Visualising 4D objects

[The Black Fox]

Is it possible to visualise four dimensional objects? I wouldn't have thought the brain is capable (I know mine isn't), but I have met people who claim they can.

Can anyone here manage it?

[Chris Haynes]

Yes... the 4th dimension is time!

So, bounce a ball on the floor with a bit of a twist. It will go up and down (z), along the floor (x), and to the side (y), and move as time (t) goes on. The movement will be described as a 2nd order differential equation as a function of x, y, z with respect to t.

[epepke]

Is it possible to visualise four dimensional objects? I wouldn't have thought the brain is capable (I know mine isn't), but I have met people who claim they can.

Can anyone here manage it?

I had the good fortune to do a demonstration at SIGGRAPH using the CAVE 3-D virtual environment. It's basically a zeroth generation holodeck.

I was just doing a meteorology display, but of course we used each other as guinea pigs, so I got to see a 4-D scene, illuminated with 4-D light projected into 3-D. That really helped, and since then I've been able to visualize 4 spatial dimensions, though I have to squeeze my brain pretty hard to do it.

[Jon the Geek]

Yes... the 4th dimension is time!

So, bounce a ball on the floor with a bit of a twist. It will go up and down (z), along the floor (x), and to the side (y), and move as time (t) goes on. The movement will be described as a 2nd order differential equation as a function of x, y, z with respect to t.
Or wave your hand in front of your face.

However, I have heard of 4D, space-only objects. Do some research on tesseracts (http://www.webster.com/cgi-bin/dictionary?sourceid=Mozilla-search&va=tesseract). And then, once you find something that explains them, post it so I can know what the heck it is :)

So if you can visualize a tesseract moving, I guess you're visualizing 5 dimensions...

[Chris Haynes]

Or wave your hand in front of your face.

However, I have heard of 4D, space-only objects. Do some research on tesseracts (http://www.webster.com/cgi-bin/dictionary?sourceid=Mozilla-search&va=tesseract). And then, once you find something that explains them, post it so I can know what the heck it is :)

So if you can visualize a tesseract moving, I guess you're visualizing 5 dimensions...

A better reference: http://mathworld.wolfram.com/Tesseract.html

It seems to be more of a mathematical concept than a physical one. I, as a former lowly dynamics engineer, am more familiar with equations of motions using 4 dimensions... and sometimes several degrees of freedom.

[Dark Jaguar]

I personally saw an interesting demo that used color to illustrate moving in the 4th dimension. So, if I envision intersection as only being possible between objects of the same color, and make one direction red and the other blue, I can imagine 4D space in that manner.

However, the idea of using that cave room (and actually I think I saw what you are talking about on the Science channel a month or so ago) sounds interesting. I'm up for a 3D display of a 4D space.

(For the purposes of this thread, I'm pretty sure what is meant is a 4th SPACIAL dimension.)

[Chris Haynes]

I had the good fortune to do a demonstration at SIGGRAPH using the CAVE 3-D virtual environment. It's basically a zeroth generation holodeck.

I was just doing a meteorology display, but of course we used each other as guinea pigs, so I got to see a 4-D scene, illuminated with 4-D light projected into 3-D. That really helped, and since then I've been able to visualize 4 spatial dimensions, though I have to squeeze my brain pretty hard to do it.

Since I am stuck in the physical world (quantum physics stuff drives me nuts), I can actually imagine what kind of other variables that would be need to be shown in a graphical representation of meteorology... Not only is there movement in three-dimensional space with respect to time, but there would also be temperature, humidity, air density... and the interactions between them. Which is really cool (and makes my head hurt, one of the many reasons why I hated thermodynamics and fluid dynamics... fortunately bolted, welded, riveted and otherwise connected structures that bounce, rotate, translate, vibrate and otherwise move are much easier to deal with --- except for that bit about "sheer flow").

[Chris Haynes]

...(For the purposes of this thread, I'm pretty sure what is meant is a 4th SPACIAL dimension.)

Spoilsport. Why do you have to clarify the terms? :p

Anyway, the explanations adn animations of n-dimensional cubes at Mathworld are giving me a headache.

[Mercifull]

Is it possible to visualise four dimensional objects? I wouldn't have thought the brain is capable (I know mine isn't), but I have met people who claim they can.

Can anyone here manage it?

Maybe they should apply for the JREF prize? :D

[epepke]

Since I am stuck in the physical world (quantum physics stuff drives me nuts), I can actually imagine what kind of other variables that would be need to be shown in a graphical representation of meteorology... Not only is there movement in three-dimensional space with respect to time, but there would also be temperature, humidity, air density... and the interactions between them. Which is really cool (and makes my head hurt, one of the many reasons why I hated thermodynamics and fluid dynamics... fortunately bolted, welded, riveted and otherwise connected structures that bounce, rotate, translate, vibrate and otherwise move are much easier to deal with --- except for that bit about "sheer flow").

Shear flow.

It's a chalenge, all right. Too much information, and the brain can't handle it. Also, the information we get from simulations is often of a different kind than what we get from Doppler radar. Sometimes the goal is to simplify the display enough that the important information is visible.

One of my early successes was kind of fun. We had a thunderstorm model, and it was predicting these narrow, spiky updrafts, and so the model was thought to be wrong. So, we did this. There's a mountain range near Socorro, New Mexico where a convection thunderstorm forms almost every day. There are a number of doppler radars pointed at where the storm forms, and so we get density information (which translates to cloud density and also rainfall), and 3-d information almost everywhere (with some missing data).

So I took data for about an hour of one thunderstorm. I used the density information to produce isosurfaces for the general storm outline and rainfall. But rather than use a classical visualization for velocity, such as flow lines or moving particles, I took just the vertical component of the velocity and put isosurfaces around them. The updrafts were visible. It turns out they had always been there, but nobody had seen them, because the visualization techniques had not been to the point.

[malaka]

Edwin Abbott gave a fun look at dimensions in Flatland (http://www.ibiblio.org/eldritch/eaa/FL.HTM).

[Chris Haynes]

Shear flow.

....

:p My defense for this obvious stupidity was it was late, I had had a very nice dinner with lots of wine, there was a 20 pound cat trying to get on my lap with the laptop... and I've not worked for 17 years (see my sig). Plus, I really was getting cross-eyed looking at the Mathworld depictions of n-dimensional cubes.

Thanks.

It sounds like a challenge. Once upon a lifetime ago I knew someone who majored in physical oceonograpy. Similar type of graphs, only they moved slower and contained variations in salinity along with temperature and density.

[homer]

Using mathematics it's easy enough to work with any number of extra dimensions , but visualising more than three physical dimensions ? I studied many wierd surfaces in topology including some that could not exist without a 4th dimension ( not time ) but I could never visualise more than 3 dimensions .

[Cecil]

I can do this. It took me quite a while, but with lots of practice and the help of several websites, I learned how to visualise hypercubes and hyperspheres. I'm still working on other shapes.

This (http://www.geocities.com/jsfhome/Think4d/think4d.html) is a great reference for starting to think in 4-D.

This (http://www.geom.uiuc.edu/docs/holt/tesseract/top.html) site takes you step by step through the process of rotating a hypercube around a plane. It's fascinating.

Google will turn up lots of results if you're interested further.

[malaka]

Aha! I took me a while to remember, but...

I haven't had time to browse the other liks in this thread, but if it hasn't already been mentioned, Charles Hinton's colored cubes (http://banubula.blogspot.com/2005/06/hintons-cubes-from-c.html) may be another method of "visualizing" the 4th dimension.