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Friends,

If I could make genetic modifications to order—What kind of modifications would I need to make to the human brain to allow it to "See" in multi-dimensions? Why? Mainly because 3-D Solid Geometry is very beautiful. Geometry in 4-D; 5-D; 6-D and 7-D would probably be even more Beautiful… I want full-color and true dimensions—like in CAD… While these spaces would be purely abstract, does anyone think that many/some thorny Mathematical Problems—like Riemann's Hypothesis—would become self-evident to someone who could visualize in 7-D—or even 4-D? Saxon Violence

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  • $\begingroup$ I don't think this allows for a useful answer, because a) higher dimensions aren't represented in the visual world, and b) it calls for baseless speculation regarding mathematical hypotheses. Flagged to be closed as too broad. $\endgroup$ – jdunlop Aug 27 '17 at 3:42
  • $\begingroup$ Additionally, there's no reason to presuppose that there is anything genetic that limits human visualization to the experiential four dimensions; our brains are incredibly versatile. It seems more likely that what we perceive shapes what we can visualize. $\endgroup$ – jdunlop Aug 27 '17 at 3:44
  • $\begingroup$ Related: How to train humans to think in 4D? $\endgroup$ – Laurel Aug 27 '17 at 4:16
  • $\begingroup$ Assuming time is the fourth dimension, you see it every day. You see it in the same way 2D critters see a 3D object... one slice (moment) at a time. $\endgroup$ – JBH Aug 27 '17 at 5:44
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    $\begingroup$ First, you'd need a 4-D or higher brain. It's not a software issue, your hardware is lacking $\endgroup$ – nzaman Aug 27 '17 at 11:07
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If by "seeing" you are talking about the capacity to visualize higher dimensional spaces. Because poor three dimensional creatures like ourselves live in a world of three dimensions of space and cannot observe anything with more spatial dimensions. Considering time as a fourth dimension can be neglected for this exercise.

if it is possible, and this is by no means certain, to modify to order parts of the brain, then it is possible to genetically reorganize the visual cortex this might be adapted for the visualization of higher order spaces. In which case, it may be possible that people with modified visual cortices will be able to visualize 4d, 5d, 6d and 7d and possibly even higher dimensional spaces.

If so, this make geometry a much easier branch of mathematics for them. Mathematicians can dealt with higher order spaces including infinite dimensional spaces in their equations as abstract qualities. Whether there is any empirical evidence that the capacity to visualize spaces leads to improved geometers is an open question.

In theory, if we understood how the visual cortex worked, and knew how to modify it by genetic engineering to order, then creating people with higher dimensional visualization should be possible. But whether this will make better at geometry remains an open question.

ADDENDUM:

As point of clarification, this answer discusses genetic modification to the structure and function of the visual cortex. This should not be taken as an improvement in the actual perception of the spatial dimensions in which humans exist. Everything in their environment would be seen as spatially three dimensional. The improved visual cortex was always intended, in this answer, to be the platform with which people could be able to visualize, that is to say, through an act of imagination to conceptualize higher dimensional spaces.

Thank you to @L.Dutch for his perceptive comment.

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  • $\begingroup$ Trained people (a.k.a. mathematicians and other ) can "visualize" iperdimensional or even infinite dimension spaces without being genetically different. It's not really about viewing with eyes, but figuring with the mind. $\endgroup$ – L.Dutch - Reinstate Monica Aug 27 '17 at 7:05
  • $\begingroup$ @L.Dutch Great comment! I wasn't talking seeing as in actually seeing something, a point I had hoped I had made clear, obviously not, the modifications to their visual cortices was intended to improve their visual imagination not their actual eyesight. Personally I'm not sure if mathematicians actually visualize higher dimensional spaces or simply know how to manipulate the mathematical concepts describing those spaces. Although it would be fun finding out. $\endgroup$ – a4android Aug 27 '17 at 8:45
  • $\begingroup$ I think visualization is an entirely brain related process. At the very end our eyes only see the 2D retinal projection. It's the brain that infers the 3D structure behind. $\endgroup$ – L.Dutch - Reinstate Monica Aug 27 '17 at 9:05
  • $\begingroup$ I read an article recently stating that scientists had modelled some neuron pathways in the brain and found several higher dimensional geometries. So it could be that the genetic modification of the visual cortex, as you suggest, would just need to link itself somehow to already existing brain structures. Ie it doesn't have to reinvent the wheel, just find a way to see/conceptualize the existing wheels! $\endgroup$ – EveryBitHelps Aug 27 '17 at 9:23
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    $\begingroup$ @EveryBitHelps. So, the brain has higher dimensional geometries embedded in its neural pathways. That would make higher dimensional conceptualization easier to achieve. Thanks for the link. $\endgroup$ – a4android Aug 27 '17 at 9:46

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