Hi!

On 9/19/2011 5:24 AM, Bruno Marchal wrote:

On 19 Sep 2011, at 08:27, nihil0 wrote:

Hi everyone,

This is my first post on the List. I find this topic fascinating and
I'm impressed with everyone's thoughts about it. I'm not sure if
you're aware of this, but it has been discussed on a few other
Everything threads.


Welcome to the party! Please feel free to express your ideas and thoughts. :-)

Norman Samish posted the following to the thread "Tipler Weighs In" on
May 16, 2005 at 9:24pm:

"I wonder if you and/or any other members on this list have an opinion
about the validity of an article at http://www.hedweb.com/nihilism/nihilfil.htm
. . ."

I would like to continue that discussion here on this thread, because
I believe the article Norman cites provides a satisfying answer the
question "Why does anything exist?," which is very closely related to
the question "Why is there something rather than nothing." The author
is David Pearce, who is an active British philosopher.

Here are some highlights of Pearce's answer: "In the Universe as a
whole, the conserved constants (electric charge, angular momentum,
mass-energy) add up to/cancel out to exactly zero. . . Yet why not,
say, 42, rather than 0? Well, if everything -- impossibly, I'm
guessing -- added up/cancelled out instead to 42, then 42 would have
to be accounted for. But if, in all, there is 0, i.e no (net)
properties whatsoever, then there just isn't anything substantive
which needs explaining. . . The whole of mathematics can, in
principle, be derived from the properties of the empty set, Ø" I think
this last sentence, if true, would support Tegmark's Mathematical
Universe Hypothesis, because if math is derivable from nothing (as
Pearce thinks) and physics is derivable from math (as Tegmark thinks)
and, then physics is derivable from nothing, and presto we have a
theory of everything/nothing.

I think Pearce's conclusion is the following: everything that exists
is a property of (or function of) the number zero (i.e., the empty
set, nothing). Let's call this idea Ontological Nihilism.

Russell Standish seems to endorse this idea in his book "Theory of
Nothing", which I'm reading. He formulates an equation for the amount
of complexity a system has, and says that "The complexity [i.e.,
information content] of the Everything is zero, just as it is of the
Nothing. The simplest set is the set of all possibilities, which is
the dual of the empty set." (pg. 40) He also suggests that Feynman
acknowledged something like Ontological Nihilism. In vol. 2 of his
lectures, Feynmann argued that the grand unified theory of physics
could be expressed as a function of the number zero; just rearrange
all physics equations so they equal zero, then add them all up. After
all, equations have to be balanced on both sides, right?

Personally, I find Ontological Nihilism a remarkably elegant,
scientific and satisfying answer to the question "Why is there
something instead of nothing" because it effectively dissolves the
question. What do you think?

Thanks in advance for your comments,

I think I could agree with this reasoning so long as the explanation does not go to an argument for meaninglessness. While we can accept that in the totality of existence all differences dissolve and this the expressibility itself of our questions vanishes, this should not be used as a reasoning to abandon the possibility of meaningfulness at our level of existence. A similar argument and response exists on the nature of Time. While all notions of temporal transitivity vanish in the limit of a total system, as exemplified by the Wheeler-Dewitt equation <http://arxiv.org/abs/physics/9806004>, this does not act to void finite subsets of the Totality from having a real notion of time as a measure of change <http://faculty.uca.edu/rnovy/Aristotle--Time%20is%20the%20Measure.htm>. A great article discussing this particular reasoning can be found here: http://arxiv.org/pdf/gr-qc/9708055


We have of course already discussed this a lot.
In a nutshell, you cannot derive anything just from the empty set alone: you need some mathematical principles or axioms, like the comprehension and the reflection axioms. This leads to an axiomatic set theory, which is nice but somehow too much powerful. But OK, set theory is already a Löbian observer, and you can derive everything from this, although you still need some definition, notably of the internal observers. Assuming mechanism, to proceed in that direction, then, as I have often explained, you get the derivation of everything including a notion of "God" (truth), souls and the precise laws of physics (but this is a sequence of hard number theoretical problems, yet the conceptual solution already exist. Note that such a derivation is not a derivation from nothing: it is a derivation from the empty set + rich powerful axioms. I use traditionnally 0, successor, addition, and multiplication (in this list), but the combinators + application are quite handy for that task too. Note also, that, contrary to what Tegmark defined, if mechanism is correct, the physical universe is not a mathematical structure, but more the border of something which can be made 99% into a mathematical structure, together with a non reductible element, which is related to the theological aspect of consciousness. The theory of everything becomes the mind theory of the (universal) numbers, and physics appears to be a sum or measure on all computations. In that setting nothing and everything are equivalent dual notions, but they makes sense only in some theory with some rules of manipulation of the concept of nothing (like 0, or the empty set, or the quantum vaccum: but this last one is assuming too much, and I have provided an argument showing that we have to derived it from numbers (or from combinators) if we want to be able to explain both the qualia and the quanta. See my URL for proof of those statements if you are interested.

What about the axiom of choice? Is it included in the collection of necessary mathematical principles that are needed for our derivations/explanations of cosmogony <http://en.wikipedia.org/wiki/Cosmogony>? It is becoming clear that we need a principle that acts to induce a measure algebra on our universes of entities as the usual axiom of choice has a fatal flaw <http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox>. One possibility is to use the property of compactness to generate the needed finiteness via the idea expressed here:

http://en.wikipedia.org/wiki/Locally_compact

"All discrete spaces <http://en.wikipedia.org/wiki/Discrete_space> are locally compact and Hausdorff (they are just the zero <http://en.wikipedia.org/wiki/0_%28number%29>-dimensional manifolds). These are compact only if they are finite."

My thought is that the requirement that the Stone duals of our abstract algebras (which would include all of our notions of mechanism!) are given as compact and (via Pontryagin duality <http://en.wikipedia.org/wiki/Pontryagin_duality>) discrete spaces. When and if compactness does not naturally exist, the compactness can be induced by the use of the Stone-C(ech compactification <http://en.wikipedia.org/wiki/Stone-Cech_compactification>.

Some notes on this idea:
From http://en.wikipedia.org/wiki/Locally_compact


     The point at infinity

"Since every locally compact Hausdorff space /X/ is Tychonoff, it can be embedded <http://en.wikipedia.org/wiki/Embedding_%28topology%29> in a compact Hausdorff space b(/X/) using the Stone-C(ech compactification <http://en.wikipedia.org/wiki/Stone-Cech_compactification>. But in fact, there is a simpler method available in the locally compact case; the one-point compactification <http://en.wikipedia.org/wiki/One-point_compactification> will embed /X/ in a compact Hausdorff space a(/X/) with just one extra point. (The one-point compactification can be applied to other spaces, but a(/X/) will be Hausdorff if and only if <http://en.wikipedia.org/wiki/If_and_only_if> /X/ is locally compact and Hausdorff.) The locally compact Hausdorff spaces can thus be characterised as the open subsets <http://en.wikipedia.org/wiki/Open_subset> of compact Hausdorff spaces.

Intuitively, the extra point in a(/X/) can be thought of as a *point at infinity*. _The point at infinity should be thought of as lying outside every compact subset of /X/._ Many intuitive notions about tendency towards infinity can be formulated in locally compact Hausdorff spaces using this idea. For example, a continuous <http://en.wikipedia.org/wiki/Continuous_function_%28topology%29> real <http://en.wikipedia.org/wiki/Real_number> or complex <http://en.wikipedia.org/wiki/Complex_number> valued function <http://en.wikipedia.org/wiki/Function_%28mathematics%29> /f/ with domain <http://en.wikipedia.org/wiki/Domain_%28function%29> /X/ is said to /vanish at infinity <http://en.wikipedia.org/wiki/Vanish_at_infinity>/ if, given any positive number <http://en.wikipedia.org/wiki/Positive_number> /e/, there is a compact subset /K/ of /X/ such that |/f/(/x/)| < /e/ whenever the point <http://en.wikipedia.org/wiki/Point_%28geometry%29> /x/ lies outside of /K/. This definition makes sense for any topological space /X/. If /X/ is locally compact and Hausdorff, such functions are precisely those extendable to a continuous function /g/ on its one-point compactification a(/X/) = /X/ ? {?} where /g/(?) = 0.

The set C_0 (/X/) of all continuous complex-valued functions that vanish at infinity is a C* algebra <http://en.wikipedia.org/wiki/C-star_algebra>. In fact, every commutative <http://en.wikipedia.org/wiki/Commutative> C* algebra is isomorphic <http://en.wikipedia.org/wiki/Isomorphic> to C_0 (/X/) for some unique <http://en.wikipedia.org/wiki/Unique> (up to <http://en.wikipedia.org/wiki/Up_to> homeomorphism <http://en.wikipedia.org/wiki/Homeomorphism>) locally compact Hausdorff space /X/. More precisely, the categories <http://en.wikipedia.org/wiki/Category_theory> of locally compact Hausdorff spaces and of commutative C* algebras are dual <http://en.wikipedia.org/wiki/Duality_%28category_theory%29>; this is shown using the Gelfand representation <http://en.wikipedia.org/wiki/Gelfand_representation>. Forming the one-point compactification a(/X/) of /X/ corresponds under this duality to adjoining an identity element <http://en.wikipedia.org/wiki/Identity_element> to C_0 (/X/)."

Querry:

Is this idea invertible such that we can consider the notion of an observer as 'existing at' or 'being a homunculus' at the point as infinity. What would allow the 'Cartesian Theater' schemata a means to generate this identification, if possible? Does the 'infinite regress' that we see in the hall of mirrors act as a finite approximation of the property of"lying outside every compact subset of X" ?

This follows the line of reasoning that Bruno explained above in the sense that the missing .0000..1% is that "point at infinity" necessary for compactness of manifolds as used in our physics to represent space-time and its content. Additionally, it makes the concept of an ideal 'observer at infinity' coherent and resolves the kinds of problems that people like Daniel C. Dennett have pointed out. It also gives us a natural way of expressing the sets of sets of sets of .. that we see in the representation of numbers as " empty set + rich powerful axioms" that Bruno mentions. For example see: http://www.math.utah.edu/~pa/math/sets.html


In a nutshell: we have still to postulate some primitive elements. Assuming the empty set + some rules, is equivalent with assuming all the sets, or all the numbers. Once you have all the numbers (or all the sets) you can derive the quanta and the qualia, by assuming the mechanist hypothesis (or any of its multiple weakenings).

Bruno, I am unable to read your paper titled "Theoretical computer science and the natural sciences", as it is behind a paywall. (http://www.sciencedirect.com/science/article/pii/S1571064505000242 ) therefore I need an alternative source that discusses the mechanism thesis that we can quote from to avoid unintentional straw men. Would the wiki article, found here http://en.wikipedia.org/wiki/Mechanism_%28philosophy%29 and/or http://en.wikipedia.org/wiki/Digital_philosophy, suffice?


We cannot explain the numbers (or the sets) in any theory which does not postulate them. This is well known by mathematical logicians. So it looks like the numbers constitute an irreducible mystery.

Bruno



Would it not be a wonderful coincidence if this irreducible mystery of number was just a counterpart of the apparent irreducibility of matter? Any finite expression of existence would have both a concrete implementative expression and an abstract qualitative expression once we understand the relation between the abstract (for example: numbers) and the concrete (for example: particles).

A nice article on the problem that we are considering can be found here: http://www.spiritone.com/~brucem/666.htm

Onward!

Stephen





Jon

On Aug 8, 2:40 am, Roger <roger...@yahoo.com> wrote:
    Hi.  I used to post to this list but haven't in a long time.  I'm
a biochemist but like to think about the question of "Why isthere
something rather than nothing?" as a hobby.  If you're interested,
some of my ideas on this question and on  "Why do things exist?",
infinite sets and on the relationships of all this to mathematics and
physics are at:

https://sites.google.com/site/ralphthewebsite/

An abstract of the "Why do things exist and Why istheresomething
rather than nothing?" paper is below.

    Thank you in advance for any feedback you may have.

Sincerely,

Roger Granet (roger...@yahoo.com)

Abstract:

   In this paper, I propose solutions to the questions "Why do things
exist?" and "Why istheresomething rather than nothing?"  In regard
to the first question, "Why do things exist?", it is argued that a
thing exists if the contents of, or what is meant by, that thing are
completely defined.  A complete definition is equivalent to an edge or
boundary defining what is contained within and giving “substance” and
existence to the thing. In regard to the second question, "Why istheresomething rather than nothing?", "nothing", or non-existence, is
first defined to mean: no energy, matter, volume, space, time,
thoughts, concepts, mathematical truths, etc.; and no minds to think
about this lack-of-all.  It is then shown that this non-existence
itself, not our mind's conception of non-existence, is the complete
description, or definition, of what is present.  That is, no energy,
no matter, no volume, no space, no time, no thoughts, etc.,  in and of
itself, describes, defines, or tells you, exactly what is present.
Therefore, as a complete definition of what is present, "nothing", or
non-existence, is actually an existent state.  So, what has
traditionally been thought of as "nothing", or non-existence, is, when
seen from a different perspective, an existent state or "something".
Said yet another way, non-existence can appear as either "nothing" or
"something" depending on the perspective of the observer.   Another
argument is also presented that reaches this same conclusion.
Finally, this reasoning is used to form a primitive model of the
universe via what I refer to as "philosophical engineering".

--



http://iridia.ulb.ac.be/~marchal/




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