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We consciously know and feel the first three dimensions and with some thinking time as well. But according to literature like String theory etc., we have many many more dimensions. We can readily express them in paper. But why can't we realize them? Why can't we experience them like the first three dimensions?

PS. I was pondering on this when I saw the movie Interstellar where even the fourth dimension 'time' is expressed using the first three dimensions for Cooper. PPS. The first three dimesnions being the X, Y and Z axes.

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  • $\begingroup$ Most people aren't even very good with three dimensions. Why not? That's more of a question for biology than physics. Why do humans not need detailed three dimensional mental maps for survival? Probably because we are normally living on a flat surface and understanding the structure of the third dimension above our heads doesn't do much for us, so nature didn't waste neural cells on it. And why not four dimensions? Because it does even less for survival to be able to map objects that do not exist in our immediate reality. $\endgroup$ – CuriousOne Jun 10 '15 at 9:22
  • $\begingroup$ @CuriousOne So you're saying that survival determines how much we want to perceive right? I agree $\endgroup$ – Srikanth Guhan Jun 10 '15 at 9:39
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    $\begingroup$ Its always my favorite sentence in mathematics that an n dimensional shape is the "shadow" of an n+1 dimensional shape. Ie like that of a point/line/square/cube/tesseract/general hypercube $\endgroup$ – Triatticus Jun 10 '15 at 11:34
  • $\begingroup$ Wow! Never knew that tesseract was actually something in the academic world. Shadow analogy seems to be working fine till 4th dimension. After that, my mind cannot comprehend $\endgroup$ – Srikanth Guhan Jun 10 '15 at 12:16
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    $\begingroup$ I think it is not impossible to visual a 4th (or even more) dimensions in the case of simpler forms, we only have to encode the extra cordinates into some other attribute (for example, into the color of the pixels). Furthermore, it would require a little bit of learning (for us) to understand such images. In the case of descriptive geometry, we've already learned it long, this is why we can "extrapolate" the 2d image into a 3d object. $\endgroup$ – peterh - Reinstate Monica Dec 2 '16 at 13:19
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Why can't we experience them like the first three dimensions?

The usual explanation is that these additional dimensions, if they exist, are tightly curled up or compacted. Humans can't move around in them like we can move through the three "normal" spatial dimensions we are familiar with.

Why are we not able to visualize Dimensions beyond 3

Mostly because as our brains develop they don't experience sensory input corresponding to movement in more than three spatial dimensions. Therefore we don't build up the mental structures needed to intuitively comprehend more spatial dimensions.

Also our major senses, our eyes, are intrinsically two dimensional. Information about the third dimension has to be synthesized in our brains. Proprioception is, I suppose, provides three dimensional information - but we rely on that less.

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  • $\begingroup$ Can you please elaborate on 'curled up or compacted'? They are dimensions after all, they should exist endlessly right? Like the space is infinite $\endgroup$ – Srikanth Guhan Jun 10 '15 at 9:36
  • $\begingroup$ @SrikanthGuhan Just so as an example of being curled up a circle can be compact and endless. Now what he means to say is that the dimensions are way too odd for us interact directly with them. $\endgroup$ – AadityaCool Jun 10 '15 at 9:41
  • $\begingroup$ The operative term in the above answer is "if they exist". Nobody knows if that is the case. For myself, all I am going to say is that I take an extremely dim view of "string theory", and leave it at that. $\endgroup$ – Pirx Dec 1 '16 at 21:51
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Actually I recently published a paper on Mathematical Intelligence trying to answering that question

Why are we not able to see beyond three dimensions?

Abstract:

This is perhaps a philosophical question rather than a mathematical one, we do not expect to give a full answer, even though we hope to clarify some ideas. In addition, we would like to provide a new perspective on the subject. We will find curious analogies with the way we perceive color and make some imaginary experiments showing that, even living imprisoned in three dimensions it could be different.

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