By James Bailey
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Extra info for After Thought: The Computer Challenge To Human Intelligence
Geometric diagram courtesy of the Trustees of the Boston Public Library. P. Kraus catalogue Monumenta Codicum Manuscriptorum, p. 44, with permission. PART ONE OF" TH-E BOOK OF" NATURE - fl· • LACE , ~~ ..... x:8.. ,.. 'T}e/J. ;;i)"» ,TOln-u'l"« :T",pir~ . eNlXtT"l~ V ... ( tU rl/v. :'" "'T... 0>. -'j. .... " The reason the Greeks were successful in mathematically orienting themselves in their universe, but not in physically moving the earth, was that the reference point did not have to be real to be effective.
For classical scientists, the vocabulary of rate of change, or pace, was out of reach because they had no clocks. Similarly, for Industrial Age scientists, the vocabulary of adaptation was out of reach because they had no electronic computers and few data to train on. The new adaptive maths presuppose massive amounts of computing power, far more than was available even fifty years ago, when all computers were still people. More fundamentally, the new intermaths presuppose computers that are willing to change their minds over and over again, holding nothing constant.
In the words of his student: "The hypotheses of my learned teacher correspond so well to the phenomena that they may be mutually interchanged, like a good definition with the thing defined. " 10 Plato's dictum that computations spoke only to appearances, not realities, had in fact been a boon to the early practitioners. It gave them the freedom to innovate, grow, and mature. Within a few constraints, which they tended to agree with anyway, they could tryout all manner of weird formulations, justifying them not on their merits but simply on the results they produced.