On 01 Feb 2014, at 14:39, Edgar L. Owen wrote:
Bruno,
You have a very strange view of arithmetic if you think it "is full
of processor cycles".
It is the standard understanding of computer science. That is
understood (by the theoricians) since Gödel 1931 (symbolically, as
some have seen this before, and some have made the point more
transparent, and stronger later).
Can you explain how that works? It seems to imply an innate notion
of time.
You need the ordering 0, s(0), s(s(0)), ... that you can derive from
the first axioms:
0≠s(x) (for all x)
x≠y -> s(x) ≠ s(y), (for all x, and y).
and
x + 0 = x (for all x)
x + s(y) = s(x + y), (for all x, and y).
x < y van be defined by
Ez(y + z = x & (z ≠ 0))
This gives already a digital time which can be used to defined the
step notion for the computations.
A computation is the sequence of steps of a universal machine when
emulated by another universal machine.
As elementary arithmetic is Turing complete, we can take elementary
arithmetic as the base system, and define computation in term of all
the universal numbers that we can define in arithmetic (we get them
all, by Church thesis).
It is long to define a universal numbers, and its computations, just
in terms of 0, s, + and *, but that can be done, and is done in most
textbook in theoretical computer science.
Note that I agree with this, it's my p-time, but block universe and
your block comp seem to be lacking it...
I still don't know what is your p-time. I still don't know if it is 1p
or 3p, mathematical or physical, etc.
PLease explain in PLAIN ENGLISH rather than your usual cryptic
notations and (undefined in the context) terminology..
Just ask when you don't understand, but you seem to ignore what is a
computation for a computer scientists.
You might read the original papers assembled by Martin Davis 1964. It
exists in the Dover edition now.
Or a good introductory book like the one by Neil Cutland. Or wait that
I rexplain the real basic 5cantor and Kleene diagonal) which unlike
logic, are rather simple, I think.
But a priori, computability has nothing to do with physics, or
physical implementation of computer. A computation is an intensional
relative (relational) number property.
Bruno
Edgar
On Saturday, February 1, 2014 3:27:08 AM UTC-5, Bruno Marchal wrote:
On 31 Jan 2014, at 13:13, Edgar L. Owen wrote:
Liz,
Your mouth sure has to move a lot to tell us it's not moving!
The problem is not that static equations DESCRIBE aspects of
reality. The problem is that you are denying the flow of time.
We deny a *primitive* and *ontological* flow of time. We don't deny
the internal experience of flow of time.
For equations to compute (not just describe) reality, there must be
active processor cycles. There is simply NO way around that...
Arithmetic is full of active processor cycles.
Bruno
Edgar
On Thursday, January 30, 2014 10:24:48 PM UTC-5, Liz R wrote:
Why do some people have such a problem with "how change can emerge
from something static" ? It's as simple as F = ma - a static
equation describing something changing. Change is by definition
things being different at different times. If you map out all the
times involved as a dimension, you will naturally get a "static"
universe, just as putting together all the moments making up a
movie gives you a reel of film - but only from a "God's eye
perspective". This is the perspective science gives us, the
perspective given by using equations and models and maps to
describe reality; it isn't the world of everyday experience, which
(at best) views those equations and so on from within (assuming for
a moment they are so accurate as to be isomorphic to reality).
Obtaining change from the static view used by science is a non-
problem, and has been since Newton published his Principia.
There are problems with comp, of course, like the "white rabbit"
problem. Does anyone have any new views on the real problems,
rather than worrying about straw men?
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