On 05 Jun 2015, at 20:35, John Clark wrote:
On Fri, Jun 5, 2015 Bruno Marchal <[email protected]> wrote:
> "Event" is a physical notion. Algorithmic non compressibility is
an mathematical notion.
An event is just a place and a time; are you saying that mathematics
is incapable of handling 4 coordinates?
Of course, applied mathematics exists, and you can represent event in
mathematics, but you shopuld not confuse something (a physical event)
and its mathematical representation.
>> Nothing caused the 9884th digit of a random number to be a 6
rather than some other digit, and that is the one and only reason it
is NOT algorithmically incompressible. But something did cause the
9884th digit of PI to be a 4 and not some other digit, and that's
why PI IS algorithmically compressible.
> I have a counter-example to your claim. Fix a universal system. It
determines completely its Chaitin number, yet it is algorithmically
incompressible.
I don't know what you mean by "fix"
I mean choose one. If you take a Fortran universal interpreter, you
can define its Chaitin number. The Chaitin number is relative to the
choice of a universal system.
but if something requires an infinite number of steps to determine
what it will do its not very deterministic.
It is, when you agree to apply the excluded middle on the arithmetical
proposition, or actually it is enough to believe that a closed Turing
machine stop or does not stop.
> In some post you argued once that comp1 is trivial,
Bullshit. I have never argued anything about "comp1" and never will
because I'm sick to death with "comp" of any variety.
?
I remember you said that comp as I meant it is trivially, true, is
wrong (btw). If you don't remember what you post, the conversation
might loss its meaning.
Bruno
>> If time or space is quantized as most physicists think it is then
the real numbers are just a simplified approximation of what happens
in the physical world.
> Typically, physical quantization is defined by using complex
numbers.
Because even if space and time are quantized the discrete steps are
so little that complex numbers are a good approximation of the
physical world unless you're dealing with things that are ultra
super small.
> But again, the point was just that CT does not refer to physics.
Bullshit.
>> Computationalism says you can make matter behave intelligently if
you organize it in certain ways,
> That is a rephrasing of computationalism, and what you say follow
from it, but the more precise and general version is that you stay
conscious [...]
To hell with consciousness! Figure out how intelligence works and
then worry about consciousness.
>> maybe that matter is primitive and maybe it is not but there has
been a enormous amount of progress in recent years with AI
demonstrating that Computationalism is probably true. There has been
zero progress demonstrating that mathematics can behave intelligently.
> Mathematics does not belong to the category of things which can
behave.
That is a HUGE admission on your part, if it is true (and I don't
know if it is or not) then the debate is over and physics is more
fundamental than mathematics. End of story.
> But mathematics, and actually just arithmetic can define relative
entities behaving relatively to universal number
And I can define a new integer that has never been seen before, I
call it "fluxdige" and it's definition is that it's equal to 2+2 but
it's not equal to 4. You can't make a calculation with a definition!
>> Nobody has shown the existence of primitive mathematics either.
> Primitive means that we have to assume it. Logicians have prove
that arithmetic, or universality, is primitive in the sense that you
cannot derive arithmetic, or the existence of universal numbers,
without assuming less than that.
When Peano came up with the integers he had to first assume that the
number 1 existed and then he came up with rules to generate its
successor, but if the physical universe did not exist, if there were
ZERO things in it, then it's not at all obvious that the number 1
would exist. Maybe it would and maybe it wouldn't, I don't know. One
of your Greek buddies Socrates said that the first step toward
wisdom is knowing when you don't know. So if Socrates was right
then I'm wiser than you are.
> Computations have been discovered in mathematics. All textbooks in
the filed explains that.
You can't make a computation with a textbook!
> You can't make a calculation with a definition!
> You can.
Then stop talking about it and just do it!
> And if it is simple enough, you can do that mentally. You will
tell me that in this case we still need a physical brain
Indeed I will.
> but this can be a local relative notion,
Local? A good rule of thumb is that if a theory says "Local" means
the entire multiverse then things may be getting out of hand.
>> I say "compute" means figuring out an answer, nobody has ever
done this without using matter that obeys the laws of physics.
> You are right, but this does not prove that the notion of matter
is used in the definition of computation.
Who cares about the damn definition? You can't make a computation
with a definition!
> To do something materially we need matter
Yes, but if mathematics is more fundamental than physics it's not
obvious why that should be the case.
> PA and formal systems compute things without doing the computation
physically.
Bullshit.
> Kleene invented his famous predicate and got his normal form
theorem for the computable function by using the arithmetical
existence of the computations only.
Then why isn't there a Kleene Computer Corporation with a trillion
dollar valuation?
>> If you know how to make such a calculation don't tell me about it
just make the calculation. Just do it.
> KKK ===> K
Oh I see the light at last, that explains everything! If you want
to be a trillionare you'd better file a patent on "KKK ===> K"
immediately.
> That arithmetic is more fundamental than physics will be a non
trivial consequence of computationalism. The point is that this is
testable.
That is true it's testable, the test is to make a computation, any
computation, without using matter that obeys the laws of physics. Do
that and the debate is over, mathematics is more fundamental than
physics. End of story.
John K Clark
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