Personally the notion that all that exists is comp & information - encoded
on what though? - Is not especially troubling for me. I understand how some
cling to a fundamental material realism; after all it does seem so very
real. However when you get right down to it all we have is measured values
of things and meters by which we measure other things; we live encapsulated
in the experience of our own being and the sensorial stream of life and in
the end all that we can say for sure about anything is the value it has when
we measure it.
I am getting into the interesting part of Tegmark's book - I read a bit each
day when I break for lunch - so this is partly influencing this train of
thought. By the way enjoyed his description of quantum computing and how in
a sense q-bits are leveraging the Level III multiverse to compute every
possible outcome while in quantum superposition; a way of thinking about it
that I had never read before.
Naturally I have been reading some of the discussions here, and the idea of
comp is something I also find intuitively possible. The soul is an emergent
phenomena given enough depth of complexity and breadth of parallelism and
vastness of scale of the information system in which it is self-emergent.
Several questions have been re-occurring for me. One of these is: Every
information system, at least that I have ever been aware of, requires a
substrate medium upon which to encode itself; information seems describable
in this sense as the meta-encoding existing on some substrate system. I
would like to avoid the infinite regression of stopping at the point of
describing systems as existing upon other and requiring other substrate
systems that themselves require substrates themselves described as
information again requiring some substrate... repeat eternally.
It is also true that exquisitely complex information can be encoded in a
very simple substrate system given enough replication of elements... a simple
binary state machine could suffice, given enough bits.
But what are the bits encoded on?
At some point reductionism can no longer reduce.... And then we are back to
where we first started.... How did that arise or come to be? If for example we
say that math is reducible to logic or set theory then what of sets and the
various set operations? What of enumerations? These simplest of simple
things. Can you reduce the {} null set?
What does it arise from?
Perhaps to try to find some fundamental something upon which everything else
is tapestried over is unanswerable; it is something that keeps coming back
to itch my ears.
Am interested in hearing what some of you may have to say about this
universe of the most simple things: numbers, sets; and the very simple base
operators -- {+-*/=!^()} etc. that operate on these enumerable entities and
the logical operators {and, or, xor}
What is a number? Doesn't it only have meaning in the sense that it is
greater than the number that is less than it & less than the one greater
than it? Does the concept of a number actually even have any meaning outside
of being thought of as being a member of the enumerable set {1,2,3,4,... n}?
In other words '3' by itself means nothing and is nothing; it only means
something in terms of the set of numbers as in: 2<3<4... <n-1<n
And what of the simple operators. When we say a + b = c we are dealing
with two separate kinds of entities, with one {a,b,c} being quantities or
values and {+,=} being the two operators that relate the three values in
this simple equation.
The enumerable set is not enough by itself. So even if one could explain the
enumerable set in some manner the manner in which the simple operators come
to be is not clear to me. How do the addition, assignment and other basic
operators arise? This extends similarly to the basic logic operators: and,
or, xor, not - as well.
Thanks
>>Those kind of questions are more less clarified. You cannot prove the
existence of a universal system, or machine, or language, from anything less
powerful, but you can prove the existence of all of them, from the
assumption of only one. I use elementary arithmetic, because it is already
taught in school, and people are familiar with it.
Sure..... keep it simple; I am all for the KISS principle - an American
programmer's vernacular which stands for "keep it simple & stupid" or the
more abrasive version "keep it simple stupid" - either way KISS
I am all for distilling away intervening complexity and orthogonal aspects,
in order to drill down into a problem space and abstract out the essential
qualities of interest.
Even as simple as:
0, 1
00, 01, 10, 11
000, 001, 010, 011, 100, 101, 110, 111
Incredible software is built from this simple base operating with an equally
spare simple set of basic logic gates.
>>The "TOE" extracted from comp assumes we agree on the laws of addition and
multiplication, and on classical logic. From this you can prove the
existence of the universal numbers and or all their computations, and even
interview the Löbian numbers, on what is possible for them, in different
relative sense.
I am not disputing this. More than most I understand how vast complex
layered, nuanced systems can and in fact are built up from just a few very
simple elements. And our universe has just a few score naturally occurring
elements; and all elements are comprised of a few kinds of quarks (6) and
leptons (2).
I would say the evidence points to complexity as being an emergent phenomena
arising from vast parallelization and z-order over-laying of systems over
systems (like an onion) of a sparse simple set of basic blocks or perhaps
bits.
It seems both logical to me that this is so - the evidence for this emergent
quality for complex systems can be found everywhere - the language of life
itself (as we know it) has but four letters for example.
So, math comes from arithmetic, and arithmetic can explain why it is
impossible to explain arithmetic from less than arithmetic, making
arithmetic (or Turing equivalent) a good start.
I understand how hard it would be to explain arithmetic without employing
it... that it is fundamental in this way. Perhaps one could attempt to do so
using set theory - if one accepts the notion that a mathematical theory is
reducible to say a set theory.
But - whatever - at some point there is a simplest system/theory that cannot
be reduced to being an emergent phenomena of an even more simple
system/theory... in this I suspect we more or less agree.
God created the Integers. All the rest came when God added "Add and
Multiply".
Basically.
I could ask the four year old question and ask then who created "God?"
But fair enough - although my wife might disagree at times I am not four
years old and I believe you are using the metaphor "God" as the ineffable,
foundation of everything... or am I mistaken?
Chris
Bruno
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