Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

November 28, 2016

Gottfried Wilhelm Leibniz: The Philosopher Who Helped Create the Information Age


                                                      



When did the information age begin? 

One might point to the winter of 1943, when British engineers started using a room-sized machine dubbed “Colossus,” the world’s first electronic digital programmable computer, to break Nazi codes during the World War II.

Or perhaps it was February 1946, when the U.S. Army unveiled the faster, more flexible Electronic Numerical Integrator and Computer (aka ENIAC) at the University of Pennsylvania. History buffs may push it back further, perhaps bringing up key 19th-century figures like Charles Babbage and Ada Lovelace who pioneered programmable calculating machines in Victorian England.

But we should look back even earlier, to the work of a towering but often overlooked intellect—to Gottfried Wilhelm Leibniz, the German philosopher and polymath who died 300 years ago on Nov. 14, 1716. Though you may not have heard of him, he was a man who envisioned the systems and machines that would define the digital revolution.

Something of a prodigy, Leibniz was just 8 when he started reading the books in his father’s library. (His father was a professor of moral philosophy at Leipzig University.) He quickly learned the classics, once boasting that he could recite Virgil’s Aeneid by heart. 

At school, he excelled in logic; by 17 he had defended his master’s thesis, and three years later he had qualified for his doctorate. Leibniz would go on to work as a historian, librarian, legal adviser, and diplomat. He wrote on biology, medicine, geology, theology, psychology, linguistics, and of course philosophy. The king of Prussia, Frederick the Great, described Leibniz as “a whole academy in himself.”

Famously, Leibniz clashed with Isaac Newton over the invention of calculus. Historians now believe that the two men discovered calculus independently, though it’s Leibniz’s elegant and compact notation system, not Newton’s clunkier version, that we use today.

Of course, there was no such thing as “computer science” in Leibniz’s day. But by developing the binary number system, a way of representing numerical information using zeroes and 1s, he became the father of all computer coding. (Computers don’t have to run by manipulating zeroes and 1s—but it’s a lot easier if they do.) 

Leibniz believed that machines, not people, should be crunching numbers and worked on a prototype for a device that could add, subtract, multiply, and divide. He tweaked and improved the design over many years; one of these contraptions looked like a primitive pinball game, with numbers represented by tiny spheres, rolling along grooves and going through gates that open and close. In London, his fellow scientists were so impressed with the device that they elected him to the Royal Society. He designed another machine that could do certain kinds of algebra, and yet another for cracking codes and ciphers.

Leibniz envisioned these machines would be used in accounting, administration, surveying, astronomy, the production of mathematical tables, and more. 

Tedious work that had kept human beings awake far into the night, working by candlelight, could now be mechanized.


Unfortunately, the technology of the day didn’t allow for the precisely machined parts, such as uniform screws, that Leibniz’s devices required. (For instance, as historians later discovered, something as simple as “carrying the one” turns out to be maddeningly difficult to implement in hardware.) Despite 45 years of work and many prototypes, his calculating machine was never fully functional.

But for Leibniz, computation was just the beginning: He believed that all kinds of problems could be reduced to the manipulation of symbols and tackled just as though they were mathematical problems. He imagined a kind of alphabet of human thought, whose symbols could be manipulated according to precise, mechanical rules, the work carried out by devices. He called them “reasoning machines” and envisioned the pursuit we know today as artificial intelligence.

Once the system was perfected, he believed, humanity would have “a new kind of tool, a tool that will increase the power of the mind much more than optical lenses helped our eyes, a tool that will be as far superior to microscopes or telescopes as reason is to vision.” We would weigh arguments, he said, “just as if we had a special kind of balance.” Linguistic barriers between nations would fall, and the new universal language would usher in an era of understanding, peace, and prosperity. (Leibniz was, needless to say, an optimist—he also had ambitions to reunify the Catholic and Protestant churches.)

Leibniz, however, was right in foreseeing the extent to which we would come to see our world in terms of numbers. (Even just a century ago, who would have imagined that creating and manipulating visual images, or recording a symphony, would boil down to processing certain arrangements of zeroes and 1s?) He even worried about “data overload,” as individuals and governments struggled to process, store, and retrieve the vast amounts of data that would soon be generated.

Leibniz never became a household name, and many of his ideas, like the notion of a universal symbolic language, never bore fruit. 

Much of it had to be re-discovered by later thinkers, such as the 19th-century English mathematician and philosopher George Boole, who more fully developed the idea of a logical system based on binary arithmetic. 

(You may have run across his name before: Boolean algebra, Boolean searches, Boolean system.) But, in imagining a world in which machines could be used to supplement or supplant human computation, Leibniz’s way of thinking paved the way for the information age that blossomed 250 years after his death.


By Dan Falk

With many thanks to Slate


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October 02, 2016

The Nobel Prizes In Numbers


                                                             


                                                                  
Five prizes were created by Alfred Nobel in his 1895 will, for medicine, physics, chemistry, literature and peace, which were awarded from 1901. A sixth prize in economics, “in memory of Alfred Nobel,” was created by Sweden’s central bank in 1968.

Six laureates have declined the prize. The only two to do so of their own will were France’s Jean-Paul Sartre, who turned down the 1964 literature prize, and Vietnam’s then-prime minister Le Duc Tho, who refused to share the 1973 Nobel Peace Prize with US Secretary of State Henry Kissinger. 

Adolf Hitler forbade three German laureates -- Richard Kuhn (chemistry 1938), Adolf Butenandt (chemistry 1939) and Gerhard Domagk (medicine 1939) -- from accepting the prize, while Soviet authorities forced Boris Pasternak to decline the 1958 literature prize.

Eight laureates were born on February 28 and May 21, the two most popular birthdates for laureates. Other dates have produced no laureates, including January 2 and October 13.

Twelve is the number of times the medicine prize jury considered the nomination of Sigmund Freud, the father of psychoanalysis, rejecting it each time.

His work had no scientific value, an expert concluded in 1929. 

The nomination of Mahatma Gandhi, who also famously never won a Nobel, was considered four times, excluding the year of his assassination in 1948.

The youngest laureate to be honoured was 17 years old — Malala Yousafzai of Pakistan (peace 2014). The oldest laureate was Russian-born American Leonid Hurwicz (economics 2007), who was 90.

Eighteen laureates have been affiliated with the two universities claiming the most Nobels: Stanford and the University of California, Berkeley.

Myanmar’s Aung San Suu Kyi had to wait 20 years before she could travel to Oslo to collect the peace prize she was awarded in 1991.

 Also deprived of their liberty: German pacifist Carl von Ossietzky (peace 1935), who died in 1938 without being allowed to leave his country; and Chinese dissident Liu Xiaobo (peace 2010), is still behind bars.

Twenty-seven English-language writers have won the literature prize, ahead of French (14), German (13) and Spanish (11) laureates.

Forty eight women have won a Nobel prize, including Marie Curie who won it twice (physics 1903 and chemistry 1911). 

The economics prize, with only one female laureate, in 2009, and the physics prize, with only two laureates in 109 years, remain the most inaccessible prizes for women.

 A total of 822 Nobel laureates are men.

The various juries have decided to not award the prize 49 times. The peace prize has had no recipient 19 times, most recently in 1972.

Fifty years must pass before the juries’ top secret deliberations are opened to the public.

The average age of the economics prize laureates is 67, the oldest average age, while the youngest average age can be found among physics laureates, at 55.

There were 376 nominations for the 2016 Nobel peace prize, a record with almost 100 more than in 2014 when the previous record was set. In 1942, 1943 and 1944, no nominations were accepted.

870 people have won a Nobel prize, including four scientists who won it twice. Twenty-six groups or organisations have been honoured with the Nobel peace prize, such as Tunisia’s National Dialogue Quartet in 2015.

1,350 people are typically invited to the Nobel gala banquet celebrating the laureates, held each year at Stockholm’s city hall on December 10, in honour of the death of Alfred Nobel. 

At the first dinner in 1901, 113 people were invited.

Each laureate is awarded 8 million Swedish kronor ($1.2m) which is shared if several laureates are honoured in the same field. 

Literature laureates are the ones most likely to take home the whole sum: on 104 occasions there has been just one literature winner.
With many thanks to The Australian 


                                                            

Source. 

                                                              

                                                                   

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September 17, 2016

Albert Einstein's Legacy




                                                                           



Without us realising it, we encounter Albert Einstein in different fields of everyday life.
The GPS system in our cars guides us safely through the traffic. Our purchases in the supermarket are registered by a scanner cash register. And we took our latest holiday snaps using our new digital camera.

Even if Einstein himself did not write his most important essays for practical use or personal profit, his abstract thoughts on light, space and time have led to many technological innovations which appear to us today to be quite normal. Whether it be a CD player, a television set or a modern computer, these new “inventions” are often based on one of Albert Einstein’s theories.

Many people associate Einstein with the development of the atomic bomb or nuclear energy. In 1905, Einstein was indeed the first person to prove that atoms actually do exist, not just hypothetically. And in his most famous formula, E = mc², he showed that the mass of atoms contains enormous quantities of energy. But this theory was only of indirect importance for the atomic revolution.

Einstein’s ideas had a much more direct influence on inventions such as the television, for example. It is thanks to his Special Theory of Relativity that we are able to receive such sharp images today. Electrons are accelerated in a television and, according to the Theory of Relativity, the mass of electrons thereby increases measurably. If one did not take this increase in mass into account, the electrons on the screen would show divergences in the millimetre range. All the images would be blurred.

Another type of picture would not be possible without Einstein’s theories, either. Digital cameras can only take pictures because they contain a small sensor which converts light into electricity. The principle can be traced directly back to Einstein, who explained the Photoelectric Effect in 1905. Not only does this work form the basis for the development of all equipment which converts light into electricity – from digital cameras to solar cells – it also earned him the Nobel Prize in November 1921 (awarded 1922).

All technologies which involve the use of laser beams are based on Einstein’s theories. In 1924, Einstein was the first person to recognise the principles of monochrome, bundled laser light. Satellite-assisted positioning systems on earth, so-called GPS, make use of Einstein’s ideas.

Pieces of equipment which can relay their position with an accuracy of less than 30 metres divergence take into account the effects of relativity on time measurement by atomic clocks when these circle the earth at great speed in satellites.

Einstein’s influence on present-day inventions is still huge even 50 years after his death. Physicists are already dreaming of quantum computers. Einstein also played a key role in this technological revolution. In 1935, he recognised that particles can be in different states at the same time. This observation developed into a future-oriented research area, and it is possible that quantum computers will revolutionise the world in the 21st century.

With many thanks to Einstein Jahr.De

                                                                  



                                                              

                                                              
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