Mapping Infinite world ....
A simple question: how many 3-letter words can be formed with 26 alphabets?
Equally simple answer: 26 x 26 x 26 (as each time we get a choice to choose from 26 alphabets).
Now, lets extend our counting problem little further. How many symbols do newspapers use usually? Lets say 100 (A-Z, a-z, 0-9, punctuation marks, special characters).
How many such symbols can a line accommodate? Make a guess!
Lets say its 200 (just for the sake of discussion).
And how many such a line a newspaper can carry in general?
Lets assume the number is: 5000 (again, for the sake of discussion).
Now, in how many ways can such a newspaper be filled with available 100 symbols?
100 x 100 x 100 ... (200 x 5000 times).
In short it is 100 raised to the power of (200 x 5000).
(Note: This count also includes weird combinations like all words starting with 'AAA' etc. However, this doesn't bother us as the sole purpose is to present an argument and a new insight. Also, the accuracy of figures like 200 alphabets per line is not our concern).
Now, think of the newspaper on the day:
[100 raised to the power 200 x 5000] + 1 (though large, of course this is a finite number)
The newspaper on that day HAS to be a repetition!!!
See the implications? We just proved that there can exist two days with SAME newspaper. What does this mean? How do we 'interpret' this? Perhaps, the contexts might be different. Perhaps the 'world' has changed. But, if 'Team A has beaten Team B in some sport' then it’s recurring again!
Not every newspaper will find its 'duplicate'. But, if we are to cut down on the number of newspapers who have 'duplicates' then we effectively increase the number of 'repetition' a newspaper can undergo!
Where is the hitch? The problem is with 'function' that tries to map presumably 'infinite' domain of real world to 'finite' range of 'newspaper'.
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When you eliminate all that is impossible; whatever remains however improbable must be the truth!
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Equally simple answer: 26 x 26 x 26 (as each time we get a choice to choose from 26 alphabets).
Now, lets extend our counting problem little further. How many symbols do newspapers use usually? Lets say 100 (A-Z, a-z, 0-9, punctuation marks, special characters).
How many such symbols can a line accommodate? Make a guess!
Lets say its 200 (just for the sake of discussion).
And how many such a line a newspaper can carry in general?
Lets assume the number is: 5000 (again, for the sake of discussion).
Now, in how many ways can such a newspaper be filled with available 100 symbols?
100 x 100 x 100 ... (200 x 5000 times).
In short it is 100 raised to the power of (200 x 5000).
(Note: This count also includes weird combinations like all words starting with 'AAA' etc. However, this doesn't bother us as the sole purpose is to present an argument and a new insight. Also, the accuracy of figures like 200 alphabets per line is not our concern).
Now, think of the newspaper on the day:
[100 raised to the power 200 x 5000] + 1 (though large, of course this is a finite number)
The newspaper on that day HAS to be a repetition!!!
See the implications? We just proved that there can exist two days with SAME newspaper. What does this mean? How do we 'interpret' this? Perhaps, the contexts might be different. Perhaps the 'world' has changed. But, if 'Team A has beaten Team B in some sport' then it’s recurring again!
Not every newspaper will find its 'duplicate'. But, if we are to cut down on the number of newspapers who have 'duplicates' then we effectively increase the number of 'repetition' a newspaper can undergo!
Where is the hitch? The problem is with 'function' that tries to map presumably 'infinite' domain of real world to 'finite' range of 'newspaper'.
-----------------------------------------------------------------------------
When you eliminate all that is impossible; whatever remains however improbable must be the truth!
-----------------------------------------------------------------------------
posted by Shrikrishna at
1:32 PM
2 Comments:
dont you think you havenot considered that the AAA is diffrent than AAAA and again different than AAAAA and so on so its a countably infinite set. So, no duplicate news paper for you buddy(?).
By
Anonymous, at Fri Feb 18, 05:04:00 PM 2005
The life span of the universe is only 311 trillion years, which is far too little from 100^(200*5000)/365 years. So the repeated newspaper will never occur.
By
Anonymous, at Wed Sep 07, 07:34:00 PM 2005
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