# Why Can't We Visualize More Than Three Dimensions?

Physicists and mathematicians who think about higher-dimensional spaces are, if they allow their interest to somehow become public knowledge, inevitably asked: “How can you *visualize* more than three dimensions of space?” There are at least three correct answers: (1) You can’t. (2) You don’t have to; manipulating abstract symbols is enough to help you figure things out. (3) There are tricks to help you pseudo-visualize higher-dimensional objects by cleverly projecting them into three dimensions; see here and here.

But really, why can’t we visualize things in more than three dimensions of space? Could a Flatlander, living in a world with only two spatial dimensions, learn to visualize our three-dimensional world? Could we somehow, through practice or direct intervention in the brain, train ourselves to truly visualize more dimensions?

I can think of a couple of explanations why it’s so hard, with different ramifications. One would be simply that our imaginations aren’t good enough to project our consciousness into a constructed world so very different from our own. Could you, for example, really imagine what it’s like to live in *two* dimensions? Sure, you can visualize Flatland from the outside, but what about asking what it’s like to really be a Flatlander? The best I can do is to imagine a line, flickering with colors, surrounded by darkness on either side. But the darkness is still there, in my imagination.

The other possible explanation is that the process of visualization takes up a three-dimensional space in our actual brain, preventing us from “tuning a dimensionality knob” on our imaginations. The truth is certainly more complicated than that (and I’m not experts, so anyone who is should chime in); the visual cortex itself is effectively two-dimensional, but somehow our brain reconstructs a three-dimensional image of the space around us.

Maybe this could be a new tantric discipline: visualization in higher dimensions. Or maybe the Maharishi already offers a course?

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