Re: Has anyone made a real conlang?

Christophe Grandsire wrote:

> En réponse à Tristan McLeay :
>
>> And what, pray tell, is the purpose of these beasts? What problem can't
>> be solved with real numbers that it requires us to take the sqrt of -1?
>
> A lot! And modern physics just can't be correctly presented without using
> complex numbers. From electricity-magnetism to Quantum Mechanics
> passing by
> system technology, you just can't solve any problem without resorting to
> complex numbers. They are vital for anything that has to do with waves.
> They are also extremely practical to solve trigonometric problems, and
> simplify greatly calculations involving sines and cosines (both things
> are
> related of course). And for things like optics (and dynamics too,
> although
> there people tend to avoid using them ;)) ), you even have to go further
> and resort to Quaternions, which resort not to one but three roots of -1,
> all perpendicular to each other, and get rid of the commutative
> assumption
> of multiplication.
So in other words they're like women: totally evil but absolutely
necessary?[1]

[1]: I hope the women who read this take it in the spirit it was
intended, which is about as far removed from insulting as possible.

>>  and how about the sqrt of -5?
>
> Easy: -5 can also be written 5*-1, and thus the square root of -5 (the
> sign
> for the square root isn't used with complex numbers under it as it often
> leads to incorrect statements) is simply sqrt(5)*i.
>
>> or the 4th root (is that the right term?) of -1?
>
> You mean the square root of the square root of -1? It's
> (1/sqrt(2))*(1+i).
> Just take its square according to the usual rules (not forgetting i^2=-1)
> and you'll see it's correct :) .
Indeed it is.

> As you may guess from the shape of the
> thing, the connection with trigonometry is appearing quickly :) . To
> confuse you even more, a common way to write it down is exp(i*Pi/4)
> ;)))) .
exp(x)=e^x?

>> [1]: I don't know how one might define that, so you can be generous.
>> [2]: I haven't officially come across imaginary numbers, but I've heard
>> a bit about them. Basically that i=sqrt(-1) and not much more... We're
>> supposed to come across them sometime in one of the Maths I'm doing this
>> semester...
>
> Well, if you need more of a proof that complex numbers are necessary,
> well,
> let me say that in the last five years of my scientific cursus
Been cursing science a lot, have you? or just cursing in a scientific
way? :P

> I've had to
> use complex numbers nearly everyday. They are vital for modern science.
Wow. I'm impressed. I'd asked this question to a few people, but no-one
could answer it (the best I'd got was from my father: 'something to do
with trigonometry' I think (he used to be a mechanical engineer)). I
hadn't really asked anyone who would really know, though, I don't think.

>> Nevertheless, I'm going to have to work on a language that has it! I
>> wonder if it's compatible with Pidse! :)
>
> LOL. First learn about complex numbers, and then include a language that
> uses their polar form ;))) .
I'll see what I can do :)

--
Tristan                  <kesuari@...>

"Dealing with failure is easy: Work hard to improve. Success is also easy to handle:
You've solved the wrong problem. Work hard to improve."

- Alan Perlis

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