Conservapedia - User contributions [en]

Design detection

2009-04-26T16:31:16Z

Rationaldebate:

'''Design detection''' is the science of how to recognize patterns arranged by an intelligent cause for a purpose. It is used in a number of scientific fields, including [[anthropology]], [[archeology]], forensic sciences, [[cryptanalysis]] and the [[Search for Extra-Terrestrial Intelligence|search for extraterrestrial intelligence]].<ref>http://www.seti.org/site/pp.asp?c=ktJ2J9MMIsE&b=178025</ref> An inference that certain cosmological and biological features of the natural world may be the product of an intelligent cause can be tested or evaluated in the same manner as scientists daily test for design in other sciences.<ref>For example, Stephen C. Meyer, Senior Fellow of the Center for Science and Culture at the Discovery Institute, notes at idthefuture.com (http://www.idthefuture.com/2005/10/a_note_to_teachers_part_3_science_and_th.html) the problem with limiting explanations to only "natural" causes: "Archaeologists routinely distinguish manufactured objects (e.g., arrowheads, potsherds) from natural ones (e.g., stones), even when the differences between them are very subtle. These manufactured objects then become important clues in reconstructing past ways of life. But if we arbitrarily assert that science explains solely by reference to natural laws, if archaeologists are prohibited from invoking an intelligent manufacturer, the whole archaeological enterprise comes to a grinding halt."</ref>

Design detection can be very difficult or impossible because God must not provide proof for his existance to nonbelievers because then faith would no longer be required, and Christianity would become a science rather than a religion.
==Notes==
{{reflist}}

==See also==
* [[intelligent design]]
[[Category:Science]]

Alan Turing

2009-04-26T16:12:34Z

Rationaldebate:

[[Image:Ture.jpg|right|thumb]]
'''Alan Turing''' (1912 - 1954) was an atheist homosexual British mathematician considered to be the founder of modern [[computer]] science and [[cryptography]].<ref>Http://www.turing.org.uk/bio</ref>

In the 1930s Turing proposed the concept of a "Universal [[Turing Machine]]". Turing had, first, proposed that the operations needed to calculate any formula could be broken down into a base set of instructions (or primitive recursive functions) that could in principle be followed by a machine: the "Turing Machine". Once fully formalized the calculations needed to derive the instructions themselves were capable of being run by a Turing Machine. The looped [[logic]] allowed the conception of a Turing Machine that could create its own instruction and, in principle, run a huge variety of calculations. Turing then used the concept of Universal Turing Machine to prove the undecidability of the [[halting problem]].

During [[World War II]] Turing was assigned to the codebreaking unit at Bletchley Park, where he worked on the decoding of the German's [[Enigma machine]]. Turing and his colleagues played a significant role in the Allied victory in WW2, allowing Allied forces access to German communication networks throughout much of the war.

In his 1950 paper "[[Computing]] Machinery and Intelligence" (Mind 49: 433-460) Turing proposed a test (apparently heavily influenced by [[Logical Positivism]]) for establishing whether a computer could think.

Turing was arrested in 1952 for [[homosexuality|homosexual acts]] and subsequently lost his security clearance. He was allowed to stay out of prison by agreeing to be injected with female hormones (which would supposedly decrease his sex drive). He later confided to a friend that the hormones caused him to grow breasts.<ref>''Oddballs and Eccentrics''. Shaw, Karl. Edison, New Jersey: Castle Books, 2004</ref> This may have contributed to his suicide by [[cyanide]] poisoning in 1954.<ref>http://www.turing.org.uk/turing/index.html</ref>
==References==

Online biography: http://www.turing.org.uk/bio/

Computing Machinery and Intelligence: http://cogprints.org/499/00/turing.html

''Oddballs and Eccentrics''. Shaw, Karl. Edison, New Jersey: Castle Books, 2004.

<references/>

{{DEFAULTSORT:Turing, Alan}}
[[Category:Mathematicians]]

Super Mario Bros.

2009-04-26T15:52:54Z

Rationaldebate:

'''Super Mario Bros.''' ([[ESRB]] ratings: E) is one of the most well known [[video games]] in the industry. It is a platform game created by [[Nintendo]] for the [[Nintendo Entertainment System]], first released in 1985. It features the intrepid [[Mario]] in his adventures through Mushroom Kingdom to save [[Princess Peach]] from [[Bowser]]'s hands. It is the game that has sold the most copies worldwide and numerous ports, sequels and other merchandise has been made out of it.

It lacks any kind of realistic [[violence]] and can possibly be enjoyed safely by the whole family; however, several enemies throw dangerous objects (e.g. hammers and spiked balls) and impressionable players should be warned that these actions are harmful to others, illegal, and go against God's word.

The player controls Mario (or possibly [[Luigi]] in two-player mode) and must reach the goal in each side-scrolling level which is populated by numerous obstacles such as enemies, pitfalls and other hazzards. The player may obtain a red [[mushroom]] (increasing Mario's side and allowing him to be hit twice before losing a life), a fire flower (allowing Mario to throw bouncing [[fire]] [[ball]]s to eliminate some enemies), a bouncing [[star]]called Starman (making Mario invisible and eliminating enemies he comes in contact with), a green mushroom (giving Mario an extra life) or coins (collecting 100 of these will grant Mario an extra life). Most enemies are defeated by jumping on them directly and by throwing fire balls or [[shell]]s (obtained by jumping on Koopa Troopas, turtle-like enemies and Buzzy Beetles, a beetle-like equivalent) at them or The player travels through eight worlds, each consisting of four levels, the last one being a castle where an impersonation of Bowser dwells and must be defeated by reaching an [[axe]] and destroying the bridge he is standing on or by throwing enough fire balls at him, when he does, the player encounters a humanoid mushroom who tells him that the princess is in another castle (with the exception being the last one, where he finds the princess). The player may encounter warp [[pipe]]s that allow him to skip levels or even whole worlds.

==See Also==
*[[Mario]]

[[Category:NES Games]]

Prime number

2009-04-26T15:48:53Z

Rationaldebate:

[[File:Eratosthenes.jpg|thumb|[[Eratosthenes]].]]
A '''prime number''' is a [[natural number]] greater than 1 that is [[divisible]] by only 1 and itself. Equivalently, the number has exactly two [[factor]]s, 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13...

[[Leonhard Euler]] wrote: <blockquote>
''Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate.''
</blockquote>

There are infinitely many primes. The only [[even]] prime number is 2.

==Sieve of Eratosthenes==
{|class="wikitable" align="right"
|{{User:ClementB/SieveOfEratosthenes}}
|-
|Here, '''n''' equals 144
|}
To construct a table of all prime numbers less than ''n'', you can use a method called the [[Sieve of Eratosthenes]]. Simply write down an ordered list of all counting numbers from 1 to ''n''. Beginning with 2*2 = 4, cross out every second number:

:2 3 <s>4</s> 5 <s>6</s> 7 <s>8</s> 9 <s>10</s> 11 ...

then beginning with 3*3 = 9 cross out every third number:

:2 3 <s>4</s> 5 <s>6</s> 7 <s>8 9 10</s> 11 ...

Beginning with 5*5 = 25, cross out every fifth number, then repeat for the primes 7, 11, 13, etc. until <math>\sqrt{n}</math>.

The number of primes smaller than a given number <math>N</math> is roughly <math>\frac{N}{\ln(N)}</math>, where <math>\ln(N)</math> is the [[natural logarithm]] (base ''[[e]]'') of <math>N</math>.<ref>http://home.att.net/~numericana/answer/primes.htm</ref> This is a formulation of a more general statement known as the [[Prime Number Theorem]].

==How many prime numbers==
{{main|Prime Number Theorem}}

It is easy to prove that there are an infinite number of primes using Euclid's second theorem: Imagine there is a finite set consisting of all the primes. Multiply them all together, add 1, and call this N. N would not be divisible by any number in the set--there would always be a remainder of 1. Because all non-prime numbers can be decomposed into a product of underlying primes (by the [[Fundamental Theorem of Arithmetic]]), N must be divisible by some prime not in the set (possibly itself), thus contradicting the assumption that the set contained all of the primes.

Another proof that there are infinitely many primes shows something stronger, namely the sum of the reciprocals of primes less than n "grows like" log(log(n)):
<math>\sum_{p\le x}p^{-1}\approx\log\log x</math>

==Unique Factorization==
{{main|Fundamental Theorem of Arithmetic}}

According to the [[Fundamental Theorem of Arithmetic]], proven by [[Carl Friedrich Gauss]], every positive integer has a unique [[factorization]] into prime numbers.

This means that every integer larger than 1, can be expressed as a product of one or more primes in only one way. For example, 132 = 2 * 2 * 3 * 11. There is no other product of primes that equals 132. This would not work if 1 were defined as a prime number.

Finding the prime factors for large numbers (having hundreds of digits) can take considerable time (millions of years) even with the most advanced computers.

==Alternative Definition==
Beyond the integers, mathematicians are interested in other structures with addition and multiplication; they are called [[Ring_(mathematics)|ring]]s. When working in rings, mathematicians use a different definition for a "prime" element: <blockquote>''A prime element is a non-unit (i.e., not 1 or -1 for the integers) which whenever it divides the product of two numbers will divide at least one of the factors.''</blockquote>

Or in symbolic notation:

<math>p \in \mathbb{Z} \quad prime :\Leftrightarrow p \not\in \{-1, 1\} \wedge (\forall a,b \in \mathbb{Z}: p \vert ab \Rightarrow p \vert a \vee p \vert b) </math>

For the integers, this definition is equivalent to the one stated above. However in general the two definitions are not equivalent. The earlier definition is still important in rings, and is given the name [[irreducibility]], since it literally states that the element cannot be broken into smaller pieces.

The preference for this alternate definition of "prime" is that this definition gives you unique [[factorization]] theorems analogous to the [[Fundamental Theorem of Arithmetic]]. For more information, consult an abstract algebra book<ref>'''Abstract Algebra: An Introduction''', Thomas Hungerford. Brooks Cole; 2 edition (1996)</ref>

==Primality testing==
To determine whether a number is prime, you can use the trial division method, provided the number you are testing is not too large. Let ''N'' be the number being tested and ''s'' be its square root. Divide ''N'' by each number in the prime table, beginning with 2. If there is no remainder, stop--N is composite. Otherwise, test again with the next largest prime in the table. If the next largest prime is greater than ''s'', stop--''N'' is prime.

For larger values of ''N'', a method based on Fermat's theorem can be used, though it usually requires a computer. Start with the number 1, and double it ''N-1'' times. Divide this number by ''N'', keeping only the remainder. If the remainder is greater than 1, ''N'' is composite. Unfortunately, the converse is not true--if the remainder is 1, ''N'' is ''probably'' prime, but not necessarily. Algorithms which improve on this method exist, and primality testing is today an active subject of mathematical research.

Testing for Mersenne numbers is much easier than for other numbers, because an intelligently-designed algorithm exists.

==Open Problems about Prime Numbers==

===The Largest Known Prime===

The largest known prime is ''232582657-1''; it was discovered by the '''Great Internet Mersenne Prime Search''' ('''GIMPS''')<ref>http://www.mersenne.org/</ref>, a distributed computing project launched by George Woltman in early 1996.<ref>http://primes.utm.edu/largest.html</ref>

===Mersenne Prime===
A '''Mersenne prime''' is a prime number ''M'' that is of the form ''M = 2n − 1'', where ''n'' is some [[prime number]]<ref>[http://mathworld.wolfram.com/MersennePrime.html Mersenne Prime] from Wolfram</ref>. As of April, 2007, only 44 Mersenne Primes have been found. The largest known prime ''232582657-1'', is a Mersenne Prime. The concept of a Mersenne Prime was discovered by the French theologian, philosopher and mathematician [[Marin Mersenne]].

===Twin primes===
{{main|twin primes}}

[[Twin primes]] or '''prime twins''' are pairs of prime number which differ from each other by only 2. Since all primes other than 2 are odd numbers, this is the closest two primes can be to each other, with the exception of 2 and 3. The first few twin primes are 3 and 5, 5 and 7, 11 and 13, 17 and 19, and 29 and 31.

Twin primes become increasingly scarce among larger numbers. For example, there are twenty-four sets of twin primes between 0 and 500, but only eleven sets between 500 and 1000. Computer programs have calculated some extremely large sets of twin primes. While there are undoubtedly an unlimited number of primes, opinions differ among mathematicians whether there is also an infinite number of twin primes or whether there is an upper limit. This debate is captured by the [[twin primes conjecture]]

Mathematicians have long been fascinated by twin primes and the biblically-approved relationships between them. There seems to be no distinct pattern in their occurrence. For example, there are no twin primes between 700 and 800, or between 900 and 1000, but there are five sets between 800 and 900 (809 and 811; 821 and 823; 827 and 829; 857 and 859; 881 and 883).

===Goldbach's conjecture===

Goldbach's conjecture asserts that every even integer greater than two is the sum of two prime numbers. For example: 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, and so on.

This conjecture is one of the oldest unsettled statements in mathematics. For centuries mathematicians have attempted to prove this statement, without success. The conjecture is known to hold for numbers less than 3 <math>\cdot</math>1017.

===Riemann hypothesis===
{{main|Riemann hypothesis}}

The [[Riemann hypothesis]] is related to patterns in the distribution of prime numbers. ''The Clay Mathematics Institute'' has offered a one million dollar prize for a proof of the Riemann hypothesis.<ref>http://www.claymath.org/millennium/Riemann_Hypothesis/</ref>

===Predicting Primes===
Large prime numbers are very difficult to find in comparison to large composite numbers, which can be found simply by multiply two large primes together. One of the largest known (legitimate) numbers, Graham's Number, has to be expressed using Knuth's up-arrow notation, while the largest known prime liberal mathematicians have discovered using socialist distributed-computing methods is only about 10,000,000 digits long and can be expressed with exponential notation.

==Cryptography==
The security of [[public-key cryptography]] schemes such as [[RSA]] depend on the difficulty of prime factorization, if a pattern in the distribution of prime numbers is discovered, then such [[cryptographic]] schemes could become vulnerable to attack. Cryptography is very important for keeping important data secure on the internet from atheist hackers.

==See also==

* [[Composite number]]
* [[Fibonacci sequence]]
* [[Perfect number]]

==External links==
*[http://www.mersenne.org/ ''Great Internet Mersenne Prime Search'' project website]
*[http://primes.utm.edu/ Prime Number resource Archive]
*[http://educ.queensu.ca/%7Efmc/december2003/Sieve.html Sieve of Eratosthenes]

==References==
<references/>

[[Category:Number Theory]]