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There is no math in a calculator. It’s a pile of logic gates assembled in a way to appear to perform mathematical operations. An ALU has no “understanding” of
by hamburglar 4y ago
There is no math in a calculator. It’s a pile of logic gates assembled in a way to appear to perform mathematical operations. An ALU has no “understanding” of arithmetic, it’s just a canned, finite set of inputs and outputs. Not an axiom to be found.
- jstanley 4y agoI expect the argument would go like: The pile of logic gates is an encoding of the axioms. The fact that it evaluates mathematical expressions correctly is both necessary and sufficient to show that it understands arithmetic. Therefore the calculator knows the axioms and understands arithmetic.
- hamburglar 4y agoExcept it doesn’t implement the axioms of math, it implements a crude facsimile of them for a certain subset of numbers, because what it’s really doing is a non-mathematical physical process.
- Gordonjcp 4y ago> It’s a pile of logic gates assembled in a way to appear to perform mathematical operations In what way is Boolean logic not maths?
- hamburglar 4y agoIf you want to argue that an ALU is performing “boolean logic” just because it’s made of logic gates, be my guest, but in my opinion that’s a bit like saying a bucket is “doing math” because if you put 5 rocks in and add 7 rocks, it’s smart enough to contain 12 rocks when you’re done.