A romance of many dimensions

[eric2006]

In flatland it appears it was not possible for any of the characters to enjoy the full degree of freedom offered by all of their existing dimensions. Take for instance the characters in the 2D world. They could only perceive the 2D objects from a 1D perspective. If a triangle approached them from its angle they would only see a line. Only through deep thinking and math could they even comprehend their own world. I still do not understand how they could even view a single dimension without some form of a third dimension being visible. How could they view a line straight on without it having any height? I believe the sphere described it as them seeing the 3rd dimension of height as a "shade" or something like that. I also didn't understand until much later what they meant by "there was a slight pull to the south" and "all the rain came from the north. It made perfect sense to me if flatland was standing up on earth. Then the slight pull to the south would be gravity and the rain would fall from what they considered the North. <br /><br />The whole story of flatland left me with many thoughts. Since a 2D object could not fully enjoy his 2D world (viewing it from a 1D angle) could this apply to a 3D world? Could we not enjoy all of the degrees of freedom in a 3D world? What I mean is that it appears we actually do live in a 4D universe since we are limited to a 3D view (2D was limited to a 1D view).<br /><br />If we do actually live in a 4D universe I am not quite sure if time would be the fourth dimension we are looking for. Since we can only travel one direction in it then it appears that it is only a half of a dimension. Is that possible? Would that make time the 3rd and 1/2 dimension? I'm not sure if fractional dimensions are possible. Mathematically I don't see why this couldn't be possible. Anyway it seems you would have to be a 4th dimensional object to fully enjoy all a 3D world would offer.<br /><br />Am I off my rocker?<br />

 

[scull]

Might it not be possible to travel back? Wormholes provide this possibility. Didn't someone work out the math already? I think I read somewhere someone did. If so, I guess it's up to the engineers now to build time machines.

 

[eric2006]

I think you can only travel back as far as when the worm whole was first created.<br /><br />For instance if you opened a worm hole and went some where far away in the universe. You stayed there for 3 years. If you traveled back through the worm hole you would pass yourself comming in the first time.

 

[newtonian]

scull - organic gardening is indeed like going back in time.<br /><br />That is how our ancestors did it!<br /><br />Wormholes are indeed extremely important to the organic gardener!<br /><br />Seriously, you are correct.<br /><br />In fact proof of this was televised recently on Star TreK!

 

[newtonian]

Eric2006 - Ah! Great minds travel the same paths!<br /><br />Time travel to when the whole worm was created?<br /><br />You posted:<br /><br />"I think you can only travel back as far as when the worm whole was first created." <br /><br /><br />

 

[eric2006]

I had to read your post a couple times to understand what you where getting at. <br /><br />Now that I see my error- I find the Whole thing to be quite amusing.

 

[newtonian]

Eric & scull - Sorry - I get silly when I'm tired.<br /><br />Please forgive.<br /><br />To make amends, here is a nice link on wormholes:<br /><br />http://www.pbs.org/wnet/hawking/strange/html/wormhole.html

 

[scull]

What the hell is a white hole?

 

[harmonicaman]

White Holes<br /><br />White holes are similar to black holes except white holes are ejecting matter verses black holes are absorbing matter. In 1916, Karl Schwarzschild derived the first model of a black hole using Einstein's theory of general theory of relativity. Nothing, not even a particle moving at the speed of light, can escape the gravitational pull of a black hole. The existence of white holes is implied by a negative square root solution to the Schwarzchild metric for space-time-matter continuum.. It is important to remember that black and white holes can be composed from matter or antimatter. <br /><br />A worm hole, which joins white holes, is known as the Einstein-Rosen bridge and is one of the most fascinating concepts in theoretical physics. In 1962, John Wheeler discovered the Einstein-Rosen bridge space-time-matter metric. Theoretically, a worm hole could be stabilized to allow a safe equilibrium between matter and antimatter white holes. To stabilize the worm hole, the throat of the singularity contains matter and antimatter white holes, which are spherical in nature. The antimatter has a negative mass and exerts a positive surface pressure. <br /><br />Scientists have questioned the existence of black holes for decades. On May 27, 2004, Edward Churchwell, a University of Wisconsin-Madison astronomer, announced their findings using NASA's Spitzer Space Telescope that the Milky Way Galaxy was churned out hundreds of new stars. The black holes in the center of galaxies are composed of condensed matter and antimatter. The black holes have the mass of a billions of suns. The Einstein-Rosen Bridge keeps the matter and antimatter black holes separated. The oscillations between the black holes at opposite ends of the wormhole force the black holes to become white holes that eject matter and antimatter in opposite directions forming the spiral arms of stars within the galactic disk. <br /><br />The antimatter negative mass ensures the throat of the worm hole

 

[scull]

*light flashes* Newtonian-- I'm just getting it now: you're an organic gardener.<br /><br /><br /><br />

 

[scull]

harmonicaman-- Thanx for the cut and paste; much appreciated; it saved me googling time. <br /><br /><br /><br /><br />

 

[bobw]

<font color="yellow">Take for instance the characters in the 2D world. They could only perceive the 2D objects from a 1D perspective.</font><br /><br />They could go forward/backward and left/right; they could go around a pentagon and count the sides. I call that experiencing all their dimensions. If a circle looks like a line isn't that really two dimensional? If you look through a drinking straw you see what I would call one dimensionally so you couldn't see the line all at once, just one point at a time. I liken that to a graph where looking forward is a line in the +y direction. In order for your field of view to be some angle greater than zero you need the x direction too. In flatland their field of view would be like us looking through a slot instead of a straw. I think it takes 2D to do that.<br /><br />They probably would have done better with depth perception if they had two eyes <img src="/images/icons/smile.gif" /><br /> <div class="Discussion_UserSignature"> </div>

 

[eric2006]

Interesting interpretation. But how could they know a triangle was not a line? From what a I understood from the book was that only the "higher thinkers" understood they were 2D. From our perception we could see they were in fact 2D and "look into their insides". What I am thinking is that a 3D object could appreciate and understand a 2D world better than a 2D object could.. SO I am thinking this works the same higher up. I understand what you are saying- I just think I am not finding the correct words to express what I am thinking.

 

[tdamskov]

We are in fact quite capable of imagining things in four dimensions, if you consider time the 4th dimension. For example, do you have any problem thinking of an empty balloon versus an inflated balolon or any of the intermediate stages? The balloon being inflated over time is really a single 4-dimensional object.<br /><br />It should be noted that what you're really doing here is imagining 'slices' of the hyperballoon, which could be argued is not exactly the same as visualising it as a whole. But most people can still mentally go forward and backward through the sequence of slices while keeping a fairly good overview of the total state of the "hyperballoon". It's what 3D animators do!<br /><br />For the hypothetical beings of Flatland, they would have a similar advantage to us when having a third dimension/time available for mental processing (consciousness?).<br /><br />If we take the 4th dimension as time idea a step further, any "transdimensional" beings would, from our point of view, necessarily exist out of time, existing as well as interacting with all points in our timelines simultaneously. And still retaining a "metatime" or imaginary time apart from our own. Looking at spacetime as complete 4D object (from Big Bang to .. when all threads of matter and energy have diffused endlessly into vacuum) everything that ever happened would be contained within this 4D object.<br /><br />Oh, my point? The Flatlanders have an implicit time dimension as well as their two dimensions.

 

[eric2006]

"Oh, my point? The Flatlanders have an implicit time dimension as well as their two dimensions"<br /><br />That is an interesting thought. <br /><br />If the Flatlanders would have an implicit time dimension then should we not be able to travel through all points in their history (as a 4D person/object could do in ours)?<br /><br />If time were our 4th dimension would it not appear to the 4D person/object that our time was an implicit dimension to us?<br /><br />I am thinking in terms of a spatial dimension as in a hypercube has 2^4 = 16 nodes. I can't see how time would fit this idea. Not that I don't recognize it as a dimension. Rather, I am wondering if it could be a fractionalized dimension or even raised to another power. Could it be possible if something were reduced by one dimension that it's time dimension could be reduced fractionally? Or if something was increased by a dimension it's time dimension could be raised by a higher exponent?<br /><br />If you were brought into a 4th dimensional plane by a 4D man and witnessed your 3D world I assume you could see all points in our time exist at once. If so then I guess you would be "ticking" in the 4D man's implicit time dimension.