Well, for all that effort, the results were fairly grotesque and incomprehensible. Renaissance European notation. But actually, there was a more serious conceptual problem with the letters-as-numbers idea: it made it very difficult to invent the concept of symbolic variables—of having some symbolic thing that stands for a number. And I’ve long thought that it would be very nice to be able to use actual special characters for these, rather than combinations of ordinary ASCII characters. And I think there’s a fundamental principle here: one wants just so much notation, and no more. | Graphical notation | Fonts and characters

Ask a mathematician if they understand. In talking about the correspondence of mathematical language and ordinary language, I was going to mention the question of parts of speech. Because anything you type will be unambiguously understandable. I will discuss the extent to which mathematical notation is like ordinary human write Sin–2x because

And in general, for big numbers, schemes like this get in a lot of trouble.

five hundred years old. I will review how it developed, with precursors in antiquity Here’s an example of a typical page from Principia Mathematica. One might imagine that it would somehow be useful to distinguish variables that are different colors. 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. But at a cosmetic level, there are things that are different from the way they’d look in a traditional math textbook. I am currently reading the Algorithm Design Manual, but my mathematical notation has become a little rusty. Empirical laws How to break the cycle of taking on more debt to pay the rates for debt I already have? But Leibniz was a different story. And basically the way that people seem to communicate anything sophisticated that they want to communicate is by using some kind of language. They mostly look too fragile and not blobby enough to be binary operators.

So, for example, in Egyptian the symbol for a thousand was a lotus flower icon, and a hundred thousand a bird, and so on. We tried all sorts of other graphical forms. One thing to realize is that these three traditions probably came from rather different things, and that’s greatly affected the kinds of notation they use. Do mirrors extend a Medusa's Petrifying Gaze? So that means that there are various obsolete Greek letters left in their number system: like koppa for 90 and sampi for 900. Well, as I hope I’ve shown you, the notation we have today has arisen through a pretty haphazard historical process. I mean, I certainly know that if I think in Mathematica, there are concepts that are easy for me to understand in that language, and I’m quite sure they wouldn’t be if I wasn’t operating in that language structure. That’s something that’s certainly discussed in ordinary linguistics. Here’s a sample: Actually, in the 1880s Peano ended up inventing things that are pretty close to the standard notations we use for most of the set-theoretical concepts. Boole had shown around 1850 that one could represent basic propositional logic in mathematical terms. Making statements based on opinion; back them up with references or personal experience. powers of things instead of one over things and so on. But there isn’t an analog of something like Fowler’s Modern English Usage for math. Here’s what we ended up with for the Greek letters. The Big-O notation is at its heart a mathematical notation, used to compare the rate of convergence of functions. I think it's time for me to brush up on my discrete math.

Let’s take a simple example, “i”. What I have ended up doing is to build a notation for Nand that is based on one of the standard ones, but is “interpreted” so as to have a better visual form. The output side was pretty straightforward: after all, TROFF and TeX already did a moderately good job with that. After all, we already know English so we wouldn’t have to learn anything new to talk to Mathematica. There were other people who had thought about similar kinds of things, mostly from the point of view of ordinary human language and of logic.

Is it possible Alpha Zero will eventually solve chess? But here’s the surprising fact—that certainly surprised me a lot. Well, like many other of his projects, Leibniz never brought this to fruition. Find the probability that a 4 will appear on the second dice. RomanNumeralForm[%]. Reference request: Examples of research on a set with interesting properties which turned out to be the empty set. Well, one has to qualify that a bit. Actually, we have a few hundred rules that are heuristics for understanding traditional form expressions. proofs in Mathematica. Dana Scott suggested one possibility: a trend towards the removal of explicit parameters. In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.The word "permutation" also refers to the act or process of changing the linear order of an ordered set. In Mathematica 3 we went to a lot of trouble to develop fonts for over 1100 characters of relevance to mathematical and technical notation. And in the book I’ve been writing for many years about the science project I’m doing, I use only Mathematica StandardForm to represent things.

In particular, it emphasized using notation whenever one could, and somehow minimizing the amount of potentially imprecise text that had to be written. But as we all know, that didn’t happen. I think Whitehead and Russell probably win the prize for the most notation-intensive non-machine-generated piece of work that’s ever been done. Thanks for contributing an answer to Mathematics Stack Exchange!

But he pretty much followed what Leibniz had set up.

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