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Hoping Frank can help me with more maths... (Read 3512 times)
abyssoft
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Hoping Frank can help me with more maths...
09/26/10 at 15:29:51
 
given the following in Knuth's notation
 
[(10!↑↑1083)!↑↑1047]
(10!↑↑1083)

 
What is the simplification of the above number in scientific notation?
I am imagining that this is both difficult to do and will result in an extremely large exponent.
 
I understand the following about this number... (10!↑↑1083) can be represented as the following series  
            10!
        ⋰1083 - 3 times
    10!
10!


 
I found this listed in a scifi book as a reference to the amount of time in years to equal the fullness of time. and I'm just curious as to what it equates to.
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frankuitaalst
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Re: Hoping Frank can help me with more maths...
Reply #1 - 09/26/10 at 22:59:12
 
really big number Abby !  
 
If 10 fac= 3628800
and you raise it 80 times with this exponent , its the same as to raise it  once to the exponent 80*3628800= 290304000
 
So one gets : (3628800)^(290304000)
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abyssoft
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Re: Hoping Frank can help me with more maths...
Reply #2 - 09/27/10 at 08:11:05
 

I'm having difficulty with this concept.
      2^2
2^2^2^
 
You say would be the equivalent of 2^(2*4) which would be 256
however if you work it out by step you get
 
      4
2^2^2^
 
2^2^16
 
2^65536 which is a lot more then 256


So what am I either missing or misconceiving?  
 
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frankuitaalst
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Re: Hoping Frank can help me with more maths...
Reply #3 - 09/27/10 at 09:46:25
 
Quote from frankuitaalst on 09/26/10 at 22:59:12:
really big number Abby !

If 10 fac= 3628800
and you raise it 80 times with this exponent , its the same as to raise it  once to the exponent 80*3628800= 290304000

So one gets : (3628800)^(290304000)

 
Sorry , I was to quick   Sad ; youre right  
It should be : (3628800)^((3628000)^80) which is in fact ...unexpressible ...
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abyssoft
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Re: Hoping Frank can help me with more maths...
Reply #4 - 10/01/10 at 08:57:06
 
I've almost been able to get my computer to represent 10!^10! let's just say it's a really big number, I've got 2 more calculation rounds to complete before it's done and it's already over 2 million digits in length I Figure the last 2 round will be completed by weekends end. I am now very much believing that given current technology, storage and processing power, and the progress of said technologies it will be quite some time until it can be expressed.
 
I did figure a way to calculate faster while I was typing this message, and for those curious enough about it I'll attached a zip of the text output in a following message. trailing zeros will have been striped and be presented in scientific notation.
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abyssoft
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Re: Hoping Frank can help me with more maths...
Reply #5 - 10/02/10 at 12:53:30
 
Calculation complete and so attached is 10! ^ 10!
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frankuitaalst
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Re: Hoping Frank can help me with more maths...
Reply #6 - 10/02/10 at 13:58:50
 
waw !! how did you do this ?
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abyssoft
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Re: Hoping Frank can help me with more maths...
Reply #7 - 10/02/10 at 22:21:25
 
I created a small .Net Window Application that utilized C# BigInt found at http://www.emilstefanov.net/Projects/GnuMpDotNet/ which gives access to integers of arbitrary length and several math functions and operations.
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abyssoft
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Re: Hoping Frank can help me with more maths...
Reply #8 - 10/02/10 at 22:33:11
 
given the size of just 10! ^ 10!  
 
10!^^1083 is quite unfathomably large and (10!^^1083!)^^1047 is beyond mind-blowingly large.
 
 
(10!^^1083) ^ [(10!^^1083!)^^1047] Is beyond all possible comprehension as this point in human evolution.
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