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
    Commented Apr 18, 2019 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
    Commented Apr 18, 2019 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
    Commented Apr 20, 2019 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
    Commented Apr 20, 2019 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
    Commented Apr 20, 2019 at 3:08

3 Answers 3


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.

  • I'm using Searle's concept of symbol as a tokenized shape and the shape has a meaning, or interpretation. So the shape (not the substance of the token but a value of a property of the substance) is the first term in a 2-term relation, the 2nd of which is a meaning (ignoring the problem of universals!). A human has perceived the shape and assigned a meaning to it. So the 1st term is really an inner representation of a shape. Representations of voltage levels and semiconductor states can't be 1st terms of this type of relation since humans can't perceive them. That's the issue, I think.
    – Roddus
    Commented May 26, 2019 at 0:28
  • When you get to this level of philosopy, you can't just take someone else's definition (not to mention someone who was only 4 years old when the paper in question was written!) Turing takes care to distinguish output symbols which communicate something to the human (that is binary numbers, I don't think he'd much mind whether they were represented as '0' and '1' or as on and off lights or something else) from "symbols of the second kind" which are for representing the internal state of, and are only meaningful to, the machine. A human is not required to perceive Turing's definition of symbols.
    – Josiah
    Commented May 26, 2019 at 7:10
  • I can't see how the things computers process could be meaningful to the current sort of machine. Values of properties have meanings. Shapes have meanings because humans assign meanings to them. But no one (or thing) has assigned meanings to the values of any property of the items computers process. Newell and Simon tried to sell the idea that inner "symbols" represented inner states, and failed. Calling inner items "symbols" doesn't magically give them referential power. Why call these inner things "symbols"? Doing so just seems a big (really big) conceptual mistake.
    – Roddus
    Commented May 30, 2019 at 1:45

Computers are machines. They process. Something (input) goes in, internal processing done, something comes out (output).

Data goes in, information comes out. Both represented by symbols.

What are symbols? Numbers, pictures, alphabets.

You can add two numbers together, in your head, in a computer. The result, the third number is also a symbol.

"Why wasn't the human idea of computing with external shapes simply applied to the machine?"

Because we process same input differently even when give same output. For example summing two numbers.

Human minds manipulate images. When we think of a number we think of a particular shape, such as this: "1". Computers have different way of internal storage of the symbol. We represent it by zeros and ones.

Again, those zeros and ones are symbols for us. Computers just work because current flows in them in a particular way (deep down our brains also work on electric current but we dont have conscious access to that depth). Computers dont have minds, no internal representation, no symbols in their "heads".

  • Hi, Can I ask a question? You say "data goes in". So what is data? Not linguistic symbols. They're inscribed on the top surfaces of the plastic keys of the keyboard (assuming typing) and that's where they stay. So what "goes in"? Clocked continuous current where, within a clock "tick", there is one of either two voltages called "high" and "low" or (confusingly) called "0" and "1". Of Course there are no 0s and 1s inside the wire leaving the keyboard - just moving electrons and their EMR field effects. How are these binary differences inside the wire "represented by symbols"?
    – Roddus
    Commented Jan 3, 2023 at 23:40
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    Symbols are for us. For any processing machines the input is always whatever it senses tells it. Our input is by our senses, what we see, what we touch, what we smell and so on. For us those inputs are always in form of electrical signals that our brains understand. We don't have access to that data, we only have access to their symbols. For computers its raw electrical signals all the way, input, processing, output; no symbols for computers.
    – Atif
    Commented Jan 4, 2023 at 4:13

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.

  • I probably take a different approach to progress, one based on analysis of concepts. So it's not just a matter of having explanatory power, it's also a matter of identifying logical errors, contradiction, begging the question, etc. So it's analysis as well as synthesis, and analysis comes first and in fact usually establishes the groundwork for synthesis.
    – Roddus
    Commented May 26, 2019 at 1:56

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