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:
> 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
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
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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