On 25 Dec 2013, at 21:35, Edgar L. Owen wrote:
Bruno,
Correct me if I'm wrong about where you are coming from in your
basic approach.
OK. Some other did already a good job.
Bruno seems to believe that mathematicians discover a math that
already exists in reality (as opposed to math being a human
invention which is the alternative view).
Compared to most scientists, I am realist on only a tiny part of
arithmetic. Comp can be much less realist than most scientists, but
sometimes being more realist shorten the proofs, and indeed that is
how the observers accept new axioms from times to times.
Thus he believes that reality itself is a mathematical structure
Not at all. You miss the main point.
The doctor needs realism in arithmetic to just explain to the patient
what is meant by a digital brain, and what is Church's thesis.
Then I just show that IF you believe that you can survive with it (in
whatever reality exists making the turing emulation relatively
possible) THEN the TOE is given arithmetic (or any Turing equivalent
universal system), and physics become an arithmetical relative
measure problem.
It is a theorem. Not an idea that I propose because I would find it
elegant.
which 'contains' in some sense all of the math that mathematicians
have come up with, and no doubt much more to be discovered. Thus he
believes that ANY correct mathematical theory can be validly applied
to reality to generate true results, which he does with facility.
On the contrary, no mathematical theory at all can exists on numbers
and machines. You confuse the mathematical theories, and the intended
reality describe by those theories. We know today that the
arithmetical reality cannot be described entirely by any effective
theories.
However there are a number of problems with this theory.
I don't want to look presumptuous, but it is a theorem, thus in a
theory, which assumes *much* less than most existing theories.
It seems you do favor computationalism, so you apply or not the
theorem. Or if you disbelieve it you can search a flaw.
For one thing the edifice of human math is static, it just sits
there waiting for humans to apply it to something,
Now you are more realist than me. mathematicians evolves all the time,
and the human mathematics changes all the time.
It even deepened vertiginously.
whereas the math that actually computes reality is active and
continuously runs like software.
Math does not compute. It is mathematicians which proves theorems.
They don't compute either, even if *they* are computed at some level.
A computer computes. Universal numbers can compute relatively to
universal numbers. Computations can be seen as type of arithmetical
relations.
There is, in my view, no evidence at all for any math in reality at
all except for what is actually running and computing reality's
current state.
Hmm, Read the UDA. here you are close to digital physics, or the idea
that reality is a computation, but the UDA shows that this cannot
work. We cannot singularize first person by their computational
states. They are distributed in many computations.
Therefore most of human math is NOT going to be applicable to the
math of reality. One can't just apply the results of any human math
theory to reality and expect it accurately describe reality. Instead
of trying to applying Godel, Church, etc. etc. etc. to reality one
has to actually look at the actual computations reality is executing
and see what they tell US, as opposed to what mathematicians try to
tell them. This is basic scientific method and is the correct
approach.
Gödel, Church concerns digital processes, and many of their extensions
on constructive ordinals. It is very general. It has nothing to do
with humans, I mean, no more than the Boson H, or the galaxy Andromeda.
Church thesis makes the notion of universal machine very general, and
completely arithmetical, and independent of us or any aliens.
That is much more independent of us than Andromeda.
Anyway, I don't defend a truth, only a theorem. What I explain is not
a question of agreeing or disagreeing, but of understanding or finding
a flaw, which can be fatal or corrigible.
So my repeated point is that human math and reality math are
different.
Of course, and doubly so, as human math is plunged in "reality math".
Of course they share some fundamental logic. But human math is a
structure that was first approximated from the math of reality,
The math of reality, or the real math?
I think that you confuse mathematical structures and the theories
describing such mathematical structures. this will not help you to get
the nuance when we treat the study of mathematical theories,
mathematically. It is the difficulty of mathematical logic.
but then widely generalized and extended far beyond what reality
math is actually computing in the process losing some of the actual
essentials of reality math.
For example all computations in reality math are finite with no
infinities nor infinitesimals since reality is granular at its
elemental level and nothing actual can be infinite.
You seem to assume a finite primitive physical universe? Frankly, it
is not clear what you assume.
The human math number system is a generalized extension of reality's
number system which is more subtle as there are no numbers that just
keep going forever (pi) to greater and greater accuracies far
greater than the scale of the universe. And there may well be no
zeros in reality math, since we could expect reality math to compute
only what actually exists.
You seem to talk like if you knew what is reality.
But if you do science, you should make clear what you assume, what is
your theory, what are the method allowed in your derivation, etc.
Basically reality math is a particular program running in reality
that computes the current state of reality.
That is digital physics. It can't work.
All the other programs that don't actually run and whatever math or
logical results they may be based upon have no relevance and cannot
be blindly applied to reality math.
Programs don't run or not run. That is a relative notion in the
arithmetical reality.
The programs can be implemented in the physical reality, in which
case, they run relatively to our running, relatively to our most
probable computations, among infinities of them.
Therefore let me respectfully suggest that Bruno needs to examine
the actual math of reality that is actually computing reality, and
use his mathematical skills to elucidate that, rather than
automatically trying to apply the results of human math without
examining whether they actually apply.
Study the theorem before making patronizing remarks.
And then never do patronizing remarks, as they weaken your point in
the infinite. Always focus on the point.
Bruno
Edgar
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