What is dimension? And how can there be more than 3 of them ?

[aphh]

You only need 2 angles to define coordinates and location in 3D space. Hmm... without knowing actual radius you would only get relative location.

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I've always had a problem with the way on programs about string theory when they talk about extra dimensions they always fail to explaint the reason why. I've always wondered why in the hell dimensions infinitely more vast then ours would be curled up in an incredibly small space. In my opinion its complete BS. These are mathemiticians devising these theories not scientist. Math can help to calculate phenomenon, but it can not replace science. Einstien changed our view of spac-time. it shattered ideas of Euclidean space. However that doesn't mean that everytime someone is trying to figure something out they need to try and redefine the universe. In my oppinion the society of particle physicist have given the mathemiticians to much freedom. Mathematics will take us down the path towards the infitismal and the infinite so that even by the time these M theories, A Theories, and D Theories reach a conclusion the mathematics will be to complex for the real scientist to find any use of the equations. They are losing their connection to reality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Whats the point of writing the universe in an equation if the equation is 1000 characters long, infinitely complex, and can no longer be applied to reality? Where is the beauty in that. What happened to parsimony? What happened to always taking the easiest approach? Where have all the scientist gone?&nbsp;&nbsp;&nbsp; <br />Posted by why06</DIV></p><p>The people working on these theories are primarily physicists and not so many mathematicians.&nbsp; I think that mathematicians are more likely to be skeptical than are the physicists. </p><p>The reason for the addition of the extra dimensions has to do with an attempt to formulate a theory that incorporates the known forces and does not provide answers that are infinite.&nbsp; In the current standard model there is a procedure used in the calculations called renormalization.&nbsp; The electroweak theory and the theory of the strong force are all renormalizable theories,&nbsp; Renormalization basically throws out a bunch of infinities and winds up with amazingly accurate predictions,&nbsp;but it is not on firm mathematical ground.&nbsp; Attempts to develop a quantum theory of gravity have faile because the resulting theories are not renormalizable and you end up with infinities in the answer.&nbsp; The addition of extra dimensions is done to try to come up with a unified theory that can either be renormalized or not have infinities in the first place.</p><p>Now that said, I must admit to being skeptical that this approach will ever result in a useful physical theory.&nbsp; But I am probably in a minority in that opinion.&nbsp; On the other hand I think Roger Penrose is in the same minority, and I consider that rather good company.&nbsp; Penrose is a mathematician.&nbsp; So am I. We could still both be wrong. </p><p><br /><br />&nbsp;</p> <div class="Discussion_UserSignature"> </div>

 

[vandivx]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Dimensions higher &nbsp;than 3+1 is also the main foundation of String theory.&nbsp; Their argument is all dimensions above 3+1 are 'curled' up.&nbsp; My question is did they really mathematically find&nbsp; dimensions &nbsp;'curled' up? I wonder what kind of math can predict curling up of dimensions? What I think is they set all dimensions except 3+1 to zero (or set to length below planck's length), and when they did this they found the results agreed with 'things' known in our world.&nbsp; I wonder if this is what they term as 'curled up'?&nbsp;Because no 'reason of curling up'&nbsp; is ever given.&nbsp; <br />Posted by emperor_of_localgroup</DIV></p><p>'curled up' means 'hiden' as in curled hair which is really much longer than it appears to casual look, meaning that true length of the hair is hidden from view, physicists take this as analogy except that for them 'curling up' when they talk of dimensions instead of hair means hiding from view completely - its like if you didn't see the curled up hair at all and in one sense you really don't see the hair's 'length' at all which is thus completely hidden from view (you don't see any piece of straight hair which it really is and could exist as such under different conditions) </p><p>&nbsp;</p><p>curled up dimensions then mean(s) hidden dimensions in the sense that we don't see or otherwise detect them but they may still play some role in this world of ours nonetheless helping to make it what is is via their influence (acting like an invisible hand and if that looks like harking back to religious view of the world is for anybody to decide), and the idea is to build theories based on higher dimensional reality by trial and error (guesswork really) in the hope that if we should happen to guess the true number of dimensions actually existing out there in nature and put together a theory based on them that the theory would as a result of that have predictive powers and be generally usefull despite being puzzling to commonsense</p><p>&nbsp;</p><p>it is somewhat as the situation where primitive man postulated existence of gods (equivalent of hidden or curled up reality) and his 'theory' would have predictive powers if you interpreted world by its light - sinners would get comeuppance from just God(s) etc. </p><p>&nbsp;</p> <div class="Discussion_UserSignature"> </div>

 

[SHU]

<p>Consider this unusual concept.&nbsp; Suppose that dimensions unfold from "lesser" dimension space.&nbsp; Zero dimensions being the absolute.&nbsp; More like abstractions than actual physical space.&nbsp; Perhaps we can only perceive a limited number of abstractions. Perhaps the universe is capable of additional abstraction but they are unstable.&nbsp; Stability or cohesiveness is the issue, even with 4 dimensions, and&nbsp;maybe it isn't on the Plank scale or&nbsp;even the&nbsp;subatomic scale.&nbsp; Implications abound.</p>

 

[UncertainH]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Consider this unusual concept.&nbsp; Suppose that dimensions unfold from "lesser" dimension space.&nbsp; Zero dimensions being the absolute.&nbsp; More like abstractions than actual physical space.&nbsp; Perhaps we can only perceive a limited number of abstractions. Perhaps the universe is capable of additional abstraction but they are unstable.&nbsp; Stability or cohesiveness is the issue, even with 4 dimensions, and&nbsp;maybe it isn't on the Plank scale or&nbsp;even the&nbsp;subatomic scale.&nbsp; Implications abound. <br />Posted by SHU</DIV></p><p>I think this is a interesting point of view it is a little bit like 'flat land' being wrapped up inside 3-d land. You could take it a little further and consider that the laws of physics must hold true not only in all frames of reference but also within all dimensions that are folded up inside the higher dimensions. There is a common thought experiment that is often talked about being what would a 'flatlander' see if a sphere were to pass through his land, usually the response is the sphere would appear as a point, turn into a line and dimish back to point again. Well that makes sense from the perspective of our 4-d world that we live in. The problem I have with this is that it presupposes certain commonalities between the dimensions. Relativity tells us that clocks and dimensions to not appear to be the same in all frames of reference. What would happen if clocks in flat land did not match the clocks in sphere land yet the interaction must make sense from both points of view. Consider also that there might be concepts in sphere land (mass for instance) that do not and cannot exist in flat land. Perhaps then the flat lander would see nothing as the sphere passes through. I don't have any answers here just questions but I liked your post.</p>

 

[SHU]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I think this is a interesting point of view it is a little bit like 'flat land' being wrapped up inside 3-d land. You could take it a little further and consider that the laws of physics must hold true not only in all frames of reference but also within all dimensions that are folded up inside the higher dimensions. There is a common thought experiment that is often talked about being what would a 'flatlander' see if a sphere were to pass through his land, usually the response is the sphere would appear as a point, turn into a line and dimish back to point again. Well that makes sense from the perspective of our 4-d world that we live in. The problem I have with this is that it presupposes certain commonalities between the dimensions. Relativity tells us that clocks and dimensions to not appear to be the same in all frames of reference. What would happen if clocks in flat land did not match the clocks in sphere land yet the interaction must make sense from both points of view. Consider also that there might be concepts in sphere land (mass for instance) that do not and cannot exist in flat land. Perhaps then the flat lander would see nothing as the sphere passes through. I don't have any answers here just questions but I liked your post. <br />Posted by UncertainH</DIV></p><p>&nbsp;<font size="2">Glad you liked it.&nbsp; Got tired of spacetime being used as the canvas for Euclidean/quantum painting.&nbsp; This concept makes spacetime dynamic and I like to think of it as a possible bridge between relativity and quantum mechanics.&nbsp; However, it only applies to very small scales or immense energy.&nbsp; At a macro scale, it all gets generalized... specifically so.&nbsp; As far as the perceptions between flatland and sphereland, maybe the question should be whether photons and electrons "see" the same.&nbsp;</font></p><p><font size="2">What happens to the laws of physics as they enfold into less dimensions?&nbsp; They integrate in some way.&nbsp; Obviously, we can do some calculus or linear algebra&nbsp;on a formula, like converting volume to area,&nbsp;and get nonsense.&nbsp; Needs a different kind of math,&nbsp;maybe something boolean, considering subatomic properties.</font></p><p><font size="2">Think about the big bang with this concept.&nbsp; "Nothing", then one change and BOOM...&nbsp;a whole and governed&nbsp;universe with instant rules.&nbsp;&nbsp;How about the uncertainty principle?&nbsp; Causality?</font></p><p><font size="2">Here's the big one: If spacetime is active does that make it the inverse of matter/energy or does it humble matter/energy into merely consistent events?&nbsp; In other words,&nbsp; if we could describe the spacetime at any one spot, in absolute terms, would we not be describing what exists there?</font></p><p>&nbsp;</p><p>&nbsp;</p>

 

[yevaud]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>The people working on these theories are primarily physicists and not so many mathematicians.&nbsp; I think that mathematicians are more likely to be skeptical than are the physicists. The reason for the addition of the extra dimensions has to do with an attempt to formulate a theory that incorporates the known forces and does not provide answers that are infinite.&nbsp; In the current standard model there is a procedure used in the calculations called renormalization.&nbsp; The electroweak theory and the theory of the strong force are all renormalizable theories,&nbsp; Renormalization basically throws out a bunch of infinities and winds up with amazingly accurate predictions,&nbsp;but it is not on firm mathematical ground.&nbsp; Attempts to develop a quantum theory of gravity have faile because the resulting theories are not renormalizable and you end up with infinities in the answer.&nbsp; The addition of extra dimensions is done to try to come up with a unified theory that can either be renormalized or not have infinities in the first place.Now that said, I must admit to being skeptical that this approach will ever result in a useful physical theory.&nbsp; But I am probably in a minority in that opinion.&nbsp; On the other hand I think Roger Penrose is in the same minority, and I consider that rather good company.&nbsp; Penrose is a mathematician.&nbsp; So am I. We could still both be wrong. &nbsp; <br /> </p><p>Posted by <em>DrRocket</em></DIV></p><p>I agree, I have often wondered how "real" extra dimensions are, or are they merely abstractions useful only for mathematical or physical descriptions?&nbsp; Then again, as many very convoluted theories simplify greatly when extra dimensions are factored in, there must be at least something to it.&nbsp; Consider Maxwell's ugly equations (*shudder*), for example.</p> <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>'curled up' means 'hiden' as in curled hair which is really much longer than it appears to casual look, meaning that true length of the hair is hidden from view, physicists take this as analogy except that for them 'curling up' when they talk of dimensions instead of hair means hiding from view completely - its like if you didn't see the curled up hair at all and in one sense you really don't see the hair's 'length' at all which is thus completely hidden from view (you don't see any piece of straight hair which it really is and could exist as such under different conditions) &nbsp;curled up dimensions then mean(s) hidden dimensions in the sense that we don't see or otherwise detect them but they may still play some role in this world of ours nonetheless helping to make it what is is via their influence (acting like an invisible hand and if that looks like harking back to religious view of the world is for anybody to decide), and the idea is to build theories based on higher dimensional reality by trial and error (guesswork really) in the hope that if we should happen to guess the true number of dimensions actually existing out there in nature and put together a theory based on them that the theory would as a result of that have predictive powers and be generally usefull despite being puzzling to commonsense&nbsp;it is somewhat as the situation where primitive man postulated existence of gods (equivalent of hidden or curled up reality) and his 'theory' would have predictive powers if you interpreted world by its light - sinners would get comeuppance from just God(s) etc. &nbsp; <br />Posted by vandivx</DIV></p><p>&nbsp;The usual analogy for the "curled up" dimensions is a garden hose.&nbsp; From a distance the hose appears to be a string -- one dimensional.&nbsp; One sees that it is three dimensional only when very close to it or under high magnification as with a telescope.</p><p>The general thought with respect to "curled up" dimensions in string theory and similar theories is that the extra dimensions occur on such a small scale as to be undetectable to us in the macroscopic world.<br /></p> <div class="Discussion_UserSignature"> </div>

 

[xmo1]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>dimensional spaces. Posted by DrRocket</DIV></p><p>Could it be that people are talking about the construction of matter? Certainly there is nothing constructed in less or more than 3 dimensions. Our universe is 3D, the simplest truth. Are there any experiments that resolve construction to 4D or 2D? I don't think such a thing could exist.<br /></p> <div class="Discussion_UserSignature"> <p>DenniSys.com</p> </div>

 

[UncertainH]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>&nbsp;The usual analogy for the "curled up" dimensions is a garden hose.&nbsp; From a distance the hose appears to be a string -- one dimensional.&nbsp; One sees that it is three dimensional only when very close to it or under high magnification as with a telescope.The general thought with respect to "curled up" dimensions in string theory and similar theories is that the extra dimensions occur on such a small scale as to be undetectable to us in the macroscopic world. <br />Posted by DrRocket</DIV></p><p>Would not any extra dimensions be non-spatial and thus scale is not applicable? Back to your original example of the theatre when we are standing inside the theatre could we not say that the ticket price is curled up inside ? You can't look at it but it does contribute to the description of our state or position.<br /></p>

 

[yevaud]

<p>Consider that you are house-bound; you may never leave your home, even for an instant.&nbsp; You experience the three familiar dimensions of your home, plus the fourth of time.</p><p>Now you're a smart guy.&nbsp; Even though you can never see them, you know that a roof and a basement must exist, from what you know about structures.&nbsp; Yet you may never actually see them; they are cut off from you.&nbsp; But the science of architecture implies that they must exist, even though they will forever be a mystery to you.</p><p>It's similar to this with extra dimensions.&nbsp; They pop right out of theory that otherwise has worked admirably well describing the world.&nbsp; Thus we can imply they exist, even if they are compactified at or below the Planck Length and, like the shut-it's roof, forever denied actually being seen or touched by us.</p><p>That's how I look at it.&nbsp; Though they may exist it's a difference without a distinction, since for all practical purposes, I must treat them as a mathematical and physical abstraction and little more.&nbsp; They are forever cut off from me. </p> <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[emperor_of_localgroup]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>IThere is a common thought experiment that is often talked about being what would a 'flatlander' see if a sphere were to pass through his land, usually the response is the sphere would appear as a point, turn into a line and dimish back to point again. Well that makes sense from the perspective of our 4-d world that we live in.Consider also that there might be concepts in sphere land (mass for instance) that do not and cannot exist in flat land. Perhaps then the flat lander would see nothing as the sphere passes through. I don't have any answers here just questions but I liked your post. <br />Posted by UncertainH</DIV></p><p><font size="2">Glad this thread has come back. Nothing is more brain-teasing than thinking about dimensions. Your comment "<font color="#ff0000">Consider also that there might be concepts in sphere land (mass for instance) that do not and cannot exist in flat land",</font>is interesting because it hints to a possibility that 'mass may be a product of a dimension". For this and other reasons I'm beginning to think number of dimensions are finite but unbounded, and different types of 'intelligence' perceive different dimensions. Flatlanders intelligence is different from 3D or 4D&nbsp; or 5D-landers intelligence. </font></p><p><font size="2">I have no problem with string theory except the dimension part. It is most probable that basic building blocks of everything are energy string. But why 9 or 11 dimensions? They sound too convenient to be correct. I once did permutation/combination that showed only a few hundred or thousand (forgot the exact number) universes are possible with 11 dimensions.&nbsp; Nature shouldn't play with numbers.<br /></font></p><p><font size="2" color="#ff0000">Even though you can never see them, you know that a roof and a basement must exist, from what you know about structures.&nbsp; Yet you may never actually see them; they are cut off from you. [mod]</font></p><p><font size="2">Sorry, a house is not a good example for 'hidden dimensions', because we have a previous knowledge about structure of a house. It is more like being within a container and unaware of its whereabouts.&nbsp;</font></p> <div class="Discussion_UserSignature"> <font size="2" color="#ff0000"><strong>Earth is Boring</strong></font> </div>

 

[yevaud]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Sorry, a house is not a good example for 'hidden dimensions', because we have a previous knowledge about structure of a house. It is more like being within a container and unaware of its whereabouts.&nbsp; </p><p> Posted by <em>emperor_of_localgroup</em></DIV></p><p>But it is.&nbsp; We have previous knowledge of the the structure of spacetime via theory, theory which has so far appeared to be correct.&nbsp; These suggest the presence of A multiplicity of "other" dimensions.&nbsp; Thus the analogy is cogent. </p> <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Would not any extra dimensions be non-spatial and thus scale is not applicable? Back to your original example of the theatre when we are standing inside the theatre could we not say that the ticket price is curled up inside ? You can't look at it but it does contribute to the description of our state or position. <br />Posted by UncertainH</DIV></p><p>The "extra" dimenions in string theory, brane theory, etc. are spatial.&nbsp; They are simply too small to notice.</p><p>One might in principle cook up other theories in which extra dimensions are not spatial, but the theories currently being contemplated involve extra dimensions that are spatial.</p><p>There is no problem dealing with additional dimensions mathematically.&nbsp; None at all.</p><p>But for a physical theory the heart of the problem is whether the theory permits predictions of phenomena that are beyond the reach of current theories with only 3 spatial dimensions and 1 time dimension.&nbsp; This is itself a bit oversimplified since the space-time of general relativity is not a Euclidean space but rather a curved 4-manifold nad one cannot cleanly separate spatial dimensions from time dimensions in a global manner.<br /></p> <div class="Discussion_UserSignature"> </div>

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Glad this thread has come back. Nothing is more brain-teasing than thinking about dimensions. Your comment "Consider also that there might be concepts in sphere land (mass for instance) that do not and cannot exist in flat land",is interesting because it hints to a possibility that 'mass may be a product of a dimension". For this and other reasons I'm beginning to think number of dimensions are finite but unbounded,</DIV></p><p>There is no such thing, with regard to number of dimensions as "finite but unbounded".&nbsp; The choices are finite-dimensional (in which case you can assign a specific natural number unambiguously as the dimensionality) or infinite-dimensional (in which case you can also talk about local homeomorphism or diffeomorphism to a topological vector space and you can unambiguously talk about the dimensionality of that vector space as well, though you may need to be specific about what you mean and may need to use cardinal numbers to describe dimension.)</p><p>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>and different types of 'intelligence' perceive different dimensions. Flatlanders intelligence is different from 3D or 4D&nbsp; or 5D-landers intelligence. I have no problem with string theory except the dimension part. It is most probable that basic building blocks of everything are energy string. But why 9 or 11 dimensions? They sound too convenient to be correct. I once did permutation/combination that showed only a few hundred or thousand (forgot the exact number) universes are possible with 11 dimensions.&nbsp; Nature shouldn't play with numbers.Even though you can never see them, you know that a roof and a basement must exist, from what you know about structures.&nbsp; Yet you may never actually see them; they are cut off from you. [mod]Sorry, a house is not a good example for 'hidden dimensions', because we have a previous knowledge about structure of a house. It is more like being within a container and unaware of its whereabouts.&nbsp; <br />Posted by emperor_of_localgroup</DIV></p><p>Your permutatin calculation must have missed something.&nbsp; Even a finite-dimensional space has an infinite (in fact an uncountably infinite) number of points.&nbsp; And you can make an infinite number of possible universes of any finite dimensin whatever, depending on what you might take to be an equivalence relation amont universes.&nbsp; <br /></p> <div class="Discussion_UserSignature"> </div>

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Consider that you are house-bound; you may never leave your home, even for an instant.&nbsp; You experience the three familiar dimensions of your home, plus the fourth of time.Now you're a smart guy.&nbsp; Even though you can never see them, you know that a roof and a basement must exist, from what you know about structures.&nbsp; Yet you may never actually see them; they are cut off from you.&nbsp; But the science of architecture implies that they must exist, even though they will forever be a mystery to you.It's similar to this with extra dimensions.&nbsp; They pop right out of theory that otherwise has worked admirably well describing the world.&nbsp; Thus we can imply they exist, even if they are compactified at or below the Planck Length and, like the shut-it's roof, forever denied actually being seen or touched by us.That's how I look at it.&nbsp; Though they may exist it's a difference without a distinction, since for all practical purposes, I must treat them as a mathematical and physical abstraction and little more.&nbsp; They are forever cut off from me. <br />Posted by yevaud</DIV></p><p>&nbsp;I don't have any problem with your house analogy (or is it House ?)&nbsp; But the extra dimension do not pop out of any theory that has been working very well.</p><p>The extra dimensions arise in an attempt to unify the quantum field theories of the electroweak force, the strong force and gravity.&nbsp; At this point they are pure conjecture and the candidate theories that use them have not been able to make any good physical predictions that are not already handled by existing theories.&nbsp; As someone (can't remember who at the moment) observed, " The problem with string theory is not that it does not make predictions.&nbsp; The problem is that they are all wrong."</p><p>Maybe the extra dimensions will prove useful in developing a unified theory.&nbsp; Maybe not.&nbsp; It is research and research typically has many dead ends before it finds success.&nbsp; <br /></p> <div class="Discussion_UserSignature"> </div>

 

[yevaud]

Analogy is always suspect. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Analogy is always suspect. <br />Posted by yevaud</DIV></p><p>Yes, but often useful.&nbsp; Anyone with your avatar knows that.&nbsp; <img src="http://sitelife.space.com/ver1.0/content/scripts/tinymce/plugins/emotions/images/smiley-wink.gif" border="0" alt="Wink" title="Wink" /><br /></p> <div class="Discussion_UserSignature"> </div>

 

[SHU]

<font size="2">Aside from string theory, there was a good article in the July '08 Scientific American, Quantum Universe, that came up with four (4.02 +/- 0.1) finite dimensions using causal structures.</font>

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Aside from string theory, there was a good article in the July '08 Scientific American, Quantum Universe, that came up with four (4.02 +/- 0.1) finite dimensions using causal structures. <br />Posted by SHU</DIV></p><p>4.02 +/- 0.1 ?</p><p>There is a notion of fractional topological dimensions, but that doesn't work very well for differentiable manifolds, so if the dimension is within the specified range it had damn well better be 4.0000000000000000000000000000000000000&nbsp; +/- 0<br /></p> <div class="Discussion_UserSignature"> </div>

 

[SHU]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>4.02 +/- 0.1 ?There is a notion of fractional topological dimensions, but that doesn't work very well for differentiable manifolds, so if the dimension is within the specified range it had damn well better be 4.0000000000000000000000000000000000000&nbsp; +/- 0 <br />Posted by DrRocket</DIV><br /><br /><font size="2">You know magazines, all generalizations and oversimplification.&nbsp; I'm not sure how they came up with that but I assumed it was statistical, based on computer models.</font></p><p><font size="2">I&nbsp;already filled my quota of&nbsp;annoying conjecture but I have one more.&nbsp;&nbsp;We often refer to time as a dimension.&nbsp;&nbsp;I have also heard it argued that it's a product, like entropy.&nbsp;&nbsp; As a dimension, it has a unique restriction of travel,&nbsp; forward only, more like a vector.&nbsp; A vector can just as easily be 2 dimensional.&nbsp; Since&nbsp;one restriction has already been established, why not more?&nbsp; No, I'm not referring to science fiction multiple time lines or&nbsp;a picture of Schrodinger's lost cat on a telephone pole.&nbsp; Even a time plane, as opposed to line, would imply more than one common source and&nbsp;is disqualified.&nbsp; It could allow for curves in time.</font></p><p><font size="2">Is it&nbsp;possible that time&nbsp;has more than one dimension?</font>&nbsp;</p>

 

[SHU]

<p><font size="2">I take that back.&nbsp; A time plane might be possible using a function like z= x^1/2 + y^1/2.&nbsp; That plane would be sloped upward on all axis from 0,0,0.&nbsp; Pythagorus strikes again.</font></p><p><font size="2">This free download can demostrate.</font></p><p>http://calculator.runiter.com/graphing-calculator/</p><p><font size="2">There's an obvious flaw in this but I'll let you work that out and maybe suggest a possible remedy.</font></p>

 

[emperor_of_localgroup]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>You know magazines, all generalizations and oversimplification.&nbsp; I'm not sure how they came up with that but I assumed it was statistical, based on computer models.I&nbsp;already filled my quota of&nbsp;annoying conjecture but I have one more.&nbsp;&nbsp;We often refer to time as a dimension.&nbsp;&nbsp;I have also heard it argued that it's a product, like entropy.&nbsp;&nbsp; As a dimension, it has a unique restriction of travel,&nbsp; forward only, more like a vector.&nbsp; A vector can just as easily be 2 dimensional.&nbsp; Since&nbsp;one restriction has already been established, why not more?&nbsp; No, I'm not referring to science fiction multiple time lines or&nbsp;a picture of Schrodinger's lost cat on a telephone pole.&nbsp; Even a time plane, as opposed to line, would imply more than one common source and&nbsp;is disqualified.&nbsp; It could allow for curves in time.<font color="#ff0000">Is it&nbsp;possible that time&nbsp;has more than one dimension?&nbsp; </font><br /> Posted by SHU</DIV></p><p><font size="2">2D time? Now you are talking. This universe is complicated enough for this lowly mortals, lets not make it more unthinkable. 2D time would be real fun for mathematicians and hell for average guys/gals. 'Curves of time' will also imply time intervals are not equal.&nbsp; But I like the comparison of time with entropy, there is one similarity between this two - the direction. </font></p><p><font size="2">My current idea is we are 3+1 dimensional. Period. We are completely integrated into this (3+1)D universe, there is no way of escaping this reality. We are not (3+1)D beings trapped in 11 dimensions (or 11 dimensional body). If a universe with 11 dimensions exist, the things of that universe would have ZERO similarity with us.&nbsp;</font></p><p><font size="2">I still don't understand why everyone thinks we humans are 'complete' , we have all we needed. We have only 5 or 6 senses, even time may be the result of another sensory process. There can be sensory systems in universes of higher dimension which is even beyond our imagination. Universes with higher dimensions may exist but they will contain 'higher lifeform'. That's why I said the number of dimensions might&nbsp; be unbounded.</font></p><p><font size="2">DrRocket's infinite universes remind of of Evertt's parallel universe theory. Anyway, next NOVA (10-28-08) will have a show on something like 'hunting for hidden dimensions'. Gotta watch this. </font></p> <div class="Discussion_UserSignature"> <font size="2" color="#ff0000"><strong>Earth is Boring</strong></font> </div>

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>You know magazines, all generalizations and oversimplification.&nbsp; I'm not sure how they came up with that but I assumed it was statistical, based on computer models.I&nbsp;already filled my quota of&nbsp;annoying conjecture but I have one more.&nbsp;&nbsp;We often refer to time as a dimension.&nbsp;&nbsp;I have also heard it argued that it's a product, like entropy.&nbsp;&nbsp; As a dimension, it has a unique restriction of travel,&nbsp; forward only, more like a vector.&nbsp; A vector can just as easily be 2 dimensional.&nbsp; Since&nbsp;one restriction has already been established, why not more?&nbsp; No, I'm not referring to science fiction multiple time lines or&nbsp;a picture of Schrodinger's lost cat on a telephone pole.&nbsp; Even a time plane, as opposed to line, would imply more than one common source and&nbsp;is disqualified.&nbsp; It could allow for curves in time.Is it&nbsp;possible that time&nbsp;has more than one dimension?&nbsp; <br />Posted by SHU</DIV></p><p>Vectors are in fact points and really don't have a dimension.&nbsp; What has a dimension is a <u>vector space,</u> which is an algebraic structure whose elements are vectors with the additional notions of vector addition and subtraction and scalar multiplication.&nbsp; That additinal structure is what is responsible for the notion of dimension (see a text on linear algebra for the details).</p><p>Once you have a notion for the dimensin of a vector space, that notion provides the notion of dimension for Euclidean spaces, which are just vector spaces with additional structure that allows the measurement of distance (also angles), which in turn provides a topology, and multi-variable calculus.&nbsp; That in turn permits the development of the theory of topological and differentiable manifolds which is the theory required for general relativity (Riemannian geometry).</p><p>There would be a problem with a multi-dimensional notion of time, the inability to provide, even locally, the ordering necessary to what we experience as the "flow" of time.&nbsp; There have been some speculations to the contrary -- I seem to recall Hawking contemplating complex time, but I don't think it ever went anywhere.&nbsp; You can already think about curves related to time and that is&nbsp;pretty much what happens in general relativity with curved space-time, and in fact time gets a bit mixed up with space over large expanses.</p><p>The bottom line is that time is not all that well understood, and in particular the reason that time seems to flow in one direction is not explainable from more fundamental principles.&nbsp; It is a topic of research.&nbsp; Einstein was of the opinion that time is basically statistical in nature, but no one has ever provided a rigorous and useful formulation of that notion as a predictive theory.&nbsp; <br /></p> <div class="Discussion_UserSignature"> </div>

 

[SHU]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I take that back.&nbsp; A time plane might be possible using a function like z= x^1/2 + y^1/2.&nbsp; That plane would be sloped upward on all axis from 0,0,0.&nbsp; Pythagorus strikes again.This free download can demostrate.http://calculator.runiter.com/graphing-calculator/There's an obvious flaw in this but I'll let you work that out and maybe suggest a possible remedy. <br />Posted by SHU</DIV></p><p><font size="2">Ready for some more fun?&nbsp; Let's replace the "+" with a "*" in the previous equation.&nbsp; Maybe factor the scale by c^2, just for example.&nbsp; Time isn't so linear anymore.&nbsp; Just a thought, or a fraction&nbsp;of a thought,&nbsp;about the accelerating universe.&nbsp; Is that any less plausible than dark energy?</font></p><p><font size="2">You&nbsp;might notice the similarity to&nbsp;a hyperbolic topology.</font></p>