On 01 Mar 2014, at 07:16, Chris de Morsella wrote:
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;
If you agree that 1+1=2, then you can prove that universal numlbers
exists, and those will defined the relative implementations of
computational histories.
We have top start from some theory, in all case. And the TOE that we
can derived from comp are just the minimal part common to basically
all scientific theories.
Then we can explain even why we cannot explain where our beliefs in
the number comes from. The theory of Lakoff presumes implicitly
numbers, and much more.
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.
We can start from:
0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
We don't need more. Just definitions.
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?
Elementary arithmetic is enough. But the two axioms Kxy=x + Sxyz =
xz(yz) too.
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?
Math is not reducible to a theory. machine's math is already not
reducible to a theory. Nor are machine's knowledge.
Computationalism refutes reductionism of most conception we can have
on numbers and machine.
What of enumerations? These simplest of simple things. Can you
reduce the {} null set?
What does it arise from?
In this case you can reduce it to number theory.
Your point seems to be that we must start from something non trivial,
and you are right on this. My point is that if we believe that the
brain is a sort of machine, then arithmetic is not just enough, but
more is non sensical or redundant at the basic level.
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.
Arithmetic is enough if you can believe in comp, and plausibly too
much or not enough if comp is false.
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}
You need much less. I will soon (or a bit later) explain explicitly
how to derive matter and mind from
0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
with comp at the meta-level.
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.
You seem to be unaware that the whole computer science is part of
arithmetic. the axioms above can already proves all you need for the
ontology, and then physics/psychology is explained as internal
appearance for relative numbers.
But if comp is true we can prove that we will never understand where
the numbers come from. We must suppose at least one Turing universal
system, and I chose numbers as people are familiarized with them.
Bruno
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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