My granddaughter will soon be two years old. It's okay for her to believe in Santa Claus and the Easter Bunny. She is also able to identify a circle from a square.
If she grows up to have common sense, she will one day believe that Santa and the Easter Bunny don't really exist. She will, however, go to her grave believing circles and squares do exist.
I should qualify that. They may really exist, but we can't see them.
What she identifies as a square is really the direct view of one side of a cube, or, perhaps, the bottom of a pyramid. What she identifies as a circle is a direct bottom or top view of a cylinder, a direct view of the bottom of a cone, or a direct view the cross-section, split at the halfway point or greater, of an orb.
Even things we see as two dimensional objects, like walls or paper, have depth, length, and height.
The common person can intellectually accept that there are things that aren't visible to the naked eye, like germs, cells, and molecules. It is accepted mostly because those things can be proven to exist. Those things are three-dimensional, just minute.
However, you cannot prove that squares and circles exist without drawing them in three dimensions on a three-dimensional object.
Socrates would ask a question, and find an hypothesis without conflict.
Aristotle would look at something, apply his prejudices, discount anything that seemed too large, and pretend he knew everything.
Einstein said reality is just an illusion - albeit a very persistent one.
Reality is only what we perceive it to be. To my granddaughter, Santa is very real because she perceives him to be real.
It is much easier to prove something exists than to prove it doesn't exist. To presume that the lack of proof that it exists is the same as it not existing is to presume germs didn't exist until they were discovered.
Lineal math would suggest that to have a two-dimensional object, one only needs to take one of the three dimensions away. That is short-sighted. We also wouldn't be able to see four-dimensional objects, though following the same lineal thought process, the four dimensions would include length, depth, and height plus one more.
We found germs looking very minutely in our three-dimensional world. I don't know if anyone knows what to look for in a two-dimensional or four-dimensional world. I don't know if anyone would know where to look for it. I certainly don't, but that doesn't mean they don't exist.
So perhaps you're not convinced that 'common sense' is short-sighted. If you believe there is no number greater than ∞, how about ∞2?
The more we know, the more we realize how little we know.
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