paper or film. So we've managed to find a way to interpret standard mathematical notation. But anyway, he was serious about notation. Well, the most obvious possibility is notation for representing programs as well as mathematical operations. Well, of course that would be absurdly confusing. So what's involved in that? Generally, this failure to see that one could name numerical variables is sort of an interesting case of the language or notation one uses preventing a certain kind of thinking. But if you want to see if you can interpret mathematical notation, you have to know what kind of grammar it uses. One of them has to do with entering things like powers as superscripts. The Future Perhaps to finish off, let me talk a little about the future of mathematical notation. Since most of the people who use Mathematica already know at least some mathematical notation, it seems like it would be really convenient if we could just have Mathematica understand ordinary familiar mathematical notation. And the most basic thing for arithmetic is numbers.

Unlike with ordinary human natural language, it is actually possible to take a very close approximation to familiar mathematical notation, and have a computer systematically understand. It's fairly hard to read. On-screen notation Graphical notation Fonts and characters Searching mathematical formulas Non-visual notation Proofs Character selection Frequency distribution of symbols Parts of speech in mathematical notation Empirical laws for mathematical notations In the study of ordinary natural language there are various empirical historical laws that have.

### Population and sample standard deviation review

I guess baked clay is a more lasting medium that papyrus, so one actually knows more about what the original Babylonians wrote than one knows what people like Euclid wrote. But then, when the Bourbaki movement in France started taking root in the 1940s or so, there was suddenly a change. I guess the main reasonapart from the fact that it's not very extensibleis that it somehow doesn't make clear the mathematical correspondences between different polynomials and it doesn't highlight the things that we think are important. You see, more than 5000 years ago, the Babyloniansand probably the Sumerians before themhad the idea of positional notation for numbers. There are about half a million of these little Babylonian tablets that have been found. It's kind of like what's often done in linguistics of ordinary natural languages. And he ended up writing a kind of summary of mathematicscalled Formulario Mathematicowhich was based on his notation for formulas, and written in this derivative of Latin that he called Interlingua. The most challenging proofs to present are probably onessay in logicthat just involve a sequence of transformations on equations. Or at least it isn't if you try to make it decently general. It's pretty unreadable too. So let's talk about notation that was used in the different early traditions for mathematics. Physiologically, I think it works by using nerve impulses that end up not in the ordinary visual cortex, but directly in the brain stem where eye motion is controlled.