[Fredrick]

Well, purveyor,

Let me start out with saying that I do like both visualizations, and they do make sense to me intellectually. I have an idea where you are going.

But...

I have bumped my nose once too often on people using words, symbols or numbers, and the communication about them turning out to not be correct. I will admit immediately that I have found myself on both sides, with being the one who correctly understood the word and its context, and being the one who had it wrong.

When I look at your circle, you are using the numbers 1 and 0. I have all by itself no problem with that. Yet I now realize that these two numbers cannot be used in one context with 1 indicating the whole, and 0 indicating the nothing. The problem is that 1 (with meaning the whole) already includes the zero, so using the zero yet again is superfluous. Ordinarily, there is no problem with using 1 in a combination with 0, but that normally only happens when 1 stands for something else than the whole.

The image I am using is the donut, or the bagel. We all know it comes with a hole, otherwise it would not be a donut. But to indicate that only the edible part is 1 and the hole the 0 is incorrect. The donut comes with the hole, so the 1 (the donut) includes the hole. So, if the hole is already included, what the heck is the 0 doing around there?

The other example is that of a car, with a spacious interior. We cannot say that the car is 1 and the spacious interior 0, because we would have then doubled the 0. As you can understand, this does not matter one singe bit for the outcome, because two times zero is still zero, but it is not well used language from a logical perspective. We wouldn't be saying: here is the car plus the steering wheel, because we know that the steering wheel is already captured by the term car.

There are therefore two levels involved: the whole and the parts. At the level of the parts we find the steering wheel, the tires, the back seat, and the spacious interior. On this level, we cannot place the car too. The car belongs to the overall level. And the nothing belongs to the part level.

I don't know if you read my posts to this thread (I am sorry, I always seem to use so many words to get the idea across), but I can come up with only two distinct mathematical systems: the binary system and the decimal system. (I can create an 8-based system, but in reality that is only a different but similar version.)

In both systems, there is no such thing as a 1 that is the whole. In the binary system, many 1s are used to express information, and not a single one of these 1s is the only 1.

In the decimal system, the 1 is not the whole, but the first, the winner, the best, the unification (which is an occasional, unusual situation). Number 1 can be: me, the guy to beat, the odd person out, the vague and generalized one (as in: one should be aware of these things). But 1 in the decimal system is not to be confused with the whole (because there is 2, and 3, and 4, and etcetera).

In philosophy, and in religion, and in stories, 1 can be magical. 1 can be god, 1 can be the finish (all's well that ends well). 1 can be the whole. But in science, the word universe is not uni, it is uni-verse. There is a component of duality hidden in this word. In Dutch the word for universe is whole-all (I believe the old English word is similar to this word); clearly, when words were created, the word whole was not enough to say it all — as if they knew the whole cannot exist as unified.

So, Purveyor, I think I have a good idea where you're heading, but I simply want to check what it is that you are saying. Does your 1 stand for the whole and does 0 stand for absolutely nothing? Because then we have a communication problem.

I would like it very much though if you are willing to discover this together with me!