I came across this concept while i was doing a course in probability and random process.It was something that really caught my fascination.So i did some kind of a research work,and i was fascinated by the way the theorem and the Theory of evolution are correlated....
For starters,what is Infinite Monkey Theorem??.The infinite monkey theorem states that "a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type or create a particular chosen text, such as the complete works of William shakephere". The term 'almost surely' is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey; rather a random sequence generator.
The infinite monkey theorem can be proved in a very straight forward manner.If two events are statistically independent,then the probabilty of both happening equals the product of the probabilities of each one happening on its own.Let A&B be the two statistically independent events then,P(a,b)=P(a)*P(b).Suppose we have a typewriter with say '50'keys,then the probability for each letter to be typed would be 1/50.Suppose we are typing the word 'blog',then the chance that first letter typed is 'b' is 1/50,second letter typed is 'l' is 1/50,and so the total probability that the entire word is typed will be (1/50)*(1/50)*(1/50)*(1/50)=(1/50)^4
Since each block is typed independently, the chance Xn of not typing blog in any of the first n blocks of 4 letters is
Xn=(1-1/50^4)^n
As n grows, Xn gets smaller. For an n of a million, Xn is 99.99%, but for an n of 10 billion Xn is 53% and for an n of 100 billion it is 0.17%. As n approaches infinity, the probability Xn approaches zero; that is, by making n large enough, Xn can be made as small as one likes.
The Infinite Monkey Theorem is used as an argument against Darwinism.. According to Darwinism all complex organism (including humans) evolved as the product of random mutations..
Infinite theorem says tat this is impossible.. coz some random mutations cannot produce a complex organism like human beings.. Ill use an example Richard Dawkins used in his book Climbing Mount Improbable. Its like letting a tornado blow through a junkyard and producing a fully connected aeroplane from the debris. such an event is so improbable. which is stated by the Infinite Monkey Theorem..
But that is not how Darwinism works.. A tiny mutation is produced and it is propagated along the generations if this mutation proves advantageous to the species.. if its bad the mutation is rejected simply bcoz the organisms having tat mutation is not as successful as the ones tat don't have it. This is just like a tiny step at a time. and this way natural selection finds a way around the difficulty posed by creationist's argument. Tiny successful mutations get selected and this produces the development of a complex organism from simpler ones.
So i think i have been able to address the issue in a very precise manner,so that it can be understood by people who haven't had any exposure to Probability too...
For starters,what is Infinite Monkey Theorem??.The infinite monkey theorem states that "a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type or create a particular chosen text, such as the complete works of William shakephere". The term 'almost surely' is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey; rather a random sequence generator.
The infinite monkey theorem can be proved in a very straight forward manner.If two events are statistically independent,then the probabilty of both happening equals the product of the probabilities of each one happening on its own.Let A&B be the two statistically independent events then,P(a,b)=P(a)*P(b).Suppose we have a typewriter with say '50'keys,then the probability for each letter to be typed would be 1/50.Suppose we are typing the word 'blog',then the chance that first letter typed is 'b' is 1/50,second letter typed is 'l' is 1/50,and so the total probability that the entire word is typed will be (1/50)*(1/50)*(1/50)*(1/50)=(1/50)^4
Since each block is typed independently, the chance Xn of not typing blog in any of the first n blocks of 4 letters is
Xn=(1-1/50^4)^n
As n grows, Xn gets smaller. For an n of a million, Xn is 99.99%, but for an n of 10 billion Xn is 53% and for an n of 100 billion it is 0.17%. As n approaches infinity, the probability Xn approaches zero; that is, by making n large enough, Xn can be made as small as one likes.
The Infinite Monkey Theorem is used as an argument against Darwinism.. According to Darwinism all complex organism (including humans) evolved as the product of random mutations..
Infinite theorem says tat this is impossible.. coz some random mutations cannot produce a complex organism like human beings.. Ill use an example Richard Dawkins used in his book Climbing Mount Improbable. Its like letting a tornado blow through a junkyard and producing a fully connected aeroplane from the debris. such an event is so improbable. which is stated by the Infinite Monkey Theorem..
But that is not how Darwinism works.. A tiny mutation is produced and it is propagated along the generations if this mutation proves advantageous to the species.. if its bad the mutation is rejected simply bcoz the organisms having tat mutation is not as successful as the ones tat don't have it. This is just like a tiny step at a time. and this way natural selection finds a way around the difficulty posed by creationist's argument. Tiny successful mutations get selected and this produces the development of a complex organism from simpler ones.
So i think i have been able to address the issue in a very precise manner,so that it can be understood by people who haven't had any exposure to Probability too...
1 comment:
If any1 is reading this, i would recommend them to read the book "The Selfish Gene" by Richard Dawkins.. It will change the way u view the world. If any of my friends want the book just ask me :)
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