General theory on dimensions

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

General theory on dimensions

Postby headcircus » Fri May 04, 2007 4:13 am

(lessons learned: dont use the words f-o-r-m or t-e-r-m in posts.. blah!

Summary:
About the concept of "moving into a higher dimension" which i hear people say: My idea is that every dimension is already represented for the object, so once an object pops into existence into n dimensions on behalf of the observer, it is fixed indefinitely with those dimensions....

Coined Phrases:

    :arrow: "collapsing the dimension function" obviously a derived phrase (except collapse actually means collapse, literally), but it is analogous to the idea that observing a wavefunction causes a system to emerge from possibilities. Instead of just observing superpositioned particles and establishing a reliable order, observing a particle also establishes its dimensional properties at the same time from a near infinite set of dimensional possibilities, with the moderating factor being the observers dimensional limitation (aka, the highest meaningful dimension the observer can accurately perceive)


Assumptions:

    :arrow: Time is not a spatial dimension, nor a degree of movement. In fact, collapsing the dimension function of an object cuts out time completely.
    :arrow: Viewing an object in your highest dimension is collapsing the wave function of an object without relativism, or time. By the time we are done establishing an object, it has depth. By the time Xr7-9 finally establishes an object, it has trength. The object always had depth, trength, pength and sength, but xr7-9 can only perceive trength as his highest perceivable dimension. (but they are all there, existing as potentialities)
    :arrow: The dimension we are in is always a collapsed dimension function of an object whose dimension is 1 lower (thus, the 3rd dimension is a collapsed dimension function of a 2 dimensional object). So, the third dimension is depth (i guess), but a cube is just an infinite series of squares lined up on an axis called depth. A tetracube is just an infinite series of cubes lines up on an axis called trength. However, viewing the tetracube collapses the dimension function of the object so that all cubes within instantly create one tetracube.
    :arrow: Thus, visualizing a higher dimension can be done by imagining all instances of an object (sans relativism, aka time) like a series of paper dolls. So, a tetracube is all instances of a cube viewed at once, just like a cube is all the squares viewed at once. To do this, take the object and split it apart into all the instances of it, like paper dolls then collapse it back into one object. It is not necessary to know what "all instances are".. just picture as many as you can.. and that will be enough of a symbol meaning "all"



Detail:
It makes more sense to me that every particle in the universe already has the potentiality (or already does) exist in infinite dimensions. But according to quantum theory, the particles do not take a fixed position until the observer observes, aka establishes a system.

So, evolving or moving into a dimension (as some people have mentioned) makes no sense to me. If we collapse the wave function of particles, it is not a far stretch to consider that we also collapse the "dimension function" which i just made up. We just happen to only really need 3.

Another creature could collapse particles to 4,537 dimensions, but their "brains" are wired to understand that many dimensions...

And a note about collapsing: (bare with me)

In my logic, collapsing the dimension function as already stated is collapsing all the instances of an object of a dimension 1 lower. By doing this, you are completely removing the concept of time (aka relativism, because everything is there at once).

When you look at a cube, you are viewing all the possible instances of the squares that makes up the cube *at once*. But this happens automatically, its not something you consciously do. When a 4d person looks at a tetracube, he/she is doing the same thing but with cubes, not squares. Since time (i think) is only the occurrence of observing a particle and causing it to take up a fixed position in space (collapsing the wave function and thus instituting relativism which we perceive as time), then time does not apply when observing an amalgamation of all squares in a cube, or all cubes in a tetracube or all tetracubes in a pentacube. It simply appears as one object. Its easy when we do this for a square or a cube, but the problem we have with tetracubes is that its hard to imagine what all instances of a hammer could be. Or all instances of a block of chewing gum. What we have to do is slow things down and imagine the process as happening in a series of steps instead of all at once.

So, net net...

The dimension we are in (the highest one that we are privy to) is always the collapsed dimension function of a dimension 1 lower. (Collapsing all lines into a square just by observing it for a 2d person. Collapsing all squares into a cube just by observing it for a 3d person. Collapsing all cubes into a tetracube just by observing it for a 4d person. Collaping all tetracubes into a pentacube for a 5d person, etc). And this goes on forever...

It just requires one to observe an object and poof, the highest dimension the viewer can perceive is brought forth. But once brought forth, it is immutable. And that is why we have such a hard time going up into 4d or 5d... because we apply our imagination to what we know of as 3d objects and try to move them up (but these are immutable dimensionally). All attempts to view a 4d object are limited to 3d versions because our dimensional limitation is 3.

If we can somehow find a way to "uncollapse" the dimension we are in, then we'd have to close our eyes (unobserve the cube) and then with the wildest imagination possible, re-establish the object from a set of potentialities and increase your dimensional limitation to 4. You can do this by pretending you are a creature that has this as their limitation, which might mean your going to have to take a couple of hits of acid, or something the like, which i do not condone.
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Re: General theory on dimensions

Postby Hugh » Fri May 04, 2007 10:28 pm

Hi headcircus, welcome to the forum. :)

headcircus wrote:It makes more sense to me that every particle in the universe already has the potentiality (or already does) exist in infinite dimensions. But according to quantum theory, the particles do not take a fixed position until the observer observes, aka establishes a system.

This is fascinating to think about. I hope someday we will understand how it all works. :)
headcircus wrote:All attempts to view a 4d object are limited to 3d versions because our dimensional limitation is 3.

Would an indication of a 4d object's existence be that we can see similar 3d views of it from perpendicular directions? (Have you ever experienced a VRI?) :)

headcircus wrote:If we can somehow find a way to "uncollapse" the dimension we are in, then we'd have to close our eyes (unobserve the cube) and then with the wildest imagination possible, re-establish the object from a set of potentialities and increase your dimensional limitation to 4. You can do this by pretending you are a creature that has this as their limitation


There are those that can attain an awareness of space much greater than normal through meditation. Others, like Wendy here on the forum, have a trained mathematical visualization ability, to see in higher dimensions.

A lot of interesting ideas headcircus, glad to have you here. :)
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Re: General theory on dimensions

Postby headcircus » Fri May 04, 2007 11:32 pm

Hugh wrote:Hi headcircus, welcome to the forum. :)


Hi hugh.. thanks! I'm glad the forum is around. It looks like it can cater to the mathematically talented and the mathematically challenged both (I am the latter).

Hugh wrote:This is fascinating to think about. I hope someday we will understand how it all works.


Yes.. I have a feeling that day is a long, long time from now, but it is incredibly fun to try in the meatime

Hugh wrote:Would an indication of a 4d object's existence be that we can see similar 3d views of it from perpendicular directions? (Have you ever experienced a VRI?)


Not sure a what VRI is? :\ Sorry I think there is no way to prove without math that a 4d object actually exists. Our dimensional limitation will not allow it.


Hugh wrote:There are those that can attain an awareness of space much greater than normal through meditation. Others, like Wendy here on the forum, have a trained mathematical visualization ability, to see in higher dimensions.


I agree.. I have this chart that shows that some people can achieve this level of awareness without drugs and I hear it takes a lot of discipline.


Hugh wrote:A lot of interesting ideas headcircus, glad to have you here. :)


Hey thanks! Well received :P
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Re: General theory on dimensions

Postby Hugh » Fri May 04, 2007 11:51 pm

headcircus wrote:Yes.. I have a feeling that day is a long, long time from now, but it is incredibly fun to try in the meatime.


I hope it's within our lifetime, but it may be much longer than that. There is an incredible amount of work being done though, and a lot of interesting experiments.

headcircus wrote:What is a perpendicular dimension? Not sure a what VRI is? :\ Sorry
I think there is no way to prove without math that a 4d object actually exists. Our dimensional limitation will not allow it.


We may find the right experiment to prove it's existence. String theory postulates many higher dimensions, and the math actually works out well, it's just that they need better experiments to test for it.

A VRI is a Visual Reorientation Illusion. It's something that I think is an indication of existing higher dimensional space. There is a thread about them in this same forum. If you google it, you can find links to other threads in other forums where I talk about the idea. I'm curious if you've ever had one yourself. You can post any ideas about them in that thread if you'd like. :)

headcircus wrote:I have this chart that shows that some people can achieve this level of awareness without drugs and I hear it takes a lot of discipline.


Can you post the chart picture up, or post a link to it? I can post it up here if you'd like. I use imageshack, and post the direct hotlink here. It's free and easy. :)
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Re: General theory on dimensions

Postby headcircus » Sat May 05, 2007 12:16 am

Hugh wrote:Can you post the chart picture up, or post a link to it? I can post it up here if you'd like. I use imageshack, and post the direct hotlink here. It's free and easy. :)


Here you go. I think I've made it to #9 once when the nurse gave me benadryl intravenously, which makes me trip... and I freaked out. That lasted 10 minutes and I wanted to die pretty much. So, no thanks going higher. As far as lower, maybe the cusp of alpha, once, after a long long time.


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Postby Hugh » Sat May 05, 2007 12:52 am

That's an interesting picture. I think I've only ever briefly been at 11 being anxious, and on the other end probably where you were, near alpha, in a conscious state.

I don't think I'd ever want to go into the schizophrenic states or higher, but the calmer states might be fun to achieve.

Hey, I saw your picture was from headcircus.com and when I went there I saw some of your artwork - wow, great stuff - you've been drawing for a long time and it's very interesting to look at. I'll be back a few times to check out more. You've got a myspace too. Ari right? :)
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Postby headcircus » Sat May 05, 2007 12:57 am

Hugh wrote:That's an interesting picture. I think I've only ever briefly been at 11 being anxious, and on the other end probably where you were, near alpha, in a conscious state.

I don't think I'd ever want to go into the schizophrenic states or higher, but the calmer states might be fun to achieve.

Hey, I saw your picture was from headcircus.com and when I went there I saw some of your artwork - wow, great stuff - you've been drawing for a long time and it's very interesting to look at. I'll be back a few times to check out more. You've got a myspace too. Ari right? :)


yes... the link to the profile on myspace is the little myspace graphic itself on the bottom. Thanks for checking it out! I'm uploading 4 or 5 new pix in the next week or so. :P
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Postby Hugh » Sat May 05, 2007 1:05 am

headcircus wrote:I'm uploading 4 or 5 new pix in the next week or so. :P

Cool! I'll be back then. :)

There may be more information in here to help you with more 4d and higher dimensional drawings if you need any.
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Postby Victoria » Sat May 12, 2007 6:48 am

I love it Headcircus. :D Really great thoughts, not just because I agree with where you are going here. I think your ideas are well formed and presented too, so thanks for sharing.

Now you refer to the idea of perception acting a certain way which is purely objective, so that say, we are looking at the wavefunction, it collapes into what we see not because it is making some physical change in itself, but because we are physically translating it. And while I say that has to be the best way I have ever seen someone interpret the phenomenon, it remains that you have confined it to three dimensionality, I'd like to consider it in four. First I agree with the way you have taken time out of the equation and put three dimensions in an inertial reference. But our perception does extrude three into four so I think it follows from your objectivity that that fourth space is translated in the same way as the third space.

So lets say we have your inertial translation of three dimensions, and lets say that the translation is pulled out into a fourth dimensional space represented by time so lets say you see the wavefunction and to translate it in four dimensions, it exists in n-d your translation has the dimensions of time to it. I guess you could say that would be you translating the wave function into causality. Yeah? The theory of decoherence fits all these musings, I guess we are both probably agreeing with that.

ANyhow... gotta run now, sorry to cut off short. Nice to talk with you.
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Postby headcircus » Sat May 12, 2007 7:27 am

Victoria wrote:I love it Headcircus. :D Really great thoughts, not just because I agree with where you are going here. I think your ideas are well formed and presented too, so thanks for sharing.


Hey there.. thanks a lot :) Glad you took the time to read... I'd love to discuss some of this stuff...

Victoria wrote:Now you refer to the idea of perception acting a certain way which is purely objective, so that say, we are looking at the wavefunction, it collapes into what we see not because it is making some physical change in itself, but because we are physically translating it. And while I say that has to be the best way I have ever seen someone interpret the phenomenon, it remains that you have confined it to three dimensionality,


Yes, but only because of one of my initial conjectures is that there is such a thing as a hard limit to the perception of dimensionality, meaning it stops at 3-spatial for us. It could be 4, 5, 1000, whatever... but for *us* anyway, it seems to be 3. Although we experience 4 - I am not entirely convinced that the "fourth" dimension is time. I think it is just another spatial dimension. There is a dimension called time, but is it #4? or #76? I think its in its own category.

When string theorists talk about dimensions, (like Briane Greene), they say it like this: "We think there are 11 dimensions based on M-theory" - 3 spatial dimensions, 6 or 7 "extra dimensions" (depending on what theory you are looking at) and one "time" dimension. They are clearly illustrating that the time dimensions is not spatial, per se, but rather in its own category.. more on that later.

Victoria wrote:I'd like to consider it in four.


Lets... :)

Victoria wrote:First I agree with the way you have taken time out of the equation and put three dimensions in an inertial reference. But our perception does extrude three into four so I think it follows from your objectivity that that fourth space is translated in the same way as the third space.



Well.. the way I see "extrustion" is that when we extrude 0 to 1, 1 to 2, or 2 to 3, we extrude "up" meaning the object's position in spacetime is relevant to our perceptions. Extruding up, even if it means drawing lines on a square to make it into a cube, is still going up because in my language "up" means "moving into a dimension that is still relevant to our perceptions". When you extrude 3 to 4, sure you are still drawing the object by pushing it into a perpendicular dimension (what i guess is "trength" on here)... but the object is fake. It is not relevant. Meaning, if you could take the drawing and wave a magic wand on it and bring it to life, this would only work up to 3. Once you go 3 to 4 and wave the magic wand, the object will practically disappear. Only a sliver will be shown.

So, in my language, when we extrude 3 to 4, we always extrude "down" or, say "left", just not up. Meaning, dimensions are lost because we cannot perceive them. By throwing an object into a 3-sphere or by making a hypercube - the extrusion is still in 3 dimensions; in fact its a completely faked visual of what "one side of a 4-dimensional object (cell) may look like", but still its in 3 dimensions. Every time we extrude into 4 or more, we extrude down.

Here are some examples of my hypothesis

Penteract: a 5 dimensional hypercube that has been projected through 3 filters (and by the way, this image blows my mind every time I see it)

http://en.wikipedia.org/wiki/Image:Penteract_projected.png

The penteract is still being shown in 3 dimensions. The stereographic projection of 4d to 3d (good luck picking out which one that is!) has taken the 4th dimensional lines and curved them into infinity and back (the 3-sphere). So, if you waved a magic wand on the object; the 3-sphere would dissolve, and the lines of the 4th dimension would spread out to infinity all over again; and the object would cease. Not so when we extrude from 0 to 3.

Sorry to go on so long on that... Having said all of that, I am completely capable of looking at it from another point of view; for arguments sake; but I thought I would point that out as where I am coming from...

Victoria wrote:So lets say we have your inertial translation of three dimensions, and lets say that the translation is pulled out into a fourth dimensional space represented by time so lets say you see the wavefunction and to translate it in four dimensions, it exists in n-d your translation has the dimensions of time to it. I guess you could say that would be you translating the wave function into causality. Yeah?


I'm not entirely sure what you are asking, I'm sorry... I'll postpone an answer...

Victoria wrote:The theory of decoherence fits all these musings, I guess we are both probably agreeing with that.


Yep, it sure does. And I have lately been linking (thanks to Brian Greenes books) the causal relationship of decoherence on behalf of the observer with the second law of thermodynamics which states that systems always move towards higher entropy. I have been trying to crack this nut... because it appears that although the law does not predict with 100% accuracy that high entropy will ALWAYS occur.... It puts into question our seemingly inherent ability to decohere a system (i just made that word up) just by observing it. Both concepts apply to systems.. on the quantum level, we are talking about infinite potentialities; on the entropic level we are talking about a level of potentiality that is directly related to the size of the system.

The size of any system at the quantum level is not even worth trying to contain in numbers; and think of how perfectly low the entropy is once the wavefunction collapses. Just by observing; we institute perfect entropy from the most highly entropic of all systems. Now that is power!

The problem I have is still the same one I always did... if I am responsible for observing a particle to position it in space; then why do I always lose the battle against systems that fall into high entropy...

Or put another way... when i spill a glass of coke on the counter; why can I not choose to collapse the wavefunction of the particles that i think should be spilled and place them back in the bottle? all I have to do is close my eyes and the system should reset itself.

Wow, I just really got off topic.. my apologies...
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Postby Victoria » Sat May 12, 2007 10:26 am

Yep, I see what you're saying about extrusion, I'd agree that was backwards to your conjecture. So if I understand you correctly, which I'm fairly sure of, you are saying to turn it in the other direction we equally "squash" n-d into 3 spatial + 1. I still like it :)... With the exception of one thing... I don't think we are "in" 3s + 1t. In my theory dimensions come in pairs, there is no odd man out, so we are in 2D + 2D = (1ms*1p) + (1ms*1p) where ms is metric space and p is polar space. I think this explains why a fourth metric space disappears, because it is without it's pair pole, it can't be translated.

Now on entropy, yes I think it will always occur. When you pin energy down into an eigenstate, IMHO, it comes with the vector (<--- by this I mean a 1s*1p couple), no exceptions. That vector is that vector. However, I do think entropy isn't what it seems; when it is placed in the 2*2d terms it looks much less foreboding 8) But it still works in one direction only. So to say, with the glass of coke, imagine you're standing in the multi-wave and you have this device that hooks into one stream and 'pulls it down' in one vector, and that vector is the line with the spilled glass of coke. Because it's just one vector it couldn't have gone any other way, you'd have to have used your device 'pull down' a different line in the same vicinity. So there's your entropy, each line of translation has it's orientation built in. You just look at a segment of it, a coordinate. Now the question is then with your coke scenario, where does a change in orientation occur? We know so much as we can postulate a device that results in an orientation, but next we need to decide where the orienting of the device takes place, and how (or if) it switches poles.... and moreover, if we figured that out, would we even bother with spilled coke..? or would we have greater ambitions.. ? :XP:
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Postby bo198214 » Sat May 12, 2007 11:07 am

I think this explains why a fourth metric space disappears when you analyse it metrically, because it is without it's pair pole, it can't be translated.


Hm Victoria, for me you sound a bit like you express all your feelings in scientific-philosophical speech. But it has not much to do with the truth of those things when verified logically.

How does a four dimensional (I hope you mean this when you say "fourth") metric space disappear when you analyse it metrically? *headscratch*
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Postby Victoria » Sat May 12, 2007 12:41 pm

bo198214 wrote:
I think this explains why a fourth metric space disappears when you analyse it metrically, because it is without it's pair pole, it can't be translated.


Hm Victoria, for me you sound a bit like you express all your feelings in scientific-philosophical speech. But it has not much to do with the truth of those things when verified logically.

How does a four dimensional (I hope you mean this when you say "fourth") metric space disappear when you analyse it metrically? *headscratch*



LOL sorry, I forgot to erase that. I meant to leave in only the first 'metric'.
And no I didn't mean the whole four dimensional space disappears, I mean to say the fourth metric and up 'disappear' only in the manner implied by headcircus.

bo198214 wrote:Hm Victoria, for me you sound a bit like you express all your feelings in scientific-philosophical speech. But it has not much to do with the truth of those things when verified logically.


LOL I've heard that before. I'm not here to fight about it, I just happen to be quite sure it has everything to do with the truth about these things verified logically. What exactly do you think is wrong.. before we go on.

headcircus wrote:
Victoria wrote:So lets say we have your inertial translation of three dimensions, and lets say that the translation is pulled out into a fourth dimensional space represented by time so lets say you see the wavefunction and to translate it in four dimensions, it exists in n-d your translation has the dimensions of time to it. I guess you could say that would be you translating the wave function into causality. Yeah?


I'm not entirely sure what you are asking, I'm sorry... I'll postpone an answer...


It took me a little while to figure out what might not be clear here.
I've just noticed I used "-" as a hyphen, bit dumb to do on a maths board, sorry. Excuse me while I get used to the local convention.. I meant the wave has ndimensions to translate, thus when you are capable of translating four.... (and sundry)

Okay so what I meant when I said inertial is that when you say take time out, we do have to take out motion with it because time is the degree of freedom for motion, metric space is just the degrees of freedom for mass (even positioning is difficult in three orthogonal axes and requires polar coordinates).

So when you say 3d+no time, I see it as inert mass, without time it can't move, because time equals a degree of freedom in terms of motion (ie d/t=v, d(theta)/dt = w or a parametric x=t y=ct path).... so then if you add time to that you are spreading out perception over a dimension of time, if that dimension is a linear axis, then what you have in my opinion is the degree of freedom for motion. And there is no motion without some acting force; ie classic classic causality. Hence what you view over the time is a dimension of pure causality.

I've merged your triple post into one. ~Keiji
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Postby Nick » Sat May 12, 2007 10:04 pm

Please don't double or triple post (or more). It wears down my scroll key and pointlessly raises your post count.
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Postby headcircus » Mon May 14, 2007 3:58 am

Victoria wrote:Yep, I see what you're saying about extrusion, I'd agree that was backwards to your conjecture. So if I understand you correctly, which I'm fairly sure of, you are saying to turn it in the other direction we equally "squash" n-d into 3 spatial + 1.


I am not sure what 'other direction' means in this context.

Victoria wrote:I still like it :)... With the exception of one thing... I don't think we are "in" 3s + 1t. In my theory dimensions come in pairs, there is no odd man out, so we are in 2D + 2D = (1ms*1p) + (1ms*1p)



Hrm.. interesting! What is your theory? I am curious to find out how the pairings work...

Victoria wrote:where ms is metric space and p is polar space. I think this explains why a fourth metric space disappears, because it is without it's pair pole, it can't be translated.


Ok, i am completely lost.. I think you've moved past me in this discussion.. maybe if I heard your theory I could have some context... what you are saying is really interesting to me, but you might as well be speaking another language. Can you help get me back on track by first establishing your theory and then using examples from it?

Thanks, though :)
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Postby Victoria » Mon May 14, 2007 5:47 am

headcircus wrote:
Victoria wrote:Yep, I see what you're saying about extrusion, I'd agree that was backwards to your conjecture. So if I understand you correctly, which I'm fairly sure of, you are saying to turn it in the other direction we equally "squash" n-d into 3 spatial + 1.


I am not sure what 'other direction' means in this context.


It's figurative. Sorry, I have to remember to keep metaphorical math terms out of the conversation.

What I meant is I was thinking in terms of building, and you were thinking in terms of deconstructing. Opposites.


headcircus wrote:
Victoria wrote:I still like it :)... With the exception of one thing... I don't think we are "in" 3s + 1t. In my theory dimensions come in pairs, there is no odd man out, so we are in 2D + 2D = (1ms*1p) + (1ms*1p)



Hrm.. interesting! What is your theory? I am curious to find out how the pairings work...

Victoria wrote:where ms is metric space and p is polar space. I think this explains why a fourth metric space disappears, because it is without it's pair pole, it can't be translated.


Ok, i am completely lost.. I think you've moved past me in this discussion.. maybe if I heard your theory I could have some context... what you are saying is really interesting to me, but you might as well be speaking another language. Can you help get me back on track by first establishing your theory and then using examples from it?

Thanks, though :)


*runs away screaming* You ask too much! Wow you have a rare attitude, Could you be any more open?!!? I salute that in you. Namaste.

We need to start with infinity. Define a point at infinity. here are more than a few schools of thought on his one, some say infinity is indefinable, while others say it's just a point where everything converges; there are still others that subscribe to the approach that infinity should have a definition and that definition would be a set of differential points. I'm one of the latter.

Have you ever heard the ALeph Null song? It goes.. Aleph null bottles of beer on the wall.. N^0 bottles of beer, take one down pass it around... Aleph null bottles of beer on the wall.
This little ditty describes the concept of infinity wherewith if you have infinity of something you can take from it infinitely and still have infinity left over. Another thought experiment that illustrates this is Hilbert's Hotel Infinity, if you have infinity rooms in a hotel. Then simplistically put, you can introduce infinity guests and there will always be room for them... Even after the hotel is full. Now once you hae contemplated those for long enough.... *guilty*..... the definition of infinity starts to take shape. And it looks a little like the aleph null song, except you add a not so arbitrary parameter to the words.

There is a double entendre in these words, which givves closure to its meaning. Now lets say you define a line to infinity east of yourself, and you do as he Aleph null song says, you take one point on the line away, repeat, repeat....... no matter how many you take away you still have a line of infinite magnitude. However, you have held steady the variable of direction an eventually, if you keep taking away a part of infinity for infinity you must get to you eventually. The reconciliation of this paradox is to imagine that you are in hotel infinity. Or in other words. The only way infinity can get to you is if you are already on it. According to our thought experiment infinity can only be taken away in one direction, towards you. Hence it will eventually reach you... At infinity.

So the only way infinity can reach you is if you are at infinity. Therefore let us define our zero point as a point on infinity. Now some mathematicians would say, okay, that's no different to what we already do, we take a zero point and start counting.. we still don't know where on infinity we are. And that is true, but we have defined something that can start us off.

So first my own version of the Aleph null song.

Aleph null points to the i of myself, N^0 points to the i. Take one point away, what can I say, Aleph null points to the i and the j.

we have defined a vector with direction <infinity> and magnitude infinity, and we have taken a point on that vector to be ourselves on infinity, that point has magnitude 0 and direction <infinity> which defines something/0 = infinity, which muddles up maths a bit if you try to take it from there and start solving with it.... however as long as you keep that infinity defined directionally, it is differentiable and 1 does not equal 2.

So just going on with the first bit. You might notice that once you're in hotel infinity everything around you is another point on infinity, this all sounds a little like the surface curve of a hypersphere, and that is a way we can define it.

So now you place your zero point,
Its definition will be as a point on an infinite vector which extends to <infinity>

This is your first dimension. It preceeds magnitude, and has a definition.

Now you take j and k from that point as your x,y axis to define two dimensions. That is to say, you choose two rotations from your null point and rotate x and y out as vectors that are orthogonal to the first dimension. And now you know relative to your first dimension where the plane of your x y axis cuts infinity.

This is the first (1p*1ms) pair. The next pair is more complicated, but follows directly from the first assumptions.
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Postby headcircus » Tue May 15, 2007 11:25 pm

Victoria wrote:*runs away screaming* You ask too much! Wow you have a rare attitude, Could you be any more open?!!? I salute that in you. Namaste.


Well thanks...

Victoria wrote:This is your first dimension. It preceeds magnitude, and has a definition.


So far so good.

Victoria wrote:This is the first (1p*1ms) pair. The next pair is more complicated, but follows directly from the first assumptions.


Thank you for explaining. I do understand. However it is not this first pair that I am confused about. I understand this cross-section of x and y as representative of this infinite point; and that these two vectors are pairs. (what do p and ms stand for?).

Anyway, how are you generating the NEXT set of pairs? Which would be z and t? If you are swiveling on 0 once to get dimension 1 and then swiveling again to get dimension 2, then I could guess that you can swivel once more to get dimension 3. Where do you swivel to get dimension 4 and how is this paired with 3?

Thanks!
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Postby Victoria » Wed May 16, 2007 3:22 am

headcircus wrote:
Victoria wrote: Namaste.


Well thanks...


You're welcome.


headcircus wrote:
Victoria wrote:This is the first (1p*1ms) pair. The next pair is more complicated, but follows directly from the first assumptions.


Thank you for explaining. I do understand. However it is not this first pair that I am confused about. I understand this cross-section of x and y as representative of this infinite point; and that these two vectors are pairs. (what do p and ms stand for?).


P is for pole, hence it is an assumed point on a defined field. The cross section (zero point) is technically a point on an imaginary vector which has an assumable orientation toward an infinite, infinite point, but the vector has no value, Just orientation; It is a unit vector, minus the unit. We can assume in this instance that it is pointing to 0,0 on two intersecting radial maps so that our rotations are half pi distances in radians from a unit of it. But we distinguish that it is not 'actually' a unit so x and y are orthogonal not to the first dimension, but to one unit of a probable first dimension. This becomes useful eventually though it can seem a little overwhelming initially.

ms is for metric space, your x,y space This is a plane of two dimensions which is attached to a pole. So you can imagine it a little like a flag, then take away the bottom of the pole and imagine it hovering in the air with all degrees of freedom around it where the axial pole can be placed.

So basically you have a normal x y axis in an abstract space, all you have attached to it is an ambiguous tail which moves with the rotation of the plane.






headcircus wrote:
Anyway, how are you generating the NEXT set of pairs? Which would be z and t? If you are swiveling on 0 once to get dimension 1 and then swiveling again to get dimension 2, then I could guess that you can swivel once more to get dimension 3. Where do you swivel to get dimension 4 and how is this paired with 3?

Thanks!



You're quick on the uptake, HC. :) the next swivel is very particular, like 1 follows 2, it is not a random decision. The defiinition of 1 is the definition of 2, with out 1, 2 has no meaning, likewise here.

You have a defined space xy; and xy has a rotational axis orthogonal to both of your original rotations. so let xy space be pole 2; it can be defined initially as a single axis which can rotate freely between 0 and half pi across the positive xy plane. Rotations about that pole on an orthogonal axis create several versions of metric space in three dimensions. For example a 3d object as a closed metric space: Define a line F(x)= y from the base of the pole in xy to pi/8 and rotate this line as you would in 3space around z, this gets you a cone; surface points of your 3d object are: (x,y,(radius; angle)) AND inner space coordinates of it are (x,y, (radial units; angle)).

Extra dimensions to this model naturally follow, for example:The gradient of your cone is defined on x and y on multiple planes. Each of these planes are possible orthogonals of your zero vector. You have chosen one, and defined mathematically a number of others in surrounding space by looking at what three dimensional object touches what two dimensional plane in relation to your defined plane. From here you can see where your tail is in relation to that local space and take angles between two objects according to the unit vectors of two or more related first dimensional axes.

In a sense, what you are doing is lettin your origin define the space from it, so that you yourself do not define space around the origin and try to put things in it, but instead define an origin and then tell space what shape to be around it.
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Postby itzclay » Sun Jul 15, 2007 10:00 pm

Wish I had read this thread before I posted my own. I came to the exact same conclusions as the OP, and all the other posts I had read didn't treat it this way, so I posted.

I think things we only know as forces are 4D objects we can't see. The force is the part of the object we can't see. Objects which have no external force, have their 4d space existing inside it so to speak. When electrons and such are aligned, as with magnets, it moves the 4D part of the object outside the the 3d limits - but is invisible to us.

With magnets, you can move 1 without touching the other. That is the 4d part of the 2 objects touching.

Even our earth - which we only see as a sphere, carries properties of a 4d object with it's 4d space being outside the 3d object. Electric fields, magnetic poles etc. Same for the sun and other large space objects.

I obviously believe in more than 4d. And the shape of the force - if you could see it. I think would be a good tell of what dimension the force exists in. Minus any outside interference in that dimension(multiple magnets for example, or the suns pull vs the earths pull).

Just as a being only SEE's 2D in the so called 2D worlds, he still does exist on th 3D plane, as noted by the fact of a 3d object affecting him. When the 3d object passes through, he only see's the 2d object of it. But if that object is moving, then he can also see an "invisible" force. If he could attaches a 2d object(or what appears as a 2d object to him) to the 3d object passing through, he would see his 2d object leave his view. He would also see the rest of the object he was working with, as it passed by he 2d view, as what he thought was a 2d object, was likely a 3d object.
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Postby Keiji » Sun Jul 15, 2007 10:28 pm

itzclay wrote:With magnets, you can move 1 without touching the other. That is the 4d part of the 2 objects touching.


I'm a bit skeptical of that. What about when you put two magnets together?
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Postby itzclay » Sun Jul 15, 2007 10:48 pm

When 2 magnets stick, it's because they are at opposite poles, or opposite ends of the lined up electrons etc.

In which case, when the 2 are connected, they "snap" into place and the electrons are lined through both.
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Postby moonlord » Sat Jul 28, 2007 5:25 pm

I'd define force as a result of the interaction. Force does not exist. Only it's effects can be observed. I'm sure I'm not the only one with this definition.
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Postby houserichichi » Sun Jul 29, 2007 2:26 pm

There are force carrier particles, for lack of a better term, but I agree no true force exists. It's just interaction between bosons and fermions that we measure on grand scales.
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Postby wendy » Mon Jul 30, 2007 7:31 am

Don't know. It seems like black magic to me.

You can collapse 3d to 2d, while still retaining a time axis (eg films).

It is best to avoid using time as a dimension, even a representation for spatial one, because it is not that at all. There is some nonsense about a complex dimension, eg i*speed of light*time, but this i, although the square root of -1, is not the i of complex numbers. It has an ambient direction, which complex i does not.

It is pretty pointless in trying to 'compress' dimensions, unless the process is to greatly simplify things. I do this, but often i wander "out" and look at the real thing.

You need a lot of logic, intuition and maths to do four dimensions. It is also about understanding what things are for.

For example, a knife cuts. It does this by making a partition with the sweep of the blade. Since a partition is N-1 dimensions, and time is 1 dimension, it gives that the blade must be N-2 dimensions, for N=3, this gives the linear edge.

Much of mathematics is infested with the notion that a thing has a fixed dimension. This is not so: some things do, by way of bridges, and others do not, by way of walls. So it's as much guessing if the thing you are looking at is a bridge or a wall.

A road in 3d, serves to unite and to divide blocks. Since the primary reason is to unite, we see that the dimension is 1d, rather than N-2. A fence serves to divide (ie a wall), so its dimension is not 1d (on the ground), but N-2, so a 4d fence is N-2 = 2 dimensional (on the ground).

Some people talk of 2 sets of analogues of left/right. This does not hold up. We have up/down, because of gravity, and front/back because of time, and the rest is a kind of 'across-space'. You can imagine that there is no restriction on how circles on the across-space might be arranged, and so the left/right + etc does not work.

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Postby bo198214 » Mon Jul 30, 2007 10:14 am

wendy wrote:Some people talk of 2 sets of analogues of left/right. This does not hold up. We have up/down, because of gravity, and front/back because of time, and the rest is a kind of 'across-space'. You can imagine that there is no restriction on how circles on the across-space might be arranged, and so the left/right + etc does not work.


I discussed the topic of left-right etc in 4d in more detail in the thread reading. Would be more appropriate if you could reply there.
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Postby Keiji » Mon Jul 30, 2007 10:48 am

wendy wrote:A fence serves to divide (ie a wall), so its dimension is not 1d (on the ground), but N-2, so a 4d fence is N-2 = 2 dimensional


Surely a fence would be N-1? Otherwise you can just walk right over it.
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Postby wendy » Tue Jul 31, 2007 7:49 am

The purpose of a fence is to create a division on the ground. Making a fence higher makes no extent to its effect of dividing ground.

So, the fence is a limitation or division of space - gravity, that is, space - gravity - bounding = N-2 dimensions.

A road in 3d also seeks to divide the city into blocks, yet this happens without height: a road is a linear divice, and this serves to divide the ground in 3d.

Note that a road (or river or snake) is 1d, regardless of dimension, so in the space of the planiverse, the road, river share the same space (the surface), and the snake is a flying thing (because it becomes an aerofoil).
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Postby moonlord » Tue Jul 31, 2007 7:57 am

No. The fence IS N-1. Otherwise it's a line on the ground.
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Postby wendy » Tue Jul 31, 2007 8:14 am

And indeed some are! Yet we note that in English, the word line serves both as a division (line in the sand, dead-line, front-line) as well as a union (eg bus line, bee-line, railway line). Edge is likewise divided into the division (technical edge, to the edge). It has the etymology of corner, cf german Ecke (corner, edge), much as edge of a cube.

The act of drawing a line in the sand is to create a division, which divides (space divided by height = gravity), which really is N-2. The height of the fence is an instrument that adds no extent to the fence in its function to divide, but to make the division more clear.
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Postby bo198214 » Tue Jul 31, 2007 8:25 am

Isnt this a bit philosophical nit picking?
We agree that the "lines" resticting the court of ball games are N-2.
(Btw. anyone there, who wants to develop a 4d tennis game? ;) ).
However a fence is not a line in that sense and is also meant to divide the space not merely the ground.
Anyway, in the usual understanding a fence is 2d in our world and it would contradict the conventional use of the word "fence" to call it 1d. There is also no gain in clarity or simplicity (for a certain theory) to define a fence as being N-2 dimensional.
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