A Hawking Perspective on the Mysterons
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A Hawking Perspective on the Mysterons
by DocBrown » Mon Jul 12, 2004 12:48 am
Originally posted on MSN forum 05/06/2004
To try to get myself up to speed on current thinking about Life, the Universe and Everything, I've been reading "A Brief History of Time" - some of which I think I've actually understood, though the concept of time being inextricably bundled with the Euclidean dimensions is so deeply ingrained into my consciousness that I'm having enormous difficulty getting away from it. (As Adams evidently discovered during the writing of "The Hitch Hiker's Guide", it's perfectly possible to grasp the whole thing about time being an illusion and then shake your head and say "Right, now it's time for lunch..."!) Perhaps inevitably, I came across a number of things that reminded me of various aspects of the CS canon along the way, so I wrote them out in the form of a set of notes for myself and/or anybody else who might find them useful in fan-fics - or alternatively would like to have some fun squabbling over them. Either way, this is what I think I understand to date:
The universe is currently expanding. Contemporary thinking on the subject is that it will continue to expand indefinitely, though that view could change. The universe had a beginning, at which point it was a highly ordered structure. As it expands, the amount of disorder present in it (i.e. its entropy) increases. The universe has no boundary: an attempt to travel through it in a straight line would simply result in one returning to one’s starting point in the same way that an attempt to walk around the Earth would. This is because the universe – at least the universe as we perceive it on an intuitive level using Euclidean nomenclature as a descriptive tool - exists in four spatial dimensions, being the three-dimensional surface of a four-dimensional structure. That structure is probably roughly hyperspherical, though this cannot be assumed, and possesses blemishes on its hypersurface in the form of dense concentrations of matter such as stars and black holes which cause the continuum to become locally distorted, or warped. The effect of such distortions upon the tendency of the objects causing them to attract one another and coalesce into larger concentrations is interpreted by us as “gravity”.
There is no such thing as “time”. What we interpret as “time” is the tendency of the universe to become increasingly disordered (i.e. the Second Law of Thermodynamics). As sentient beings, we are capable of recording in our brains the state of any part of the universe that we can perceive. To do this, however, we expend more energy than we use to record the given state, resulting in a net increase in entropy, as required by the Second Law. We interpret our ability to record more highly ordered states in our brains as “time”. A more highly ordered state is interpreted as having happened “in the past”, whereas a less well-ordered state is anticipated “in the future”. Time is effectively a measure of the difference in the level of disorder in the universe when we make the observation and that recorded in our memories. That measure is affected by our passage through the universe in accordance with Relativity. Since we cannot anticipate in which of an infinite number of ways disorder is going to increase, we cannot accurately predict the future (though our very existence requires continual short-term anticipation of this). We cannot travel in time – because there is no “time” through which to travel. It is meaningless to talk about what happened prior to what is colloquially referred to as the Big Bang, because time is defined only in terms of the increase in entropy of the universe since that event.
Recent experiments on elementary particles have demonstrated that protons and neutrons, which were previously thought to be indivisible, are actually created from smaller particles called quarks. Quarks come in a number of varieties, each of which has different characteristics, one of which has been termed its “spin”. The spin of a particle can take a number of values: 0 (the particle looks the same from all directions); 1 (requires a complete 360° revolution before it looks the same); 2 (looks the same if you rotate it 180°) and most remarkably, ½ (which means that it has to be rotated through two complete revolutions before it looks the same). Matter is composed of particles with spin ½; the others give rise to forces between the matter particles.
That much I’ve gleaned from the book. Now I’ll take a flight of fancy and move on to the Mysterons. I’ll say at the outset that I’m assuming that the Mysterons are not only extraterrestrial, they’re extrauniversal – that is, they are not native to our universe. Any sentient being whose origin lay outside the universe as we understand it would have a completely different perception of time, which would presumably be based upon the change in entropy of its own universe (assuming that their universe possessed such a concept as entropy, that is). An interface of universes might provide such a being with both a reason to explore and the need to replicate structures in the other universe as a means of interacting with it. Such structures would possess the entropy state of an identical structure already present in that universe, but could lack what we might for want of a better word call “consciousness”. Alternatively, the “consciousness” might be that imposed by the alien. It might be necessary to eliminate the “consciousness” from such an entropy state prior to effecting such a duplication (i.e. kill it) in order to impose an alternative consciousness, or it could be that the process of analysing the entropy state in the first place requires that consciousness be absent.
Another possible consequence of the Mysterons’ being not native to the universe is that while we cannot travel in time (i.e. manipulate entropy) since we ourselves are an integral part of it, the Mysterons might possibly be able to manipulate a portion of in such a way that a net decrease in entropy resulted (presumably at the expense of a corresponding increase in entropy in their universe). Such a capability could permit the Mysterons to manipulate what our consciousness interprets as “history” - which is effectively what the occupants of the MEV experienced in the immediate aftermath of the attack on the complex, albeit on a very localised scale.
If a mysteronised construct is composed of elementary particles, it makes sense to ask of what type those particles are. We understand that a construct is not indistinguishable from the original, and yet it resembles the original in many superficial respects. The construct is composed of matter, i.e. elementary particles of spin ½. It is reasonable then to suppose that the elementary particles of which the construct is composed differ in some material way – and an obvious possibility is that they have been given just one of the two rotations needed to duplicate the original perfectly. All such constructs have been created in this way – with one exception. That one exception is of course Scarlet himself, who is a construct created from elementary particles that have been given the necessary double spin to duplicate the original perfectly. Whether this is a consequence of an error on the part of the Mysterons at the time of his creation, or a side-effect of the fall from Car-Vu as I have speculated in earlier postings, remains an unresolved question at this time (or perhaps I should say at this specific entropy state of the universe).
Now I think I'll go and read it all over again, and see if I interpret it the same way next time round!
DocBrown
To try to get myself up to speed on current thinking about Life, the Universe and Everything, I've been reading "A Brief History of Time" - some of which I think I've actually understood, though the concept of time being inextricably bundled with the Euclidean dimensions is so deeply ingrained into my consciousness that I'm having enormous difficulty getting away from it. (As Adams evidently discovered during the writing of "The Hitch Hiker's Guide", it's perfectly possible to grasp the whole thing about time being an illusion and then shake your head and say "Right, now it's time for lunch..."!) Perhaps inevitably, I came across a number of things that reminded me of various aspects of the CS canon along the way, so I wrote them out in the form of a set of notes for myself and/or anybody else who might find them useful in fan-fics - or alternatively would like to have some fun squabbling over them. Either way, this is what I think I understand to date:
The universe is currently expanding. Contemporary thinking on the subject is that it will continue to expand indefinitely, though that view could change. The universe had a beginning, at which point it was a highly ordered structure. As it expands, the amount of disorder present in it (i.e. its entropy) increases. The universe has no boundary: an attempt to travel through it in a straight line would simply result in one returning to one’s starting point in the same way that an attempt to walk around the Earth would. This is because the universe – at least the universe as we perceive it on an intuitive level using Euclidean nomenclature as a descriptive tool - exists in four spatial dimensions, being the three-dimensional surface of a four-dimensional structure. That structure is probably roughly hyperspherical, though this cannot be assumed, and possesses blemishes on its hypersurface in the form of dense concentrations of matter such as stars and black holes which cause the continuum to become locally distorted, or warped. The effect of such distortions upon the tendency of the objects causing them to attract one another and coalesce into larger concentrations is interpreted by us as “gravity”.
There is no such thing as “time”. What we interpret as “time” is the tendency of the universe to become increasingly disordered (i.e. the Second Law of Thermodynamics). As sentient beings, we are capable of recording in our brains the state of any part of the universe that we can perceive. To do this, however, we expend more energy than we use to record the given state, resulting in a net increase in entropy, as required by the Second Law. We interpret our ability to record more highly ordered states in our brains as “time”. A more highly ordered state is interpreted as having happened “in the past”, whereas a less well-ordered state is anticipated “in the future”. Time is effectively a measure of the difference in the level of disorder in the universe when we make the observation and that recorded in our memories. That measure is affected by our passage through the universe in accordance with Relativity. Since we cannot anticipate in which of an infinite number of ways disorder is going to increase, we cannot accurately predict the future (though our very existence requires continual short-term anticipation of this). We cannot travel in time – because there is no “time” through which to travel. It is meaningless to talk about what happened prior to what is colloquially referred to as the Big Bang, because time is defined only in terms of the increase in entropy of the universe since that event.
Recent experiments on elementary particles have demonstrated that protons and neutrons, which were previously thought to be indivisible, are actually created from smaller particles called quarks. Quarks come in a number of varieties, each of which has different characteristics, one of which has been termed its “spin”. The spin of a particle can take a number of values: 0 (the particle looks the same from all directions); 1 (requires a complete 360° revolution before it looks the same); 2 (looks the same if you rotate it 180°) and most remarkably, ½ (which means that it has to be rotated through two complete revolutions before it looks the same). Matter is composed of particles with spin ½; the others give rise to forces between the matter particles.
That much I’ve gleaned from the book. Now I’ll take a flight of fancy and move on to the Mysterons. I’ll say at the outset that I’m assuming that the Mysterons are not only extraterrestrial, they’re extrauniversal – that is, they are not native to our universe. Any sentient being whose origin lay outside the universe as we understand it would have a completely different perception of time, which would presumably be based upon the change in entropy of its own universe (assuming that their universe possessed such a concept as entropy, that is). An interface of universes might provide such a being with both a reason to explore and the need to replicate structures in the other universe as a means of interacting with it. Such structures would possess the entropy state of an identical structure already present in that universe, but could lack what we might for want of a better word call “consciousness”. Alternatively, the “consciousness” might be that imposed by the alien. It might be necessary to eliminate the “consciousness” from such an entropy state prior to effecting such a duplication (i.e. kill it) in order to impose an alternative consciousness, or it could be that the process of analysing the entropy state in the first place requires that consciousness be absent.
Another possible consequence of the Mysterons’ being not native to the universe is that while we cannot travel in time (i.e. manipulate entropy) since we ourselves are an integral part of it, the Mysterons might possibly be able to manipulate a portion of in such a way that a net decrease in entropy resulted (presumably at the expense of a corresponding increase in entropy in their universe). Such a capability could permit the Mysterons to manipulate what our consciousness interprets as “history” - which is effectively what the occupants of the MEV experienced in the immediate aftermath of the attack on the complex, albeit on a very localised scale.
If a mysteronised construct is composed of elementary particles, it makes sense to ask of what type those particles are. We understand that a construct is not indistinguishable from the original, and yet it resembles the original in many superficial respects. The construct is composed of matter, i.e. elementary particles of spin ½. It is reasonable then to suppose that the elementary particles of which the construct is composed differ in some material way – and an obvious possibility is that they have been given just one of the two rotations needed to duplicate the original perfectly. All such constructs have been created in this way – with one exception. That one exception is of course Scarlet himself, who is a construct created from elementary particles that have been given the necessary double spin to duplicate the original perfectly. Whether this is a consequence of an error on the part of the Mysterons at the time of his creation, or a side-effect of the fall from Car-Vu as I have speculated in earlier postings, remains an unresolved question at this time (or perhaps I should say at this specific entropy state of the universe).
Now I think I'll go and read it all over again, and see if I interpret it the same way next time round!
DocBrown
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DocBrown
by DocDenim » Mon Jul 12, 2004 12:58 am
I knew you'd like Hawking if you read him!
(spin, however, is an instrinsic property of each sort of particle - if you change the spin, you get a different particle. so just doubling the particle spin won't get you a slightly different or more exact Scarlet it'll get you something else altogether.)
Doc Denim
(spin, however, is an instrinsic property of each sort of particle - if you change the spin, you get a different particle. so just doubling the particle spin won't get you a slightly different or more exact Scarlet it'll get you something else altogether.)
Doc Denim
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DocDenim
by DocBrown » Mon Jul 12, 2004 1:01 am
This may well be true. But then... these quark thingies with a spin of ½ really are a bit on the small side*. I'd guess therefore that if you put a lot of them together, you'd probably get something which at a macroscopic level at least would be indistinguishable from the original - and that's your mysteronised construct. For dabblers in Scarlet pseudo-sceince such as ourselves, it seems to me that the mystery becomes not why when you give 'em a double spin you get a Scarlet, but why the reconstructed Scarlet should retain any Mysteron characteristics at all. After all, the theory says that with a double spin you get right back to where you started - so why is Scarlet impervious to X-rays?
Perhaps it's got something to do with the presence or absence of "consciousness", whatever that is. I've already come to the conclusion that consciousness - whatever it is - is fundamentally tied up with the perception of "time", since if I've understood it correctly, its only consciousness that allows a perception of time to exist at all, since it's essentially our brains' mechanism for interpreting entropy increase. During those six hours immediately following his death, I'll guess that Scarlet either lacked what we call "consciousness" (which is why he can't remember anything about it), or had an alternative consciousness imposed on him throughout that period. Though some mechanism that we don't understand, he got his original "consciousness" back. How did that happen? Was it there all the time, but suppressed in some way? Did the Mysterons confiscate it, and then return it? Or was the presence of "consciousness" incompatible with the elementary particles of which the ½-spin copy of Scarlet was created?
Over to you, Doc...
[* Possibly the biggest understatement in the history of the universe.]
DocBrown
Perhaps it's got something to do with the presence or absence of "consciousness", whatever that is. I've already come to the conclusion that consciousness - whatever it is - is fundamentally tied up with the perception of "time", since if I've understood it correctly, its only consciousness that allows a perception of time to exist at all, since it's essentially our brains' mechanism for interpreting entropy increase. During those six hours immediately following his death, I'll guess that Scarlet either lacked what we call "consciousness" (which is why he can't remember anything about it), or had an alternative consciousness imposed on him throughout that period. Though some mechanism that we don't understand, he got his original "consciousness" back. How did that happen? Was it there all the time, but suppressed in some way? Did the Mysterons confiscate it, and then return it? Or was the presence of "consciousness" incompatible with the elementary particles of which the ½-spin copy of Scarlet was created?
Over to you, Doc...
[* Possibly the biggest understatement in the history of the universe.]
DocBrown
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DocBrown
by DocDenim » Mon Jul 12, 2004 1:04 am
Doc B!
(You're a dangerous man with a little knowledge!)
Yes, quark thingys are very small - but the cannot under any circumstances exist alone outside of some other elementary particle - it's the quantum chromodynamics thing I mentioned in another thread - they form in their various configurations the stable elementary particles from which everything else is made but can't 'stand alone'. (You're rather misinterpreting this 1/2 spin concept. 1/2 spin properties give rise to 'matter' whole interger spin properties give rise to 'forces'. (Fermions and bosons respectively, if you need to know, but it's more complicated than that.)
As far as time and conciousness goes, well, things were proceeding to evolve on a cosmic level a long time before anything, anywhere had the chance to evolve some sort of consciousness to notice.'Our' perceptions are certainly very important for 'us' to be able to interpret and interact with the Universe at large out there, but our perceptions/consciousness certainly can't in any way be a prerequisite for the existence of said Universe and it's entropic properties
and that's all I have time for! Revisit the other thread and really try to check out the Elegant Universe link. (It's all string theory anyway - that's what the quarks are made of.....)
gotta run!
Doc Denim
(You're a dangerous man with a little knowledge!)
Yes, quark thingys are very small - but the cannot under any circumstances exist alone outside of some other elementary particle - it's the quantum chromodynamics thing I mentioned in another thread - they form in their various configurations the stable elementary particles from which everything else is made but can't 'stand alone'. (You're rather misinterpreting this 1/2 spin concept. 1/2 spin properties give rise to 'matter' whole interger spin properties give rise to 'forces'. (Fermions and bosons respectively, if you need to know, but it's more complicated than that.)
As far as time and conciousness goes, well, things were proceeding to evolve on a cosmic level a long time before anything, anywhere had the chance to evolve some sort of consciousness to notice.'Our' perceptions are certainly very important for 'us' to be able to interpret and interact with the Universe at large out there, but our perceptions/consciousness certainly can't in any way be a prerequisite for the existence of said Universe and it's entropic properties
and that's all I have time for! Revisit the other thread and really try to check out the Elegant Universe link. (It's all string theory anyway - that's what the quarks are made of.....)
gotta run!
Doc Denim
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DocDenim
by DocBrown » Mon Jul 12, 2004 1:06 am
[Holds up hands in surrender]. Fair enough - I'll come back when I've watched it. At least the video player on this PC appears to be working at the moment, which simplifies the process somewhat.
However, to paraphrase Captain Oates, "I may be some time..."
[Link for anyone else who wants to try their luck with a crash course in String Theory: http://www.pbs.org/wgbh/nova/elegant/]
DocBrown
However, to paraphrase Captain Oates, "I may be some time..."
[Link for anyone else who wants to try their luck with a crash course in String Theory: http://www.pbs.org/wgbh/nova/elegant/]
DocBrown
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DocBrown
by DocBrown » Mon Jul 12, 2004 1:09 am
I’m still reading, but I’ve a few observations to throw back. One concerns the graviton – the only elementary particle with the exception of the Higgs Boson (see http://www.pbs.org/wgbh/nova/elegant/ under “Elementary Particles”) that has been postulated but hasn’t apparently actually been observed, either directly or indirectly. Rather than interpreting this as a particle that causes things to attract one another, I’m reading this as the structure of the universe we’re talking about here. The fabric of the surface of the expanding four-dimensional soap bubble that we live in, if you will*, in which case it’s perhaps not so surprising that we’ve never observed it, since we ourselves are presumably an integral part of that fabric. Spots and blemishes are one thing, but the fabric of space-time itself is rather another.
Incidentally, continuing with the bubble analogy for a moment, it occurs to me that the effect of blemishes like stars on the surface of the universal hypersphere is necessarily to warp space “inwards”, i.e. towards the interior of the hypersphere. If it were otherwise, i.e, space were warped away from the interior to create a “pimple” on the hypersurface, it’s not hard to see that we’d have created antigravity: just imagine that instead of the balls sinking into the pool table in the analogy we’re familiar with, they were pulled upwards instead, then imagine rolling the cue ball along it. So why are masses pulled in towards the centre of the hypersphere, eh? Presumably there’s a pressure being exerted on the fabric of the universe from the “interior” which becomes countered more effectively by the presence of a “blemish” in space-time.
I’m not actually too happy with the use of dimensions to explain strings at all, come to think of it. I’ve got this vague idea at the back of my head that dimensions are nothing more than an idealised descriptive tool in all of this – rather the same way that “time” was treated as an absolute reality before Einstein discovered that it was nothing of the kind. I mean, we say that in spatial terms the universe is a three-dimensional structure – but we do that simply because we need three co-ordinates to specify any point within it, using the Euclidean convention that useful co-ordinate systems lie at right-angles to one another. Better to say simply that the universe just is. (Assuming that that’s true, of course!)
[* Which raises the question of WHY the universe is expanding. Not wishing to sound too facetious, the idea of an expanding four-dimensional bubble does rather conjure up the issue of whether there’s someone outside it blowing it up with a mechanical pump. And that raises the inevitable question of how long it’ll be before it goes “bang”. Douglas Adams’s vision of the universe being sneezed out of the nose of a being called the Great Green Arkleseizure springs to mind – to say nothing of the understandable terror of the inhabitants at the event colloquially known as “The Coming of the Great White Handkerchief”. Perhaps God really DOES have a sense of humour after all – though not necessarily one we would wholeheartedly appreciate!]
DocBrown
Incidentally, continuing with the bubble analogy for a moment, it occurs to me that the effect of blemishes like stars on the surface of the universal hypersphere is necessarily to warp space “inwards”, i.e. towards the interior of the hypersphere. If it were otherwise, i.e, space were warped away from the interior to create a “pimple” on the hypersurface, it’s not hard to see that we’d have created antigravity: just imagine that instead of the balls sinking into the pool table in the analogy we’re familiar with, they were pulled upwards instead, then imagine rolling the cue ball along it. So why are masses pulled in towards the centre of the hypersphere, eh? Presumably there’s a pressure being exerted on the fabric of the universe from the “interior” which becomes countered more effectively by the presence of a “blemish” in space-time.
I’m not actually too happy with the use of dimensions to explain strings at all, come to think of it. I’ve got this vague idea at the back of my head that dimensions are nothing more than an idealised descriptive tool in all of this – rather the same way that “time” was treated as an absolute reality before Einstein discovered that it was nothing of the kind. I mean, we say that in spatial terms the universe is a three-dimensional structure – but we do that simply because we need three co-ordinates to specify any point within it, using the Euclidean convention that useful co-ordinate systems lie at right-angles to one another. Better to say simply that the universe just is. (Assuming that that’s true, of course!)
[* Which raises the question of WHY the universe is expanding. Not wishing to sound too facetious, the idea of an expanding four-dimensional bubble does rather conjure up the issue of whether there’s someone outside it blowing it up with a mechanical pump. And that raises the inevitable question of how long it’ll be before it goes “bang”. Douglas Adams’s vision of the universe being sneezed out of the nose of a being called the Great Green Arkleseizure springs to mind – to say nothing of the understandable terror of the inhabitants at the event colloquially known as “The Coming of the Great White Handkerchief”. Perhaps God really DOES have a sense of humour after all – though not necessarily one we would wholeheartedly appreciate!]
DocBrown
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DocBrown
by DocDenim » Mon Jul 12, 2004 1:11 am
well, yes, it does get a bit complicated, doesn't it. However, to address one or two of these points:
I know it's difficult to visualize, and often 2D illustrations are used as analogies for it, but when you talk about the hypersphere, you're not really talking about a 'bubble' with an interior or an exterior. The other dimensions don't exist either inside or outside of that 'surface' because you have to try to imagine the 'fabric' as a three dimensional grid and when it warps, it's warping off a direction that we can't 'see'.
As to the graviton; there is at least one school of thought that says it has to exist, simply because gravity does and that should be all the proof we need. But gravity has been the odd-force out for some time - because Einstein's theories say that gravity is the warping of the geometry of space, and quantum theory says that gravity is created by the exchange of massless, spin-2 particles called gravitons. So far, string theory is the only one that ties the relativity and quantum theories together, and to make that work you need the extra dimensions. (According to theory, compactified at every point of space-time as toplogically twisted little Calabi-Yau spaces - it's where the strings hide.)
Extra dimensions, which happen to be - for this dabbler of Mysteron powers speculation - damn handy things to have kicking around. Mysterons can't be seen (for the most part) and they have the ability to move things in three dimensions (changing the object's co-ordinates in 3D) and can vanish into thin air - which I like to interpret as the object or being funneling 'down' into or 'up' out of the aforementioned compactified dimensions. I'm not going to repeat myseld here (I've explained most of this in other threads) but if you review some of my previous speculations armed with some of your recent readings, you may actually see some sort of pseudo-scientific
sense in them.....
all I ahve time for right now...must go!
Ciao
Doc Denim
I know it's difficult to visualize, and often 2D illustrations are used as analogies for it, but when you talk about the hypersphere, you're not really talking about a 'bubble' with an interior or an exterior. The other dimensions don't exist either inside or outside of that 'surface' because you have to try to imagine the 'fabric' as a three dimensional grid and when it warps, it's warping off a direction that we can't 'see'.
As to the graviton; there is at least one school of thought that says it has to exist, simply because gravity does and that should be all the proof we need. But gravity has been the odd-force out for some time - because Einstein's theories say that gravity is the warping of the geometry of space, and quantum theory says that gravity is created by the exchange of massless, spin-2 particles called gravitons. So far, string theory is the only one that ties the relativity and quantum theories together, and to make that work you need the extra dimensions. (According to theory, compactified at every point of space-time as toplogically twisted little Calabi-Yau spaces - it's where the strings hide.)
Extra dimensions, which happen to be - for this dabbler of Mysteron powers speculation - damn handy things to have kicking around. Mysterons can't be seen (for the most part) and they have the ability to move things in three dimensions (changing the object's co-ordinates in 3D) and can vanish into thin air - which I like to interpret as the object or being funneling 'down' into or 'up' out of the aforementioned compactified dimensions. I'm not going to repeat myseld here (I've explained most of this in other threads) but if you review some of my previous speculations armed with some of your recent readings, you may actually see some sort of pseudo-scientific
sense in them.....
all I ahve time for right now...must go!
Ciao
Doc Denim
-
DocDenim
by DocBrown » Mon Jul 12, 2004 1:12 am
To pick up on just the first point, I'm not happy with this apparent absence of an "interior" to the universe. I've no problem with the concept of warped space: that's just an extension into a fourth spatial dimension of the notion that the Earth isn't flat. I've also no problem with the statement that if you were to set off in a straight line in a spaceship in any direction into the universe and keep flying for long enough you'd eventually arrive back where you started: again, that's essentially just a theoretical extension into a fourth spatial dimension of what Magellan's expedition did when it circumnavigated the Earth. The problem is that in order to do something like that, you've got to go "round" something. Haven't you? It seems to me that proving that ought to be a relatively straightforward exercise in topology*, irrespective of the number of spatial dimensions needed to do it. In three dimensions that something is the Earth; in four dimensions it becomes the "interior" of the universe. If I'm mistaken on that point, can you supply me with a reference which discusses it?
This question will be tied up with the notion of wormholes, no doubt: I've seen observations about wormholes joining discontinuous points within the same universe (which I can't reconcile with the above - using the analogy, even if one were able to pass freely through the Earth's core, it's still a long way from here to Australia), and also observations about wormholes joining points in different universes (which is perfectly consistent with the above - another universe could be an infinitesimally small fraction of a millimetre from here if we permit movement in 4-space). I've also seen at least one comment about a wormhole joining discontinuous points in time - and I can't accept that one at all, on the grounds that if time doesn't really exist, then moving in it makes no sense.
[* But then, topology is concerned with the mathematics of spatial structures only. Whether it applies equally to space-time is another question.]
DocBrown
This question will be tied up with the notion of wormholes, no doubt: I've seen observations about wormholes joining discontinuous points within the same universe (which I can't reconcile with the above - using the analogy, even if one were able to pass freely through the Earth's core, it's still a long way from here to Australia), and also observations about wormholes joining points in different universes (which is perfectly consistent with the above - another universe could be an infinitesimally small fraction of a millimetre from here if we permit movement in 4-space). I've also seen at least one comment about a wormhole joining discontinuous points in time - and I can't accept that one at all, on the grounds that if time doesn't really exist, then moving in it makes no sense.
[* But then, topology is concerned with the mathematics of spatial structures only. Whether it applies equally to space-time is another question.]
DocBrown
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DocBrown
by DocDenim » Mon Jul 12, 2004 1:14 am
Greetings again Doc Brown:
Well, I do have a short reading list for you, and I know you've heard me mention a few of these before:
Brian Greene - The Elegant Universe, in particular chapter 8, More Dimensions Than Meet the Eye. You'll find quite a lucid discussion about 'where' the hidden dimensions are. But as a teaser, the other dimensions we're referring to aren't outside of our 3 'extended' macroscopic dimensions, they are contained within it - they're just so small we can't see them.
You can also google search (or go to Wikipedia or Mathworld) and search keyword: Calabi-Yau space.
Also be sure to google (and it's included in the above mentioned chapter) Kaluza-Klein Theory. That's got an interesting twist or two in it, and it's a theory that Einstein himself found very intriguing (it dates back to the 1920's, so additional dimensions are not really all that new a concept.)
Enjoy your research! Have fun! Hope you can track the book down or find a computer that will let you watch the Nova version.....
Doc Denim
Well, I do have a short reading list for you, and I know you've heard me mention a few of these before:
Brian Greene - The Elegant Universe, in particular chapter 8, More Dimensions Than Meet the Eye. You'll find quite a lucid discussion about 'where' the hidden dimensions are. But as a teaser, the other dimensions we're referring to aren't outside of our 3 'extended' macroscopic dimensions, they are contained within it - they're just so small we can't see them.
You can also google search (or go to Wikipedia or Mathworld) and search keyword: Calabi-Yau space.
Also be sure to google (and it's included in the above mentioned chapter) Kaluza-Klein Theory. That's got an interesting twist or two in it, and it's a theory that Einstein himself found very intriguing (it dates back to the 1920's, so additional dimensions are not really all that new a concept.)
Enjoy your research! Have fun! Hope you can track the book down or find a computer that will let you watch the Nova version.....
Doc Denim
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DocDenim
by DocBrown » Mon Jul 12, 2004 1:16 am
Okay, I’ve been doing a little more reading. One of them - http://people.cs.uchicago.edu/~mbw/astr ... sions.html - is helpful (and remarkably artistic too: I love that Escheresque visualization of 6-dimensional Calabi-Yau space in Figure 5). But as to http://mathworld.wolfram.com/Calabi-YauSpace.html and http://en.wikipedia.org/wiki/Calabi-Yau_spaces... ulp. It’s a long time since I’ve had to cope with this sort of thing, and I’m rather rusty (or to put it another way, I can’t understand a word of it). That aside however, I still can’t shake off this gut feeling that the evident need to reduce the problem to one of dimensions is barking up the wrong tree. Regardless of how well it works, it’s still a mathematical model, and like all mathematical models it’s necessarily an approximation to the truth – and I have this feeling at the back of my mind that the “reality” is that there aren’t any dimensions as such at all. We attempt to decompose the Universe into simple linear dimensions in our heads because that’s the way we think, and that style of thinking is necessarily reflected in our mathematical notation. (It would be rather like trying to solve problems in corporate accountancy using Roman numerals. The subject just couldn’t be tackled at all until the whole system used for representing numbers was replaced by the Arabic notation that’s currently in use.) I suppose what I’m effectively saying is that mathematics as we understand it is probably the wrong tool to tackle the problem – which is not a helpful comment, since it prompts the instant retort “So what’s the right tool to tackle it, then?”, and I obviously haven’t got the faintest idea.
I was interested to see at the top of the Mathworld article the apparent use of a simple cross-product of the space-time manifold and the Calabi-Yau space to generate the 10-dimensional Universe. On an intuitive level, isn’t that rather close to just adding Time to Space to generate Spacetime, with the implicit associated assumption that the two don’t interact in any obvious way? But then, I suppose since the object of the exercise was presumably to unify the actions of macroscopic forces with microscopic ones into a single theory, I have to assume that the end result does represent the observed combined actions of the two sufficiently well to be generally accepted as a workable theory.
Incidentally, I’ve been chewing over that earlier point of mine about the 4-dimensional “interior” and “exterior” of the Universe. You’re right – there doesn’t have to be an “interior”: if the spatial structure of the Universe were to resemble a five-dimensional analogue of a Klein bottle (http://www.math.rochester.edu/misc/klein-bottle.html) the inside and the outside would be synonymous. That would imply however (I think) that space would have to warp in both concave and convex forms to be able to be a closed system – so if gravity is simply a by-product of the curvature of spacetime, there would need to be parts of the Universe in which antigravity is the overriding macroscopic force. That would imply a completely alien structure of matter, since absolutely nothing would be attracted to anything else, other than by electromagnetic forces. Interesting to contemplate, eh?
Back to the reading material...
DocBrown
I was interested to see at the top of the Mathworld article the apparent use of a simple cross-product of the space-time manifold and the Calabi-Yau space to generate the 10-dimensional Universe. On an intuitive level, isn’t that rather close to just adding Time to Space to generate Spacetime, with the implicit associated assumption that the two don’t interact in any obvious way? But then, I suppose since the object of the exercise was presumably to unify the actions of macroscopic forces with microscopic ones into a single theory, I have to assume that the end result does represent the observed combined actions of the two sufficiently well to be generally accepted as a workable theory.
Incidentally, I’ve been chewing over that earlier point of mine about the 4-dimensional “interior” and “exterior” of the Universe. You’re right – there doesn’t have to be an “interior”: if the spatial structure of the Universe were to resemble a five-dimensional analogue of a Klein bottle (http://www.math.rochester.edu/misc/klein-bottle.html) the inside and the outside would be synonymous. That would imply however (I think) that space would have to warp in both concave and convex forms to be able to be a closed system – so if gravity is simply a by-product of the curvature of spacetime, there would need to be parts of the Universe in which antigravity is the overriding macroscopic force. That would imply a completely alien structure of matter, since absolutely nothing would be attracted to anything else, other than by electromagnetic forces. Interesting to contemplate, eh?
Back to the reading material...
DocBrown
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DocBrown
by Hazel K » Mon Jul 12, 2004 1:18 am
Cripes… in the immortal words of Python – "My brain hurts."
I speak as someone who, on reading Stephen Hawking's ‘A Brief History of Time’, thought, with great satisfaction, "AT LAST I understand the Uncertainty Principal!" As soon as I turned the page, however… gone. Ever since I was in primary school, struggling to understand how you could tell numbers apart (still not sure about 4, 6, 8 and 0 – they all look far too alike to me. I think it's called dyspraxia), I’ve had trouble with basic arithmetic, let alone higher mathematics. Still, I shall take pride in my mastery of the apostrophe and semi-colon. Everyone has their own talents.
Hazel K
I speak as someone who, on reading Stephen Hawking's ‘A Brief History of Time’, thought, with great satisfaction, "AT LAST I understand the Uncertainty Principal!" As soon as I turned the page, however… gone. Ever since I was in primary school, struggling to understand how you could tell numbers apart (still not sure about 4, 6, 8 and 0 – they all look far too alike to me. I think it's called dyspraxia), I’ve had trouble with basic arithmetic, let alone higher mathematics. Still, I shall take pride in my mastery of the apostrophe and semi-colon. Everyone has their own talents.
Hazel K
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Hazel K
by Marion W » Mon Jul 12, 2004 1:19 am
A quick shufty in the files reveals Dyspraxia is 'clumsy child syndrome'. How are you at ball games, Hazel? 
The Beeb claims problems with numbers (and here I hold up my hand too) is called dyscalculia (or number blindness)
I am switching off my Librarian-mode switch and going to do something useful now.....
Marion W
The Beeb claims problems with numbers (and here I hold up my hand too) is called dyscalculia (or number blindness)
I am switching off my Librarian-mode switch and going to do something useful now.....
Marion W
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Marion W
by DocDenim » Mon Jul 12, 2004 1:21 am
Mornin' all!
Just a very quick clarification, for those who may be wondering:
I too, can be very firmly numbered amongst the mathematically disinclined. I will admit to the occassional micro-epiphany or short-lived flash of insight when it comes to crunching the numbers, but mostly I am a physics groupie with a decent grasp of the concepts. I Don't Do the Math. (Quantum stuff is just a hobby for me, that is.)
And for Doc B: you seem to be hitting the correct websites; the uchicago-dimensions one in particular has lifted it's info/illustrations directly from Greene's book (Greene is obviously an Authority in this area) and when you finally manage to locate the book, you will find that he addresses verbatim your concern about whether or not other dimensions actually exist or if they're just a useful conceptual crutch. (I would quote the appropriate paragraph, but the book had to go back to the Library yesterday....) And I agree with you, the Calabi-Yau diagram is pretty darn cool, isn't it?
All I have the time for right now!
ciao all!
Doc Denim
PS - Hazel & Marion! Nice to see you popping into the conversation! And I do recommend Hawking anytime....
Just a very quick clarification, for those who may be wondering:
I too, can be very firmly numbered amongst the mathematically disinclined. I will admit to the occassional micro-epiphany or short-lived flash of insight when it comes to crunching the numbers, but mostly I am a physics groupie with a decent grasp of the concepts. I Don't Do the Math. (Quantum stuff is just a hobby for me, that is.)
And for Doc B: you seem to be hitting the correct websites; the uchicago-dimensions one in particular has lifted it's info/illustrations directly from Greene's book (Greene is obviously an Authority in this area) and when you finally manage to locate the book, you will find that he addresses verbatim your concern about whether or not other dimensions actually exist or if they're just a useful conceptual crutch. (I would quote the appropriate paragraph, but the book had to go back to the Library yesterday....) And I agree with you, the Calabi-Yau diagram is pretty darn cool, isn't it?
All I have the time for right now!
ciao all!
Doc Denim
PS - Hazel & Marion! Nice to see you popping into the conversation! And I do recommend Hawking anytime....
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DocDenim
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