Well, I'm sure you're right, but it seems to me that .5 would be clearer on the one hand, "in" half on the other, since a fraction can apply to other figures than one, and seems to ask, half of what? The reason you would multiply, it seems to me, is only because your calculator doesn't have a handy 1/2 key, while your head does. One doesn't multiply it in one's head, but simply halves it with a mental knife. Because it was phrased in a sentence, the adjective relation of half-to-ahundred seemed just as reasonable to me, but I seem to be alone in thinking it.

Yes Amos, I see that, but it doesn't help you do complex problems with roman numerals.
I agree that symbols only seem to "mean" whatever they are used to represent, through association, and I feel the same way about analyzing dreams. There's no reason to think they should explain anything, and if they did, why would they do it in some portentious code? My dreams are plainspoken and always say "Boy, you sure have a lot of dust-bunnies and junk laying around here in your head, dude." Still, however arbitrary, the signs and symbols we make and use have peculiar properties that come into play when we use them. It's the Sapir-Wharf hypothesis, I think, that suggests that different sets of symbols, different languages, don't simply re-name things, but construct meaning in different ways. English is a great language in which to see that language is arbitrary and a mess. Greek is supposedly more misleading in that it seems very logically inter-related.

Whatshisname, Chomsky, tried to determine an underlying universal language of syntax, but only got so far and the car broke down. It seems that the symbols and tools might have some residual peculiarity, which leads mental development this way or that.

There was test that showed Asian students performed differently in terms of western class-discussion. It annoys their learning process.Western students do about as well at solving puzzles while talking through it, Asian students suffer. And their essays are not so linear, but sort of encircling. I'm guessing western students very often do much the same thing, but here we call it Poor Work, and don't develop it. Kind of like how high western art for generations now has tried to escape commodification and materialism, but the test of success at this strange game remains "Success." It's very easy to merely succeed at it, success is all around us, it's called "Failure."

If symbols have any effect on brain development and so on, they aren't quite utterly arbitrary and immaterial from a scientific point of view. Scientists can study that stuff. It's empirical, because we are, and our tools for understanding are--we aren't in some other world, above it, or across a real dividing line, looking at everything else. The idea that we are, or that science really quite puts us in that position, is fanciful--it's the fantasy of science, its airbrush unicorn.

I still can't think of much boring science stuff I believe. Maybe because I'm trying to think of INTERESTING "boring science stuff I believe," to post, which defeats the idea.