A Matrix View of Space-Time
What if the universe is an nth-dimensional hyperspacial matrix?
Background - Neural Networks
Back in grad-school, my lab took a semester to discuss neural-network models of learning and memory, of the sort that cognitive neuroscientists and artificial intelligence researchers have been developing in hopes of simulating the activities of the human brain/mind. Some of these models utilize a matrix involving nth-dimensional hyperspace (where n is a variable indicating the number of dimensions represented by the matix). Such models are hideously complex, but that complexity is attractive when attempting to model something as mysterious as the human mind.
Without getting into too much depth, one of the strengths of these models is that they can simulate the learning of categories through the presentation of exemplars ("examples" of a category to be learned). After a learning period during which numerous exemplars are presented to the input function of the matrix, a set of novel exemplars is presented for classification. The network produces at its output function a unique pattern of excitation for each unique category, and will, for the most part, correctly categorize new exemplars presented to it. What happens within the matrix during the learning process is that a specific set of interconnections gets created - a prototype - for each category. When new exemplars are tested, the excitation patterns across the net are "compared" to the various prototypes, and depending upon that "comparison", the appropriate category is output.One of the reasons that I like this idea is that it implies that the mind functions in more dimensions than we can normally percieve. Although we experience "reality" in only 4-dimensions (3 of space and 1 of time), the mind may by it's very nature be operating in ways we can't easily concieve of. I will return to the elegance of this supposition shortly.
Why Not Reality?
If the mind can operate in n dimensions, it seems reasonable that "reality" - of which it is part - can as well. If so, is there any evidence that it does? I think so. Picture, if you will, the following scenario:
There is a cube, which has three dimensions: horizontal, lateral, and vertical. Now toss a ball
inside the cube and let it bounce around. The ball is now moving in 4 dimensions: 3 of space and
1 of time. As time moves forward, the ball moves around the cube.
Notice that the balls movement is "causal". You impart energy to the ball, it bounces off the walls at angles appropriate to its trajectory and momentum, taking into account gravity, friction, etc. Newtonian physics in a cube. The ball's movements are determined by "what came before". Time, as we percieve it, is linear and unidirectional. Always forward - cause and effect.
Let's continue to assume that time is linear, but let's remove the requirement of unidirectionality. Now the ball may move both backwards and forwards in time along its linear axis. Unfortunately, there is no evidence that this is possible as of yet. Maybe someday someone will discover tachyons, move faster than light, or discover genuine communications from the omega-point entity. Until, then, I leave the possibility open, just for fun.
Dimensions in Time
Now let's take this one step further and propose another dimension of time, which functions at "right angles" to our original timeline, i.e. "laterally". This is the basic concept behind the "alternate timeline" themes so popular throughout modern science fiction. It is also similar in scope to the "Many Worlds Hypothesis" proposed by certain quantum physicists, in which each binary choice causes a "splitting" (or more correctly, duplication) of the universe.
Is there any evidence for this "lateral" dimension of time? Subjective experiences aside (for this I recommend the essay "If You Find This World Bad", by Philip K. Dick), the best evidence for a "lateral" dimension of time involves the experience of synchronicity (i.e. "meaningful coincidence"). While this nearly always manifests with a strong subjective component (much like deja vu - which might also be considered evidence, if one were so inclined), quite often the subject is able to document the synchronic data points in such a way as to be independently verifiable (for a foray into this form of madness I highly recommend Cosmic Trigger by Robert Anton Wilson). Events of this nature can be truly mind-boggling as to the depth of the stacked "coincidences". It is no wonder that science steers well clear of such things.
[To return to my point of elegance in regards to the human mind: think of linear, cause-effect, "horizontal" time as analogous to "left-brained", logical thought. "Lateral" time would then be analogous to "right-brained", intuitive thought. Logic plods onwards, one foot after another, while intuition leaps of the track to suddenly find itself in possession of the answer. The elegance, then, is in the implied isomorphism between mind and reality, or more poetically, between the wanderer and the landscape.]
How might such a lateral movement in time appear in our example of the bouncing ball? The ball itself might suddenly appear in a different part of the cube or suddenly veer off at an angle it should not, given its trajectory. It might change color, or become dimpled. Or worse yet, you might notice that the ball is bouncing at precisely the same frequency at which your heart is beating. More likely, the effect would be so subtle as to be unnoticeable. It would likely take a physicist will sophisticated measurement devices to declare that the ball is behaving "erratically" at the millionth decimal place where regards behavior expected according to classical Newtonian physics. And even then, he would probably write it off to "noise" in the measurement apparatus, or perhaps some chaos function.
So if we have "lateral" movement in time, why not "vertical"? If so, how would it function? In what ways might it manifest? Honestly, I haven't a fucking clue, but I think it's a neat idea, and I like the symmetry (3 of space to 3 of time) as well as the implied isomorphism between the two "levels".
Sub-Dimensions
Care to make it an even 9? In truth, n could be anything up to infinity, but I like 9 for its trilateral symmetry, references to the "World Tree", and its interesting numerical and numerological properties. But where do we stick these 3 extra dimensions?
Super-string theory gives us a clue. It posits the existence of other dimensions, some of which are "smaller" than our "own". Smaller? Yes, in the sense that 3-dimensional space "moves" within the "larger" dimension(s) of time, these sub-dimensions might "move" within the dimensions of space. Because of the way our "wetware reality interfaces" our designed, it's incredibly difficult (for me, anyways) to picture such a thing. I think at this point in our evolution, the best we can do is to describe them mathematically. Sadly, I cannot do this for you because matrix algebra makes me hurt in ways even I cannot fathom. I suspect, however, that if the physicist and mathematicians can create equations to describe them, that these dimensions can and likely do exist.
Evidence for sub-dimensions? I suspect it is to be found at the quantum level. It is interesting to note here the phenomenon of quantum indeterminacy: if one aspect of a particle (i.e. position or momentum) is measured [exactly], then the other aspect can only be derived as a statistical probability. Prominent physicists (e.g. Heisenber, Schroedinger, von Neuman) have taken this as evidence of an "inherent lawlessness" of matter at the quantum level. Here, the laws of Newtonian physics break down.
But we know that Newtonian physics is based upon the behavior of objects in our standard 4-dimensional universe. If quantum events are affected by the laws of sub-dimensions as well, this may begin to explain the indeterminacy effects observed here.I find it interesting to note that David Bohm (Wholeness and the Implicate Order) attempted to at least begin to explain quantum behavior in terms of "hidden variables". his hope was that if such variables could be determined, not only would they explain quantum behavior as well as current theories, but that they would also provide testable predictions that the existing theories cannot.
What better place to find hidden variables than in some [hidden] sub-dimensions where Newtonian physics have no sway?
"number nine... number nine... number nine..."
-sk
Background - Neural Networks
Back in grad-school, my lab took a semester to discuss neural-network models of learning and memory, of the sort that cognitive neuroscientists and artificial intelligence researchers have been developing in hopes of simulating the activities of the human brain/mind. Some of these models utilize a matrix involving nth-dimensional hyperspace (where n is a variable indicating the number of dimensions represented by the matix). Such models are hideously complex, but that complexity is attractive when attempting to model something as mysterious as the human mind.
Without getting into too much depth, one of the strengths of these models is that they can simulate the learning of categories through the presentation of exemplars ("examples" of a category to be learned). After a learning period during which numerous exemplars are presented to the input function of the matrix, a set of novel exemplars is presented for classification. The network produces at its output function a unique pattern of excitation for each unique category, and will, for the most part, correctly categorize new exemplars presented to it. What happens within the matrix during the learning process is that a specific set of interconnections gets created - a prototype - for each category. When new exemplars are tested, the excitation patterns across the net are "compared" to the various prototypes, and depending upon that "comparison", the appropriate category is output.One of the reasons that I like this idea is that it implies that the mind functions in more dimensions than we can normally percieve. Although we experience "reality" in only 4-dimensions (3 of space and 1 of time), the mind may by it's very nature be operating in ways we can't easily concieve of. I will return to the elegance of this supposition shortly.
Why Not Reality?
If the mind can operate in n dimensions, it seems reasonable that "reality" - of which it is part - can as well. If so, is there any evidence that it does? I think so. Picture, if you will, the following scenario:
There is a cube, which has three dimensions: horizontal, lateral, and vertical. Now toss a ball
inside the cube and let it bounce around. The ball is now moving in 4 dimensions: 3 of space and
1 of time. As time moves forward, the ball moves around the cube.
Notice that the balls movement is "causal". You impart energy to the ball, it bounces off the walls at angles appropriate to its trajectory and momentum, taking into account gravity, friction, etc. Newtonian physics in a cube. The ball's movements are determined by "what came before". Time, as we percieve it, is linear and unidirectional. Always forward - cause and effect.
Let's continue to assume that time is linear, but let's remove the requirement of unidirectionality. Now the ball may move both backwards and forwards in time along its linear axis. Unfortunately, there is no evidence that this is possible as of yet. Maybe someday someone will discover tachyons, move faster than light, or discover genuine communications from the omega-point entity. Until, then, I leave the possibility open, just for fun.
Dimensions in Time
Now let's take this one step further and propose another dimension of time, which functions at "right angles" to our original timeline, i.e. "laterally". This is the basic concept behind the "alternate timeline" themes so popular throughout modern science fiction. It is also similar in scope to the "Many Worlds Hypothesis" proposed by certain quantum physicists, in which each binary choice causes a "splitting" (or more correctly, duplication) of the universe.
Is there any evidence for this "lateral" dimension of time? Subjective experiences aside (for this I recommend the essay "If You Find This World Bad", by Philip K. Dick), the best evidence for a "lateral" dimension of time involves the experience of synchronicity (i.e. "meaningful coincidence"). While this nearly always manifests with a strong subjective component (much like deja vu - which might also be considered evidence, if one were so inclined), quite often the subject is able to document the synchronic data points in such a way as to be independently verifiable (for a foray into this form of madness I highly recommend Cosmic Trigger by Robert Anton Wilson). Events of this nature can be truly mind-boggling as to the depth of the stacked "coincidences". It is no wonder that science steers well clear of such things.
[To return to my point of elegance in regards to the human mind: think of linear, cause-effect, "horizontal" time as analogous to "left-brained", logical thought. "Lateral" time would then be analogous to "right-brained", intuitive thought. Logic plods onwards, one foot after another, while intuition leaps of the track to suddenly find itself in possession of the answer. The elegance, then, is in the implied isomorphism between mind and reality, or more poetically, between the wanderer and the landscape.]
How might such a lateral movement in time appear in our example of the bouncing ball? The ball itself might suddenly appear in a different part of the cube or suddenly veer off at an angle it should not, given its trajectory. It might change color, or become dimpled. Or worse yet, you might notice that the ball is bouncing at precisely the same frequency at which your heart is beating. More likely, the effect would be so subtle as to be unnoticeable. It would likely take a physicist will sophisticated measurement devices to declare that the ball is behaving "erratically" at the millionth decimal place where regards behavior expected according to classical Newtonian physics. And even then, he would probably write it off to "noise" in the measurement apparatus, or perhaps some chaos function.
So if we have "lateral" movement in time, why not "vertical"? If so, how would it function? In what ways might it manifest? Honestly, I haven't a fucking clue, but I think it's a neat idea, and I like the symmetry (3 of space to 3 of time) as well as the implied isomorphism between the two "levels".
Sub-Dimensions
Care to make it an even 9? In truth, n could be anything up to infinity, but I like 9 for its trilateral symmetry, references to the "World Tree", and its interesting numerical and numerological properties. But where do we stick these 3 extra dimensions?
Super-string theory gives us a clue. It posits the existence of other dimensions, some of which are "smaller" than our "own". Smaller? Yes, in the sense that 3-dimensional space "moves" within the "larger" dimension(s) of time, these sub-dimensions might "move" within the dimensions of space. Because of the way our "wetware reality interfaces" our designed, it's incredibly difficult (for me, anyways) to picture such a thing. I think at this point in our evolution, the best we can do is to describe them mathematically. Sadly, I cannot do this for you because matrix algebra makes me hurt in ways even I cannot fathom. I suspect, however, that if the physicist and mathematicians can create equations to describe them, that these dimensions can and likely do exist.
Evidence for sub-dimensions? I suspect it is to be found at the quantum level. It is interesting to note here the phenomenon of quantum indeterminacy: if one aspect of a particle (i.e. position or momentum) is measured [exactly], then the other aspect can only be derived as a statistical probability. Prominent physicists (e.g. Heisenber, Schroedinger, von Neuman) have taken this as evidence of an "inherent lawlessness" of matter at the quantum level. Here, the laws of Newtonian physics break down.
But we know that Newtonian physics is based upon the behavior of objects in our standard 4-dimensional universe. If quantum events are affected by the laws of sub-dimensions as well, this may begin to explain the indeterminacy effects observed here.I find it interesting to note that David Bohm (Wholeness and the Implicate Order) attempted to at least begin to explain quantum behavior in terms of "hidden variables". his hope was that if such variables could be determined, not only would they explain quantum behavior as well as current theories, but that they would also provide testable predictions that the existing theories cannot.
What better place to find hidden variables than in some [hidden] sub-dimensions where Newtonian physics have no sway?
"number nine... number nine... number nine..."
-sk