re: #607 zombie

I once got into a contentious discussion with a math PhD about rudimentary arithmetic. I said, only half-joking, that my real problem was the “identity equation,” i.e. 1 = 1 . It is the corollary upon which most higher math rests. But, I argued, how can you really know that 1 is in fact 1? I mean, there is no physical analog to the theoretical concept of 1. He challenged me and used as an example a carrot (we were in a kitchen at a party) — if you have a carrot, it is one carrot.

But, I countered, picking up the carrot and sniffing it, the carrot faintly smells of carrot. And since smell is composed of molecules, not radiation or waves like light or sound, that when I smell the carrot, I am absorbing some subset of that carrot. Which means that the apparently solid unitary-ness of the carrot is an illusion: there is in reality a faint cloud of carrot-osity surrounding the carrot, which our noses can detect in the form of smell. Which means there is no distinct boundary between carrot and not-carrot. At what point to we declare carrotness to end, at what density of carrot molecules? Whatver we decide, it will be arbitrary.

And the same concept applies to every”thing.”

In order for him to prove his point that “1” was a reality-based concept, I demanded that he give me an irrefutable example of one-ness in the real world. Before long, we had gotten down to the quantum level, him claiming that quanta are indivisible, hence a single quantum is an example of 1. But then i broched the subject of Heisenberg, and then strings (i.e. that quanta are just bundled up energy bits in compacted dimensions), and the argument began all over again.

He was unable to convince me of anything. Though I was half-joking when I started, I became serious, and I came away with the inescapable conclusion that arithmatic was just as theoretical as algebra, and that “1” was no more real than “x.”

The perfection of the number system does not depend on the imperfections of the real world. Plato knew that. Too bad your PhD did not.

I’m no expert on this, but a logician or number theorist could recite this stuff. The symbol for 1 is a perfect one - because we say it is! If we say we have one carrot, then that’s what we say. But then, we lie a lot, and are mistaken more often, it sometimes seems it’s almost luck when we get something right.

The number one plays its role in various algebraic or logical systems.

In Russell and Whitehead’s Principia Mathematica, I believe they spend a lot of time on establishing these things. What the status of their writing is today, I’m not sure. I think something like my arguments above, insofar as I got it at all right, are newer.