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Our panel of 90 professional philosophers has responded to

Question of the day

My short answer is that we don't need to be able to visualize higher-dimensional spaces in order to reason about them. I'd be quite astonished if Stephen Hawking could visualize 11 or 26 or even 5 dimensions. In fact, visualizing even three dimensions is not as easy as people think, as one realizes when trying to think through certain "ordinary" geometrical descriptions. But there are tricks that can sometimes give you the sense of visualizing higher dimensions, as with various diagrams of a four-dimensional "hypercube." Here's an example:

https://plus.google.com/117663015413546257905/posts/VteWm45DCff

Turns out that what I've said is more or less what the well-known physicist Sean Carroll says here:

http://www.preposterousuniverse.com/blog/2009/03/30/why-cant-we-visualiz...

though he adds some speculations that you can evaluate for yourself. But on the question you ask, it's (1) you can't, (2) you don't need to, and (3) there are all the same some tricks.