Dialog with an Adding Machine
On the same topic, a reader writes:
“(quoting me) abstract thought cannot possibly be described or defined except in terms of symbols.”
[wrf3] But software can.
… Define a line of software merely in terms of quantitative measurement of mass, length, duration, or other physical properties without reference to the language or other non-physical symbolic correspondence that language contains but that empirical objects do not?
It’s just 0’s and 1’s in the right pattern and all digital logic can be represented by NAND (or NOR) gates wired in the proper sequence. Do you want me to give you the NAND gates that are equivalent to (INCF X)? Or the NAND gates that are equivalent to a LISP compiler? We build abstraction on top of abstraction on top of abstraction, but it’s just NAND gates connected the right way. You’ve built your argument on the claim that the representation of the thing is not the thing, but I’ve given you two counter-examples, which you haven’t yet addressed.
Let me address it now as best I may:
“It’s just 0’s and 1’s in the right pattern and all digital logic can be represented by NAND (or NOR) gates wired in the proper sequence.”
The word “it”in this sentence refers to the object I asked you to provide me an example of: a line of software merely in terms of quantitative measurement of mass, length, duration, or other physical properties without reference to the language or other non-physical symbolic correspondence that language contains but that empirical objects do not.
I asked you for the physical properties of a line of code lacking all symbolic properties.
In your answer, you used the word “represented”, and used it to refer to “and” and “or” which are not physical properties but symbolic properties (purely symbolic, namely, symbolic logic).
But a symbol has no meaning outside of someone to read it. A symbol has no physical properties whatsoever.
By “physical properties” I mean properties that can be reduced to mass, length, duration, temperature, moles of amount, candlepower, amperage.
I am not talking about the most abstract imaginable symbols of all, the symbols of pure mathematics base two. I am not talking about purely symbolic logic.
An open circuit is not a “zero”; a closed circuit is not a “one” — an opened circuit or a closed one is a physical object that has only physical properties. It is not a symbol of anything unless and until a symbol-using creature, be he man, martian or angel, makes an association in his mind between the object and the symbol.
Consider an adding machine:
Let us suppose I have a simple clockwork machine, with numbers written on the teeth of the gears, and the wheels of the machine are arranged so that turning the first two wheels will force the third wheel to turn. On that third wheel I inscribe the sum of the numbers showing on the first two wheels. It is I, not the machine, who makes the mathematical deductions that allow me to inscribe the wheels.
I then give the machine to my clerk, Bob C ratchet. He turns the first two wheels and find, lo and behold, the adding machine “adds” the sums faster than he can do it in his head.
(1) Is the machine really adding any numbers? The machine is not aware of any numbers, so how can it add anything?
(2) If Bob were not there to read the marks inscribed on the wheels, would the numbers mean anything to anyone? Suppose the marks inscribed on the teeth were removed, but the mechanism was otherwise still intact. Would the machine’s wheel-motions still be described as “adding numbers together”? If not, the idea that the adding machine can add is a symbol we, human observers, bring to the machine, not something in the machine itself.
(3) If I had made a mistake, such as putting down a circle to represent ‘naught’ rather than putting down a straight line and a circle to represent ‘ten’, would the machine still behave the same way when the wheels were turned? But the machine adds falsely. Clicking the first wheel to the tooth inscribed with the “1” and clicking the second wheel with the tooth inscribed with a “2” forces the third wheel to click and display the tooth inscribed with a “0”.
(4) Suppose instead of fixing the machine, I tell Bob: “interpret the zero as a ten.” No PHYSICAL property of the adding machine has changed. The machine now adds truly. No physical property has changed, only the symbolic property has changed.
(5) Is there any essential difference between string of computer code and little wheels and gears in an adding machine? If not, the computer code is no more self-aware than the adding machine.