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From: Archimedes Plutonium on 6 Jan 2010 14:33


Robert wrote:
> what is 10^500 + 1?
>
> there be dragons.


Pray tell, is it prime? Is this number

10000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000001

A prime number?

And with a definition, a precise definition of Finite as the Planck
Unit
of 10^500

Then 10^500 +1 is no longer a finite number but is in the Incognitum
where numbers have "no meaning" because there is no longer a reliable
physics going on to test and experiment.

So the structure of mathematics becomes this:

Finite -- 10^500 and below and where all of math is carried out
Incognitum -- little beyond Finite and the answers that lie here
are not mathematical because they are not trustworthy
Infinite -- beyond the Incognitum such numbers as 9999....9997
where they are undecidable as to whether they are prime or
composite and most other concepts of mathematics.

Physics logic is duality and only in the Finite region can we
have Aristotliean logic of linear logic and so mathematics
is a subject that can only be precise within the confines
of Aristotlean logic of 10^500 or less.


Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
From: Owen Jacobson on 6 Jan 2010 16:11
On Jan 6, 2:33 pm, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> Robert wrote:
> > what is 10^500 + 1?
>
> > there be dragons.
>
> Pray tell, is it prime? Is this number
>
> 10000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000001

That is not 10^500 + 1 (it's 10^499 + 1 -- remember, 10^n has n+1
digits, not n digits). This is 10^500 + 1:

10000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000001

And, the quotient when divided by 73:

136986301369863013698630136986301369863013698630
136986301369863013698630136986301369863013698630
136986301369863013698630136986301369863013698630
136986301369863013698630136986301369863013698630
136986301369863013698630136986301369863013698630
136986301369863013698630136986301369863013698630
136986301369863013698630136986301369863013698630
136986301369863013698630136986301369863013698630
136986301369863013698630136986301369863013698630
136986301369863013698630136986301369863013698630
1369863013698630137

> A prime number?

No. You can verify this with a short Python snippet:

>>> import decimal
>>> (decimal.Decimal('1E500') + 1) / 73

(The decimal module is an arbitrary-precision math library.)

-o
From: mike3 on 6 Jan 2010 21:38
On Jan 6, 12:33 pm, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> Robert wrote:
> > what is 10^500 + 1?
>
> > there be dragons.
>
> Pray tell, is it prime? Is this number
>
> 10000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000001
>
> A prime number?
>
> And with a definition, a precise definition of Finite as the Planck
> Unit
> of 10^500
>
> Then 10^500 +1 is no longer a finite number but is in the Incognitum
> where numbers have "no meaning" because there is no longer a reliable
> physics going on to test and experiment.
>
> So the structure of mathematics becomes this:
>
> Finite -- 10^500 and below and where all of math is carried out
> Incognitum -- little beyond Finite and the answers that lie here
> are not mathematical because they are not trustworthy
> Infinite -- beyond the Incognitum such numbers as 9999....9997
> where they are undecidable as to whether they are prime or
> composite and most other concepts of mathematics.
>
> Physics logic is duality and only in the Finite region can we
> have Aristotliean logic of linear logic and so mathematics
> is a subject that can only be precise within the confines
> of Aristotlean logic of 10^500 or less.
>

Hmm. So beyond some magic threshold, rules like those of arithmetic
are no longer "trustworthy"?! So I guess you can't trust that


10000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000001 + 1 =

10000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000002

then, right? It could equal
32975092734097329040239749023704323927408237402374
89235892369560976509236406027931632646203140622347
32720314702340732407347803427340783873528705084380
48743874387043784387042387047283874238794238742398
74327434872437802734878042748374237804278478043870
43078234807432807423087423807408727402780423807423
87480487042080428394830965904619756209164790327659
08621379564378567093265873467659734985623652736837
82365943675097289562459276237590837248905346343243
43248963246346394327983427324934293131247932575623
79156793254732547013527048523784783254780352078406
23863824768321774032750325407532078463207846732014
67082316470231674021678450872347802136407823647062
03140236409430006660006660006660006660006660006660
00666000666066606660666066606660666066606660666066
606660666
or something, for all we know. It could equal 42. It could equal
something
else altogether. It might be a non-number. Yeah, right, I don't THEENK
so,
matey.
From: Robert on 7 Jan 2010 10:59
On 6 Jan, 19:33, Archimedes Plutonium <plutonium.archime...(a)gmail.com>
wrote:
> Robert wrote:
> > what is 10^500 + 1?
>
> > there be dragons.
>
> Pray tell, is it prime? Is this number
>
> 10000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000001
>
> A prime number?

No idea. Is that the test for whether numbers have meaning? Whether
you can tell if they're prime. No.

> And with a definition, a precise definition of Finite as the Planck
> Unit
> of 10^500
>
> Then 10^500 +1 is no longer a finite number but is in the Incognitum
> where numbers have "no meaning" because there is no longer a reliable
> physics going on to test and experiment.

You can reliably tell that 10^500 + 1 is an odd number. Totally
trustworthy, with total cognition. You can do mathematics with numbers
bigger than 10^500. Not all mathematics it's true, but you shouldn't
have a tantrum about that.


> So the structure of mathematics becomes this:
>
> Finite -- 10^500 and below and where all of math is carried out
> Incognitum -- little beyond Finite and the answers that lie here
> are not mathematical because they are not trustworthy
> Infinite -- beyond the Incognitum such numbers as 9999....9997
> where they are undecidable as to whether they are prime or
> composite and most other concepts of mathematics.
>
> Physics logic is duality and only in the Finite region can we
> have Aristotliean logic of linear logic and so mathematics
> is a subject that can only be precise within the confines
> of Aristotlean logic of 10^500 or less.
>
> Archimedes Plutoniumwww.iw.net/~a_plutonium
> whole entire Universe is just one big atom
> where dots of the electron-dot-cloud are galaxies

 | 
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