For instance, I have a programmable watering system for outside. It has knobs for frequency and duration. Is it really computing anything, or is it full of non-computing electronics?
In: Engineering
Mathematicians and computer scientists have an abstract model of a computer called a Turing machine (TM for short). TMs are pretty simple machines. They have a line of memory cells, a read/write head that can read from and write to which ever cell it’s at, a state (basically a way to keep track of what its currently doing), and a table that tells it “If you’re in this state and reading that symbol from memory, overwrite the memory with this new symbol, move the head over to there, and put yourself in state yada-yada.”
It’s a lot simpler to describe than all of the components of a physical computer, but never-the-less it’s all that you need to compute anything that is computable. And what’s most significant is that you can design a universal Turing machine, which is a TM that will simulate the operation of any other TM if you put a description of the other machine into the universal machine’s memory. So not only can you design a particular TM that will compute something for you, you can design a TM that will compute anything that it is possible to compute for you, given the right input.
That’s the key difference between computers and other complex electronics. A proper computer can do anything (within its memory limits) that a TM can do; it can run arbitrary programs; it can even simulate other computers. Other circuits can’t do that. They generally only do 1 or 2 things, and can’t do anything beyond that.
There’s another distinction we can make. Any system – electronic, mechanical, or otherwise, that can simulate a TM can be considered a computer. Games like Magic the Gathering, Minecraft, and Conway’s Game of Life have been shown to be able to do this. A pencil and a sheet of paper can be used to simulate a TM. So, computers don’t even have to be electronic.
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