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Its refreshing to meet a product again with such a brutally logical backbone of design something that was much sought-after in the Sixties and exemplified by systems like LISP and Prolog. This contrasts strongly with the APL view of the world, where the whole time youre conscious of handling vectors of binary numelements. Indeed if you compute 1023 1023 or 1000!, what comes out is an extremely long integer, suggesting to me that its all done symbolically.
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Although one of the chief features of release 5.2 is full support for 64 bit computing, I imagine the binary stage is put off as late as possible. If you want the system to give you numbers, then at some stage a semantic function like N must cut-in and start converting symbolic numerals to binary.
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An expression breaks down into function calls, like Sin and Exp, and if at the end of the day you want the system to do something more than simply spit out a string of characters you have what used to be called semanticfunctions (although I havent seen the term used in the vendors literature) functions like Plot and Play, plus all the GUI furniture youll ever want. And an expression is a string of ASCII characters to be filtered (you can see the C/Unix world view coming through strongly here). In Mathematica everything, but everything, is an expression. Note the tabs, which list the chief sources of information to learn about Mathematica. The Help Browser, showing "Everything is an expression". Glancing at the publications produced by the Mathematica team, judging by the titles alone it seems theyve had the same idea, and I look forward to getting hold of Mathematica for keeps in order to wallow in their investigations. It never got very far, but I saw no barriers that couldnt have been overcome if Id had the time to spend on it that Salah had done on his differentiator. Artificial Intelligence was then all the rage, at least among those of us short on the natural variety, and the idea appealed to me of applying a communications engineering technique of looking for a signal-in-noise in a system which actually had symbols for what it was looking for in other words one that had thoughts. I quickly got the idea and tried writing a symbolic Fourier analyser. But I had been retreaded as a computer programmer and Id somehow got it into my head that this was how it had to be done. The symbolic differentiator never handled a mathematical variable as a binary quantity at all it certainly never performed finite difference, in circumstances fraught with rounding errors, and pretended it was doing calculus.
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As a mathematician I should have been suspicious of the Babbage school of computing which saw a mathematical formula as the (unwieldy) specification for a series of instructions to be performed in sequence on a numeric accumulator. I was awed by the power of the technique.
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This was built on top of a macro-processor, not unlike the C preprocessor. In 1973 at the Peterlee scientific centre I came across Salah Mandil and his symbolic differentiator.
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For nowadays the Mathematica engine has a top end! For the six months Ive had Mathematica to play with, Ive scarcely typed a line of Mathematica language like the above. How blinkered I was! Nobody criticises Dreamweaver because HTML is so ugly to type. as any APLer might be who had been forced to use C/C++. I remember thinking then that insofar as it was like APL it was good, insofar as it wasnt it was bad. I first came across Mathematica at an educational exhibition nearly 15 years ago. This article therefore is aimed at jobbing APLers like myself whose exposure to Mathematica may be slight. But Mathematica needs no promotion from me its user base is huge and extensive, far beyond the provenance of Mathematics, pure and applied, as a typical university department understands it. As a rank beginner addressing other rank beginners where Mathematica is concerned, this is hardly a review of 5.2 so much as a review of Mathematica itself.
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When I sent away for the free Mathematica trial disk, version 5.2 hadnt yet been released.