Re: Numbers

From: Georges Quénot <Georges.Quenot.domain.name.hidden>
Date: Sat, 11 Mar 2006 10:59:14 +0100

John M wrote:
>
> Georges: please, have merci on me! 'my' English is
> the 5th of my acquired languages, so to read - and
> realize what it stands for - that long a post is
> (almost) beyond my mental endurance.

I understand that but the point is highly unusual
and unintuitive and I felt that a "critical mass"
was necessary for it to make is way.

> I try to pick some of your remarks as non-conform to
> how I feel. Consider please the rest as agreed. (At
> least for now - ha ha - which means the <G> I wrote, a
> usual WEB-abbreviation for <Grin>.

Sorry, I dont even know <Grin>.

> Thanks for taking so much time to respond.

It helps me too to formalize things and indentify
weaknesses and limitations. Thank to ypou too.

>> [...]
>> I think I have the same kind of feeble thinking tool
>> as you have. However I am not sure that common sense
>> is of much help for questions like "why is there
>> something?". Rather it is likely that it would
> confuse >us on such topics. It simply did not evolved
> for that. >Our common sense is more a handicap than a
> good guide >to understand quantum mechanics. The
> situation is even >worse here. My common sense also
> says that to me. Of >course it does not follows that
> nothing (or everythng) >makes sense.

Strange hashing of text here. ?

> QM is not for me: it is a linear way to perpetrate the
> reductionist model of physical sciences in ways not
> too approachable for common sense - as you said.
> Q-science: IMO (=in my opinion) an extension of the
> QM-nightmare.

Yes. But this is not only QM as a human mind activity.
It really seems that the world in which we live is just
like that (Who can be cruel enough to design a world
like that and have sensible creatures living into it?).

Yes also and indeed, the way of thinking I presented
fits within a reductionist framework. Nobody is required
to adhere to such a framework (and therefore to the way
of thinking I presented). If one rejects the reductionist
approach, all I can say isn't even worth reading it for
him. And, again, all of this is pure speculation.

> A physicist once retorted: "I can live with paradoxes"
> well, I cannot. I rather rely on MY common sense, even
> if it is "not on the level".

You are free to rely on whatever you want. However, it
seems that we have no choice about the world we live in.

>> [...]
>> I would not say that. I don't believe that numbers
>> are "there" for any purpose. They just are there (or
>> exist). But their existence might be all that we
>> need to explain the (perceived) existence of
>> everything else.
>
> Right you are: not the 'numbers' are there for any
> purpose, we use the idea of numbers in our logic for
> explanations substituting paradoxes with other ones.
> My question: "Are they (numbers) really there?" 0r
> they only exist in our sophistication and usage?
> [...]
> Of course they exist: we invented them so they exist.

I would say that we discovered them. The argument (a
weak one I concede) is that we did not have so much
freedom while doing so. We find and proved that the
Fermat's conjecture was true and we *could not* find
that is was false. This constraint is intemporal and
it exists whether there are men or not and even
whether there is something or not (but there cannot
be nothing because there is least this constraint).
The set of such constraints is likely to include or
define that natural numbers themselves.

>> not only natural numbers but also real numbers,
>> Hilbert spaces and all the "higher level objects"
>> that "comes with".
>
> As you said above: "this is speculation indeed".

Indeed, I identified at least four speculations on
which the explanation rely upon. I don't see for
any of them any way to rationally make an opinion.
I did not find for any of them any decisive argument
for or against and I can't even imagine on what such
an argument could rely upon (indeed, common sense is
excluded). Furthermore, it happens that many people
sharing the same biology and even the same culture
have very different opinions about them.

>> Let's also consider the possibility that the
>> universe in which we live strictly follows some
>> "mathematical rules" and that it is completely
>> determined by them (this is another speculation).
>
> I don't think this is attributable to English: in all
> languages people speak in reverse: The universe (or
> whatever Bruno may call it) does not FOLLOW any rules
> that humans derive from their ways of thinking -
> explaining the (easily misunderstood) observations. We
> observe, evaluate (right or wrong) and deduct "rules"
> (again right or wrong). As long as they do not bounce
> into contradiction, we pride ourselves by "nature is
> following our rules". When the tachyons showed higher
> speed than 'c' the verdict was "wrong observation",
> not a speed exceeding Einstein's assumed limit for
> nature.

This is a speculation. It might be that the universe
in which we live is completely ruled by mathematical
laws. Indeed one can doubt of that or believe it but I
can't see how this can be either proved or refuted.

>> This is equivalent to say that this universe is
>> isomorphic to one of the above mentionned "higher
> level objects".
>
> Nice words. Do they mean something?

This means something to me. I would say that meaning
is relative to individuals or group of individuals.
I understand that this might not mean anything to
other people just as what other people sometimes
refer to has no precsie meaning to me.

>> The last and hard point is that, from a mathematical
>> point of view, all the objects that are isomorphic
>> one to another are the same mathematical object (just
>> as there is only one set of natural numbers, no
>> matter how is is built) and, if the universe is
>> isomorphic to a mathematical object, it could just be
>> this mathematical object.
>
> I think I can decipher what you wrote (?), firstly:
> "from a mathematical point of view" (if not, not).
> Isomorphic requires the ONE set of characteristics we
> are 'allolwed' to use, while 'nature' is unrestricted.

I don't understand you here.

> Then do not miss your "IF" - and 'if not'?
> I still do not understand "mathematical object" but
> that is the feebleness of my common sense mind.

This a bit strange. Usually common sense tends to
have people believe in such things as mathematical
objects (like natural numbers or Hilbert spaces for
instance). Mine do so for me. Commen sense is a
strange thing.

>> Let's consider an outrageously simplified view of
>> the universe as particles interacting with each
>> others according to a set of mathematical laws. The
>> mathematical structure of the universe is likely to
> be >much more complex than that but the following
> might >still be correct when applied to a more complex
>> structure.
>
> I don't know about 'particles', they are the figments
> of the explanations for ununderstood phenomena. Try to
> reduce them into their ingreients: no particle is
> left, unless you call a (hypothetical?) quark a particle.

That was the idea. That particles might not exist
as such does not prevent the universe to have a
mathematical structure and I mentionned that this
was a (possibly very) simplified view.

> I "made" macromolecules for 50 years: now I see that
> there are no such 'things' - only we assume them for
> effects (phenomena?) we think to perceive. No atoms
> either. But they have their mathematics.

I agree on that. But that do not prevent the universe
as a whole to have its own mathematics too (and even
a mathematics that would be "reflected" in many
"phenomenons" that can be observed/conceived by us).

>> The problem with the idea that the universe could
>> simply be a mathematical object is that our common
>> sense strongly suggest that a physical universe has
>> to be different from a mathematical object because
>> there is to be "something in the particles" to
>> "make them real". ...
>
> I skip the rest, this is NOT my way of thinking, so I
> do not discuss it here.

OK. Is this because you reject a reductionist view?

>> ...why should there be some "magical substance"
>> inside the particles? Isn't that enough that they
>> follow the rules? What more could bring the presence
>> of "something else" inside the particles? What the
>> idea of an "internal substance" could add to any
>> explanation? Isn't this idea just irrational and
>> similar to the concept of "soul" in a dualist view?
>> Isn't even that a kind of dualism?
>
> I like that a lot, thank you Georges.

Thanks to you too.

> Unfortunately my mailbox did not take more and wrote:
> == message truncated ===

Strange. I forward the remaining in another post.

Georges.

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Received on Sat Mar 11 2006 - 05:00:46 PST

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