On 11/8/2012 10:04 AM, Richard Ruquist wrote:
The compact manifolds, what I call string theory monads, are more
fundamental than strings. Strings with spin, charge and mass, as well
as spacetime, emerge from the compact manifolds, perhaps in the manner
that you indicate below.


Hi Richard,

OK, but then you are thinking in terms that are different from the formal models that are in the literature. You will have to define all of the terms, if they are different. For example. How is the property of compactness defined in your idea? Why are the Calabi-Yau manifolds are topological objects that are part of a wide class of "minimal surfaces". There is a huge zoo of these in topology. See http://www.scholarpedia.org/article/Calabi-Yau_manifold

  The one difference from what you are
considering and the compact manifolds (CMs) that I can see is that the
CMs are fixed in the emergent space and not free floating- which in
itself implies a spacetime manifold.

If you have a proposal that explains how space-time emerges from the CMs, cool, but you have to explain it to us and answer our question. One question that I have is: What fundamental process within the compact manifolds enables them to generate the appearance of space-time. I think that you are assuming a substantiabalist hypothesis; that substance is ontologically primitive. There is a long history of this idea, which is by the way, the idea that Bruno and others -including me- are arguing against. This article covers the debate well: http://plato.stanford.edu/entries/substance/

Perhaps another is that from your discussion, it appears that all your
monads can be identical, whereas the CMs are required to be different
and distinct in order for consciousness to emerge from an arithmetic
of real numbers.

Why? What is acting to distinguish the CMs externally? You seem to assume an external observer or consciousness or some other means to overcome to problem of the identity of indiscernibles. http://plato.stanford.edu/entries/identity-indiscernible/ I think that your idea is not that much different from that of Roger and mine. I just would like to better understand some of your assumptions. You seem to have some unstated assumptions, we all do. Having these discussions is a good way of teasing them out, but we have to be willing to consider our own ideas critically and not be too emotionally wed to them.

  However since from wiki "Each Boolean algebra B has
an associated topological space, denoted here S(B), called its Stone
space" and "For any Boolean algebra B, S(B) is a compact totally
disconnected Hausdorff space" and "Almost all spaces encountered in
analysis are Hausdorff; most importantly, the real numbers",

No, actually. Real numbers are not Stone spaces. P-adic numbers, OTOH, are. http://en.wikipedia.org/wiki/Totally_disconnected_space#Examples


I contend
that your monads as well as mine must be enumerable-that is all
different and distinct.

Yes, they would be, but the idea that they are distinct cannot just be assumed to exist without some means for the information of that partitioning of the aggregate comes to be knowable. One thing that consciousness does is that it distinguishes things from each other. Maybe we are putting in the activity of consciousness into our explanations at the start!


I apologize for using wiki. But I confess that what it says is the
limit of my understanding.

I love Wiki, but I prefer other references if they can be found. It helps people to get a better idea of what is being discussed if they wish to drill down into the complicated ideas that we discuss here in the Everything List.

Any way what I propose is that all of what you say below may more or
less be appropriate for the compact manifolds of string theory if we
replace the dust with an array.

A dust is more simple - has less structure to be explained than an array. We can add structure to a dust to get an array, but we can get lots of other things as well. We need to be able to get smooth fields in some limit. Can an array do this?

Richard


--
Onward!

Stephen


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