Mathematics, the study of totally constructed concepts like numbers, time, logic and all that, is the closest thing we’ve got to a universal language. Highly intuitive symbols are included, if not universal, and let me point out a few and critique them:

- ‘Square foot’, exactly like it says on the box. Not that a foot is a good unit of measurement – a human foot is of course not a standard base for a system the way the size of our watery Earth is – but this symbol is excellent in its simplicity and expressiveness anyway.

- ∠ An ‘angle’! Very nice. Just a drawing of the referenced thing. Conveniently, this one is extensible – you can mark it up to show that you mean the measure or that your angle bisects another one, or what three points describe it.

- ƒ ‘Function of’, pretty daft as it’s just an initialization. At least it’s scripted, so you can tell it’s not
*just*an F, I guess. This is precisely the kind of thing we should stay away from. A better symbol? ☡ would at least show the process of something undergoing a path, ⍆ shows a thing passing a threshold.

- ∞ ‘Infinity’. Well, I guess this one works. I’ve never been a huge fan of the ‘lazy eight‘, as it in no way indicates to me an unlimited amount of anything. But as an enormously abstract concept, it’s not easy to symbolize without encoding, so this arbitrary, somewhat rationalizable symbol (it keeps going!) works well enough.

- Δ ‘Delta’, commonly indicating a change in something over time. Pragmatically, an arrow describing the path of the sun, phases of the moon, tides, plants, something like that would be better. However, I
*do*think it’s great that, in English, a delta is a change in a river over time. A*triangle*shaped change. Is this intuitive? No. But for being referential in form, it’s way better than ‘Function of’.

- ¬ ‘Not’. One of the absolute simplest, and best. One has taken the straight tally representing ‘a thing’, and broken it in just such a way that negates it in form, function, and concept. One of the most intuitive, least encoded symbols we have.

- ∧ ‘And’ shows the logical joining of two concepts into a higher, compound version. + is still useful as it shows two tallies in combination, but rather than depicting them together, a∧b is clearly the union between. while it’s not as intuitive as +, we at least have a demonstrative picture of a joining, more indicative of the idea that ‘both of these are required’.

- ∨ ‘Or’ is another logical operator, used as a∨b. The deficit of this and ∧ is that, while they’re wonderful in their logical inversion of one another, they are not referential of anything, and require some prior knowledge of their meaning. Good, but not perfect.

- ∅ ‘Null’, a very difficult concept to represent in mathematics: a group of nothing. I’m very pleased with this one, which is so intuitive that it’s more often reddened and superimposed on another symbol to show that it is not allowed. What a fantastic and practical use! Another, even more definite success where symbols are concerned.

- ∴ Here’s another terrific one. While not immediately intuitive, ‘therefore’ is an abstract concept. But if abstract concepts were shaped like dots, this symbol would show two of them with a third built on top, perfect units of reasoning being built on one another. Genius.

– ∧∨

I always thought something divided by zero should be infinity. If the query is “How much nothing can fit in that thing?” the answer would be an emphatic “Why, an infinite amount of nothing can fit into that thing!” Of course then 0/0 would still be undefined. How much nothing can fit into nothing? Probably 1.

I also think the relative sizes of infinity should be taken into account… although the set of all integers is infinitely large and the set of real numbers is infinitely large, the set of reals is most definitely larger than the set of integers… similarly although an infinite amount of 0 would exist in both 1 and 2, twice the amount of 0 would fit into two… so I think we probably need coefficients for infinity… so 1/0 would give

∞ and 2/0 would give 2∞, or something like that. Oh, and a subscript providing the distance between two numbers in that infinity would be nice to have… so the number of integers within the infinity of 2/0 would be something like 2∞[sub]2[/sub]whereas the number of real numbers within the infinity of 55/0 would be 55∞[sub]1/∞[/sub]… because, you know, measuring the size of different infinities is bound to be interesting to someone somewhere. And that is how much I hated division by zero errors as a child. Sub tags don’t work in blogger comments, bah.