On 18 Nov 2014, at 18:34, John Clark wrote:
On Mon, Nov 17, 2014 Bruno Marchal <marc...@ulb.ac.be> wrote:
>> Maybe Schrodinger's Wave Equation doesn't interfere either, only
other worlds do,
> ?
!
>> and maybe the wave equation is just a way, and certainly not the
only way, humans have of describing that interference between worlds.
> Indeed,
Then why the "?" ?
Probably because I did not parse well the sentence above, and the term
"world" is a but fuzzy in this context. But I guess we are OK.
> You know positivist physicians still alive? Who?
Every physicist alive uses both Heisenberg's Matrices and
Schrodinger's Wave;
OK, and other pictures and formulations of QM too.
none use Positivism or any other school of philosophy because no
philosophical franchise is of the slightest help in doing what
scientists want to do, figure out how the world works.
I disagree. The collapse axiom, which is still in amost textbook, and
which is used by bad pedagog to avoid hard question, is a
philosophical axiom relying on a religious belief: the belief that
there is only one physical universe, and that we are unique.
Some physicists used it as a rule of thumb, and as a way to not do
philosophy, but of course, that is eventually like a use of God-gap
type of explanation.
> In math and physics, it is frequent that two apparantly different
theories are equivalent,
Yes, just like Heisenberg's Matrices and Schrodinger's Wave, they
both tell a story with a identical plot they just use different
symbols in the vocabulary of mathematics to do so, just as 2 books
about World War 2 tell the same story but use different symbols in
the vocabulary of the English language to do it; however neither
book about World War 2, no matter how good, is World War 2. I said
it before but it's worth repeating, maybe we should take seriously
and think through the implications of what mathematicians have been
saying for years, mathematics is a language.
Mathematics use a mathematical language, but is not a language itself.
You can use different language to describe a similar mathematical
reality. You can use the combinators, or the sets, to *represent* the
natural numbers, and admit quite different axioms, but you will get
the same facts, for example that the number of ways to write an odd
natural number as a sum of four square is given by 24 times the sum of
its odd divisor. Like the product scalar does not depend of the
orthonormal base, in linear algebra, the truth of the arithmetical
statements do not depend on the theory and language used to describe
them. It is the same for computer science, which is actually a branch
of number theory. Some machines will stop on some input independently
of the language used to describe those machines and input.
> but that does not make the thing described into a convention or
language.
True. A electron is not a convention or a language, but what about
a description of the electron written in a particular dialect of the
language of mathematics, like the Schrodinger Wave Equation? Yes
Schrodinger's Equation does a good job describing the behavior of a
electron, but Dirac's Equation does better, and Feynman's sum over
histories even better. And some equations do a terrible job
describing the electron even though the are grammatically correct
sentences in the language of mathematics, that is to say they are
logically self consistent. So maybe you can not only write true
descriptions of the electron in the language of mathematics maybe
you can also write the equivalent of a Harry Potter novel in the
language of mathematics. Maybe Cantor's infinities and the Real
Numbers are mathematical Harry Potter novels. Actually I kinda doubt
it but maybe.
Sure. but may be electron are only useful fiction to get the voltage
right for the working of my fridge. Here math and physics are alike,
and it asks some familiarity with the subject to develop an intuition
of what might be conventional and what might be a deep truth
independent of the subject.
> On the contrary, it points on something real beyond the language.
But that's exactly what I was getting at, maybe it points to
something real beyond the mathematics.
I was meaning "it points on something real and mathematical beyond the
language.
I don't insist that is true, maybe mathematics is more than just a
language, but maybe not, I believe it's worth thinking about. Unlike
philosophers who are always certain but seldom correct I just don't
know.
The choice of a theory might be conventional, but some truth will not
depend on that choice. And with computationalism, I explain that even
physics is "theory independent". You can use the axiom of arithmetic,
or the axiom on combinators, and the existence of 24, or of electron,
will not depend on it. A bit like most truth in linear algebra don't
depend on the choice of the base.
It is not a convention that 17 is prime. It really means that you
cannot divide 17 to make some rectangle from it. If math was
conventional, there would not be any conjecture, like the Riemann
hypothesis, or the twin prime conjecture. Then Gödel's theorem
justifies that the arithmetical truth is beyond all possible
theoretical formalization of it, and this, imo, gives grain to realism
in math, against conventionalism.
Bruno
John K Clark
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