Zero is Not Less Than One
This morning over Sunday coffee I was thinking about thinking. What are the components of thought?
I landed on the following:
Identifying. This is here, that is not. “An apple exists.”
Grouping. These are similar to those. “These are all apples.”
Relating. This item is linked to an item on another dimension. “There is a thing called an apple. There is a thing called red. The apple is red — or, the apple has redness.”
From there I thought, well, of course this is logic, mathematics, right?
So — what tools do we have? Well, each of these is a dimension.
The first dimension of identifying is a dimension that spans from “less existing” to “more existing.” The least amount of existence we call “zero.” The most amount we call “one.” We move here from negation to affirmation.
The second dimension of grouping is called counting. The “least amount” of anything in this dimension is “one” and the most is “many.” We move from singular to plural.
The third dimension of relating is really simply linking something from one dimension to another dimension. There are two kinds of linking: is and has — and that maps to the above. “Is” links to identifying and “has” links to grouping.
In other words, when we think we can do one of three operations: identify, group, or relate.
What I find interesting here out of this is that our idea of “zero” doesn’t fit into the grouping dimension. Zero is a “level of existence” not a “level of grouping.” You can’t have a group of zero.
Which means (I believe) that the number line (0, 1, 2, 3…) we were taught in elementary school is incorrect. There are, in fact, three “number lines” — one mapping to each of the above dimensions. Imagine the first as the x-dimension, the second as the y-dimension and the third as the z-dimension.
What’s cool to me is the so-called challenge of physics in the past century has always seems to be that we’re trying to merge the very small (quantum physics) with the real world (Newtonian physics) with the very large (relativistic physics.) And so this falls out nicely:
Quantum physics is the study of the “level of existence” and goes from zero (it does not exist) to one (it fully exists.)
Newtonian physics is the study of “how much” and goes from “one” to “many.” Here we have calculus.
Einsteinian physics is the study of “relating” (literally: relativity) and shows “level of connectivity” from one dimension to another.
Why is it so hard to get our heads around the first and the last? Because we’re using “grouping” and “counting” tools to try to analyze them. Foolish! Imagine listening to a symphony and trying to describe the sound of a tuba as “greenish-blue.” Or imagine smelling a fresh-baked apple pie and describing the smell as “loud.” We can sort of “make the leap” but it’s not natural. We should use the language that maps to the domain.
And here’s the beauty of this. It’s not that there are three planes of the universe — it’s that our minds have three senses.
We believe our body has five senses: sight, hearing, touch, taste, smell. Here I propose our mind has three senses: identifying, grouping, and relating. So it’s not that the universe is “quantum” or “Newtonian” or “relativistic.” It’s that just as we might touch, smell and taste a chocolate chip cookie, we are identifying, grouping, and relating our environment.
So: three number lines, three dimensions, all intersecting not at “zero” but at what I’ll call more generally the “origin.”
Zero is not less than one any more than “sour” is less green than “blue.” Two different parts of the brain sensing two different things.