Much further along than what I'll call
arithmetic rather than
mathematics.
I'm perfectly comfortable with the fact that 1+1=2, and that it always will. Afterall, these numbers are simply place-holders for any given object, whether it's apples or nuclear submarines.
I'm pretty comfortable with geometry and even simple algebra as well. At least as far as if 1+x=20, then x must = 19. That's straightforward enough, x is simply the unknown in the equation, which can be deduced by simple logic, (or trial and error.
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I can survive statistics too, which gives me a handle on probability, (Stats A was a required subject at Varsity for me, (and the only one that I ever struggled with (my own lazy-ass fault) but I passed it eventually.
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Even there, the expressions of the formula are simply placeholders for variables which we can determine, right? Like those old "triangular" formulae which I can't reproduce here, with the representation of, say, force in the top, and time and speed say, at the bottom, where one is the sum of the others, and therefore, a different one must be the product of the remainder, etc. (Yes, I know, those example don't work out, but you know what I'm talking abot, right?)
I can "see" how all those work on the whole.
It's when we get into the "pure" mathematics that I lose all coherence. Where a mathematical proof of something serves to underscore an observed event/whatever.
When it comes to these more complex expressions, the way it looks to me is that the person has taken an observed event, (say gravity, although even that is probably too simple to really count here) and then played with numbers until he gets an answer that matches what he's observed.
In other words, they
start with an answer, and then reverse engineer it so that the equation comes out to that answer.
(I'm not sure if this makes it easier to understand my problems with math, but let's see what happens. At least it's a starting point so you can point out any misconceptions I may be under.
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Don't get me wrong, I find it very interesting. But like statistics, I think the answers seem not only inferential, but easily manipulable.
--A