From: everything-list@googlegroups.com
[mailto:everything-list@googlegroups.com] On Behalf Of Bruno Marchal
Sent: Saturday, March 01, 2014 12:44 AM
To: everything-list@googlegroups.com
Subject: Re: If it's all math, then where does math come from?
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.
What about sets {0,1…n}? Isn’t the conceptual entity of the set necessary in
order to map orders of operation for example grouping operations of lower
precedence to ensure they are performed first for example; or for ordering
enumerable or at least identifiable entities into groups that have some set of
characteristics.
Also are you arguing that the ≠ & = comparators suffice? What about “<”? A
lot of algorithms (sorting for example) are implemented in terms of the “<”
comparator, that would seem very difficult to do without.
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.
I am unfamiliar with this axiom.
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.
Given enough parallelism and depth of recursion; given a vast enough networked
system, it is amazing what emerges. I agree in principal that all that is
really required is some very basic computationally self-catalyzing system and
the rest emerges.
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.
Okay that one stretched my brain like a balloon as it waved trough my neural
net. What if one admits the possibility retro-causality? Physicist as eminent
as Wheeler & Feynman have speculated on it and Huw Price has suggested that it
could explain quantum entanglement.
Maybe there is no base… and reality itself emerges out of some process of
retro-causality … okay maybe this is a little far out…. The serpent eats its
tail.
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.
I am meta-interested J
Chris
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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