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**Science Discussion Forum / Re: অন্ধ করে দিতে পারে কন্ট্যাক্ট লেন্স!**

« **on:**June 25, 2012, 11:54:14 AM »

Thanks for sharing the information.

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Thanks for sharing the information.

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"Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to take the switch?"(Assuming, of course, that you are after the car, not the goat)?

This popular puzzler created a stir in 1991 when it appeared in the newspaper^{1} and received a lot of wrong answers from readers, even from some who were mathematicians. How do we think about a problem like this, aÂ¬nd why is it so tricky?

^{1}**Tierney, John** "Behind Monty Hall's Doors: Puzzle, Debate, and Answer?," New York Times, July 21, 1991.

http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html?pagewanted=all&src=pm

Further reading

**Isaac, R.** *The Pleasures of Probability*, Undergraduate texts in Mathematics, Springer, 1995.

This popular puzzler created a stir in 1991 when it appeared in the newspaper

http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html?pagewanted=all&src=pm

Further reading

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Consider the following problem to test our skills with conditional probability:

*The king comes from a family of two children. What is the probability that the other child is his sister?*

The sample space for this problem can be considered to be the set S of four pairs (B, B), (B, G), (G, B), (G, G), where B stands for "boy" and G stands for "girl" and the first and second positions in the pair denote first and second born children, respectively. To be able to do the problem some assumptions must be made. Once again, we shall assume each of the four outcomes is equally likely.

This problem is tricky-a lot of people think the answer should be 1/2. If the question had been "what is the probability that a person's sibling is a sister," then the answer would be 1/2. But in the given problem you are sneakily given the information in the wording of the problem that one child, the king, is male, and that information eliminates the outcome (G, G) in the sample space as a possibility. The remaining three outcomes of S become the conditional, or updated, sample space S' of which two outcomes have a B and a G, (B, B), (B, G), (G, B).

Therefore, the probability that the other child is his sister is 2/3.

Further reading

**Isaac, R.** *The Pleasures of Probability*, Undergraduate texts in Mathematics, Springer, 1995.

The sample space for this problem can be considered to be the set S of four pairs (B, B), (B, G), (G, B), (G, G), where B stands for "boy" and G stands for "girl" and the first and second positions in the pair denote first and second born children, respectively. To be able to do the problem some assumptions must be made. Once again, we shall assume each of the four outcomes is equally likely.

This problem is tricky-a lot of people think the answer should be 1/2. If the question had been "what is the probability that a person's sibling is a sister," then the answer would be 1/2. But in the given problem you are sneakily given the information in the wording of the problem that one child, the king, is male, and that information eliminates the outcome (G, G) in the sample space as a possibility. The remaining three outcomes of S become the conditional, or updated, sample space S' of which two outcomes have a B and a G, (B, B), (B, G), (G, B).

Therefore, the probability that the other child is his sister is 2/3.

Further reading

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(1912â€“1954)

Alan Turing (1912-1954)

At the dawn of the computer age, Alan Mathison Turingâ€™s startling range of original thought led to the creation of many branches of computer science, ranging from the fundamental theory of computability to the question of what might constitute true artificial intelligence.

Turing was born in London on

As a youth, Turing showed great interest and aptitude in both physical science and mathematics, although he tended to neglect other subjects. One of his math teachers further observed that Turing â€œspends a good deal of time apparently in investigations of advanced mathematics to the neglect of elementary work.â€

When he entered Kingâ€™s College, Cambridge, in 1931, Turingâ€™s mind was absorbed by Einsteinâ€™s relativity and the new theory of quantum mechanics, subjects that few of the most advanced scientific minds could grasp. At this time, he also encountered the work of mathematician JOHN VON NEUMANN, a many-faceted mathematical genius who would also become a great computer pioneer. Meanwhile, Turing pursued the study of probability and wrote a well-regarded thesis on the Central Limit Theorem.

Turingâ€™s interest then turned to one of the most perplexing unsolved problems of contemporary mathematics. Kurt GÃ¶del had shown that in any system of mathematics there will be some assertion that can be neither proved nor disproved. But another great mathematician, David Hilbert, had asked whether there was a way to tell whether any particular mathematical assertion was provable.

Instead of pursuing conventional mathematical strategies to tackle this problem, Turing reimagined the problem by creating the Turing Machine, an abstract â€œcomputerâ€ that performs only two kinds of operations: writing or not writing a symbol on its imaginary tape, and possibly moving one space on the tape to the left or right. Turing showed that from this simple set of states, any type of calculation could be constructed. His 1936 paper â€œOn Computable Numbers,â€ together with ALONZO CHURCHâ€™s more traditional logical approach, defined the theory of computability. After publishing this paper, Turing then came to America, studied at Princeton University, and received his Ph.D. in 1938.

Turing did not remain in the abstract realm, however, but began to think about how actual machines could perform sequences of logical operations. When World War II erupted, Turing returned to Britain and went into service with the governmentâ€™s secret code-breaking facility at Bletchley Park. He was able to combine his previous work on probability and his new insights into computing devices, such as the early special- purpose computer COLOSSUS, to help analyze cryptosystems, such as the German Enigma cipher machine, and to design specialized code breaking machines.

As the war drew to an end, Turingâ€™s imagination brought together what he had seen of the possibilities of automatic computation, and particularly the faster machines that would be possible by harnessing electronics rather than electromechanical relays. In 1946, after he had moved to the National Physical Laboratory in Teddington, England, he received a government grant to build the Automatic Computing Engine, or ACE. This machineâ€™s design incorporated such advanced programming concepts as the storing of all instructions in the form of programs in memory without the mechanical setup steps required for machines such as the ENIAC. Another of Turingâ€™s important ideas was that programs could modify themselves by treating their own instructions just like other data in memory. However, the engineering of the advanced memory system ran into problems and delays, and Turing left the project in 1948 (it would be completed in 1950). Turing also continued his interest in pure mathematics and developed a new interest in a completely different field, biochemistry.

Turingâ€™s last and perhaps greatest impact would come in the new field of artificial intelligence. Working at the University of Manchester as director of programming for its Mark 1 computer, Turing devised a concept that became known as the Turing test. In its best-known variation, the test involves a human being communicating via a Teletype with an unknown party that might be either another person or a computer. If a computer at the other end is sufficiently able to respond in a humanlike way, it may fool the human into thinking it is another person. This achievement could in turn be considered strong evidence that the computer is truly intelligent. Since Turingâ€™s 1950 article, â€œComputing Machinery and Intelligence,â€ computer programs such as ELIZA and Web â€œchatter botsâ€ have been able to temporarily fool people they encounter, but no computer program has yet been able to pass the Turing test when subjected to extensive, probing questions by a knowledgeable person.

Turing also had a keen interest in chess and the possibility of programming a machine to challenge human players. Although he did not finish his chess program, it demonstrated some relevant algorithms for choosing moves, and led to later work by CLAUDE E. SHANNON, ALLEN NEWELL, and other researchersâ€”and ultimately to Deep Blue, the computer that defeated world chess champion Garry Kasparov in 1997.

However, the master code breaker Turing himself held a secret that was very dangerous in his time and place: He was gay. In 1952, the socially awkward Turing stumbled into a set of circumstances that led to his being arrested for homosexual activity, which was illegal and heavily punished at the time. The effect of his trial and forced medical â€œtreatmentâ€ suggested that the coroner was correct in determining Turingâ€™s death from cyanide poisoning on June 7, 1954, a suicide.

Alan Turingâ€™s many contributions to computer science were honored by his being elected a Fellow of the British Royal Society in 1951 and by the creation of the prestigious Turing Award by the Association for Computing Machinery, given every year since 1966 for outstanding contributions to computer science.

In recent years, Turingâ€™s fascinating and tragic life has been the subject of several autobiographies and even the stage play and TV film Breaking the Code.

Excerpt from the book

1.

2. Alan Turingâ€™s Automatic Computing Engine The Master Codebreakerâ€™s Struggle to Build the Modern Computer

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