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  1. Hi all, I was recommended Lee Smolin's book Three Roads to Quantum Gravity, and was wondering if I could get a few thoughts on a couple selections to clarify some issues. My first question is, is Smolin's interpretation/definition of a discrete space pretty well agreed upon? What I mean to ask, is his definition of a discrete space essentially agreed upon and invariant, or are there other drastically opposed conceptions of a discrete space? In other words, when a physicist talks about 'discrete space', can it take on a fundamentally different picture than the one Smolin describes here? My second question is simply if anyone can help clarify what Smolin is trying to say. It seems I can't help but fall into what he notes is the 'wrong way to think' about it. Any help would very much be appreciated. Thanks, and peace, Mike
  2. Hi ajb, I appreciate what you say here, and your taking the time to address these questions. Trying to find the simplest and therefore most general part or aspect of reality has been physic's main goal as I understand it, extending back to the atomism of the Greeks. But I wonder if, taken to the very extreme, such a search will ultimately prove to be meaningful. Not that we shouldn't try, since the limited results obtained are always insightful. But whatever set of axioms we glean from the universe, it seems logically that there will always be more, since any proposition seems to inescapably lead to more propositions and a synthesis of these propositions ad infinitum. It seems to me that theoretical physics is ultimately trying to get us to the simplest conceivable principle or object. But how would we know it if we saw it? What would it really mean to find it? It seems that the simplest thing we can imagine, is nothing at all: zero dimensions, zero extension, etc. Such objects or whatever-you-call-its would be the ideal thing to work with. But do such objects explain nothing? But really, what would it really mean to find an elementary particle or whatever? Would they fit the category of 'object' or would it be 'something' much different than that? In my understanding, a truly "fundamental" particle or philosophical atom, which many physicists seem to identify with what are commonly called the elementary particles, cannot fit the definition of a "thing" or "object" since they would have no structure or substructure. I question whether it makes any physical or even logical sense to posit something, using the category of "object" or "thing", that is not made of anything else, that is an irreducible or intrinsic object. It stretches the meaning of the word 'object' too far for me to find any meaning in it. And it is a contradiction in terms, I feel, that has been entertained for a long time. Thanks for reading, Mike
  3. I'm interested in what this might mean philosophically and physically apart from mathematical formalisms on paper, because I realize that theoretically we can speak of zero-dimensional objects and point-particles. But it strikes me that these manifolds would exist immaterially as Plantonic- or as pseudo-objects, rather than as material/physical objects. I'm also not sure how to take these points and manifolds as being 'isolated' or 'intrinsic objects', because if they were, in the senses that I think of 'isolated' and 'intrinsic', then there'd be no sense in speaking of them. They'd be their own reality all by themselves. These are, of course, my own impressions rooted no doubt in the imprecise nature of words, and I do not project them onto the content of your responses. Thanks, Mike
  4. You can say that again. I find it very difficult to find meaning in the idea of an object (a point or a space) with zero dimension. I'm not saying there isn't any, just that I don't understand it. To my mind such spaces would be completely immaterial, and there would either be an infinite amount of space between each one or no space and therefore distinguishing between them would be meaningless. How could they ever 'add up' to the universe we see? When we speak of these points and such, are we talking about anything close to a traditional 'thing' or 'object' that composes larger, macroscopic things, or is it something fundamentally more abstract and/or immaterial than that? You've certainly given me a lot of ideas to look further into. On a philosophical level, I personally find the notion of a finite universe to be the more compelling choice. But I'm very much unable to visualize what it means to have arrived at a fundamental discrete 'part'. The question always arises, well what would that then be made of, or why can't you just make it smaller or break it apart? Of course this is assuming a very billiard-ball type object. Or any classical object. The only way, to my mind, is to find a way out of having to ask that question by a more subtle way of thinking about the problem - and I'm very sure modern physics has done quite a bit of that. Thanks, Mike
  5. Hi ajb, thanks for the response. You wrote, And Like I said I am not educated in physics. Could you help me visualize this? What does it mean for a space to have zero topological dimension, classically speaking? If it has no dimension, what is it that we're describing? As for quantum physics, what does it mean for spaces to not be 'set theoretical objects' and unable to be described by points? I guess what I'm trying to wrap my brain around the idea that there is a smallest unit of space, because I immediately visualize some thing/object with dimensions. If it is a thing with dimensions then it cannot be fundamental, can it? Mr. Skeptic calls it digital. If the idea here is that there is some limitation on how reality can operate (it must manifest itself wholly or not at all: quanta) this makes sense to me, though in a yet very fuzzy way. Forgive my metaphysics but it is my only substitute for the math. Thanks for the input, Mike
  6. Hi everybody, I have a question about the whole idea that space/spacetime is fundamentally discrete. It's been in the back of my mind since I first encountered it, because I still don't have any clear understanding of what it means. Keep in mind that I have absolutely no understanding of physics beyond some popular science books. So my question is, what does it mean, if anything, for space to be fundamentally discrete? Does it mean that space is broken up into tiny parts? Physically what can it mean to have arrived at a smallest part? Or is it something more subtle than that? Thanks for any input! Peace, Mike
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