We are three dimensional beings. Just in case you weren’t sure. Everything we do, everything we understand, is in the squishy three dimensional world we understand in. The fourth dimension for current thinkers is a wibbly-wobbly concept of space-time. Human brains, unfortunately, are currently not equipped to experience the world in space-time.
We are three dimensional beings that use negative numbers. Cavemen did not have a need for negative numbers, and the fact that our brains can conceptualize it is quite remarkable. Natural numbers (positive whole numbers) were probably difficult enough for our ancestors to understand. But the idea of less than nothing? What a remarkable concept! I’m certain that our primate cousins could not only not understand negative numbers, but they probably could not understand why they would be needed at all. But being three dimensional beings, with enough brain power, a long lifespan, and the ability to build on previous knowledge, it seems inevitable when considered.
But what if we were four dimensional beings? If we were four dimensional beings, would our view of negative numbers be the same? So I did what most people would do when daydreaming about negative numbers in the shower. I toweled off my hair and asked my friend Peter, who happens to teach physics at the University of Maryland. And his answer is: No. He believes that “negative numbers would seem pretty much the same, because even we 3-dimensional beings understand negative numbers in one-, two-, and three-dimensional coordinate systems.” Of course! It seemed so silly after reading his response for me to think that four dimensional beings would not be working in a similar fashion to us, with the basic laws of the universe being, well, universal. But, he added, “4-dimensional schoolchildren would work up from there to draw some neat 3-dimensional shapes on their 3-dimensional paper!”
And for some reason, that is more difficult for me to imagine. But that’s my downfall as a three dimensional human. Can’t quite think outside the box.