John M a écrit :
> Bruno wrote:
> "What can be said about numbers is that it is
> impossible to explain what numbers are to someone who
> does not already knows what they are..."
> <I will talk about "what numbers do, not 'are'>
> "..If a TOE does not implicitly or explicitly
> presupposes the existetnce of natural numbers, then
> the natural numbers will not be definable in that TOE,
> and for this reason that TOE will not be a plausible
> TOE. - although Hartree Field, if I remember
> correctly, makes a case for a science without
> number[s?]. ..."
> Friends, we are closer friends than any others in this
> world: we share our thoughts, the most intimae of us. 
> So I dare share this one with you all:
> *
> As I said above: "what numbers do". 
> Well, what DO numbers do? -- -THEY DO NOTHING. -  - 
> - This is my fundamental objection to the 'hard'
> number theory making numbers (and their manipulations)
> the basis of them all (I don't dare: nature, world,
> existence, etc. as very loaded words over here).
> Numbers do NOT add, subtract, etc., WE do it to (by,
> with) them. Humans, Loebian machines, whatever, but
> NOT the numbers. 
> Same argument as against the 'Intelligent Design": a
> design does nothing, it requires an operator (factor)
> to perform what the design includes. Similarly:
> Numbers require factors (operating agents) to perform
> any potential which CAN BE PEFRFORMED with/by them. 
> If there 'are' only numbers - it stays only numbers. 
> That may be a neat world, but without us thinking
> about it. Do I miss the numberculus (I don't say:
> himunculus) 
> DOING the operations.

Who said that numbers do (or have to do or could do) anything?
I am not sure Bruno did and I did not. I only suggested that
natural numbers might have to exist and their existence might
be enough to explain the existence of everything else. This is
very different.

Actually, by "numbers have to exist" I do not mean just natural
numbers. The number 2 can no more be isolated from N than N
can be isolated from R. 2 comes with N that comes with R that
comes with Hilbert spaces and so on. All for the same reason:
everywhen/everywhere they tend to appear, constraints naturally
apply to them. These constraints are always ready to apply to
them and I feel that they even contain/define them.

Finally, it might be that one of the (possibly very) complex
objects in this world of numbers just happens to host us and
all that we see.

> Do I need more faith to believe (understand?) the TOE
> based on numbers? I may choose another TOE (if I have
> to). 

I have nothing against TOEs (or against anything) without
numbers, I am just completely unable to figure out what they
might look like. I am also completely unable to imagine that
numbers could not exist. We mainly exchange speculations here
and I found that very enriching. The amount of faith necessary
to adhere to or to reject them is very dependent upon people
(biology, personla history, ...). I am not sure that in that
sort of discussion everything can be decided on a purely
rational basis so faith has large opportinities to come in.

But do we need to actually believe in any of these speculations?


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