On 11 Sep 2010, at 00:42, Stephen P. King wrote:
Hi Bruno,
-----Original Message-----
From: everything-list@googlegroups.com
[mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal
Sent: Friday, September 10, 2010 11:16 AM
To: everything-list@googlegroups.com
Subject: Re: What's wrong with this?
On 09 Sep 2010, at 14:37, Stephen P. King wrote:
Hi Bruno,
My thought is to look at the transformation group around which some
property is invariant to act as a generator of the properties of the,
say, quark.
[BM]
Good idea. That is related with the importance of group theory and
(soon) category theory in physics.
For simple numbers this would be a permutation over fields, one field
per number,
[BM]
Why? We may have use combinators instead of numbers. Their role are
intensional, and representational. Their intrinsic mathematical
structure
certainly plays some role, but I don't see why to use them directly to
mirror physics. Even if that works (by chance) it would hidden the
mind-body
problem. Of course it might be very interesting, and the relation
between
physics and number theory suggest that such approach have their
merits.
[SPK]
YES!!! You nailed it! Let me paste a little note here that I just
wrote up. I apologize in advance for the crudeness of this.
***
Integers as Arithmetic Equivalence Classes and implications
by S. P. King
9/10/2010
Zero-ness
_______
0 + 0 = 0
0 - 0 = 0
0^1 - 0^1 = 0
1 - 1 = 0
2 - 2 = 0
3 - 3 = 0
...
0 x 0 = 0
_______
One-ness
_______
0 + 1 = 1
1^1 + 0 = 1
1 - 0 = 1
1^1 - 0 = 1
2 - 1 = 1
3 - 2 = 1
4 - 3 = 1
.
1 x 1 = 1
2 / 2 = 1
3 / 3 = 1
4 / 4 = 1
.
_____
Two-ness
________
1 + 1 = 2
1^1 + 1^1 = 2
0 + 2 = 2
3 - 1 = 2
4 - 2 = 2
5 - 3 = 2
.
4 / 2 = 2
6 / 3 = 2
8 / 4 = 2
..
_______
Etc.
External symmetry = 3rd person aspect.
Each Class has aleph_null tuples and thus has the same cardinality.
We could use the permutation symmetry over the cardinality to
identify an
external or 3rd person notion of Integer. This would generate a
notion of
that is an Integer that is invariant to a change from one of the N
classes
to another.
What would be the internal symmetry?
Internal Symmetries = 1st person aspect.
Note that we can substitute equivalent elements of the tuples with
each other by the use of bracketing or some other push/pop method.
This
would ultimately show that the tuples are combinations of "images"
of each
other's elements so that there is 1) no primitive atom and 2) that the
pattern of similarities and differences over this tapestry of
combinatorics
would encode the operations of Arithmetic. Property 1 is the reason
I use
non-well founded set theory, by the way...
*************
It is difficult for me to follow. In ZF there is no atom, yet it is
well-founded. Non well-foundedness is motivate by introducing set
having themselves as elements, or having elements having elements ...
having elements having the starting set as an element.
It is my suspicion that the mind-body problem is caused by a lack of
understanding of what is involved. It is far too easy to throw up
one's
hands and settle for some silly eliminatism; Ignorance is Bliss.
Notice that
both the internal and external symmetry notions here yield a kind of
indefiniteness that Plotinus would point to, as per your
discussions, to
define Matter.
You should elaborate, but you should make clear the relation between
math and philosophy/theology.
But what about the information content itself of the
relations themselves? Is Information identical to Indeterminateness?
Information is a tricky word having different meaning in different
theories. It can be a measure of surprise, like in the old Shannon
theory, or something related to meaning, like in logics and in the
press. We can relate all that, but then we have to be almost formal
for not falling in the traps of non genuine analogies.
It
seems to me that the answer is a resounding NO! I claim that it is
its Dual.
Thus I advocate a form of mind-matter dualism in terms of an
Information-Matter dualism following the lines of the Pontryagin and
Stone
dualities. http://en.academic.ru/dic.nsf/enwiki/327868
You may elaborate, but Stone dualities are very technical hard matter.
I guess you are alluding to Vaughan Pratt's work on Chu Spaces.
but this seems to not really resolve the question entirely.
[BM]
I am not sure I have a clear idea of the question, here.
[SPK]
Am I making any sense so far?
It
makes me suspicious of the entire Platonic program, for what would
act
as the universal generator of "twoness" as distinguished from
"threeness" be in-itself? Why not some kind of nominalism that
transforms asymptotically into universalism?
[BM]
You lost me.
You know how I work. I start from an assumption about some link
between
consciousness and Turing 'machine', and from this I derived step by
step a
frame which is closer to Plato and Plotinus than to Aristotle, at
least on
the "Matter" notion.
[SPK]
Yes and I use the assumption that any 1st person "content" of
consciousness can be show to be equivalent to the content of some
virtual
reality generated by a Turing Machine (given with sufficient physical
resources)
But this has been shown not working. You cannot both capture
consciousness by Turing machine states, and at the same time to invoke
a notion of physical resource. It is the whole point of most of my
posts. Physical resource including space and time have to be recovered
from the math of (abstract) computer science.
and following your arguments will agree that while the content
itself is computable, *which one of the computations it is* that is
the
actual generator of the particular content of a particular point of
view is
not computational.
I am OK, here.
These thoughts tie back to the point about
indeterminateness that Plotinus brilliantly made and you point out.
Yes. Note that the idea of relating matter to indeterminacy is already
in Aristotle. Alas, Aristotle and/or its successors have reified it
metaphysically. That is, imo, what makes the mind-body problem
insolvable.
Your modelization so far seems to only consider a "frozen"
perspective and there is scant mention of how the model is extended
to cover
a plurality of entities, except for the diamond^alpha aspect mentioned
below. As far as I can tell, your Model offers a logical structure
to a new
version of the individual Leibnizian Monad (
http://www.iep.utm.edu/leib-met/#H8 ) that I am trying to develop,
but only
in the static sense. There is no dynamic in it.
The 'sensible' modalities, like Bp & p, and Bp & Dp & p, introduces an
internal dynamic. S4Grz is not just a logic of knowledge, it is a
logic of evolving knowledse, or time. It is due to the "& p". It makes
the first person intuitionist, the builder of its mental reality.
I think that this is
intentional since you are taking an explicit Platonic Idea stance in
the
Modelization of Plotinusian Statics. I appreciate that, but
understand that
unless we can derive change from changelessness within our
modelizing we are
doomed to eliminatism when it comes to our 1st and 3rd notions
temporal
transitivity, duration and causality.
That's right, but the nice thing is that the first person notion
automatically provides an internal dynamics.
It is my contention that it is
impossible to derive change from changelessness,
Even physicalists can accept this though. Many physicists don't
believe in time. It emerges for local observers when embedded in the
block-static reality.
Of course we accept the (non trivial) ordering of the natural numbers,
which can be seen as the Mother of all computational times.
but the converse is easy to
show.... Leibniz himself made this mistake so I do not fault you too
much.
;P
BTW, I really enjoyed reading your SIENA paper. My only comment on
it
is that I wish you would elaborate more on the diamond^alpha t aspect
because that is where plurality obtains.
[BM]
Thanks. Actually I think, but I'm still not quite sure, that the
"^alpha"
feature should explain the graded aspect of the quantum logics,
which should
explains the origin of the tensor product, of the plurality of
dimension,
and eventually the (quantum) structure of space-time. The many
worlds are
more due to the extreme redundancy of the computational histories in
arithmetic.
[SPK]
In the quantum logic that I have studied so far there is the fact
that there are an infinite number of instantiations (not sure if
that is the
right word) of Boolean algebraic structures within a sufficiently
general
Quantum Logic propositional lattice. See:
http://en.wikipedia.org/wiki/Quantum_logic This might be the place
where
plurality obtains.
One of my interests is in looking at the extension of Qlogic that
has a Local instead of a Global change (time = measure of change)
parameter.
So far I think that I have an idea but it is still only embryonic. I
am
looking at whether or not it is possible to use the notion of
families of
parameters or functors that preserve the bijective map from density
operators to density operators which is convexity preserving between
pairs
of Quantum systems, where the QM system is taken as a Monad. Right
now I
need to figure out what would generate the convexity. I know that I
lack
much of the sophisticated knowledge needed to do this quickly, so my
work is
very slow.
I wish you good luck.
Bruno
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to everything-l...@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
