Comments on: Visualizing Four Dimensions

By: Jonathan Vos Post

Jonathan Vos Post — Wed, 05 Aug 2009 20:12:48 +0000

http://math.ucr.edu/home/baez/gr/oz5.html

“Now, what does geodesic deviation have to do with curvature, exactly? Well, let’s look at a spacetime diagram of the situation. Hang on while I equip you with 4-dimensional vision.” He passes his hands over Oz’s head and mutters an almost inaudible syllable, and all of sudden Oz is shocked to find that he can see the clocks, not just in space, but in spacetime. They trace out curves in spacetime, and he sees these curves in their entirety as a static whole! Yet he is simultaneously able to see how at any given “moment” — i.e., any given slice of spacetime — the clocks occupy positions in “space” just as they did in the previous scene! Furthermore, as before, he can see, as in a movie, how as time passes the clocks begin to accelerate away from each other. Somehow he is seeing not just space but spacetime!

“Hey, how are you doing that?” he asks. “I bet if I could do this myself these problems would be a whole lot easier!”

“I’m just using my limited telepathic ability to show you how I think of these things,” the wizard says. “For you to do it too, all you need is practice.”

Oz frowns, unsure as to how he’d practice this. He decides to keep quiet and pay careful attention; maybe he’ll get the habit of 4d vision.

“Wise move,” says the wizard, smiling.

By: Jonathan Vos Post

Jonathan Vos Post — Fri, 03 Jul 2009 16:58:03 +0000

“In physics, time is the 4th dimension,…” is how H.G. Wells could summarize an idea already popularized for over a decade. But that was assuming Euclidean flat space. Minkowski and Einstein rather changed all that. “Space of itself, and time of itself, melted way, and what remained was a kind of marriage.”

By: hp

hp — Fri, 03 Jul 2009 03:54:14 +0000

In physics, time is the 4th dimension, and we move along the time axis to see how a 3D objects evolves ( for lacks of better word) —- or changes shapes. So if we have another spatial dimension, I wonder if we can use the same method? Slide along that 4th axis, and observes what happens in the other spatial axes.

By: Doug Hammer

Doug Hammer — Sun, 28 Jun 2009 23:49:40 +0000

In the context of four dimensions, the general topological considerations confuse the concept. Taken from a combinational generalization, it is second nature to consider upwards of four to seven variables in state space. To simplify matters by considering known boundaries of a given variable range, in a similar relation to confining a axis of rotation in topological space. In addition, in many linear relationships the combinational permutations or ranges of all known state configurations, can be reduced to rate functions independent of forth dimensional time, and considered directly in context to their relations and boundaries of configuration. Visualizing four dimensions is a matter of context, when the ranges and boundaries are known many systems of equations can be reduced to very few if no dimensions at all.

By: John Smith

John Smith — Tue, 02 Jun 2009 11:51:45 +0000

There is a graph type called slice can show the character of 4D volume scientific data. The coordinate x, y and z are used to show the position in the volume, and the color shows the feature of the fourth dimension.
You can see some images made by visualization software Visual Data:

http://www.graphnow.com/visual-data.html

By: Catherine

Catherine — Mon, 25 May 2009 19:11:35 +0000

My old roommate once told me that her favourite shape was a tesseract. I thought it was a clever thing to say although a physics major acquaintance was critical of her ability to have a shape that she wouldn’t be able to conceptualize as her favourite.

By: Jonathan Vos Post

Jonathan Vos Post — Mon, 18 May 2009 04:37:04 +0000

“After all, our nervous system evolved in a three dimensional world” begs the question (both as the the actual dimension of reality, and to the content of geometric imagination). Or relies on circular reasoning. And can people who DO visualize four dimensional space be said to have evolved differently? With all due respect, visual systems neuroscientist Vincent Toups, you miss the point of the real question. Not that your implicit question “[how] can [we] accurately visualize three space?” is adequately answered so far by our field.

By: Vincent Toups

Vincent Toups — Fri, 15 May 2009 14:52:45 +0000

As a visual systems neuroscientist I don’t find it odd at all that we cannot easily visualize four dimensional space. After all, our nervous system evolved in a three dimensional world (one we already have to approximate with fundamentally two dimensional data and computational machinery). You should be more surprised that we can accurately visualize three space.

By: schriAlphi

schriAlphi — Mon, 04 May 2009 20:04:04 +0000

Perhaps if the atomic structures of the material that forms some hypothetical newly evolved cortex of the brain - if this atomic material were to contain an axis lying in a fourth direction; let’s say a .0000006 seconds into the future and .0000005 seconds into the past, and with particles at these distances, then information of four space might be able to be processed into perceptual interpretation mediated through the 4-D neurons of this cortex. -scriAlphi

By: Steve Nordquist

Steve Nordquist — Fri, 17 Apr 2009 04:18:27 +0000

Sure, once we all get Baby’s First Algebraic Transformation mobiles and Russell Blocks printed on the sides of polytopes. You know, easy dot algebras….

The examples; they just look like local group projections; how am I going to formally invert a horse through itself using negative lens distance in blender (or some other renderer)? (Tens of aliens tried it the tactile way; they can’t get it either. (cough)) It is too easy to confuse dimensions (which it would be our senses’ job to reduce to a salient few aspects), and plot coupons.

We barely have 3D animations of common particles; wasn’t it only recently that we got explanations of friction that weren’t cartoons of classical mechanics? So…how about just complex/real 3D visualization, now that we have (well…for $4k, wall space, and enough computer, videocard & webcam around to track whoever leads the ‘viewpoint’ around…carbon footprint flaming…hideous distortion of MTV Sound Fields through 2D comb filters…) 3D displays.