Thread: Computers and Imaginary Numbers

Helloo.

I've been reading a Paul Davies book, and in it he suggests that human's ability to do maths is related to the physical structure of their brains and the physics of the universe in general - we can only understand maths as it is because we can only compute physically computable things, which is defined by the physics of the universe.

So, obviously humans figured out a system that included a solution to the square root of minus one - the imaginary unit. When I use my old-fashioned calculator, it has no idea what I mean. Neither does Excel. It doesn't tell me, Yes there is a solution to the square root of minus one. It tells me, What? That's not maths.

So I have two questions. Can computers solve the square root of minus one? And if they can't, why can't they when human minds can?

Can computers solve the square root of minus one? And if they can't, why can't they when human minds can?

What do you mean under "solve"? There is no solution in real numbers...

Imaginary unit has some properties (The most important one is ), but that's () not a real number. That's why Excel and your calculator can't give you a result.

Computers indeed can't invent new concepts like complex numbers. But I believe that's a matter of time. I believe human mind is just an algorithm which can be programmed on Turing machine (or any computer given it has enough memory). The last statement (about algorithmic nature of mind) is just my guess.

Humans never solved what the square root of -1 is, we simply gave it the symbol i for the sake of convinience.

If a computer is programmed to handle imaginary numbers, they can solve or easily.