How does a four-dimensional world look like?

Eric Lippert is running an eye-catcher series on High Dimensional spaces (see here part one and two). Which got me thinking. The classical laws of Optics work can be easily generqalized to N spatial dimensions. You could easily imagine things like refraction point of a material, lenses, sources of light and so on in a four-dimensional space for example. And also more advanced things like refraction, diffusion, and even the Fresnel effect!

I am sure that there are relevant images on the web, but I can’t seem to find them. Any ideas?

Comments (8)

  1. saraford says:

    I don’t know about 4-D, but if you want to see 3-D, check out Webtop is the research project i worked on senior year of college. Lasers and Reflection & Reflection are mine.



  2. Anil says:

    Don’t know about 4 dimensional but you can check out the 2 dimensional world and a point’s world in the book "Flatland: a romance of many dimensions" , available on project gutenberg.

    Maybe it has the 4 dimesional world but I have not finished the book yet 😉

  3. Hunweasel says:

    .. and the one dimensional world is shown on Fox News .. ;-P

  4. Piotrek says:

    We can see in 3 dimensions because of our two eyes

    3 dimension can be represented by an image (in two dimensions) by adding perspecive. A misrepresented image gives us the impression of 3 dimensions

    We cannot make an image in 4 dimensions just because we would be not able to see it.

    The fourth dimension in astronomy is time, it means that a tri-dimensional object can change according to time (some stars we see are already dead)

    My advice: to see 4 dimensions, go to watch the last starwars, there will be plenty of special effects with polygons moving everywhere 😀

  5. VeXocide says:

    Like a 3d with a ticking clock 🙂

  6. AdiOltean says:

    I could probably write some basic program that projects a 4D figure into 2D.

    BUT it would be much more interesting to have a 4D ray tracer…