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Author Topic:   Dimensional Discourse
Tony650
Member (Idle past 4023 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 1 of 71 (130824)
08-05-2004 7:17 PM


Time for another (hopefully) non-controversial thread. By "non-controversial" I just mean that I don't want to incite any arguments if I can help it. I know this is a debate forum, and that's cool, but as was the case with my first thread, my purpose here is not to argue, it's just to learn.
Incidentally, my first thread, Relative Motion (A Thought Experiment), is of course still available for anyone to reply to, if they wish. It kind of died about half way through, I'm afraid. This was partly my own fault for getting so far off topic. Still, if anyone thinks they can help me with it, by all means, feel free. Also, I may still be uncertain about the overall scenario but I am a little clearer on certain specifics so thank you to those who helped me out, it is greatly appreciated.
Anyway...
Of all the concepts I've pondered over the years, the one that stands out in my mind as having fascinated me the most is that of higher dimensions. Why is this? I honestly don't have a clue. Perhaps it's because the basic principles of it are so unimaginably simple, yet the consequences of it are so paralyzingly inconceivable. Who knows?
Whatever the reason, I spent years trying to grasp the reality of higher dimensions. Not to merely "understand" them in terms of extrapolated principles but to actually comprehend their true nature; to visualize four dimensional space and geometrics (naturally I am in no way averse to visualizing indefinitely more than four dimensions but let's not get ahead of ourselves ).
I long ago gave up on this pursuit, concluding that it was simply impossible. Then for a long time I didn't look into it very much, until my interest was resurrected by a comment from our resident mathman, Rrhain.
Rrhain writes:
When I was in my prime as a mathematician, I had no problem visualizing four-dimensional surfaces and if I tried hard enough, I could get fleeting glimpses of five-dimensional ones, too. We live in a three-dimensional world and it is hard to conceive of what a 4D space looks like.
Do not confuse your inability to visualize something with the idea that it cannot be done.
I nearly fell out of my chair when I read that...Seriously!
A brief exchange between us ensued in these three posts and Rrhain's replies. 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.
To that end, I thought it would be educational to open a thread on the subject. I don't really have any specific topic in mind, except the principles of dimensionality and concepts relating to higher dimensions in particular.
I hope Admin is ok with this; the point of this thread is simply for my own (and anyone else's) education on the subject. I apologize for being so vague and not really making any opening statements or asking any specific questions; I was hoping to leave the floor somewhat open for others to comment on and discuss more specific points under the general topic, and just see where it goes.
So, Admins permitting, I propose a generic dialogue on the topics of higher dimensions, dimensional constructs, properties of dimensionality, etc. If however we do need something to get us started, I might be inclined to ask if anyone else has ever been able to comprehend higher dimensions, and if so, how did you achieve this? What led to your understanding? Is there any way you can describe it (without using three dimensional analogues)? Do you think it requires a strong proficiency in the underlying math?
Incidentally, just to be clear, I'm not so naive as to think that I will learn enough from this thread to start visualizing higher dimensions. I really should amend the third paragraph above this one, to read; "To that eventual end..."
Indeed, if the mathematical fluency necessary to visualize higher dimensions is anything approaching Rrhain's then I will likely never achieve it. However it's a topic that I have always found absolutely mesmerizing regardless of my incomplete comprehension, and if I learn something new from this or gain even the smallest insight I didn't have before, then the thread has served its purpose.
Ok, having finished my ramble...
Dimensions...
Discuss!

Replies to this message:
 Message 7 by Rrhain, posted 08-08-2004 10:01 AM Tony650 has replied
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AdminNosy
Administrator
Posts: 4754
From: Vancouver, BC, Canada
Joined: 11-11-2003


Message 2 of 71 (130847)
08-05-2004 8:25 PM


Thread moved here from the Proposed New Topics forum.

  
Tony650
Member (Idle past 4023 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 3 of 71 (131001)
08-06-2004 12:01 PM


Too vague, perhaps?
AdminNosy writes:
Thread moved here from the Proposed New Topics forum.
Thank you, Ned.
So would anyone like to contribute? I realize the opening post was somewhat ambiguous but I didn't really know what to narrow it down to. If I were to simply ask how to visualize higher dimensions, I think that would end the conversation pretty quickly.
That's why I gave the thread such a wide scope; I just want to learn more about the general subject. I know I won't be able to comprehend 4D space based on the small amount of tuition this thread will give me, but every little bit counts.
Also, don't assume that you have to be knowledgeable about this to post; feel free to ask your own questions if you have any. Would anyone like to ask me anything? I can't guarantee I'll be able to answer (I am by no means an expert; my knowledge of this subject is all "self-taught", so to speak) but I'll see what I can do. And if I can't give you an answer, I'm sure there will be others capable of doing so. In any case, it's a way to kick off the discussion.
So...Questions? Comments? Anything? Anyone?
Feel free!

Replies to this message:
 Message 4 by Hangdawg13, posted 08-07-2004 4:10 AM Tony650 has replied

  
Hangdawg13
Member (Idle past 741 days)
Posts: 1189
From: Texas
Joined: 05-30-2004


Message 4 of 71 (131262)
08-07-2004 4:10 AM
Reply to: Message 3 by Tony650
08-06-2004 12:01 PM


Re: Too vague, perhaps?
Hmm... 4-D space...
You could go up, down, left, right, forwards, and backwards, ilkwards, and drekwards.
Make sense? No... I guess not.
The only way I can imagine a fourth dimension is by giving a point temperature or density, but thats not a "true" dimension in the spacial sense.
My mind just starts to meltdown if I try to imagine the 4th dimension.
Apparently, if you wanted to see higher dimensions you'd have to have a perception on the level of a billion billion billion-th of a fraction of your current size.
Anyway, sorry I don't have much to add... though I did start reading parts of the Elegant Universe again today.

This message is a reply to:
 Message 3 by Tony650, posted 08-06-2004 12:01 PM Tony650 has replied

Replies to this message:
 Message 5 by Tony650, posted 08-08-2004 9:30 AM Hangdawg13 has not replied

  
Tony650
Member (Idle past 4023 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 5 of 71 (131558)
08-08-2004 9:30 AM
Reply to: Message 4 by Hangdawg13
08-07-2004 4:10 AM


Re: Too vague, perhaps?
Hangdawg13 writes:
You could go up, down, left, right, forwards, and backwards, ilkwards, and drekwards.
Yup, that's about right!
Actually it's up and down, left and right, forwards and backwards, ana and kata (although, you'll have to forgive me, I don't remember who coined those terms).
Hangdawg13 writes:
The only way I can imagine a fourth dimension is by giving a point temperature or density, but thats not a "true" dimension in the spacial sense.
Yes, Rrhain suggested something like this to me (temperature gradient, as I recall), but as you said, it is not a true spatial dimension. It still requires what I believe Rrhain referred to as a "visual leap". Ack! How do you make that leap?
Hangdawg13 writes:
My mind just starts to meltdown if I try to imagine the 4th dimension.
Tell me about it! Did you read Rrhain's quote where he said that when he really concentrates, he can even catch glimpses of five dimensions? At the risk of sounding unscientific, how bloody cool is that?
Hangdawg13 writes:
Apparently, if you wanted to see higher dimensions you'd have to have a perception on the level of a billion billion billion-th of a fraction of your current size.
Yes, so I understand. They are there but curled up so tightly that they're too small to detect, at least with current technology. Actually that may be a good question to discuss as part of this thread; can we ever detect such "micro-dimensions"?
Mind you, I don't think there's any reason (in principle) that more dimensions couldn't exist on a macroscopic scale. It's just that it's something we've never seen, so visualizing it is tricky (to say the least).
I think the problem is that our minds are trained to think in three dimensions and we can't help but do the same when trying to imagine 4D (or higher) concepts. So it would seem that if we're ever to comprehend them we need to change the way we think about them. How we do that, though, I have no idea.
It's frustrating that I always find myself falling into this trap. No matter how hard I try, I can't seem to get away from visualizing 3D analogues. It's all my mind knows, it's all the world has taught me.
I'll attempt to visualize the fourth axis and then realize that I'm trying to align it, perpendicular to the other three, in three dimensions of space. Argh! That won't work!
The problem here is that I'm trying to visualize the fourth axis so that I can find the fourth dimension, but to place it correctly I first have to visualize the fourth dimension; it's a vicious circle.
Anyway, I'm getting a little carried away now. [ / rant mode ]
Hangdawg13 writes:
Anyway, sorry I don't have much to add...
Heh, are you kidding? Thank you just for replying! At least my other thread went a few pages before throwing it in; I thought this one was going to die after the first post.
To be honest, I was quite surprised when I came back and there were no replies; I find this subject virtually off the scale as far as fascinating concepts go. Perhaps I'm the only nut who thinks so.
Hangdawg13 writes:
...though I did start reading parts of the Elegant Universe again today.
I haven't read that one, but I know of it. I'll have to look for it some time.
I can't say I'm very familiar with the author but I've read quite a few others; Stephen Hawking, Richard Dawkins, a whole bunch of Paul Davies. And I just bought Carl Sagan's Cosmos...Woohoo!

This message is a reply to:
 Message 4 by Hangdawg13, posted 08-07-2004 4:10 AM Hangdawg13 has not replied

  
Tony650
Member (Idle past 4023 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 6 of 71 (131561)
08-08-2004 9:42 AM


A couple of questions to make things more interesting (I hope)
Ok here are a couple of questions to (hopefully) give things a bit of a push along.
The first one hit me during my last post. It's open to everyone, of course, but it might be interesting to hear from someone in the appropriate fields; particle physics or quantum theory, perhaps?
As far as I'm aware, we currently have no way to directly detect the "extra" dimensions of our universe (the non-macroscopic dimensions). They are curled up so tightly that they're smaller than the smallest elementary particles. So is there any way (even in principle) that we could ever detect them?
The clincher for me (although I may be misinformed about this) is that I understand they are believed to be on the scale of, or close to, Planck length. If this is true, doesn't it somewhat seal our fate? Considering we have nothing on that scale to work with, how would we go about "looking" for them?
Or am I on the wrong track? Is there another way we could test for their presence? Perhaps we could do away with matter altogether and "scan" for them with fields somehow? Still, even then, I can't see how we could get a meaningful result at that level. Mind you, we're starting to get into the realm of quantum physics and I'm not as well versed in that field. Hell, is anybody well versed in it?
The second topic regards one of the more "exotic" ideas I've read about; the concept of a space-time universe with more than one temporal dimension.
Ok, obviously we aren't talking about our universe here but it's an interesting concept, none the less.
To keep things "relatively" simple, let's say that this universe is the same as ours, in spatial dimensions. However, whereas our universe is four dimensional space-time with three of space and one of time, this universe will be five dimensional space-time with three of space and two of time.
Well, I guess my first question has to be; is this even possible? Or does the nature of time simply forbid such a combination?
If it is possible, what would this mean? What kinds of properties would its geometry have? What would it be like for beings living in this universe? Could anything even exist in such a realm? Or would the entire concept of cause and effect collapse into chaos?
This is another one I'm having a hard time picturing. Anybody think they can clarify it a little for me? Or is this concept simply not possible?
Incidentally, the original question about visualizing dimensions still stands; if anyone can give me any pointers, I'll be forever in your debt (and I mean that literally because I can't pay you anything ).
Ack! I need to sleep. I hope I was coherent enough. I have a hard enough time collecting my thoughts on these topics when I'm not tired.
P.S. I've passed 100 posts! What do I win?

  
Rrhain
Member
Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 7 of 71 (131562)
08-08-2004 10:01 AM
Reply to: Message 1 by Tony650
08-05-2004 7:17 PM


Well, I don't know if this will help, Tony650, but it may help stir the creative juices.
In The Elegant Universe, Greene tries to help us understand the 10-dimensional universe we might be in if certain aspects of Quantum Theory are true. While we can easily see three spatial dimensions, there are others that are "curled up" so tightly that we cannot detect them on the macroscopic scale. But how to visualize them?
Well, consider a telephone wire. From your vantage point in your room looking out the window, that line is essentially a one-dimensional object. But consider it from an ant's point of view on the line. There's still forward and back, but now there's clockwise and anti-clockwise...a second dimension that can only be seen from the scale of the wire, itself.
Now, while that is directly applicable to the "curled up dimension," it has secondary ideas to multi-dimensional thinking. When we think about three dimensions, we usually think in terms of straight lines: Forward and back, left and right, up and down. But there are other ways to think of them such as rotational: Pitch, yaw, and roll. If you are in a linear frame of mind, it's hard to think of things in a rotational sense. Those who have taken calculus may recall the unit on cylindrical and polar coordinates and how that changes the calculus.
Actually, that last could be a bit helpful. You see, if you do enough work in, say, spherical coordinates, you start to think that way. There's some of this when you work in real-life trigonometry where things are expressed in radians rather than degrees...you start to see a right angle as 1/2 pi rather than 90.

Rrhain
WWJD? JWRTFM!

This message is a reply to:
 Message 1 by Tony650, posted 08-05-2004 7:17 PM Tony650 has replied

Replies to this message:
 Message 8 by Tony650, posted 08-08-2004 2:20 PM Rrhain has not replied

  
Tony650
Member (Idle past 4023 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 8 of 71 (131632)
08-08-2004 2:20 PM
Reply to: Message 7 by Rrhain
08-08-2004 10:01 AM


Rrhain, just the mathematical dynamo I was hoping to hear from!
Rrhain writes:
But consider it from an ant's point of view on the line. There's still forward and back, but now there's clockwise and anti-clockwise...a second dimension that can only be seen from the scale of the wire, itself.
Damn! Are you sure you're not psychic? I read this exact same analogy, like, two days ago! Heh, spooky. But yes, I understand the principle.
One thing I'm not clear on, though, is whether or not the "wire analogy" is supposed to actually represent the reality of the situation or if it is merely a lower dimensional analogue, such as the three dimensional analogues of 4D primitives.
My understanding is that superstrings are only one dimensional anyway. So how does this actually constitute "extra" dimensions? Even if we allow the "clockwise/anti-clockwise" axis to count as a dimension, doesn't that just give us a two dimensional object in three dimensional space?
As I understand it, one of the properties of dimensions is that an object with dimension x cannot be contained by a space of any dimension less than x. Hence my confusion; if these "curled up" dimensions contain more than three spatial dimensions, they cannot be all there (in our space), can they? Most of their volume (hyper-volume?) must be poking out of our three dimensions along their other axes, right? Or are they so tiny that they literally squeeze all of their "extra" dimensions "flat"?
Even in this case, I'm not sure I see the distinction. If I take a cube and flatten it into a square, could the inhabitants of Flatland really say that it was three dimensional on the microscopic level? Haven't I simply turned it into a two dimensional object?
If 3D space truly has zero size along the fourth axis, the only way these other dimensions could be contained within it would be if they too were squashed down to zero size. That's fair enough but if they have zero size, how can they be a dimension? Isn't zero size dimensionless, by definition?
Or perhaps our space isn't really three dimensional at all; perhaps our space is actually three and a bit dimensional (that is to say, three and the teeniest, tiniest bit dimensional).
If it has the most minuscule (yet non-zero) size along the fourth axis then I could understand how these can be higher dimensions curled up on the smallest conceivable scale. But if it truly is without any size at all along the fourth axis, I really can't see how these dimensions, however small, can "fit" in our space. Unless they are completely flat, in which case, aren't they simply three dimensional?
Hmm...Looking back, I'm not too sure how that came across. Just to be clear, I'm not arguing with you; I'm just asking questions. I know what you're telling me will be correct and I'm just explaining what I'm having trouble understanding. Just in case I seemed like I was being confrontational; I wasn't.
Rrhain writes:
If you are in a linear frame of mind, it's hard to think of things in a rotational sense.
Yes, this is one of my problems, no doubt.
Rrhain if you don't mind telling me (because I am very curious about this), just how well can you (could you) visualize 4D? I understand that there's no way you can describe what you see but can you perhaps give me some very general examples?
For instance, you mention thinking in a linear way; can you actually picture four perpendicular axes? Can you rotate a 3D object in 4D such that you can see all of its points simultaneously?
Or 4D primitives? Can you visualize a tesseract? Not the 3D analogue but the real thing? Can you see its true form? To use another analogy, Flatland's resident mathematician has such a grasp on the properties of the "hyper-square" that he is actually able to picture, in his mind, a true-to-life, three dimensional "cube". Can you make this kind of leap from a hypercube to a true tesseract?
Ugh! I'll leave it at that for now. I greatly appreciate your reply; you're the person I really wanted to hear from in this topic. Thank you!
And I apologize for rambling so much; this is just something I love. You really picked the wrong guy to reveal your special skill in front of, didn't you? I think you've awoken a sleeping giant.

This message is a reply to:
 Message 7 by Rrhain, posted 08-08-2004 10:01 AM Rrhain has not replied

Replies to this message:
 Message 13 by Brad McFall, posted 09-22-2004 9:51 AM Tony650 has not replied

  
Tony650
Member (Idle past 4023 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 9 of 71 (132255)
08-10-2004 3:42 AM


Rrhain, Eta, anyone?
Hmm...My thread isn't that boring, is it? My apologies guys, I really thought this topic would generate more interest. It fascinates me almost to the point of obsession; I guess I just assumed it would be popular with others, too.
Well, a little bump to see if anyone's still out there. Also, I tend to ramble a bit between applicable points, so here's a brief summation of my main questions, so far.
1. Does anyone have any suggestions on visualizing/perceiving 4D, or any of its properties, beyond mere 3D analogues?
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?
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?
If any of these interest you, or something else under the general topic that I haven't mentioned, please feel free!

Replies to this message:
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Itachi Uchiha
Member (Idle past 5605 days)
Posts: 272
From: mayaguez, Puerto RIco
Joined: 06-21-2003


Message 10 of 71 (132405)
08-10-2004 2:59 PM


When I was taking my multivariable calculus course in college, I always used (and still do) to imagine what would it be like living in a 4d universe. From what ive seen here in college the subject of higher dimensions easily becomes a battleground between physicists and mathematicians. Usually mathematicians believe in higher dimensions because of the numerical evidence and physicists don't because there is no physical evidence. Even though higher dimensions cant be proved in a lab I tend to favor mathematicians on this subject. This is mostly because I believe that there is more in this world that can be apreciated in a 3d world.
In that multivariable course i was taking the profesor raised an interesting situation in class. He draw on the board a table and on top of the table a little point representing an ant and a circle that represented a cookie jar with a cookie inside. He explained that the ant in the 2d board could only go foward and backward and because of this he couldn't find the opening to the jar that was at the top. Then he said that he was some sort of god and lived in another dimension and could see what was going on with the ant. He said that he told the ant to climb up the jar and that evetually he would reach the opening. He said the ant just needed faith in what he told him but because the ant couldnt find the logic in what the professor was saying he just coninued pushing into the jar without success. When he finished the story he turned to the students and said what if there is reallly a God in a higher dimension who wants to help us with our lives but we just dont listen because it makes no sense to us. Almost the entire class raised their hands wanting to ask a question but he said just think about it and dismissed the class.
I totally agree with him

Ponlo todo en las manos de Dios y que se joda el mundo. El principio de la sabiduria es el temor a Jehova

  
1.61803
Member (Idle past 1494 days)
Posts: 2928
From: Lone Star State USA
Joined: 02-19-2004


Message 11 of 71 (132505)
08-10-2004 7:20 PM
Reply to: Message 9 by Tony650
08-10-2004 3:42 AM


1. We are 3 D creatures, it is difficult for 3D reasoning to comprehend other multiple dimentions. Mathmatical models and extravagant shapes still leave much to be desired. Your wire analogy is good. Now try to imagine the 2D present and horizon then the 3D around and go one futher and go within the large wire and within it is Hundreds of thousands of wires all with they're own dimentions.
2. No. (* not that I am aware of)
3. As for your final point..... life is stranger than fiction. In other words I do not know. *edit
This message has been edited by 1.61803, 08-10-2004 06:24 PM

"One is punished most for ones virtues" Fredrick Neitzche

This message is a reply to:
 Message 9 by Tony650, posted 08-10-2004 3:42 AM Tony650 has replied

Replies to this message:
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Tony650
Member (Idle past 4023 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 12 of 71 (133989)
08-15-2004 12:23 AM
Reply to: Message 11 by 1.61803
08-10-2004 7:20 PM


1.61803 writes:
1. We are 3 D creatures, it is difficult for 3D reasoning to comprehend other multiple dimentions.
Heh, it sure is! I've been looking around the internet and have actually come across a few others who say they can do it. The impression that I get from them, generally, is that you have to virtually retrain your mind in how to think about things.
Since our sensory input is entirely in three dimensions from the time we're born, that is how our minds are trained to codify everything. This can take quite some undoing, apparently. I've heard that even excluding learning the math and physical concepts, it can take a lot of time and patience just to get your mind thinking the right way. I don't doubt it.
1.61803 writes:
Mathmatical models and extravagant shapes still leave much to be desired.
Yes, the problem is that the models can only show us three dimensional "slices" of 4D objects. As I understand it, if a true 4D space/object is ever to be seen, the only place it can happen is in the mind; there is simply no way to do it in our spatial dimensions.
It would be like someone in Flatland trying to build a model of an actual cube; he couldn't do it because there is simply no "space" to do it in. The only place he could ever conceivably "see" a true cube is in his mind.
1.61803 writes:
Your wire analogy is good.
Well, thanks but it was Rrhain that brought it up.
1.61803 writes:
Now try to imagine the 2D present and horizon then the 3D around and go one futher and go within the large wire and within it is Hundreds of thousands of wires all with they're own dimentions.
Hmm...I'm afraid you lost me here. Could you elaborate on this? In particular, what do you mean by "the 2D present and horizon then the 3D around?"
1.61803 writes:
2. No. (* not that I am aware of)
Really? None at all? Bummer. Is there no way to even test the mathematical models to see if they're accurate?
I guess the question at this point is; are there any qualitative differences between what we should see if our model of tightly curled up dimensions is correct and what we should see if it's incorrect (even if present technology doesn't have the means to test for those differences)?
1.61803 writes:
3. As for your final point..... life is stranger than fiction. In other words I do not know.
Heh, good answer. Neither do I.
I think this question, in particular, really delves into the realm of speculation, as it's a concept that we have not only never experienced, but quite possibly, never could experience. As beings whose psyche is so intimately linked to a single, mono-directional time, I have my doubts as to whether or not we would have the capacity to make any sense of a "multi-temporal" universe, even if we were thrown into one.
That's not to suggest, of course, that we can't create models to determine the properties it ought to have, but as far as experiencing it, I really don't know if we could.
At any rate, does anyone want to take a shot at it? Any ideas on what a universe with multiple dimensions of time would be like?

This message is a reply to:
 Message 11 by 1.61803, posted 08-10-2004 7:20 PM 1.61803 has not replied

  
Brad McFall
Member (Idle past 5023 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 13 of 71 (143855)
09-22-2004 9:51 AM
Reply to: Message 8 by Tony650
08-08-2004 2:20 PM


http://www.jimloy.com/books/4d0.htm
You substantively and goodly said, "My understanding is that superstrings are only one dimensional anyway. So how does this actually constitute "extra" dimensions? Even if we allow the "clockwise/anti-clockwise" axis to count as a dimension, doesn't that just give us a two dimensional object in three dimensional space?"
I guess you are giving me reason to FINALLY get around to reading RUCKER (I have been tempted many a time but never got around to reading the likes of
http://www.jimloy.com/books/4d0.htm
etc).
I DO see why you indicate that any group of 1-D strings would not be "extra" dimensionally but indeed I might be able to suggest how in the "nothing but BM" thread is related to YOUR visualization issue. I will do some personal reading on this as you seem to be the only one here really interested in "panning" down my posts. You might be absolutely correct about there being nothing 'extra' dimensionally here but I am not certain that an old idea I had of relating the Butterfly Catastrophe to statistics of normal distributions might (not) allow me to present or demonstrate what it is you were asking about. ??
Pages perso Orange - Domaine obsolte
Let me know this. I will try.
Here are some of the problems/issues/difficulties I am noticing in linking up your visualizability and my vision.
John Archibald Wheeler in "Geometrodynamics" wrote page 129 "VII - The Central Position of the Neutrino in Elementary Particle Physics. In conclusion, the vision of RIEMANN, CLIFFORD and EINSTEIN, of a purely geometrical basis for physics, today has come to a higher state of development, and offers richer prospects - and presents deeper problems - than ever before. The quantum...between this virutal foam-like structure...seems no escape from indentifying these wormholes with <>" but the electrons I will be discussing for any attempt to build a read all about it cantor dimension WILL be in this difference of dressed vs undressed but it will be difficult to keep clear, in English, what the electron (sub)population actualy is that nonethemore would remand a macrothermodynamic equilibrium no matter the foam etc.
In other words, what Russell named 'co-superficial' WILL divide this sample of electrons that I discriminate across isothermals from what ON THE AVERAGE Gladyshev works with. (Russell THE ANALYSIS OF MATTER Space-Time Order p 311 "The further development of our geometry, so as to include surfaces, volumes, and four-dimensional regions, obviously presents no difficulty in prinicple, and I do not propose to enlarge upon it. I will merely observe that it is possible to extend the method by which we have defined points and lines so as to obtain something wihch we may call surfaces and regions, though not quite in the usual sense. Probably various ways of doing this are possible; the one I suggest is..") I have many pages of notes on using Cantors' ascending Ps that occur mathematically before he developed ordertypes in terms of READINGS OF CROIZAT (panbiogeography) (and I started to explain this, to my self (in notes) in terms of Pascal's position on propositions) but it will not be easy for me to directly relate what I DID THINK as a surface to a region that might be 4-D. I am interested in black body radiation, baraminic discontinuity and Einstein's attempts to use parralel math but it has always been easier for me to NOT THINK about Bohr and side with Einstein as to the philosophical position of clock without a rod or a rod without Poincare against Cantor etc etc...I regress to BM speak...
Nonetheless, I FULLY EXPECT, Einstein, "The meaning of Relativity" p 75 " The Riemann Tensor. If we have give a curve extending from the point P to the point G of the continuum, then a vector...otherwise, the result depends on the path of the displacement "
to remand equally for biology and physics. And just now I am trying out Russell's idea on intersection with Georgi's notion of cross time and space hierarhies phenomenologically. I have not tried to think of Popper's 3rd world but I dont suspect this is impossible "in the region" as word without denotation. I have to see if my own connotation can be ORDINaTED with your visualizability! I expect higher order vertex sets of minimal spanning trees can provide the coverage of the path but I have not attempted the maths on it. The difficulty for me, is that chance dispersal OR vicariance are not categorically rejected nor is there an explict null hypothesis currently under test. This of course does not stop one from forming notions a la Rucker but I will first be, without the fluff, noting how differently CODED 1-D symmetries might classify mutations into new cateogorizations that if indeed related to INDPENDENT magnetic properties might enable the direct use of the physical probabilites IN THE algebra of Hardy Weinberg PER EQUILIBRIUM. But whether or not catastrophe theory needs be added to the descriptive tool kit I did not, as of yet, know. The history of biology indicates to me that it does. It may even be that c/e dependent so much on joint historical disputes IS NOT the place to discuss it but that can not be determined without the virture you thought Rhain to have provisioned.
This message has been edited by Brad McFall, 09-22-2004 10:31 AM

This message is a reply to:
 Message 8 by Tony650, posted 08-08-2004 2:20 PM Tony650 has not replied

  
Brad McFall
Member (Idle past 5023 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 14 of 71 (147517)
10-05-2004 12:50 PM
Reply to: Message 9 by Tony650
08-10-2004 3:42 AM


Re: Rrhain, Eta, anyone?
I am just about finished with a response that details what conditions I need to be able to DEDUCE an extra dimension and in the process I think I have really managed to understand ALL of Georgi Gladyshev's point(s) (except how much Russian Culture itself assisted him in the formulation etc)however to be fair I still need to look into possibly one slip up on my part which did bear on your query Tony.
I state this here more for my own benefit than yours but we might end up back here after I go on. Georgi had said (I will do all the reference stuff if we HAVE to come back to this tissue) "Many investigators, as the reader knows for sure, also identify the classical Clausius Gibbs entropy and Prigogine entropy S' despite the latter has no relation to the second law of thermodyanmics.^1,4,15"&"After the author of this paper had forumulated the law of temporal hierarchies (he was first aware of its existence in 1976-77^26), it became obvious that the methods developed by Langrange,Gibbs, and ..."Following the guiding principles of Lagrange..."
The only way I can be WRONG physically, up to now, and beyond this post, is ONLY (in so far as I am aware of my own cognitive abilities (which is all any one has ever asked net wise as far as I know) if proper use of Langragians dimiss errors of the former quoted kind. It is not obvious to me that fractal TO 4D must fit within this physicality but as I have still to look into this minutae it is possible that conditioning the deductive environment as I will will still miss the sip you or I or someone else might later find in this LATTER"". (t is not d).
Hopefully if we come back to this I will remember all or enough of the analogies that are presently "coming to mind" if needed.

This message is a reply to:
 Message 9 by Tony650, posted 08-10-2004 3:42 AM Tony650 has replied

Replies to this message:
 Message 15 by Tony650, posted 10-22-2004 5:59 PM Brad McFall has replied

  
Tony650
Member (Idle past 4023 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 15 of 71 (152068)
10-22-2004 5:59 PM
Reply to: Message 14 by Brad McFall
10-05-2004 12:50 PM


Re: Rrhain, Eta, anyone?
Hi Brad. I apologize for taking so long to reply to this.
Well, as so often seems to happen, I'm afraid that much of what you said went right over my head again. I think I managed to follow some of it, but man, that was an effort. You obviously go to a lot of trouble and I apologize for getting so lost.
Perhaps we can back right up and start with my original question, as it applies to you. Are you able to visualize, in your mind, more than three spatial dimensions? Can you visualize 4D primitives or "surfaces"? Can you mentally "rotate" a 3D object in 4D space such that all of its points are visible simultaneously? Can you "see" four perpendicular axes in your mind?
These are some of the things I would eventually like to be able to do. It's not going to happen any time soon...it may never happen at all...but this is the direction I'm trying to head in. I just wanted to explain this so that you know where I'm coming from.
I was going to type more but I think I'm starting to lose coherence, myself. I've been awake for around 30 hours now and I can feel myself struggling to maintain my own clarity. Ugh! Why am I doing this when I should be sleeping?
Well, hopefully this will suffice for now. Sleepy time.

This message is a reply to:
 Message 14 by Brad McFall, posted 10-05-2004 12:50 PM Brad McFall has replied

Replies to this message:
 Message 16 by Tony650, posted 10-23-2004 9:18 PM Tony650 has not replied
 Message 21 by Brad McFall, posted 10-25-2004 1:22 PM Tony650 has replied

  
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