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Post 0

Monday, April 19, 2004 - 11:13pmSanction this postReply
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Whether or not space is Euclidean--isn't that a question for physicists, and not philosophers?



Post 1

Tuesday, April 20, 2004 - 11:38amSanction this postReply
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Mr. O'Connor,

Given that modern "fysicists" today are bent on "disproving" the Law of Identity via their "thought experiments" and inherently flawed theories on the "origin" of the Universe, I do not think them qualified to investigate this question in the slightest. Try envisioning more than three spatial dimensions or more than one time dimension. It is impossible; it is contrary to one's first and most fundamental empirical data, that which sets the stage for all further observation. It is this data that first leads to an implicit understanding of the Law of Identity and is inherently linked to it.

I am
G. Stolyarov II




Post 2

Tuesday, April 20, 2004 - 12:29pmSanction this postReply
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Though I don't agree with all possible aspects of the Stolyarov quote, I do agree with his perspective on "multiple dimensions" and would call attention to the fact that this is one of the issues outlined in my SOLO article "Errors of Modern Science," which see. I regard the issue, not as a scientific, but a philosophic one of the relation of mathematics to the realities to which it is applied.




Post 3

Tuesday, April 20, 2004 - 2:49pmSanction this postReply
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What about the idea that space is curved?  Isn't that a possibility?  I don't think a philosopher can decide whether or not space is curved--that would require actually doing some careful experiments.

I read about an experiment Gauss did once where he measured the angles on some enormous triangle, whose vertices were the peaks of three hills, or something like that, and he checked to see if the angles added up to 180 degrees.  That's the kind of experiment I'm talking about. 




Post 4

Tuesday, April 20, 2004 - 5:52pmSanction this postReply
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This is a good question, Daniel, and I will try to reply soon, perhaps by tomorrow. Of course, philosophy can never set itself up to deny real-world observations or their more direct and indubitable implications. On the other hand, the special sciences depend on philosophy in order not to go off the rails and start misinterpreting their results!




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Post 5

Tuesday, April 20, 2004 - 6:40pmSanction this postReply
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G.

...three-dimensional Euclidean space, has remained in existence infinities back.
 
Since I am not sure if your quote is meant to be entirely technical or is in part rhetorical, these questions may not apply, since I am assuming technical.

Do you mean that space itself is "three-dimensional?"

Since you say it "remained" and is "in existence" does that mean you think of space as an existent? Since every existent has an identity, which is all of its qualities, what are the qualities of space? (Perhaps you only mean space is the concept for the relationship between entities, that is their positional relationships.)

Do you imply by the plural, "infinities," there is more than one infinity, and did you actually mean eternities?




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Post 6

Wednesday, April 21, 2004 - 10:44amSanction this postReply
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The seriousness given to the multiple dimensions theory is an unfortunate development. It's purpose is to "make the math work" and I've heard arguments that the reason we don't observe 5th, 6th, and higher dimensions is because they "fold in" on each other, whatever that means; that they had greater importance during the universe's infancy than they do now. The whole notion is convoluted and I suspect it's born out of a rushed attempt to explain universal forces when there is still not enough information available.



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Post 7

Wednesday, April 21, 2004 - 11:22amSanction this postReply
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Eddie:
 
Curled higher dimensions are not that difficult to picture by analogy.  Think of the surface of a taut rope.  It would appear to have one linear (uncurled) dimension.  Upon closer inspection will see that it has a second dimension, its surface which is curled around the linear dimension.
 
You are correct that the math is driving this speculation about higher dimensions.  But this is not just any math.  It is the mathematics of superstring theory which presently offers the best prospects of unifying the laws of quantum mechanics with relativity.  In the past such unification failed because of the convention of treating the fundamental particles of matter as non-dimensional points when in fact they must occupy some minimum amount of space.
 
Only by actually accounting for the space that fundamental particles MUST occupy, by means of string theory, have we've gotten closer to unifying the laws of physics.  This has lead to some interesting ideas that spacetime may consist of 11 dimensions, only three of which are unfolded, and that space and time are not continuous but quantized.  Another interesting thought is if higher dimensions do exist at the quantum level, that may explain the appearance of uncertainty there.  We can view events at the quantum level only in three dimensions, so we may not see all aspects of a quantum event at a given point in time, because some aspects may be hidden from our view at that moment in higher dimensions.
 
Interesting stuff.  The real question is whether an experiment can ever be designed to prove any of this.  That remains the biggest challenge right now.
 
Regards,
Bill a.k.a. Citizen Rat




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Post 8

Wednesday, April 21, 2004 - 8:48amSanction this postReply
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I don't see anything wrong with invoking extra space and time dimensions as a mathematical device to simplify the laws of physics, so long as the scientists doing the postulating do not kid themselves in assuming that such dimensions have physical significance.  Of course, if a physicist manages to peform some experiment which demonstrates the literal existence of another space dimension, then so be it.

Often, the assumption of an extra space dimension can be very aesthetically beneficial; for instance, postulating an extra space dimension in which to express Maxwell's equations boils them down to a single equation.

The important thing to consider is whether a theory involving an extra space dimension (or any other non-observable phenomenon) is provable or not.  In this light, string theory is a horrible theory, since the level of energy at which one could test the validity of string theory is so high as to be unattainable to humans for the forseeable future (at least).

So, while there is nothing wrong with introducing mathematical devices into physics to help organize existing information in a coherent and aesthetically pleasing way, we must be certain to state that these devices have no physical significance unless demonstrated through experiment.

In any case, a very good way to think of the force of gravity is to suppose that space-time has been "bent" by the presence of mass (or energy, equivalently).  The term "bent space" is merely a matter of speaking; it refers to the metric used to determine the shortest distance between two lines in the presence of a gravitational field, nothing more.  Thanks to this insight, we have the General Theory of Relativity, which is spectacularly successful in predicting high energy and high gravity phenomena.

In short, just because we visualize space as being Euclidean and time as being linear and uniform does not mean that this paradigm is the most useful in describing the universe and predicting events.




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Post 9

Wednesday, April 21, 2004 - 11:51amSanction this postReply
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Mr. Firehammer,

You pose a serious challenge and several questions to which I intend to respond.

Mr. Firehammer: Do you mean that space itself is "three-dimensional?"
Mr. Stolyarov: Though "space" is not composed of matter, it can house matter of only three dimensions. It is a medium for matter's placement as well as the navigation of entities through it. In both of these respects, it does not permit more than three dimensions. The fact is, all of Euclidean space can be described by a three-coordinate (x,y,z) system. This is what I mean by its "three-dimensional" nature, though it does not have (in itself) material length, width, and height.

Mr. Firehammer: Since you say it "remained" and is "in existence" does that mean you think of space as an existent? Since every existent has an identity, which is all of its qualities, what are the qualities of space? (Perhaps you only mean space is the concept for the relationship between entities, that is their positional relationships.)
Mr. Stolyarov: Space can indeed be described as a relationship of distance between entities. It is not an entity in its own right. This is why the "Universe" can never be a single entity in itself. Space's "existence" can only be characterized in terms of the entities that inhabit it and navigate through it. My contention is that I can theoretically (given the material capacity to do so) move in one direction indefinitely in Euclidean space without ever coming to a barrier inherent to the space itself or returning to my original location.

Perhaps my use of "existence" was rhetorical in this sense. I intended to convey that space cannot be created or destroyed and is not inherently limited.

Mr. Firehammer: Do you imply by the plural, "infinities," there is more than one infinity, and did you actually mean eternities?

Mr. Stolyarov: I do actually mean "eternities." That part was indeed rhetorical.  

I am
G. Stolyarov II




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Post 10

Wednesday, April 21, 2004 - 11:58amSanction this postReply
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Like all things in string theory we'll just have to wait and see what they discover next.

I have no problem with models (using your taut rope as a model), but sometimes people confuse models with reality. Daniel stated above that space could possibly be curved. Certainly, we have models that are funnel shaped or "curved", and they are useful for understanding the trajectories of smaller objects near massive objects, but that is not the same as reality.



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Post 11

Wednesday, April 21, 2004 - 12:31pmSanction this postReply
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I concur with Mr. Stolyarov that "space can indeed be described as a relationship of distance between entities. It is not an entity in its own right" but I would like to emphasize that space can only exist between two entities. Anything outside the convex hull of entities comprising  the universe (no matter how many dimensions you're considering) is meaningless. There is nothing there, so the term 'space' or any other descriptor cannot be applied to it. Space is created by entities getting farther from each other.



Post 12

Wednesday, April 21, 2004 - 1:00pmSanction this postReply
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Eddie is saying several of the things that I will in my eventual reply, which will however cover a bit more ground. (He might find my article "'Errors of Modern Science'--A Philosophical Magic Act" to be of interest, if he can slog through its highly unusual format: a magic act in verse!)

(Edited by Rodney Rawlings on 4/21, 1:13pm)




Post 13

Wednesday, April 21, 2004 - 1:01pmSanction this postReply
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while I sympathize with the objection to certain anti-determinist, anti-identity interpretations of quantum mechanics (if not to the equations and principles as such), this hostility to string theory has got to go. with the copenhagen/indeterminist interpretation of QM, there is actually a formal point against which to argue: ie, the proposal of an anti-identity, uncertain, contradiction filled universe. (and we must remember that there are more rational interpretations of quantum mechanics, and that this whole enterprise, while involving philosophic errors, is not pseudoscience, as some objectivists seem to believe)

All of this said, however, as far as I can tell, the only real objection anyone has served up against string theory is that its counterintuitive and bizarre. to my knowledge it does not invoke any formal refutation of causality, identity, or any other axiom. and being a wierd or counterintuitive theory is not enough to condemn it as pseudoscience if evidence and argument fits for it. the math REALLY DOES suggest 11 dimensional space crumpled into a calabi -yau formation, and that particles are little tiny strings. this is not some neokantian anti-rationalist conspiracy, nor does the fact that it is a radically different picture from what "common sense" teaches us mean anything -- what matters is formal logic, not "common sense". lest you argue that we see only three dimensions with our senses, allow me to remind you that, to our senses, the earth looks flat, but observations superior to our senses proved it to be round. to our senses, it looks like the earth holds still while the sun gyrates up and down. but better measurements than our senses proved that instead it is the sun which is (contextually) stationary while our earth is what moves. to common sense, time seems constant, but can be proven to be stretched or contracted dependant on one's velocity. the upshot of all of this is that A: a wierd theory is not necessarily anti identity, and B: our common intuitions about the world do not have a very good track record when compared to the litmus test of formal science. thusly, I see no problem with string theory as a plausible hypothesis unless one objects to the mathematics behind it. of course, it is not known to be true or untrue until experimentally analyzed, but as a plausible hypothesis or educated guess and I see no problem with it.



Post 14

Wednesday, April 21, 2004 - 1:20pmSanction this postReply
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Robert: I, for one, do not for a moment doubt the value of superstring theory or its math's validity. (The section on superstring theory in my magic act article is carefully worded to avoid this implication.) My main point there is to hint at a more reasonable view of the relation of mathematics to the realities being analyzed.



Post 15

Wednesday, April 21, 2004 - 4:30pmSanction this postReply
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G.

You pose a serious challenge ...
 
I did not mean the questions as a challenge. Thanks for the interesting response. I think I may have some comments later, if you're interested.

Regi




Post 16

Wednesday, April 21, 2004 - 5:20pmSanction this postReply
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Mr. Firehammer,

I did not, by the way, mean the word "challenge" in any negative context. "Intellectual stimulation" would be another proper description of my meaning.

I would indeed be interested in hearing your further comments.

I am
G. Stolyarov II




Post 17

Wednesday, April 21, 2004 - 8:12pmSanction this postReply
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String Theory may prove to be useful, but I reject the notion that it would be the Holy Grail of Science, the Universal Theory of Everything(TUTOE).

In principle, TUTOE would be the perfect marriage of analytic and synthetic propositions like Peikoff mentions in his Analytic-Synthetic Dichotomy, able to accurately predict and explain anything and everything to full capacity.

Assume we have the TUTOE. Now, since it is TUTOE, it should be able to make predictions about humans using the TUTOE. It also should be able to predict how humans will use the TUTOE to predict how humans will use the TUTOE to predict how humans will use the TUTOE and so on forever...

However, because we're Objectivist, we reject logical nonsense because nature is sensical(!). So the TUTOE comes with a asterisk: it can only be used to explain anything unrelated to the TUTOE, otherwise it's self-referencing. It becomes TUTOE*. How does that hamper it's ability to make predictions? Who knows, but it is an interesting idea that I may explore later.



Post 18

Wednesday, April 21, 2004 - 9:05pmSanction this postReply
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So you think there's no such thing as a UTE?



Post 19

Thursday, April 22, 2004 - 5:19amSanction this postReply
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Mr. O'Connor

Unified Theory of Existence (UTE)

Another gift of Islam.

Who could doubt it?





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