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Comment by mettamage | Hacker News Reader

How about having some understanding of complex numbers? Wasn't it an Italian who started to use sqrt(-1)? I don't see how that'd be practical.

Disclaimer: I'm not a mathematician.

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The first use of complex numbers was as intermediate quantities in the calculation of the roots of cubic polynomial functions. This use is analogous to using negative numbers in a ledger even though negative amounts of physical things don't make sense.

Edit: I meant physical things like apples fam. This is an important philosophical point we don't appreciate because we are so used to them. De Morgan once wrote:

"It is not our intention to follow the earlier algebraists through their different uses of negative numbers. These creations of algebra retained their existence, in the face of the obvious deficiency of rational explanation which characterized every attempt at their theory."

Depends on the "thing." We do use negative values for, say, degrees of temperature.

> even though negative amounts of physical things don't make sense.

I beg to differ, just today, on the road, accelerating by some negative amount made a lot of sense.

I am, have a PhD in it at least, and complex numbers are 100% required to do quantum mechanics, so are physically motivated. In fact, many physicists consider the complex numbers to be the preferred number system of the universe for this reason.

Complex numbers are practical, they're everywhere in classical mechanics and circuit design, off the top of my head

The complex numbers enjoy a widespread use in physics (and electrical engineering).

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