I've spent a fair amount of time in my life thinking about numbers. Granted, I am not a mathematician, nor can I claim any understanding of the highest levels of mathematical thinking, but I'm pretty good with numbers, and I like them.
Unfortunately, numbers are not real. They are, like everything else, abstractions that help us better understand reality. There is no such thing as a one or a two. That's clear enough. But what we often don't appreciate are concepts some of the less obvious number-related truths: you can't really have more than one of anything, and you can't really divide anything into parts.
I say that as I have in front of my two apparently identical cups. I know that they are not identical, however. Aside from all the miniscule flaws in design that may make one different from another, the mere fact that I can identify them as distinct objects implies that they are not identical. One is on the left, and the other is on the right. In order for two objects to be identical, they must have no features that distinguish them from one another. In other words, they must occupy the same space at the same time while exhibiting the same traits. That is, they must be the same object.
We categorize, as I have mentioned previously, in order for our limited minds to make sense of what is around us. We find patterns and we make inferences about one pattern based on what we know of another similar pattern. As I have said before, this is good and useful for us, but we too often fall in love with the abstractions and forget that they merely describe an underlying reality. They are not the reality itself, which is continuous and essentially indivisible.
So, with this in mind, I turn my attention to human beings. In daily life, we usually feel pretty comfortable thinking of ourselves as distinct from other people. I am not you, and you are not me. However, like all other separations, even this seemingly obvious one falls apart upon more careful inspection. What makes me not you? Religious people will make claims about souls or some dualistic ideas that don't so much add to the conversation as block further discussion. I'm going to throw out the notion of a soul as an idea constructed egocentrically as a mechanism for making sense of the limitations of our consciousness. In other words, I don't buy it. I'm a scientific thinker, for the most part, and I don't like conclusions that rely on making stuff up to explain what is difficult to explain.
So what is it that separates us? Information. We recognize ourselves as distinct from other people (and other objects, for that matter) due to the lack of information flowing between us and others. Specifically, our nervous system does not extend beyond what we recognize as the bounds of our bodies. We cannot send or receive information beyond the extents of our nervous system without indirect methods. Information can be received through our senses and transmitted through our motions, but there is no neural connection, no direct, two-way flow of information like there is within the nervous system.
So what happens when you cut up a nervous system? If you lose your arm, is it a part of you anymore? Beyond a sort of sentimental attachment, I don't think most people would feel that their detached arm is still part of them. Once something is removed from the nervous system's central controls, it becomes something else.
So then, what happens if you split up the central controls themselves (for the most part, the brain)? Well, that's complicated, but it has happened. There are plenty of studies out there on the effects of brain damage and, perhaps more to the point, split-brain studies. A split-brain person is a relatively recent sort of medical creation. For the most part, fiddling with the brain is a bad idea. In cases of extreme epilepsy, though, doctors may sever the corpus callosum, which connects the two hemispheres of the brain. Naturally, the results are rather interesting. The two halves of the brain, lacking the direct communication they had, effectively become different people sharing a body, each with control of one side. There's a lot to read about this, most of which can be googled. Here is a particularly good, succinct summary.
So if you can split someone into two people, can you combine two into one? Theoretically, sure, but the mechanisms for doing so don't yet exist. You would need to be able to fuse two nervous systems, at least, and find a way to make their brains work together with a direct connection. I am not anything close to a neurologist, so I won't begin to theorize about the difficulties involved. Compatibility issues, I would think, could complicate things. But lacking any real medical reason to fuse people together, it will likely not be happening anytime soon.
The point, though, is that what we define as ourselves is not some kind of actual, separate thing from everything else. It is only a sort of sensory limitation. On an atomic level, in fact, objects are constantly moving around and switching places. There is likely not one particle of you that was in you when you were born. The continuity of self comes from the continuity of information flow. It is, therefore, as much an illusion and a simplification as anything else.
I realize this negates many of the world religions, particularly Abrahamic ones that depend on ideas like individuality and personal salvation. I'm not out to negate religions. I don't really care much about religion beyond examining its role within society and such. I'm an atheist, but I don't care if you are. I'm just out to make sense of the world based upon my observation of it.
I'll get into ideas like ethics and morals in a later post.