Thanks to David Seaman and Bruno Marchel for acknowledging my posts.
Bruno wrote in response to:
>All
>mathematical structures necessarily have in common an existence.
This does not necessarily help. You could have said that all
mathematical structure have in common the fact that they ere equal
to themselves. But this does not help to give existence to the
set V = {x : x = x} in naive set theory.
You are making a mathematical structure a thing, so that the thing is
equal to itself. If you notice I write and propose ideas from what may
seem like an alien perspective to others, perhaps without normal
definitive sets. To me, infinity is not a series. Real time, for
example, distinct from measurable clock time, is simply one enormous
moment, without beginning or end.
Above I am saying that all mathematical structures exist undivided from
one another. All are here in the very same space we exist within. It is
a simple truism and for certain no argument can change this inevitable
truth. There is one physical Universe and one mathematical Universe,
un-divided by such things as universes that don't exist or mathematical
structures which don't exist. There is no meaning to the idea of
division between one structure and another, if there is no non-medium or
non-thing to divide them.
And yes, the physical and mathematical Universe are the same. Any TOE
must unify all structures into one whole, and so model the definite not
as a multiplicity of worlds or things; a grande total sum, but rather as
a synthesis of many lesser parts of one grande whole, such as positive +
negative = a neutral whole.
Because we interpret the world to be many things, we think of the
maximum universe as the maximum number of things, rather than a
synthesis of positive and negative and so two sets of infinities.
We cannot bend our ordinary math, based upon the existence of definite
things, toward understanding a Universe of infinities. The axioms do not
allow it, since zero is nothing and numbers count an endless array of
things without completion. Example: the sum total of a positive infinity
(counting up indefinitely) and a negative infinity (counting down
indefinitely) is of course an indefinite sum. As well, to make things
worse, since zero is defined as no definite things, the sum, if we allow
ourselves to imagine a sum, it produces a cancellation, a sum of
nothing, when in fact the whole is a synthesized combination, an
everything, which by nature is not relative to anything but its internal
self (as a friend of mine, Steven Kaufman would say).
Mmmh... My (humble) opinion is that "existence" is relative.
Well, definition is relative, but existence is not relative. All
positive numbers and all negative numbers are relative. But zero is not
relative . You are not alone. Collectively we see and describe only the
defined world of things as real in physics and math.
Existence appears indefinite because it doesn't have an opposite. This
is the precise reason everyone believes existence is relative, because
we think the world is made of things and that whatever is without
definition is not existent. Still, the laws of physics break down at a
singularity, where there is no longer a distinction between time and
space. It isn't that there is no such thing as a singularity. Rather it
is that infinity in nature is not a definitive process like the infinity
of ordinary mathematics. It is an actuality. And, for example, an
infinity of time (without beginning or end) is a singularity of time,
not a progression.
>There is no such thing; no meaning to the
>anomalous idea that something doesn't exist.
I like the idea, but I would put in in the relative way. Everything
exists for the genuine observer who can look at things from
some angle. I would say that there is no meaning to the
anomalous idea that something doesn't absolutely exist, except that
I don't believe in square circle or transcendantal fraction.
Good point. This is what many people say to the argument that there is
no such thing as non-existence.
Please notice that what I am saying, the argument that existence is
inevitable, without beginning or end, and is without opposite, because
non-existence cannot be, also applies to the idea of a square circle.
Separately non and existence have meaning. I can put the two words
together... non + existence and say the word non-existence, but together
the words form a contradiction in terms. No word can represent non-being
because there is no such state. There is no something that does not
exist. There is no meaning for the words to represent.
Similarly, the idea of a square circle also mixes two meanings to form
what has no meaning. There is no meaning to the idea of a square circle.
But it isn't that a square circle does not exist. For that idea, that it
doesn't exist, also has no meaning.
Hopefully you might sense just a bit what happens to one's view of
reality when the idea of non-existence is removed. You might consider
being aware of how often you use the notion and how integrated it is in
your thinking. Doing so certainly has had a profound effect on myself
and its exclusion has allowed me to be very productive in theoretical
cosmology, and some mathematical ideas, even without a good education.
This matter also has much to do with why I think of the universe and
reality as the stuff of knowing or meaning.
David Seaman wrote:
Devin, you are very welcome to make such an interesting interpretation,
but
the three equations were meant to be read from the rather dry point of
view
of information theory.
Do you mean that the statement sum(everything) = 0, means something
different than I interpreted it to mean. I interpreted 'sum' as a
combination of, 'everything' as all that exists, and then I recognized
that the use of zero was not consistent with the axiom or ordinary
meaning of mathematical zero as nothing or no things.
I don't agree with seeing fundamental issues through a complex series of
ideas, (an example being the anthropic principle) over a simple study of
the basic meaning of such words as everything, nothing, or existence.
sum(everything not known by conscious subjects) = 0
means that the parts of information space not observed by conscious
subjects are likely to be equivalent to white noise. Any tests carried
out
by a hypothetical outside observer would show zero information content.
This is because the part of information space available to conscious
subjects is probably of measure zero on the whole of information space.
Again, which 0 do you mean? 0 as nothing; white noise; no information,
or 0 as the combined sum of everything.
I would say that zero is being torn in half as we venture into MWs
theory. We are exacting a great deal of abuse to the concept of zero
these days.
Zero is in my mind is the most fundamental axiom of math, physics,
philosophy, and yet we presently use it, especially in cosmology,
without consistency, in ways that its meaning changes vaguely back and
fourth between a finite count of things and a total measure of the all.
We constantly refer to the infinity of things, worlds, whatever, and no
one is saying that its all unreal, yet the sum total is somehow seen as
void and indefinite, as we default back to zero as nothing.
The intuition that I expect everyone who believes in MWs shares yet
cannot reconcile on a mathematical or non-intuitive level is that
sum(everything) = 0. We do this because of one reason that is I admit
difficult to discuss and resolve. That which is exists. Anything that
exists is part of, and undivided from the whole of existence. There are
no border lands of non-being or non-matter separating worlds. It is all
inevitably one thing, one existence. Only from such a base can we move
forward.
Back to Bruno who responded to:
>There is no such
>alternative. There is only being. That existence becomes what we think
>of as a mathematical system and all mathematical structures are subsets
>of the one elementary math.
Euh ... This is a little too vague.
I assume you mean existence becomes what we think
of as a mathematical system... is vague.
Okay. First simple.
Everything, The Infinite, Universe, all could mean the same thing or
refer to the same base of existence. Each is a different way of saying
the same thing. Note that there is no more fundamental meaning than
existence. Out of that base comes the relative or defined. The most
basic and simple ideas or concepts are something and nothing. Like
positive and negative mathematical values they are relative and
contradictory. All that is defined is synthesized within either
something or nothing. As well, something and nothing are contained
within everything or existence. Again notice the simplicity of meaning.
Consider that there are two versions of binary coding: (0,1) and (0,-1).
Now more complex. I tried to clarify two different ways of describing
the value of 0 in a recent post. There is the 0 = nothing of ordinary
mathematics (or 0 things) and there is a very different system of values
where 0 = sum of everything which for years I have called symmetry math.
Sum(everything) = 0
Positive + Negative = 0 = neutral
Positive whole + Negative whole = 0
Infinity = 0 (Not axiomatically possible or describable in
ordinary mathematics)
New Axiom: 0 = sum of all reality =
0 does not mean nothing or non-existence, absence, vacuum,
or void
0 means indefinite, same as undefined, same as non-polar,
same as neutral
0 means whole, complete, finished, same as singularity
0 means not many but one thing, one whole, oneness
New mathematical axiom: 0 = sum of all other numbers and values
=
0 = Largest value in system
1 = Less than zero
0 = whole infinity
1 = must be smaller than 0 or infinity
1 = ?
1 = Combined sum of all real numbers also except (-1) is
missing
2 = Combined sum of all real numbers except (-2)
(-1) = Combined sum of all real numbers also except (1) is
missing
Sum of all numbers except (-2) = 2
(1,2,3...) all numerics other than zero in system are
infinite values less than 0
Counting up into larger numerics = smaller value
Larger numerics converge in value toward infinitely small
value
Smallest value in system = +oo or -oo (note: relates to
point of infinite density)
Smallest value still is an infinity
+oo = half of whole
Smallest value in system still equals half of whole
+oo or -oo both definite infinite values, not processes, but
numbers
+oo and -oo represent duality, definition, and thingness
+oo and -oo are positive and negative singularities
0 or oo is a neutral singularity (Omega zero)
(+oo) + (-oo) = 0 = oo
This is possibly difficult to accept, but I am proposing that ordinary
math reflects an abstract view of the world as many things, and that it
is secondary to a more primary mathematics. By no means am I suggesting
that the world of things is unreal or an illusion. The defined or
relative world is real but it is not fundamental. Existence is primary
or elementary. Definition and relativity is secondary.
There is a mathematical system which measures definition and there is a
mathematical system derivable from the mathematical value that is
existence i.e. infinity.
I believe the mathematical system of infinities described above is
similar to Cantor's Transfinite math, yet different. I haven't studied
Cantor as much as I would like to, but from what I have read and heard,
Cantor didn't clearly establish an absolute infinity, and am fairly
certain there is no whole spectrum, such as a smallest to largest
cardinal. I don't believe the series of cardinals was ever directly
related to the mathematical plane as an alternate set of axioms.
I said existence as a mathematical system. In Symmetry math the absolute
set or absolute infinity is very clearly defined as zero. The smallest
possible infinities are +oo and -oo, yet each is half of the whole. Each
is a synthesize of all the positive numbers and all the negative numbers
(all other numbers are formed by the combination of positive and
negative values i.e. +1 equals a synthesis of all the positive numbers
and all the negative numbers except (-1)).
I relate this system of values directly to basic meanings and the
physical universe of space-time. I believe +oo and -oo are equivalent to
something and nothing. I believe the point of infinite density
(positive) in our past is +oo, or half of the whole, and that the
universe expands and cools toward absolute zero because of an influx of
negative into that original positive.
You computer gurus should like these elementary infinite numbers, since
the same ideas relate to binary logic 0 (oo) and 1 (+oo), except that
all those bit words are countered by an alternate universe of 0 and -1
(-oo). I would think this would relate to computation theory. Has anyone
considered an inverse set of computations? I am just now reading about
computation theory in Deutsch's Fabric of Reality.
Devin Harris
Received on Mon Jul 19 1999 - 02:02:05 PDT
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