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| S D Rodrian wrote: The three dimensional aspect of space is very simple. Take an object like the tip of a pencil. Place it in a square room. You will find that three measures sufficiently represent its position relative to the room. Any more will be wasteful and any less will be broken. In this sense the Euclidean three dimensional space is an empirical discovery that takes very little to demonstrate. Do you deny this? These are the three dimensions that you are disputing. Even if more dimenions do exist this behavior must be resolved. Three dimensions are an observation. -Tim |
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| On 5 Jul 2006 17:28:48 -0700, "Timothy Golden BandTechnology.com" <[Only registered users see links. ]> wrote: An interesting way to conceptualize this is to imagine a large screened TV in front of you. Then, in your imagination, expand the width and height to infinity. Next, in your imagination, toss the hardware aside, leaving only the image in place. Persons in this image perceive their space as 3-dimensional. That is, they can move in any direction they want to. To them, a meter stick will appear to be one meter long, any way they orient it. However, from your perspective, these people are limited to something very close to two dimensional space. Granted, the image has some thickness, albeit very small. Now, in your imagination, shrink the image's thickness on down to less than a Planck Length. From your perspective it is no longer discernable, but it is still there. From your perspective, their third dimension is rolled up to less than a Planck Length. But, from their perspective their third dimension is no different than their other two dimensions. This is not a real-world kind of thing, but it does provide a rather nice way of getting the concept. Those other dimensions could very well be right her in our midst, but if they are less than a Planck Length, they are completely indiscernible to us. Gordon |
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| In article <1152130640.399740.184150@l70g2000cwa.googlegroups .com>, "[Only registered users see links. ]" <[Only registered users see links. ]> wrote: <SNIP> Are you trying for a record of some kind in uncouth Usenet behaviour? Top-posting a semi-literate, unresponsive self-promotion as a reply to a widely cross-posted thread is bad enough, but quoting the 2700 lines in full underneath is downright uncivilized. -- Odysseus |
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| > On 5 Jul 2006 17:28:48 -0700, "Timothy Golden No doubt, no doubt! Who can't count to three? Well, there ARE a number of drinks beyond which... What is a tip of a pencil! Certainly to an ant it must be a mountain top. And to our dear ole Planck Length Creature it is its universe in all! But, what is the tip of a pencil to the elephant, or to the whale! O, what is a tip of a pencil to the world! (Good Heavens, I've still got it! --The Poet In Me.] Why does it always HAVE to be a square room? Every time I am placed in a square room I feel compelled to only walk in "2" dimensions! Unless I manage to wiggle out of my strait jacket, of course. And then I can walk "3" dimensionally (via the rope my kind keepers like to leave for me tied to a hook on the ceiling). Why bother? Why not simply ask, "You can't see it?!?! It's right in front of you nose!" HINT: However way you point it out.... said "way" is all in your head: Unless your "lines" are the thickness of a Planck's Length's Planck's Length's Planck's Length's Planck's Length's (ad infinitum) your triangulation will only always ONLY succeed in giving a general direction as to where the thing is. (Cross you fingers and see just how large the area is over which they cross.) And, yes, it works both ways... or try to triangulate the position of the earth with such itty bitty "lines." We live in an approximate world only. And this is the achilles heel of all attempts by Mathematics to "rule" the universe, I'm afraid. (Who knows not this, is doomed to waste a lot of his life de-noodling his mind with infinite minutia.) --SDR And how comes it that we just happen to live in an approximate world only, you might ask. Because in reality we live IN OUR MINDS, and there's very precious little in there that's not but an estimation. Or something close to it... Certainly none of it will have to do with "dimensions" but only with different approaches to it (or, directions). START QUOTE Imagine a one-dimensional wall... From where would one even "see" such a wall? Certainly if we are NOT looking at it dead-on we are using other dimensions than its merely one to "see it" (since we would have to look at it from a little to the side). Throw a left-hook and freeze your punch in mid-air: Your floating arm is describing an impossible journey through an infinite number of (certainly more than just three) dimensions! And thus too any circumference such as the earth's... And because all it would take would be a very tiny "little" ... no huge human eye could ever see it. (And we are talking strictly theoretically here.) The wall itself would have to be infinitesimally tiny. Impossibly tiny. Let's say that a Planck's Length is the smallest thing (and that there are no lengths as small as a Planck's Length to our Planck's Length, although I do not know of any objection to that). Then the wall would have to be a Planck's Length AND the observing eye would also have to be a Planck's Length and be looking at it perfectly head-on because if it were but even the smallest fraction to any side it would have to look at it from a second, third, or additional dimension. [You can see why it's much more easy to just look at a comic strip and believe the fiction that it's a two-dimensional drawing... even though we know that no true purely two-dimensional object can exist in our reality.] HINT: It's your mind agreeing to "go along with" the fiction that the comic strip/painting/photo graphic is two-dimensional. And if no purely one-, or purely two-, or even purely three-dimensional object can exist in our reality, then any talk of the existence of ANY-numbered- dimension is also nonsense... whether in or outside our reality. And if you can't see this, you're not really very smart, no matter how clever you may be (and not even though you be even as clever as a checkers-playing computer). END QUOTE Repeat after me: IF A ONE-DIMENSIONAL ANYTHING IS IMPOSSIBLE, THEN A TWO- DIMENSIONAL ANYTHING IS TWICE AS IMPOSSIBLE. AND A 3-DIMENSIONAL ANY- THING IS 3 TIMES AS IMPOSSIBLE & SO ON. A balloon only has two-dimensions. But only because that's a convenient short-hand in mathematics: That two-dimensional balloon helps mathematics neither to add to nor to substract from REALITY anything whatsoever, though we speak about it until the Word of God at last falls silent in the universe. Amen. You are right at last, Tim: "3" dimensions ARE only a requirement of the mind (in the mind) and have nothing whatsoever to do with reality: Imagine that man has finally become extinct. Then, to the world that continues without him, what use are the methods he used to use to point out things to himself? I don't mind your use of whatever method you wish to point things out to yourself, Tim. But don't then ORDAIN that your brain commands reality, Tim! That's positively bonkers, ole boy. That would be a nice trick for such "persons" to perform, since they would have to do it with "brains" which have no "depth" at all. With "muscles & limbs" which have no "depth" at all. Well, certainly, if they try to orient it from "width" to "height" they are going to have to make it travel through a zillion dimensions other than their only "2." As I've said: I don't mind Mathematics describing every point in a circumference. But do not let then Mathematics try to describe the "dimensions" of reality! (Because, as I said, it's absurd to limit them in any way... in effect, by any number. It offends the laws of physics.) Ah! A little bit of sanity creeps into this petty pace! Not much, but a little bit does. That's a start. Does it really matter how thick the image is? And, who sez when we get to a Planck's Length's thickness we won't get bitten by an even tinier tick? "In your imagination" everything is possible, yes. A truly "really" three-dimensional "thing" could only be observed from "six" very specific, very specifically placed very infinitely infinitesimal "impossible" positions (hint: no such positions are possible in reality, ole boy): BEGIN QUOTE Imagine a one-dimensional wall... From where would one even "see" such a wall? Certainly if we are NOT looking at it dead-on we are using other dimensions than its merely one to "see it" (since we would have to look at it from a little to the side). Throw a left-hook and freeze your punch in mid-air: Your floating arm is describing an impossible journey through an infinite number of (certainly more than just three) dimensions! And thus too any circumference such as the earth's... And because all it would take would be a very tiny "little" ... no huge human eye could ever see it. (And we are talking strictly theoretically here.) The wall itself would have to be infinitesimally tiny. Impossibly tiny. Let's say that a Planck's Length is the smallest thing (and that there are no lengths as small as a Planck's Length to our Planck's Length, although I do not know of any objection to that). Then the wall would have to be a Planck's Length AND the observing eye would also have to be a Planck's Length and be looking at it perfectly head-on because if it were but even the smallest fraction to any side it would have to look at it from a second, third, or additional dimension. [You can see why it's much more easy to just look at a comic strip and believe the fiction that it's a two-dimensional drawing... even though we know that no true purely two-dimensional object can exist in our reality.] HINT: It's your mind agreeing to "go along with" the fiction that the comic strip/painting/photo graphic is two-dimensional. And if no purely one-, or purely two-, or even purely three-dimensional object can exist in our reality, then any talk of the existence of ANY-numbered- dimension is also nonsense... whether in or outside our reality. And if you can't see this, you're not really very smart, no matter how clever you may be (and not even though you be even as clever as a checkers-playing computer). END QUOTE Repeat after me: IF A ONE-DIMENSIONAL ANYTHING IS IMPOSSIBLE, THEN A TWO- DIMENSIONAL ANYTHING IS TWICE AS IMPOSSIBLE. There ya go! THAT's my whole point in a banana peel. I'm sure that as long as you understand, Gordon, the world/the universe will sleep soundly tonight. There ya go! THAT's the whole problem right there out of the safety of its banana peel: The instant you even so much as HINT at the mere possibility that it's possible to assign a (necessarily limiting) number to the dimensions of "anything" you are literally knocking all sorts of bits from "it" OUT of existence (in our reality). And THAT would be a jolly nice trick indeed. Gordon! Gordon, if something exists, it does (or, if it doesn't it doesn't). But you can't cheat on the rule by ANY means. (And I should think CERTAINLY NOT by merely shrinking the thing out of sight... or tossing a hanky over it and hollering, "Abracadabra!") Voila! S D Rodrian [Only registered users see links. ] [Only registered users see links. ] [Only registered users see links. ] [Only registered users see links. ] |
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| I hardly banish the notion of higher dimensions. In fact I believe that I have a construction that supports them while also supporitng spacetime: [Only registered users see links. ] It is not necessary to deny the 3D observations that we make. By working out the puzzle of how they come to be we may find the best theory. They are generally imposed on theories as empirically evident. But theory is supposed to predict the empirical, not rely upon it. The polysign claim is that higher dimensions are poorly behaved according to the usual concept of dimensionality. Oddly enough these heigher dimensions are very well behaved arithmetically under the polysign construction. They just don't conserve distance in their product above P3. So the usage of a ruler in the product space will only lead to cohenernt measures in three of the dimensions. Time is accounted for as well under this natural construction. There are no special laws in it. Just special behaviors as a result of those laws. -Tim |
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| The number of nonzero eigenvalues determines the dimensionality of the graph (at least the mathematical one). Hypothesis. The largest distance in the linear chain x-x-x-x is 3, similarly as the largest distance in cube. Fact kunzmilan |
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