Look at it this way, negative numbers are, in real world terms, imaginary in that you can't, for example, have "negative three apples".

Some numbers are just more imaginary than others.

I suppose you could have a negative apple, but if it touched anything you'd start tossing around battleships.

A medium sized negative apple appears to have a yield of 1.5 megatons of destructive force. About 3 megatons of actual energy.

A negative apple is what you have when Guido the loan shark is about to stop by and pick up the apple you owe him.

Math is kind of an easy subject to be able to to see how these different cultures though about things very differently than we did. There's zero. There's the idea that unit fractions are the only possibility. Negative numbers. Irrational numbers. My personal favorite, infinity. Each one really requires a paradigm shift. It's hard to think about, that they didn't just not use zero, they never conceived of the possibility of something like zero.

Yeah, really interesting.

I think that the problem with imaginary and real numbers is that those words mean very different things to the English majors among us. For me if you use the word imaginary, it has the same level of "realness" as my daydreams or "playing pretend"-- it seems that you have to have a belief (or at least a suspension of disbelief) that the "imaginary" are "real".

As if imaginary numbers are Narnia and Santa Claus and real numbers are England and our parents, and while I believe that Narnia and Santa Claus exist, I don't believe that they actually exist in the physical world, just that those ideas have something special about them that describes a human truth. And I feel like, with imaginary numbers being something you can work with to get actual electricity, I am being told that Santa Claus is an actual man who lives on the North Pole. And my brain just sort of explodiates.

I don't remember very well. I think you can use them to introduce a new dimension to a calculation. I believe one example is introducing phase into the math of AC electrical circuits.

For someone who is a very visual learner, this kind of stuff makes me want to cry. Do. Not. Understand.

History of math is way cool, though.

I think that the problem with imaginary and real numbers is that those words mean very different things to the English majors among us.

Yeah, it's unfortunate naming. You gotta think of neutral names like star-bellied numbers and plain-bellied numbers.

Some people, I'm not saying who, are bigoted against numbers that aren't in the real set.

Woot! Down with letter-appropriating imaginary "numbers"!

::runs screaming from the math talk::

I'm a big fan of quantum mechanics, so imaginary numbers don't present much of a problem. The thing I love about quantum mechanics is the ability to perfectly predict experiments and not have a clue what the fuck is actually going on.