On Jan 21, 2014, at 12:32 AM, meekerdb <[email protected]> wrote:
On 1/20/2014 6:28 PM, Jason Resch wrote:
On Mon, Jan 20, 2014 at 6:59 PM, meekerdb <[email protected]
> wrote:
On 1/20/2014 4:41 PM, Jason Resch wrote:
On Mon, Jan 20, 2014 at 11:32 AM, meekerdb <[email protected]>
wrote:
On 1/20/2014 12:25 AM, Bruno Marchal wrote:
And to answer this properly, you have to define "physical
existence of Brent" without using arithmetic.
Brent:=the being who typed this sentence. (Or next time you're in
California, come by and I'll give an ostensive definition - and a
cup of coffee.)
Thanks very much for the coffee cup, I appreciate. But frankly
this will not work. If I need to define number by invoking a being
typing a sentence in a post dated the 19 janvier 2014, oops: I am
using some numbers here.
You didn't ask to define a number, you asked to define "physical
existence of Brent". And 19 January 2014 can easily be defined as
when Brent typed the above message. I think you (understandably
as a logician) are so immersed in the axiomatic method that you
lose of sight of its connection to the physical world.
Definitions become nothing but relations between symbols if you
never ground them in pointing.
Don't ask someone who want to compute 2+2=4 to come in California
and drink four cups of coffee, if all computers have to do that I
am afraid the net will become extremely slow ...
I find much more plausible that I can explain numbers behavior,
and Brent's brain and ideas, from
elementary arithmetical axioms,
than explain arithmetic from Brent and other humans ideas. Come
on ...
I'm quite sure you can explain Brent's brain and ideas without
using any number bigger than 10^100.
Just the sentence:
"I'm quite sure
you can explain Brent's brain and
ideas without using any number bigger than 10^100."
Takes a number larger than 10^100 to represent.
No, the sentence only uses the description "any number bigger than
10^100". It's logically equivalent to, "Every explanation of
Brent's brain and ideas uses only number less than 10^100".
Okay, then you should have clarified "no single number bigger than
10^100". It is possible to represent your ideas as a series of
much smaller numbers, however their combined product will almost
certainly be bigger than 10^100, even for very short sentences.
(10^100 is less than 42 bytes of information.)
But you don't need the product to explain my brain. And in any case
there is still an unbound on the biggest number you will need. You
will never need "..." or "and so forth".
Through my computer scientist eyes it just seems like a meaningless
distinction. If your brain is backed up on a computer you can look at
that file as a large number of bytes (numbers from 0 to 255) or simply
as one very big number. On the order of 256^(10^16).
I agree there is some finite upper bound, but this whole tangent began
when Bruno speculated that your brain might not appear until the
10^10^1000th step of the UD which is also a finite number.
Jason
Brent
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