Hi Mindey,
let me put it in this way.
You seem to agree that PI exists, and I see PI indeed as an existing
machine computing PI decimals, or measuring the era of a circle (with
radius 1).
So you are realist about arithmetic and even a bit more.
Then, you can already proves the existence of the UTM in elementary
arithmetic. The Turing machine is a mathematical notion, and with
Church thesis, the universal Turing machine is only one form of a
universal machine. Amazingly perhaps, elementary arithmetic is another
one. More amazingly some diophantine polynomials, even of degree four,
are Turing universal.
So elementary arithmetic is full of universal machines, ...
We have to assume at least one universal machine, or system, if only
has a base to talk about all the other. I use elementary arithmetic,
because it is taught in high school, but to avoid idolatry of numbers,
I use also the combinators.
There are also mazing mathematical chracterization, like the creative
set (of natural numbers) by Emil Post.
So it is easy to justify the existence of the universal numbers
(entities described by number; as I choose arithmetic as the universal
base).
The real problem is this one. if we are only universal machine, as the
computationalist hypothesis suggests, then we cannot know which
universal machine run us, but we can know that below our substitution
level, we must find the result of some statistical sum on all
computations, done by all universal numbers.
The physical reality cannot select the computation without betraying
the computationalist assumption, and so the physical reality has to
result from the invariant in the sum on all computations.
Now this is very difficult to define, but we can define at a more
abstract level the "probability one" on our consistent computational
continuations, and study its logic, which should be, and seems to be,
a quantum logic.
Like the mystic says: the truth (including physics and physical
worlds) is in your head.
I generalize: the truth is "in the head" of all universal number, and
you need just to listen to them to compare with what you see, think,
believe, etc.
Although they would probably put it in that way, the interview has
begun with Gödel in 1931, and culminated with Solovay with the
axiomatization two infinite interviews, what the machine can justify,
and what is true but that the machine cannot justify (the modal logic
G and G*).
Few people seems to know that some universal machine can "know" (in a
weak technical sense) that they are universal, and those machine can
prove their own incompleteness theorem, and understand the origin of
the contradictory intuition (the many intensional variant of G* minus
G) that they have about ourselves: they can discover the mind-body
problem, and solve it in some ways.
Good books are referred in my papers and biography of my thesis, or in
this list, or ask. Good authors are Boolos, Smullyan, Smorynski.
Boolos and Jeffrey made a good book on the main technic "Computability
and Logic".
Smullyan wrote a recreative introduction to self-reference and the
modal logic G. Mendelson is one of the best introduction to
mathematical logic.
Yes, that is the bad news perhaps, the subjects of UTM, and UMs and
other UNs belongs to mathematics (mathematical logic, theoretical
computer science). In fact it belongs to arithmetic and meta-
arithmetic, which plunges itself in a large part in arithmetic. From
inside, it is vastly bigger than arithmetic.
The Church-Turing hypothesis rehabilitates Pythagorus and Plato, but
changes the Platonia in the deep, it adds the Mandelbrot set, chaos,
indeterminacy, uncertainties. Living things live on the border of the
computable and the non computable in arithmetic.
There is someting which put *uncomputably* many more mess in Platonia
than an UTM: a couple of UTMs.
The universal machine is a bit the enfant terrible of mathematics.
(and not all mathematicians likes it).
Then the debate between God/not-God hides the real debate: is physical
reality real or is physical reality the border of something else?
With comp I argue we have not so much choice, if we want stay
rationalist: the evidence are that the physical percolates (somehow)
on the arithmetical). That is already testable, and somehow tested.
With computationalism, we are in the Matrix, or in the simulacron-III,
but we are actually in infinities of matrices. That is a problem.
Universal machines gives already a big hint to the solution. It is
more close to Plato-Plotinus-Pythagorus than Aristotle.
Reality is not WYSIWYG (assuming computationalism).
So: everything from nothing physical? Yes. We need only natural
numbers or combinators at the start. But in that frame it is still an
open question if our physical history (which are coherent glued
machines' dreams) starts from some physical nothingness, like quantum
vacuum. That remains possible, and it is open if that would be
geographical or really physical: does our histories have a finite or
infinite past? I don't know. Comp might suggest infinite pasts, but I
might misinterpret what the machine says, or extrapolate too naively
from the structure of the universal dovetailing.
Bruno
On 28 Mar 2015, at 10:22, Mindey I. wrote:
Hi Everyone,
so, my background: http://mindey.com/42 -- I always wanted to know its
origin precisely.
The understanding of the origin of Universe(=Everything, Multiverse,
and our Life experience included) was likely never fully successful.
Fundamental obstacle for succeeding in it has been the logical
inconsistency of the concepts "Origin" and "Universe", because an
attempt to explain Everything by Something, makes the Something part
of Everything, which leaves us with "Nothingness", as the only viable
candidate for "Origin".
Universe to us subjectively appears as a complex and diverse
experience. In fact, except for some regularity (which we call laws of
physics), the patterns we see every day appear so complex, that only
something like a universal computer with large memory could possibly
generate it. We had recently even done so by creating 3D computer
games and worlds running on Universal Turing Machines (UTMs) -- our
computers.
From here, we can conclude:
(1) It follows that, _if_ we could come up with a UTM from
"Nothingness", we could explain pretty much everything that is
computable.
Our experiences rely on finite numbers of receptors with limited
granularity (selectivity), and limited lifespan, which seem to imply
finite number of possible experiences (as their Cartesian product) by
a being.
(2) It follows that, our life experience is likely computable.
To come up with a UTM from "Nothingness", let's:
1. assume "Nothingness"
2. conclude "Equidistance"
(because "Nothingness" means equal absence of information regarding
any aspect whatsoever)
3. see the definition of a ball
4. see the computation of Pi number with varying precision, i.e.:
Remember balls from degenerate ones in low-dimensional spaces with
special coordinate systems and weird distance metrics, to quite
standard Euclidean ones, to hypersphere, to the most near-perfect
conceivable ball regading any information aspect whatsoever.
Unfortunately, we don't know if Pi is really equivalent to UTM,
because we had not yet solved the Normality of Pi conjecture, but
assuming it is Normal, to understand how your unique experience of
life could have arisen:
1. assume that your life experience is a finite number
2. conclude that it is in Pi.
However, if Pi is normal, then then the conclusion is not informative
at all, because we will find any finite string in it many times over.
It would be much more informative, if Pi actually is _not_ normal.
Any comments/errors?
Thanks,
Mindey
Related: discussion on Halfbakery:
http://www.halfbakery.com/idea/Explanation_20of_20Origin_20of_20Universe
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