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View Poll Results: Does the square root of -1 exist? Poll!

No. The square root of -1 is a mathematical convenience and a figment of man's imagination

18

28.57%

No. As numbers don't actually exist in the real world, neither do imaginary numbers (Mwa ha!)

2

3.17%

No. They only exist if you believe in them!

1

1.59%

Yes. I saw it in a bar on Fourth Street last Tuesday drinking daquiris with Bigfoot.

7

11.11%

Yes. Because I say so.

7

11.11%

Yes. And I have this big fancy list of equations to prove it. How *clever* am I?

9

14.29%

Yes. As the universe is infinitely big, then imaginary numbers *have* to be out there somewhere!

No. The square root of -1 is a mathematical convenience and a figment of man's imagination
No. Seeing as numbers do not actually exist in the real world, neither do imaginary numbers (Mwa ha!) --->The Biologist's answer?!
No. They only exist if you believe in them! (The agnostic's answer?!)
Yes. I saw it in a bar on Fourth Street last Tuesday drinking daquiris with Bigfoot.
Yes. Because I say so.
Yes. And I have this big fancy list of equations to prove it. How *clever* am I?
Yes. Seeing as the universe is infinitely big, then imaginary numbers *have* to be out there somewhere!
Yes, we have no bananas.

The trick (from what I understand) is that we've got this framework of axioms from which everything else derives. When it works, that's good and we can build other things on top of it. When we find something that doesn't work with what we have, we put something else into our set of axioms so we can do what we need.

The reason we can do this is because math doesn't physically exist. We can't reach out and touch addition or three. Instead, math represents the real world. We can visuallize adding one set of apples to another, and we can see three oranges. So if we come across something that as yet can't be rationalized mathematically, we put that functionality into our mathematical framework.

Take zero for example. Humanity had no notion of zero for a long time; I believe the Babylonians and Mezoamerican cultures were the first to come up with it. Before that, we simply didn't need to represent a lack in that kind of nomenclature. It was more like, "Oh, no. I don't have any food. I'd better get some." But once cultures started developing the need to express that lack in mathematic terms, it was invented.

And like imaginary numbers, zero is something you can't really visualize. I mean, how do you hold zero of something? You're not really holding anything at all! The same goes for 3i+8 and lots of other things in mathematics.

So, yeah, I think imaginary numbers are "real" (pun intended) just like any other mathematical form is real. Not necessarily relevant to a lot of people, but a necessary part of the mathematical framework.

"No. They only exist if you believe in them!" is basically the same as "No. The square root of -1 is a mathematical convenience and a figment of man's imagination"

Distribution: Ubuntu, Debian, Various using VMWare

Posts: 2,088

Rep:

Complex numbers are very useful in Engineering - AC current and voltage can be convieniently expressed in complex form. Impedance is a complex quantity. Complex numbers explain why a balanced 3-phase load doesn't need a dedicated neutral line.

From my dim distant memories of advanced maths, complex numbers are also used to derive trig identities.

When people discovered 0, it was quite a scary principle. Zero is both nothing, and something. Zero added to the end of a number increases that number by an order of magnitude.

Complex numbers are extremely useful and practical in engineering, true. When I was studying EEE, a lot of problems involving alternating current/voltage used complex numbers.

So to say they don't exist is like saying electricity doesn't exist because you can't see it.

No. They only exist if you believe in them!" is basically the same as "No. The square root of -1 is a mathematical convenience and a figment of man's imagination"

Hmmm... one is a joke, and the other is not

Quote:

So to say they don't exist is like saying electricity doesn't exist because you can't see it.

Don't you wag your finger at me!
(I'm well aware of the applications in engineering / quantum physics, etc. ...)

That's not really true though, because as somebody above aptly put it:

Quote:

The reason we can do this is because math doesn't physically exist. We can't reach out and touch addition or three. Instead, math represents the real world

Mathematics merely describes our world, it doesn't technically exist in and of itself, unlike electricity, which having had numerous electrtic shocks before, I *can* authoratively tell you does exist!

Would numbers really exist by now if our universe was exactly the same as it is, but humanity didn't exist?

... This is what I was driving at with the answer No. "Seeing as numbers do not actually exist in the real world, neither do imaginary numbers (Mwa ha!)"
...as numbers don't really exist in nature. I'm surprised no-one has voted for this one (yet?).

I'd have voted for it myself but I just had to go for "Yes, we have no bananas".
Must have been all those electric shocks I've had.

Mmmmm, bananas. Banana cake. I like banana cake.

Last edited by 144419855310001; 09-23-2006 at 07:27 AM.

Would numbers really exist by now if our universe was exactly the same as it is, but humanity didn't exist?

Would 3 things be called 3 things? No, but there would still be 3 of them, it just wouldn't be quanitifed and named. Everything would still tick over obeying the laws of physics etc, just there would be no-one to write these laws down in ways that make sense to humans.

So my argument is that YES, numbers (real and imaginary) would still exist just no one would have discovered them yet

Depends on what you mean by "exist". If you mean "has real world applications", then sqrt(-1) certainly exists. If you mean "can be represented", the sqrt(-1) exists that way too. If you mean "can be detected directly or indirectly through the five senses", then sqrt(-1) and every other mathematical idea doesn't exist. That's a good excuse for not doing your math homework -- "But professor, math doesn't exist!".

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