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Visualizing 4D -- Road Race

  1. Nov 24, 2015 #1
    I've been wondering what spaces with an extra physical dimension would look like. That is, instead of our 3+1D space it would be a 4+1D space.

    In general, it can't be done. There is too much information for a human brain to handle. But some special cases can work. The main one I thought of was a 4D road race.

    Now in our world a Formula One road race is mainly a 2D phenomenon. The track is more or less flat, so all that matters is forward-back and left-right. The up-down dimension could be reused. The way this would be done is to not show the up-down dimension at all, and instead use that for the new, novel, extra dimension. The road then would like like a curved rod instead of a strip. That curved rod can wind around in all three dimensions, so it can curve as freely up and down as it does left and right, or any combination of these two directions. The road would appear on the screen as a circle extending off into the distance, turning and twisting as it will. The driver has to be careful not to exceed the the friction of the road and skid off of it. Has this already been done?

    The sky wouldn't be usually be visible, instead the round road would be surrounded all 360 degrees by buildings, trees, or whatever. The 4th dimension up-down dimension couldn't be seen directly but could be encoded topographically.

    Off-road 4D is much harder. The trouble is that a human can see only 3D slices of the 4D world, and has to construct the 4D world from that, then find an optimal path through this 4D world constructed in the imagination.

    It would be even more difficult that constructing a 3D world from 2D slices. Imagine a game where you could only see only a few one-pixel-wide vertical and a horizontal slits. It wouldn't be easy, but at least we know how to imagine a 3D world.
  2. jcsd
  3. Nov 24, 2015 #2


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    Are you looking for works of science fiction or fantasy that deal with this visualisation? If so I suggest Diaspora by Greg Egan. If not and you're just looking for a discussion on what you've posted then the thread will have to be locked as it isn't in line with sub forum rules.
  4. Nov 24, 2015 #3

    Put it anywhere you like.
  5. Dec 1, 2015 #4
    So, how does Greg Egan visualize an extra dimension? I read about Diaspora but this specific topic wasn't discussed in the summaries.

    Ever since Flatland (1895?) higher dimensional spaces have been visualized by not displaying one of the dimensions. A 3D slice of a 4D object is displayed. Nothing wrong with that, but there are other ways.

    In general, displaying 4D objects can't be done because there is too much information. Possibly the best course is to look for constrained situations that can be taken advantage of.
  6. Dec 3, 2015 #5


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    It's been a while and to be honest the descriptions are complex and take up large parts of the story (the latter third anyway). It's definitely not with the flatland analogy, it takes pains to describe the journey from a 3+1d environment to a 4+1d. One chapter features a virtual museum whose exhibits are all dedicated to explain the physical laws and features of 4 dimensional universes. I suggest checking it out to really find out.
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