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Author Topic:   Dimensional Discourse
Brad McFall
Member (Idle past 5032 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 46 of 71 (167549)
12-12-2004 9:46 PM
Reply to: Message 45 by Tony650
11-24-2004 2:53 PM


Re: Something new
Yes it would be so subject to QM. I guess that unless I can no more linear work, it is possible I will not need for sensing biology material things this small. I dont believe in ghosts and aliens. Yes, you are correct but perhaps I will have something to say of Plank's oven later.
Kant had, "But, although this rule of progress to infinity is legitimate and applicable to the subdivision of a phenomenon, as a mere occupation or filling of space, it is not applicable to a whole consisting of a number of distinct parts and constituting a quantum discretum - that is to say, an organized body. It cannnot be admitted that every part in an organized whole is itself organized, and that, in analyzing it to infintiy, we must always meet with organized parts; although we may allow that the parts of the matter which we decompose in infinitum, maybe organized. For the infinity of the division of a phenomenon in space rests altogether on the fact that the divisibility of a phenomenon is given only in and through this infinity, that is an undetermined number of parts is given, while the parts themselves are given and determined only in and through the sub-division; in a word, the infinity of the division necessarily presupposes that the whole is not already divided in se. Hence our division determines a number of parts in the whole - a number which extends as far as the actual regress in the division; while, on the other hand, the very notion of a body organized to infinity represents the whole as already and in itself divided. We expect, therefore, to find in it a determinate, but, at the same time, infinite, number of parts- which is self-contradictory. For we should thus have a whole containing the series of members which could not be completed in any regress - which is infinite, and at the same time complete in an organized composite. Infinite divisibility is applicable only to a quantum continuum, and is based entirely on the infinite divisibility of space. But in a quantum discretum the multitude of parts or units is always determined, and hence always equal to some number..."
I only wonder if the metric might get turned around at the quantum level biological to include from alegra to geography a geometry of conditioned topology that takes advantage of infinite divisibility based on non-extinction IN A discrete continuum subject as you said. This seems the only way that baramins ARE valid naturally. Else the subject is non-biological (in)organic physics and not something I will ever be expert on...
This message has been edited by Brad McFall, 12-13-2004 03:59 PM

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roxrkool
Member (Idle past 988 days)
Posts: 1497
From: Nevada
Joined: 03-23-2003


Message 47 of 71 (296681)
03-19-2006 10:45 PM
Reply to: Message 1 by Tony650
08-05-2004 7:17 PM


I didn't forget about your post.
I haven't read the entire thread, Tony, but I thought I would share my opinion and experience, although I'm not sure I can add much from a geologic perspective. And please understand, I am NO mathematician. I personally find math difficult.
Unfortunately I am no closer to achieving my goal than I was before, but in fairness, I didn't really expect to be; I don't think this is something that can simply be taught, I think you have to "get it" by having a certain depth of understanding regarding the principles and probably the math, too.
I agree with your last statement. You really have to be familiar with the underlying principles before you can visualize things in 4D space, but I also think some people can do so with less knowledge simply because they have a knack for it.
I am a visual learner, but this is something I did not realize until recently when I was reading about the different ways children/people learn. Apparently, most people are verbal learners and this is generally how teachers teach in school. Verbal techniques don't work well with visual learners and so the visual learners are generally left in the dark, often feeling stupid and getting poor grades.
I think this is the reason I did not do well in math - I need to be able to 'see' how and why math works in order to 'get it' and the teachers I had very rarely made math visible to me. That pretty much goes for any and everything I'm learning. Unless I can picture something in my head and then mentally manipulate it by changing the variables, I haven't learned it.
In Calculus, because I couldn't visually see how the concepts arrive at the correct answers, I had to memorize the steps that got me the right answers. Not a very easy thing to do, but I do seem to have a knack for memorizing numbers when need be. However, without that visual understanding of the concepts (which my brain seems to require), I soon forgot the rules and missed out on that deeper and more intimate understanding of math.
I can memorize and retain facts as long as I can picture them in my head, but if I don't, I can't retain the information.
Can you learn to visualize things in 4D or 5D space? I don't know. It almost seems this is a skill you either have or you don't. I think visualizing geological processes over time is likely a thousand times easier than what Rrhain is referring to, however, but then like I said, I don't get math.
This message has been edited by roxrkool, 03-19-2006 10:47 PM

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riVeRraT
Member (Idle past 415 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 48 of 71 (296946)
03-20-2006 8:54 PM
Reply to: Message 25 by Tony650
10-27-2004 5:35 PM


Re: Rrhain, Eta, anyone?
I actually gave up trying years ago because everything I read basically said, "Don't bother...humans can't comprehend it." Then I read Rrhain's comment, which gave me a whole new lease on life regarding the subject.
Are you ready? This is where the fun starts.
First off, I really don't think that rrhain can imagine 4d, or 5d. What he is seeing in his head is nothing more than 3d folded over a few times. But I may be completely wrong, it may in fact be possible for rrhain to imagine 4d. I would love to discuss it with him, but I don't think I would be on his level, I have to study up a little more. Plus me a rrhain have never had a rational discussion.
But there is one question I have for him, and one thing I would like to share with you. I think one thing that may help you along in your little journey is this.
Picture round pipe(cylinder), 10" diameter, 3' length, Then a round pipe 6" diameter 2' length intersecting the first pipe in the middle at a 45 degree angle. See picture to get a visual:
If you can, without looking it up in a book. layout the shape of the hole that will be in the larger pipe. Never mind the pipes themselves. The amount of triangulation that is needed will start to give you the perspective I am talking about.
Go in the opposite direction. Try to look at something 3d, and see it as 2d. You see, I am a not a college grad, but I am an accomplished sheet metal layout mechanic. Top 5 in NYC. I can cover anything in metal, or look at any 3d object and immediately know how to form it from a flat sheet of metal. I actually invented trig out of necessity. I never learned it in school. A few years after I made my formulas, I read it in a book, and recognized it as trig. I made formulas that allowed me to figure out other sides of triangles, with only knowing the angle of one corner, or the length of one side. This helped me lay out certain stuff. I used to make a lot of custom things for the hospitals, in the operating rooms.
Something happens after years of trying to do this, and I can see how our 3d world is constructed, and actually fold, and unfold it in my mind. This opens up a mental doorway.
I read some of the links provided here, and it was my understanding that the 4 dimension does not have time. Since time = distance, then we would loose all points of measure, and not see things as boxes or any of those silly java scripts in those links. It was once explained to me as being inside a 3d box, looking out one end, and actually seeing your back.
I had a vision once, that I described in detail here:
Consciousness and Dreams
In the vision, I believe what I saw was 4d, although I was constrained to not move about it. It was almost like looking through a glass jar filled with water, but without any distortion. There was no front or back. I wonder if this resembles what rrhain sees in his head.
Anyway, I just rambled a lot here, I hope it makes some sense. I am not an authority on 4d, I possess the same desire as you to be able to see it.

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ringo
Member (Idle past 411 days)
Posts: 20940
From: frozen wasteland
Joined: 03-23-2005


Message 49 of 71 (296979)
03-21-2006 12:39 AM
Reply to: Message 48 by riVeRraT
03-20-2006 8:54 PM


3D --> 2D
riVeRraT writes:
layout the shape of the hole that will be in the larger pipe.
I learned to do that in High School. It's just projecting a 3-dimensional surface into 2 dimensions.
I'm guessing there's an analogous method for projecting 4 dimensions into 3, etc.

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riVeRraT
Member (Idle past 415 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 50 of 71 (297010)
03-21-2006 8:05 AM
Reply to: Message 49 by ringo
03-21-2006 12:39 AM


Re: 3D --> 2D
I learned to do that in High School. It's just projecting a 3-dimensional surface into 2 dimensions.
I'm guessing there's an analogous method for projecting 4 dimensions into 3, etc.
Yes, I learned in Junior High School, but the fittings were not as complicated as that one is.
It takes about 1 hour and 45 minutes to lay that fitting out, and put it together, on a sheet of metal. You can just follow directions and do it, or once you reach the amount of experience I have, or if you can see things in that way, you can just do it without the directions, or plans.
The point is, once you can see things in that way, without having to follow directions, your mind is expanded.
The analogous method for projecting 4d on to 3d is probably what rrhain might see in his head. If we really know what 4d is anyway. If there is no time/distance in 4d then how do we measure it?

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 51 of 71 (297124)
03-21-2006 6:29 PM
Reply to: Message 50 by riVeRraT
03-21-2006 8:05 AM


Re: 3D --> 2D
Projecting from n dimensions to m dimensions is a relatively simple process. My favourite doodle since childhood is the classic hypercube projection onto 2d. Visualising simple 4+d objects, such as the higher-d versions of the Platonic solids (the regular polytopes) isn't too bad (once you've spent several years working with them), but in general one uses projections to understand and visualise.
However, it may surprise you to realise that you haven't even begun to visualise 3d spaces! Take the surafce of the Earth, a 2-sphere as we call it... it's a surface and hence 2d. But try and visualise it without using 3d space into which it can be embedded? You can't. This doesn't mean that a 2-sphere is 3d.
Now imagine the 3-sphere. It's a 3d space so imagine yourself inside it. You can float around, but if you float far enough in any 3d direction you eventually get back to where you started. So what does this space look like? To visualise it, you need to imagine it embedded in 4 dimensions. But the space itself is still only 3d.
This is why sci-fi wormholes (Deep Space 9, Farscape, etc) are always depicted completely incorrectly. The artists have looked at our drawings and used them directly without realising that they are dimensional reductions because a wormhole is a 3d object that can't be simply visualised. Winds me up no end

This message is a reply to:
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riVeRraT
Member (Idle past 415 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 52 of 71 (297162)
03-21-2006 10:54 PM
Reply to: Message 51 by cavediver
03-21-2006 6:29 PM


Re: 3D --> 2D
Take the surafce of the Earth, a 2-sphere as we call it... it's a surface and hence 2d. But try and visualise it without using 3d space into which it can be embedded? You can't.
But I did. This is exactly what I saw in my vision. I saw the whole earth, it was a globe but I could see the whole thing.
I have met other people with similiar visions of the earth.

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ringo
Member (Idle past 411 days)
Posts: 20940
From: frozen wasteland
Joined: 03-23-2005


Message 53 of 71 (297173)
03-21-2006 11:16 PM
Reply to: Message 52 by riVeRraT
03-21-2006 10:54 PM


Re: 3D --> 2D
riVeRraT writes:
I saw the whole earth, it was a globe but I could see the whole thing.
Sounds like cubism, piCcAssO.

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crashfrog
Member (Idle past 1466 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 54 of 71 (297182)
03-22-2006 12:53 AM
Reply to: Message 51 by cavediver
03-21-2006 6:29 PM


Re: 3D --> 2D
But try and visualise it without using 3d space into which it can be embedded? You can't. This doesn't mean that a 2-sphere is 3d.
You mean, like a map? Or like a game of Asteroids where, if I fly the ship offscreen at one side it comes back from the other in the same direction of travel?
This message has been edited by crashfrog, 03-22-2006 12:53 AM

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 55 of 71 (297207)
03-22-2006 4:30 AM
Reply to: Message 54 by crashfrog
03-22-2006 12:53 AM


Re: 3D --> 2D
Or like a game of Asteroids
Exactly! Though the Asteroids playing field is not a 2-sphere, it is a 2-torus. If you wrap it up to visualise the space you get a doughnut. Welcome to topology!
How do you know it's a 2-torus? Wrap a loop of string around a 2-sphere (surafce of the earth, a ball, etc) in any way you like, and you can always shrink it down to a point. Now take one end of your string and move off the left edge of the screen, and it appears on the right. Tie it into the loop. Now try and shrink your loop... you can't, it's stuck on the 2-torus. You can do the same in the vertical direction as well. In fact, you can count how many wraps you make in both directions, call them A and B. The 2-torus can be identified by the algebra of A+B. Welcome to algebraic topology!
You can have a 3-torus, where we live in a space that repeats itself in the 3 orthogonal directions; a bit like the 3-sphere but different for similar reasons as given above. My first research, done as an undergrad back inthe 80s, was into investigating whether our universe exhibited this kind of behaviour.

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riVeRraT
Member (Idle past 415 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 56 of 71 (297261)
03-22-2006 8:54 AM
Reply to: Message 55 by cavediver
03-22-2006 4:30 AM


Re: 3D --> 2D
You can have a 3-torus, where we live in a space that repeats itself in the 3 orthogonal directions; a bit like the 3-sphere but different for similar reasons as given above. My first research, done as an undergrad back inthe 80s, was into investigating whether our universe exhibited this kind of behaviour.
Does this have anything to do with time and space being on a curve?
Also, when I think about it, 1d, and 2d really don't exist at all, only in theory. They are immeasurable in 3d.

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 57 of 71 (297271)
03-22-2006 10:06 AM
Reply to: Message 56 by riVeRraT
03-22-2006 8:54 AM


Re: 3D --> 2D
Does this have anything to do with time and space being on a curve?
Well, yes and no Curvature of space and time is a local property, and is what we call geometry. We can see its effect all around us (we "fall" to the ground) The large scale property that we are mentioning here cannot be so easily observed. It is global and is what we call topology.
And you don't need one for the other. Crashfrog's asteroids game has a completely flat space and yet it still wraps around on itself. Any curvature here is purely an effect of visualising the space (as in wrapping it up to make a dougnut) and isn't real. We call this extrinsic curvature. The curvature of space-time that leads to you falling to the ground is very real and is intrinsic curavture.
This message has been edited by cavediver, 03-22-2006 10:07 AM

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2ice_baked_taters
Member (Idle past 5850 days)
Posts: 566
From: Boulder Junction WI.
Joined: 02-16-2006


Message 58 of 71 (321090)
06-13-2006 11:44 AM


I attempted to start a thread that directly applies to this one. I was led here by Mr. Ad-Mooseus- thank you sir.
I have scanned this thread and see what I believe to be a repeated mistake. All discussion thus far attempts to think of a fourth or greater dimension in terms of direction. This may be the limiting factor. I would like to have you consider that the process of thought is not limited to the three dimensions discussed. We opperate on a daily basis in a realm we could never express in three dimensions. Language seems to be the best tool. Our minds work on a level or levels far beyond what math can express. I am thinking to understand the fourth dimension is to leave the chains of math behind. To attempt to express it with math would be like a group of monkeys playing Bach with used car parts. To concieve and accept a greater dimension means you must stop attempting to fit it into 3 dimensional boxes.

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Scrutinizer
Inactive Member


Message 59 of 71 (321612)
06-14-2006 9:36 PM
Reply to: Message 58 by 2ice_baked_taters
06-13-2006 11:44 AM


2ice_baked_taters writes:
All discussion thus far attempts to think of a fourth or greater dimension in terms of direction. This may be the limiting factor. I would like to have you consider that the process of thought is not limited to the three dimensions discussed.
I agree with you that thought is not limited to three dimensions. In fact, one might even need to use a quadrillion-dimensional space to describe any one human mind. (I believe that there are somewhere around one quadrillion synapses in the human brain. Technically, a single point in this vast hyperspace may represent an entire state of mind, including every conscious and unconscious thought at any one time.)
However, although we may use many abstract dimensions in our thought processes, most people cannot form a mental picture of anything with more than three physical dimensions. In other words, we may use many dimensions more than four to think, but we still cannot visualize higher dimensions, in the sense of mutually perpendicular directions.
2ice_baked_taters writes:
I am thinking to understand the fourth dimension is to leave the chains of math behind. To attempt to express it with math would be like a group of monkeys playing Bach with used car parts.
I will have to disagree with you on this point. Math is a very useful tool, especially in dealing with dimensions beyond human comprehension. Certainly it's more interesting to try to visualize higher dimensions than to represent them with mathematical formulas, as true visualization would give us a more intuitive grasp of higher dimensions. But if we use math, we can at least put ourselves on the right track to understanding them, especially since we need math in order to simulate them.
2ice_baked_taters writes:
To concieve and accept a greater dimension means you must stop attempting to fit it into 3 dimensional boxes.
no argument there

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 Message 58 by 2ice_baked_taters, posted 06-13-2006 11:44 AM 2ice_baked_taters has replied

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Scrutinizer
Inactive Member


Message 60 of 71 (321651)
06-14-2006 11:18 PM
Reply to: Message 9 by Tony650
08-10-2004 3:42 AM


Re: Rrhain, Eta, anyone?
I know Tony650 stopped posting on this thread way back in 2004, but I still think it would be appropriate to answer his three main questions on dimensions.
Tony650 writes:
1. Does anyone have any suggestions on visualizing/perceiving 4D, or any of its properties, beyond mere 3D analogues?
Yes I do. I believe it is possible to retrain one's brain to be able to conceive 4D, though this would take immense focus and a long time to do. The mathematician Charles Hinton (I believe that's his name) once tried to visualize the fourth dimension by creating a mental 36*36*36 unit cube to represent the 3D retina a 4D creature would have. He then assigned each box in this cube a Latin name, and when he tried to map 3D objects into this "retina," he would recite the name of each cube (voxel) the object occupied. This was a painstaking process, and I think he may have given up this exercise, thinking 4D perception was impossible. I'm sure others have found simpler, though probably just as difficult, methods to "rewire" their perceptions, but I do not know anyone who has done so.
Virtual reality is probably a much more efficient way to learn 4D. Just as when you were a baby, you learned to perceive the world as 3D by combining perceptions from different senses (i.e., vision, audition, kinesthetic, vestibular, touch, etc.), full body immersion into a virtual 4D environment should allow faster comprehension of the fourth spatial dimension. A couple of years ago, I came across a project to create "4D Virtual Environments" where participants would wander around a complex four-dimensional spaceship and manipulate objects. Unfortunately, though, as I saw on a demo simulation of the project, the person in the VE can only see a single 3D "slice" of spaceship at a time, though they could still move in the fourth direction. A description of the project is at http://www.cvr.uci.edu/dzmura/4D/ndtech3.pdf. (The URL may be old, so you may need to use a Google cache to view the page.)
I think that if you could find a way to transform the picture on the 3D retina of the 4D virtual creature to be able to fit on our 2D retinas without losing any visual information, we could quickly learn to see as a 4D person would see. I would also suggest incorporating "4D sound" to assist in perception of the "4D-ness" of the virtual environment. Anyway, until this technology comes about, I guess we could just keep on trying to visualize the fourth dimension on our own.
Tony650 writes:
2. Is there any way (at least, in principle) that we could test for, and detect, the "extra" dimensions of our universe, curled up at the smallest level?
I haven't thought about this as much, and I would need to be more familiar with quantum mechanics and string theory to get an idea of how to do this. But I believe there is a way, it's just a matter of technology. I read somewhere that if we created super-small, super-temporary doughnut-shaped black holes from a large enough particle collision, it would prove the existance of at least 5 dimensions to our universe, and I heard that scientists are trying right now to build a large particle accelerator to do just just that. Don't worry, though; the black holes would be so small that they would decay almost as soon as they were created.
Tony650 writes:
3. Is the concept of a spacetime (not ours; just hypothetically) with more than one temporal dimension possible? If so, what would be the properties of such a universe? What would life there be like? Could anything even exist in it or would causality fragment into chaos?
This is a very interesting concept. Of course, it is relatively easy to describe a universe with multiple temporal dimensions mathematically; comprehending it is another story. Several years ago, when I first started thinking about extra dimensions, I hypothesized on the properties of extra tempral dimensions. The first dimension here would be time, composed of the "now" and the two opposite directions of past and future, just as the first spatial dimension has "here" and backward and forward. Are you with me so far? The second temporal dimension, then, would also have the "now," but it would be perpedicular to time. Instead of past and future, it would have two unique directions. You could represent multiple temporal dimensions as perpendicular axes intersecting at "now."
With two temporal dimensions, time would no longer look like a line, but rather like a plane. Movement in such a universe would also be different. Instead of moving in a line, you would move in a plane. With 3 temporal dimensions, you could move in a volume. Now imagine a simple universe with only one spacial dimension. Tiny line segments can move only back and forth in their universe. Try to visualize time as a spacial dimension, so that if a point in the 1D universe were to move back and forth repeatedly, it would look like a static zig-zag line on a plane (Remember this plane is a spacetime, so any line drawn on it is actually movement, with the slope of the equalling the speed of the object). If we add another temporal dimension, we can view this simple universe in one of two ways: either as the zig-zag suddenly beginning to move or as a static bumpy plane in a 3D spacetime (Remember, this is still just a single point moving back and forth in a universe with only 1 spatial dimension; it now only looks like a bumpy plane because we are viewing its motion with 2 temporal dimensions). If anyone cannot visualize this, I could try to post a picture of it, as long as someone tells me how to do that.
I have read before that a universe with 2 or more temporal dimensions would be inherently unstable, just as would be one with 4 or more spatial dimensions, so life probably could not exist in such a world.

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