John M wrote:
>
> Georges, your post is "on the level", I am not <G>
> I am still in common sense with my feeble
> thinking-tool.
Sorry, I am not a native english speaker, I don't understand
what "on the level" can mean (and especially with quotes).
In don't understand either what you mean by "<G>".
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.
> Which leaves me with a question - please see inserted.
> (I erase the rest of the lengthu discussion)
>
> --- Georges Quenot <Georges.Quenot.domain.name.hidden> wrote:
>> 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'>
>>>
>>> *SKIP
>>> 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.
> SKIP
>>> 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.
>
> So the numbers are only 'there' to explain the
> existence of everything else.
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.
> What else must be there to provide such existence -
We come here to the hard part of the story. My point is that
nothing else needs to be there to provide such existence (this
is a speculation indeed). I will try to keep it simple. Let's
assume that numbers exist (this is a speculation at that point),
not only natural numbers but also real numbers, Hilbert spaces
and all the "higher level objects" that "comes with".
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).
This is equivalent to say that this universe is isomorphic to
one of the above mentionned "higher level objects".
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.
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.
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". We think that particles needs to have a mass,
an electric charge, ... But do they follows mathematical rules
thanks to these properties or do these properties appear as
such because they actually follows such rules? Since the
behavior of particles is determined by the mathematical rules,
what difference can make what they actually are made of? And
do they need to be made of something? Whatever they would be
made of would have no impact at all on what we see and feel
as soon as they follow the mathematical rules. All their
properties would be defined in the same way from these rules
and only from these rules and what they are made of wouldn't
have any effect at all. The "substance" of the particles could
very well come from the rule and only from them. We feel such
a substance but it might come from the rules and only from them.
Once we have started thinking according to this point of view,
the charge of proof can be reversed. Occam's razor is here to
ask: 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?
Last but not least: this view has the advantage that we no
longer have to wonder how it comes that particles follows the
rules, how can a particle influence another particle and so on.
The situation reversed here too. There is no more necessary
magic involved.
This is the last but one speculation. The last one is that our
thinking and consciousness emerge from the operation of matter
(that particles are empty or not). This one is more common even
if not widely accepted. It might be the more puzzling one.
What can be said about it is that what needs to be explained
is not physical existence but the perception of a physical
existence. This is (much) weaker and comes quite easily from
the combination of all the previously mentionned speculations.
Indeed what we perceive comes from the "structures" occuring
from the applications of the rules and the same rules simply
makes what we perceive appear as a physical reality.
Finally, Stephen Hawking compeletely missed the point by asking
"What is it that breathes fire into the equations and makes
a universe for them to describe?". He fooled himself just as
if he asked "Who created the world?". Common sense can be very
hard to escape to. There is no need for anything/anybody to
breathe fire into the equations: the fire *is* in the equations.
> which then you want to assign to the numbers?
I do not understand what you mean here.
> What I really asked: WHAT is the operator? without one
> the numbers just 'sit there as numbers.
Not soo sure. The natural numbers jsut sit there bu so do also
the addition and multiplication as operators from NxN into N.
So do also the Hilbert space with all the operations that makes
it an Hilbert space.
> Numbers do not
> "decide" to add up or else themselves into complex
> constructs (including 'ourselves') Do they?
Indeed they do not but who said they did or the needed to?
The addition operator may just sit there with the natural
numbers. The couple that contains the second and the first
also just sit there as a semi-group and so on. Nobody has
to do any operation for that. All the complex constructs
just sit there. The fact that we perceive them as constructs
is related to the way we think of them. We ca exhibit some
relations between them that appear to us as construction
processes but that does not mean that they need us to just
sit there all together.
>> SKIP
> I feel that gap here:
>> 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.
>
>> But do we need to actually believe in any of these
>> speculations?
>
> I feel we have a discussion here. Do we just speculate
> to entertain ourselves with unbelieved ideas, or some
> of us take it seriously to speak about 'real' ideas?
I asked the question but I did not intend to suggest that
the answer should be "no". I find the above mentionned
speculations and the developments above them quite
entertaining. I am not sure that I am really willing to
believe into them but currently I did not find any better
alternative.
Georges.
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Received on Thu Mar 09 2006 - 18:58:55 PST