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<div class="row"><center><h2>ALAN TURING</h2></center>
<center><p>Alan Turing; the man who knew too much, the father of theoretical computer science & artificial intelligence, the tortured genius, modern martyr and what not. </p></center>
<center><p>A man aging 41 at the time of death really became a lot of things.</p></center>
<center><p>It's never a question of who was who but moreover what we were today without them!</center></p><br><br></div>
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<div class="col-md-6" style="border:2px;border-style: solid;border-color:white white white #FFDFC4;"><h1>So what did Turing do for us?</h1>
<p>Very firstly it shall be modest to state that Turing, nearly alone, shortened the World War II by 4 years and saved millions of lives. The catalyzed success of Allies against Nazis, yes, no armies but a mathematician made it possible by breaking the Enigma machine which was Nazi's super weapon of their secret communication.</p>
<p>Turing Test or the Imitation Game set by him still remains one of the most excellent and promising work in the field of Artificial Intelligence. </p>
<p>The modern computer which served as the most inevitable machine of modern life is nothing but a better version of Turing's universal machine.</p>
<p>Turing also went on to pick on 'Hilbert's problems' - one of the 23 unsolved problems in mathematics and solved one of the the most important mathematical challenge of the century.</p>
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We can only see a short distance ahead,<br /> but we can see plenty there<br /> that needs to be done.
<cite>Alan Turing</cite>
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<center> <br /><br /><br /><h2>TURING AND THE WORLD WAR II</h2>
<h1>ENIGMA</h1></center>
<p>The Enigma machines produced a polyalphabetic substitution cipher. During World War I, inventors in several countries realized that a purely random key sequence, containing no repetitive pattern, would, in principle, make a polyalphabetic substitution cipher unbreakable. This led to the development of rotor cipher machines which alter each character in the plaintext to produce the ciphertext, by means of a scrambler comprising a set of rotors that alter the electrical path from character to character, between the input device and the output device. This constant altering of the electrical pathway produces a very long period before the pattern—the key sequence or substitution alphabet—repeats.</p>
<p>Decrypting enciphered messages involves three stages, defined somewhat differently in that era than in modern cryptography. First, there is the identification of the system in use, in this case Enigma; second, breaking the system by establishing exactly how encryption takes place, and third, setting, which involves finding the way that the machine was set up for an individual message, i.e. the message key. Today, it is often assumed that an attacker knows how the encipherment process works and breaking specifically refers to finding a way to infer a particular key or message (see Kerckhoffs's principle). Enigma machines, however, had so many potential internal wiring states that reconstructing the machine, independent of particular settings, was a very difficult task.
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We are not interested in the fact that the brain has the consistency of cold porridge.
<cite>Alan Turing</cite>
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<br /><br /><br /><center><h1>BREAKING ENIGMA:CONSTRUCTION AND WORKING</h1>
<H1>(A MATHEMATICAL UNDERSTANDING)</H1></center>
<p>Braking Enigma was nearly impossible because, in a 4 rotor Enigma, the number of combinations, each of which could have been the initial state of the machine when it enciphers or key setting ,that would arise, is 26^4 . Each combination would be mapped to a letter. Now, the video says that the Germans did build machines which had many rotors and what's more, machines in which the arrangement of the rotors could change. That multiplies the number of possibilities for the key setting by an n! in case of n rotors. </p>
<p>They say that the codes in the naval networks used 336 wheel orders - that is, the scrambler(which enciphered) would choose 3 out of 8 rotors which can be done in 8\choose 3 = 56 ways. For each of these combinations, the rotors could be arranged in 3! = 6 ways. So, the number of wheel orders = 56*6 = 336 ways. </p>
<p>Similarly, the army and airforce codes apparently used 60 wheel orders.
Where Turing came in, from what I understand, is eliminate the brute force approach and develop an elegant solution that would go over possibilities so quickly that, well, the allies won the war.</p>
<p>The difficulties didn't end at the number of combinations to be brute forced of course. The plugboard of the Enigma swapped letters pairwise. This is known as steckering.</p>
<p>Coming back to the operator errors and the Enigma's idiosyncrasy that became its weakness that I mentioned, there are two weak points the English and the Poles exploited, according to the video:
<p>1. The Enigma, justifiably to avoid the possibility of a word being enciphered to itself, never gave back the same letter as the output given any input letter. So, a letter had only 25 possibilities for a cipher instead of 26. So, this eliminated options as shown in this picture from the wiki page on Cryptanalysis of the Enigma.</p>
<p>2. The operators of the machine, who were supposed to open it up and change choose the key setting for the day, changed the position of the rotors only a wee bit sometimes, which left the cryptanalysts testing key settings close to the recent ones with good success. </p>
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<p>But, as anyone can see, points 1 and 2 amount to nothing that can remarkably minimize the possibilities. </p>
<p>While earlier Bombes constructed by Polish cryptologist Rejewski, who worked out the complete wiring of the Enigma 1 even before he had a chance to see one, were influential in the allies intelligence that helped them win against the Germans( Technically, there was no "win" in the second world war or any war for that matter and the word is used from a purely political context), Turing made improvements to the Bombe and there were a few of them built , one of them being at Bletchley Park.</p>
<p>These improvements were extremely elegant and a mark of the genius that Turing was.</p>
<p>The difference in the approach of the two code breakers was that Turing's Bombe looked for hits for some common German words - this turned out to be very successful. </p>
<p>When the drums were so aligned that the crib used resulted in the ciphers, they would have a success. But, the catch was of course, merely brute forcing over the 26^3 possibilities didn't get one anywhere because of the steckering.</p>
<p>In fact even if 6 letters were steckered, that is, swapped with 6 other letters, the number of ways that could happen is [math] 100391791500 = [/math]
{26\choose 12} (*11 * 9 * 7 * 5* 3) . That's over a 100 billion possibilities .
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<h3>So, what did Turing's Bombe do? </h3>
<p>A good explanation in the form of a lecture by Tony Sale, curator of the Bletchley park museum, can be found here.
To sum up the lecture, both Rejewski and Turing discovered the same patterns but independently.
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<p>Rejewski did his reverse engineering starting with the fact that the codes were ciphered by using the same key twice at the start of the message.</p>
<p>Turing devised the menu that would be tested on the Bombe using common German words as cribs. </p>
<p>The Bombe was basically many Enigma's in series. In brief, it had some mechanisms to move the positions of the drums and a comparator unit that checked matching output and if there was a "logical contradiction", the drums would move on to the next pattern.
Turing's work mainly was the probability analysis which he did "without the use of electronic aids" (obviously - it was during World War II).
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I believe that at the end of the century the use <br />of words and general educated opinion will<br /> have altered so much that one will be able <br />to speak of machines thinking without expecting to be contradicted.
<cite>Alan Turing</cite>
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<br /><br /><br /><center><h2>THE IMITATION GAME/TURING TEST</h2></center>
<center><h1>(ARTIFICIAL INTELLIGENCE)</h1></center>
<p>Alan Turing, in a 1951 paper, proposed a test called "The Imitation Game" that might finally settle the issue of machine intelligence. The first version of the game he explained involved no computer intelligence whatsoever. Imagine three rooms, each connected via computer screen and keyboard to the others. In one room sits a man, in the second a woman, and in the third sits a person - call him or her the "judge". The judge's job is to decide which of the two people talking to him through the computer is the man. The man will attempt to help the judge, offering whatever evidence he can (the computer terminals are used so that physical clues cannot be used) to prove his man-hood. The woman's job is to trick the judge, so she will attempt to deceive him, and counteract her opponent's claims, in hopes that the judge will erroneously identify her as the male.</p>
<p>What does any of this have to do with machine intelligence? Turing then proposed a modification of the game, in which instead of a man and a woman as contestants, there was a human, of either gender, and a computer at the other terminal. Now the judge's job is to decide which of the contestants is human, and which the machine. Turing proposed that if, under these conditions, a judge were less than 50% accurate, that is, if a judge is as likely to pick either human or computer, then the computer must be a passable simulation of a human being and hence, intelligent. The game has been recently modified so that there is only one contestant, and the judge's job is not to choose between two contestants, but simply to decide whether the single contestant is human or machine.</p>
<p>Fora deeper understanding refer:</p>
<p><a href="http://plato.stanford.edu/entries/turing-test/">http://plato.stanford.edu/entries/turing-test/</a></p>
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No, I'm not interested in developing a powerful brain. All I'm after is just a mediocre brain, something like the President of the American Telephone and Telegraph Company.
<cite>Alan Turing</cite>
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<br /><br /><br /><center><h2>TURING MACHINE AND MODERN COMPUTER</h2></center>
<p>Alan Turing published a paper, “On Computable Numbers, with an application to the Entscheidungsproblem,” which became the foundation of computer science. In it Turing presented a theoretical machine that could solve any problem that could be described by simple instructions encoded on a paper tape. One Turing Machine could calculate square roots, whilst another might solve Sudoku puzzles. Turing demonstrated you could construct a single Universal Machine that could simulate any Turing Machine. One machine solving any problem, performing any task for which a program could be written—sound familiar?</p>
<h1> He’d invented the computer.</h1>
<p>Back then, computers were people; they compiled actuarial tables and did engineering calculations. As the Allies prepared for World War II they faced a critical shortage of human computers for military calculations. When men left for war the shortage got worse, so the U.S. mechanized the problem by building the Harvard Mark 1, an electromechanical monster 50 feet long. It could do calculations in seconds that took people hours.</p>
<p>The Turing Machine to break Enigma became one of the first pioneering computers improving upon which made the computer age possible.</p>
<p>As the 1950s progressed business was quick to see the benefits of computers and business computing became a new industry. These computers were all Universal Turing Machines—that’s the point, you could program them to do anything.</p>
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A computer would deserve to be called<br /> intelligent if it could deceive a human<br /> into believing that it was human.
<cite>Alan Turing</cite>
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<br /><br /><br /><center><h2>THE DECISION PROBLEM</h2></center>
'Decision Problem', or 'Entscheidungsproblem' in the original German, was initially expressed in 1900 as part of the famous 'Hilbert Problems'- 23 unsolved problems in mathematics.
<H4>The problem:</H4>
A general “decision problem” requires a binary answer such as “yes” or “no;” “true” or “false.” The Halting Problem is an example of a “decision problem.”<BR />
It asks whether a particular program would ever halt while processing a certain input, and provides the “yes or no” answer.<br />
Within a few years, Kurt Gödel crushed Hilbert’s hope of proving that a sufficiently strong system of mathematics could prove that it itself is complete and consistent.<br />
Would Hilbert’s Decision Problem fare better?<br />
Hilbert’s grand Decision Problem asked whether it is possible to have a fixed procedure to determine whether any specific mathematical statement can be proven within that system.<br />
This could verify an algebraic equation, an integration in calculus, or the truth of a derivation in logic.<br>
Mathematicians then had to create tools that might be capable of solving such a problem.<br />
<h4>Turing's solution:</h4>
Turing while studying mathematics at Cambridge got inspired by the lectures of Max Newman & decided to take on the Decision Problem.<br />Turing imagined a hypothetical machine, (now called a 'Turing machine' that would read a tape of symbols, one at a time, then either rewrite or erase the symbol, before then shifting the tape to the left or right. In fact, originally Turing describes a person slavishly performing these operations. He called this person the 'computer'.<br />
Some Turing machines would run forever, some would halt quite quickly, and for others it depended on the input. Turing asked if some method existed that always allowed us to determine whether a computer program and input would eventually halt, or run forever. He proved that a general algorithm to solve this problem, for all possible program and input pairs, cannot exist - making it an example of an undecidable problem. An astounding example that disproved Hilbert's question on decidability.<br />
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Machines take me<br /> by surprise with great frequency.
<cite>Alan Turing</cite>
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<br /><br /><br /><center><h2>INCARUS:IN DEATH</h2></center>
Turing was homosexual at a time when it was illegal in Britain. Caught up, he was charged with "gross indecency" under Section 11. <BR>
He opted for probation over imprisonment and went for the forced medical treatment under law to continue his work. <BR>
He accepted the option of treatment via injections of stilboestrol, a synthetic oestrogen; this treatment was continued for the course of one year. The treatment rendered Turing impotent and caused gynaecomastia, fulfilling in the literal sense Turing's prediction that "no doubt I shall emerge from it all a different man, but quite who I've not found out".<BR>
It nearly killed his senses and abilities.<BR>
At the age of 41 Turing was found dead of cyanide poisoning, considered a suicide.<BR>
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<h2>AFTER DEATH</h2>
<h4>Prime Minister Gordon Brown acknowledged the petition, releasing a statement on 10 September 2009 apologising and describing the treatment of Turing as "appalling".</h4></div>
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<center><h2>LEGACY</h2></center>
<p>Turing's legacy is huge, bigger than any of us can realise. He goes on to inspire and awe every generation of mathematicians, computer scientists and laymen with his astonishingly remarkable-magical genius.<br />
We live in a world full of computers, thanks to the work of Alan Turing. There have been many accolades and tributes to Turing since his death. Since 1966 the Turing award has been given annually by the Association for Computing Machinery, widely considered as equivalent to the Nobel Prize for computing. Recently a movie "The Imitation Game" got released featuring Turing's life, partially. In Manchester's Sackville Park there is a statue of Turing sitting on a bench, titled 'Father of Computer Science'. Before his death, Turing had taken an interest in mathematical biology, investigation the appearance of Fibonacci numbers in plant structures and pattern formation in animal markings. This work is considered seminal in the field, which goes to show the breadth of Turing's genius, and only leaves us to wonder what else he could have achieved.
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