.

Far from being a dangerous lunatic, he was ahead of his time. Nowadays thousands of lives are saved as hearts are regularly re-started using electrical pulses delivered by defibrillators.

Aldini’s controversial experiments were performed for a particular purpose, but not all science is carried out with a goal in mind.

Mary Shelley soon after wrote the classic gothic story Frankenstein, a cautionary tale of science out of control.

In the 19th Century, John Tyndall decided to work out why the vivid red and purple colours appeared when the sun is low, and why, for the rest of the time, the sky is blue.

He concluded that the colours of the sky are produced because light bounces off dust and water particles in the air. Blue light is more likely to bounce around than red, and so it is only when the sun is low and the light travels through more of the dust-filled air that the red light is bounced around to produce a sunset.

Tyndall was half right – we now know that it is mainly the air molecules themselves that scatter the light – but this didn’t really matter. Tyndall’s romantic curiosity led to a far more important discovery.

He decided to produce “pure” air with no particles in it, to see if the colours vanished, and he discovered that samples of meat didn’t rot in it. Here was evidence that infection and decay are caused by germs in the air – which Tyndall had inadvertently removed during his purification process. The discovery ultimately transformed the way that doctors dealt with infection and contamination.

Countless millions of lives were saved, because one curious scientist wanted to find out why the sky is blue. Today, the curiosity driven exploration of nature is still known as “blue skies research”.

Science has truly revolutionised our world. It is the basis of our economy and the foundation of our future. We must value our great heritage and continue to invest in education and science to ensure that we never lose our position as the best place in the world to do science.

SIR ISAAC NEWTON and me

One there is above all others,
Well deserves the name of Friend!
His is love beyond a brother’s,
Costly, free, and knows no end:
They who once His kindness prove,
Find it everlasting love!
‚ÄĒNewton.

DSCN8330Zoo 2012 100

Newton, unarguably the greatest scientist that ever lived. Even super-genius Albert Einstein acknowledged that Newton was the greatest scientist that ever lived. His contribution to science is so immennse that he saved later scientists more than 2oo years in research.

Rene Descartes – Father of Modern Philosophy

Rene Descartes – Father of Modern Philosophy & Western Philosophy

Rene Descartes (31 March 1596 ‚Äď 11 February 1650) French Philosopher & Mathematician

Rene Descartes (31 March 1596 ‚Äď 11 February 1650)
French Philosopher & Mathematician

all the sciences which have for their end investigations concerning order and measure, are related to mathematics, it being of small importance whether this measure be sought in numbers, forms, stars, sounds, or any other object; that, accordingly, there ought to exist a general science which should explain all that can be known about order and measure, considered independently of any application to a particular subject, and that, indeed, this science has its own proper name, consecrated by long usage, to wit, mathematics. And a proof that it far surpasses in facility and importance the sciences which depend upon it is that it embraces at once all the objects to which these are devoted and a great many others besides; ….
‚ÄĒDescartes.

….

Common sense is the best distributed commodity in the world, for every man is convinced that he is well supplied with it.
– Rene Descartes

“Doubt is the origin of wisdom”
~René Descartes

….

‚ÄúIt is not enough to have a good mind; the main thing is to use it well.‚ÄĚ
‚ÄēRene Descartes

……..

The greatest minds are capable of the greatest vices as well as of the greatest virtues.
– Rene Descartes

Bertrand Russell’s Philosophy

Honourable_Bertrand_RussellBertrand Arthur William Russell

3rd Earl Russell, OM, FRS (18 May 1872 ‚Äď 2 February 1970) was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these in any profound sense. He was born in Monmouthshire, into one of the most prominent aristocratic families in Britain.
(Source: Wikipedia)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Bertrand Russell’s Philosophy

A great many worries can be diminished by realising the unimportance of the matter which is causing anxiety.
– Bertrand Russell
~~~
Cruel men believe in a cruel God and use their belief to excuse their cruelty. Only kindly men believe in a kindly God, and they would be kindly in any case.
– Bertrand Russell
~~~
Drunkenness is temporary suicide.
~Bertrand Russell
~~~
If we were all given by magic the power to read each other’s thoughts, I suppose the first effect would be to dissolve all friendships.
– Bertrand Russell
~~~
If there were in the world today any large number of people who desired their own happiness more than they desired the unhappiness of others, we could have a paradise in a few years.
~Bertrand Russell
~~~
Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture.
– Bertrand Russell
~~~
Men are born ignorant, not stupid. They are made stupid by education. – Bertrand Russell ~~~ Of all forms of caution, caution in love is perhaps the most fatal to true happiness.
– Bertrand Russell

Philosophers, for the most part, are constitutionally timid, and dislike the unexpected.  Few of them would be genuinely happy as pirates or burglars.  Accordingly they invent systems which make the future calculable, at least in its main outlines.
~Bertrand Russell

Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of¬†anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is of which it is supposed to be true…. If our hypothesis is about¬†anything¬†and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
– Russell, Bertrand

…..

To teach how to live with uncertainty, yet without being paralyzed by hesitation, is perhaps the chief thing that philosophy can do.
~Bertrand Russell

To fear love is to fear life, and those who fear life are already three parts dead. – Bertrand Russell

The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it. ~Bertrand Russell

The observer, when he seems to himself to be observing a stone, is really, if physics is to be believed, observing the effects of the stone upon himself. ~Bertrand Russell

‚ÄúThere are two motives for reading a book; one, that you enjoy it; the other, that you can boast about it.‚ÄĚ
‚Äē Bertrand Russell
….
Without civic morality communities perish; without personal morality their survival has no value.
– Bertrand Russell
Bertrand_Russell_Signature

Blaise Pascal


Blaise Pascal (1623 – 1662)
French mathematician, inventor, writer and philosopher. He contributed to the theory of probability. He’s famous for the Pascal Wager. ¬†He also invented the first adding machine in 1642.


Anything that is written to please the author is worthless.
– Blaise Pascal

Clarity of mind means clarity of passion, too; this is why a great and clear mind loves ardently and sees distinctly what it loves.
– Blaise Pascal

Few friendships would survive if each one knew what his friend says of him behind his back.
– Blaise Pascal

I have made this letter longer than usual because I lack the time to make it shorter.
‚ÄĒBlaise Pascal
________________________________________

I lay it down as a fact that if all men knew what others say of them, there would not be four friends in the world.
~Blaise Pascal

It is not certain that everything is uncertain.
– Blaise Pascal

It is not good to be too free. It is not good to have everything one wants.
– Blaise Pascal
___
It is the heart which perceives God and not the reason.
– Blaise Pascal

‚ÄúKind words don’t cost much. Yet they accomplish much.‚ÄĚ
~Blaise Pascal
Let us weigh the gain and the loss in wagering that God is, but let us consider the two possibilities. If you gain, you gain all if you lose you lose nothing. hesitate not, then, to wager that He is. (Pascal’s Wager)

Most of the evils of life arise from man’s being unable to sit still in a room.
– Blaise Pascal


Man is but a reed, the weakest thing in nature, but he is a thinking reed.
– Blaise Pascal

(I love the quote. Man is weak, easily bent, but he is strong because of ability to think, to reason)


Man’s greatness lies in his power of thought.
– Blaise Pascal

Men never do evil so completely and cheerfully as when they do it from a religious conviction.
– Blaise Pascal

Nature has perfection, in order to show that she is the image of God and defects, to show that she is only his image.

To ridicule philosophy is really to philosophize.
~Blaise Pascal

The heart has its reasons of which reason knows nothing of. (The heart has its reason, which reason does not know.)
– Blaise Pascal

………

Apparently the heart is more than just a pumping machine for blood. It stores data, it has a neuro-network just like the brain.

………

When we encounter a natural style we are always surprised and delighted, for we thought to see an author and found a man.
– Blaise Pascal

……………………
When we are too young our judgment is at fault; so also when we are too old.
‚ÄĒPascal.
…………………
We are only falsehood, duplicity, contradiction; we both conceal and disguise ourselves from ourselves.
– Pascal
……………….
We find fault with perfection itself.
– Blaise Pascal

We must learn our limits. We are all something, but none of us are everything.
– Blaise Pascal

‚ÄúYou always admire what you really don’t understand.‚ÄĚ
~Pascal