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In his 1936 paper, Turing explains that humans compute by manipulating symbols that are external to the human brain (humans compute with pen and paper). Electronic digital computers do the same thing - the symbols are external to the machine: printed on or by attachments: on keys, displayed on screens, printed by printers. Why wasn't the human idea of computing with external shapes simply applied to the machine? Why did Turing say that the machines also internally manipulate internal symbols? Why apply the concept of external manipulation to what happens inside?

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    What else do you think computers do, besides manipulate symbols according to rules? – user4894 Apr 18 at 6:57
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    Because we did not know (and still do not) what our brains do internally, but we do know that computers shuffle around 0s and 1s as prescribed by their programming, because that is what we built them to do. Current neuroscience suggests that brains function differently, more like artificial neuronets. – Conifold Apr 18 at 18:11
  • @user4894 I think the idea of manipulation is pretty inaccurate for a start. But accepting the idea, what's manipulated is mostly clocked voltage levels and semiconductor switch states. None of these things are symbols in the sense of interpretable shapes. You could say everything a computer manipulates is by definition a symbol, but that just confuses various important issues. The question is still there: why apply the idea of manipulation of external interpretable shapes to the uninterpretable things on the inside? – Roddus Apr 20 at 1:18
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    @Conifold That's a key gripe. Turing machines actually do manipulate inner 0s and 1s. But with electronic digital computers, "0" and "1" are merely names of what are internally processed. There are no 0s and 1s moving along the wires in a data bus for instance, or stored in memory. The idea that computers internally process meaningful tokens I think has led to much error, for instance the CYC and SOAR myth that when a human types stuff on a keyboard, the typed symbols enter the machine and are then knowledge. The myth started with Turing and the Turing machine. But why did it start? – Roddus Apr 20 at 1:28
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    Computer storage is based on elements that have two stable states aimed to approximate 0/1s, and the processing is aimed at approximating binary arithmetic. When the approximation fails we talk of "glitches" and "fix" them. The talk of tokens as symbols is sloppy, but the difference is immaterial because the tokens are taken as symbols in a plain way. In the brain there are apparently no tokens that can be so taken. – Conifold Apr 20 at 3:08
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I think perhaps the issue at hand is the word symbol. A symbol is not a picture. A symbol is a representation of some other concept. We might talk about the queen of England being a symbol. We might talk about a gift or action being a symbolic gesture of remorse. Even when pictures are used they can represent different things: usually 5 represents the number of toes on a typical human foot but in a paint by numbers it could represent a pleasant sort of green.

It is in this broader understanding that computers, whether modern physical machines or theoretical ones like the turing machine, manipulate symbols. Those high and low voltages in the circuits of a RAM chip represent other things. What they represent could be anything from the colour of a pixel on screen to the health of a player in a game.

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Sadly I still am not yet allowed to comment, so I'll do so by an answer to @Roddus who says

The question is still there: why apply the idea of manipulation of external interpretable shapes to the uninterpretable things on the inside?

Any programmer who has had to analyse program dumps will know that at least in theory it is all interpretable.

The internal state of the human is harder to be certain about, which is maybe why he [Turing] treats them differently.

Philosophically it is informative to speculate about both kinds of data manipulation, to try to understand what goes on beneath the surface. But to do that you need to have a full set of theories covering existence, time, metaphysics, consciousness, AI, logic, and set theory probably. Maybe that was beyond the scope of his paper.

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