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<RT·section id="Section·Machine_notation">
- <RT·name>Mathematics as a machine notation</RT·name>
+ <RT·name>Introduction to Computational Naturalism</RT·name>
- <p>In March of 1826 Babbage read a paper to the Royal Society describing a language he had invented for machines.<RT·endnote>Charles Babbage, "On a Method of Expressing by Signs the Action of Machinery", <em>Philosophical Transactions of the Royal Society of London</em> 116 (1826): 250−265, read 16 March 1826.</RT·endnote> He called it the <RT·term-em>mechanical notation</RT·term-em>. It gave each part of a machine a sign, classified that part as fixed or as moveable, recorded what drove it and what it drove in turn, and set down when each motion occurred relative to the others. Given the notation for a machine, a person could say what that machine would do, and could find any part at any moment and state whether it was moving or at rest.</p>
+ <RT·section id="Section·Machine_notation·The_lamps">
+ <RT·name>The Thesis</RT·name>
+
+ <p>In March of 1826 Babbage read a paper to the Royal Society describing a language he had invented for machines.<RT·endnote>Charles Babbage, "On a Method of Expressing by Signs the Action of Machinery", <em>Philosophical Transactions of the Royal Society of London</em> 116 (1826): 250−265, read 16 March 1826.</RT·endnote> He called it the <RT·term-em>mechanical notation</RT·term-em>. It gave each part of a machine a sign, classified that part as fixed or as moveable, recorded what drove it and what it drove in turn, and set down when each motion occurred relative to the others.Babbage considered it one of his best inventions.<RT·endnote>Charles Babbage, <em>Passages from the Life of a Philosopher</em> (London: Longman, Green, 1864), 104, where he adds that he doubts machinery of comparable complexity could be contrived without that language or an equivalent one. On its mature form, comprising labeled drawings, timing diagrams, and logic diagrams, see Anthony Hyman, <em>Charles Babbage: Pioneer of the Computer</em> (Oxford: Oxford University Press, 1982), 58.</RT·endnote></p>
+
+ <p>Imagine a Universal RT Machine</p>
- <p>The engine Babbage wrote about was never built. He said plainly that without the notation he could not have invented the Analytical Engine, and he counted the notation among his best inventions.<RT·endnote>Charles Babbage, <em>Passages from the Life of a Philosopher</em> (London: Longman, Green, 1864), 104, where he adds that he doubts machinery of comparable complexity could be contrived without that language or an equivalent one. On its mature form, comprising labeled drawings, timing diagrams, and logic diagrams, see Anthony Hyman, <em>Charles Babbage: Pioneer of the Computer</em> (Oxford: Oxford University Press, 1982), 58.</RT·endnote> The signs came first and the metal was to follow. That is what makes the notation worth beginning with. Its sentences say what a machine will do, they were written before any machine did it, and they are answerable to the machine for whether they said right.</p>
- <p>Computational Naturalism holds that mathematics is a language of precisely this kind: a language about what a constructed machine will do. Babbage's notation was about one engine. Mathematics is about machinery in general. That is the whole of the difference between them, a difference of scope and not of kind. The word <em>constructed</em> carries weight, since a language about what an unrealizable machine would do is a language about nothing, which is why the first of the conditions of chapter <RT·Counter·read snapshot="Section·Three_conditions"></RT·Counter·read> is that the machine can be built.</p>
+ <p>Hence, while the clerk at the desk with his squares of paper, and a pen, works, he is merely a more general machine, a sort of Universal Machine, programmed by the language of mathematics. As he interprets the math, as a Universal Turing Machine would interpret a program, the para is a parallel machine to the RT Machine, just as Turing's Universal Machine running a program is a parallel machine to the machine with a hard coded controller.</p>
- <p>This chapter is where that claim is made good, and it starts where the machine starts, with symbols and the lamps that report them. Chapter <RT·Counter·read snapshot="Section·Grounding"></RT·Counter·read> gave the words a reader is likely to arrive with, and gave them as they are conventionally used. Nothing here is derived from that chapter. It is a table of translations, offered so that reader and author use words the same way, and it is consulted below only to say which familiar word names the thing the machine has just been seen to do.</p>
+ <p>And as mathematics is the language of for the universal machine, it can be interpreted as observations of the running base machine. As when a Universal Turing Machine program says to step a square to the right, if the parallel hard controlled machine would also be moving the head one square to the right. So to, can statements in mathematics be shown to be describing the motions of the RT Machine.</p>
+
+ </RT·section>
+
+
+ <RT·section id="Section·Machine_notation·The_lamps">
+ <RT·name>The lamps</RT·name>
+ </RT·section>
<RT·section id="Section·Machine_notation·The_lamps">
<RT·name>The lamps</RT·name>
projects / TM-2026 / commitdiff