FalloutJack said:
However, I'm going to need some citation on the part of you stating that imaginery numbers have an application beyond thought experiment.
How about the entirety of Quantum_Mechanics [http://en.wikipedia.org/wiki/Quantum_mechanics]?
Wikipedia said:
"Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an understanding of complex numbers and linear functionals."
Since 'i' is literally representing a paradox,
No it's representing the square root of -1.
"Has no solutions in the real numbers." is not the same thing as "A literal paradox."
it smacks of carelessness. "We didn't feel like figuring out where this leftover piece of the puzzle actually comes from, so here, have a Lowercase-I."
What do you mean "We didn't figure out where it came from so we just made it up."? Mathematicians
did figure it out, it comes from the complex numbers. Which aren't any more made up than the real numbers. Yeah, we choose to
label it as "i", but we labelled all the other numbers too. "1" "2" "3" etc., they're all just labels for concepts.
There was a time when people refused to believe negative numbers were any more than made up nonsense with no practical application, and then the same for irrational numbers.
...but it doesn't cry out as the pinnacle of precision anymore.
Well, you're simply wrong, mathematics is more precise nowadays than it has ever been. And no, it isn't a matter of opinion, there are mathematicians who spend their life doing almost nothing but making the definitions of concepts more precise or, more precisely, more concise.
Just because mathematics it constantly expands itself, does not mean mathematicians don't ensure it is done in a precise way.
And Discreet Mathimatics is very much this. It's the metaphysics of math that gives way to some interesting thoughts, but it's not logic and it's not science anymore.
Hardly, there are hypothesises in science today that suggest the universe is in fact discrete, not continuous as assumed, if so, then discrete mathematics is exactly what science need. Further, there are many things that exist today which require discrete models.
And this goes back to my point before. Why should mathematics wait until a concept is needed before researching it? That wastes years of time. So many times science has needed a new mathematical idea and it's been there waiting, full researched and usable, precisely because of mathematicians doing what you call pointless. Why are you advocating for that to stop?
You follow my meaning, right?
As far as I can tell, you've had a high school level of maths taught to you, or perhaps a basic university level, neither of which are nearly enough to understand
why the concepts we have exist, and yet you think you're qualified to judge why they exist.