could you apply this to humans who are 3 dimensions and discover a 4 dimensions?
I bet a lot of people have tried. I thought about this myself and it's still a mystery to me. I don't think it is possible because the brain cannot think about dimensions higher than 3.
It depends on how you define dimension. If you can imagine a 3d object moving through time, you are imagining four space as far as I'm concerned.
John, there is more to this question than first meets the eye. Initially I will confine my remarks to spacelike dimensions.
Consider first a one dimensional intelligence, moving up and down its line. Since it only has one dimension it has no second one to compare and no incentive to even conceive of a second, third one.
Now take your 2D intelligence. Because it can distinguish two dimensions (that's intelligence) it could more easily conceive of a third, fourth....
So it asks your question.
If its world was really a 2D cross section of a 3D world then it could observe shadows cast by objects with extent in the third dimension.
In the same way a 3D intelligence living in a 3D cross section of a 4D+ world could observe shadows.
Now we come to an interesting side question.
We only experience one timelike dimension are we missing something?
Consider what a person in a 2-dimensional world would see. You would ONLY have the ability to see forward, backward, up, and down. You have no ability to see left or right. Since you have no ability to see left or right, then an object directly in front of you that is in the 3-dimensional world could be seen, but as soon as that object stepped left or right, it would literally completely disappear to you.
Take note of what was previously said, however, that the objects in the 3-dimensional world could still interact with your world through things such as shadows, which would cast the shadow across your sight. You would just see a black line in front of you. Also consider if that person was strafing left and right in front of you, you would see flashes of him as he crossed your plane and then he would vanish again.
If you think about that, things like dejavu could actually be a bi-product of things in the 4th dimension crossing our plane. I tend to lean more toward the "brain-fart" theory about your brain incorrectly processing memories directly into long-term instead of into short and then long though, but it's fascinating to contemplate.
Now consider this though, what if the sun only exists in the 3rd dimension, then that would imply there would be no shadows from the 4th dimension to the 3rd, effectively eliminating the use of dimensional shadows to see the 4th dimension. This would be similar to the concept of how a sphere exists only in 3-dimensional space, as it's only a circle in 2-dimensional space and a point in 1.
Just some thoughts for you to think about.
(FYI, I don't believe in 10 dimensions. I believe in 3. I don't even consider time a dimension, but a measurement. I believe time is linear and only goes forward, or backwards, infinitely, just as the number line only goes forward and backward).
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