Re: Has anyone made a real conlang?

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.

>is it a ligitimate problem?[1]
Oh yes! If only by providing some symmetry like for solving quadratic
equations (and it's necessary, in electricity for instance, to give
solutions to quadratic equations which have no real solutions, and yet do
have solutions in the real world ;)) ).

>  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 :) . 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) ;)))) .
That's called the polar form of complex numbers, and appears in physics
everywhere you have periodicity involved :) .

>  are they both imaginary numbers
>and as useful as i? [2]
As much as 5 is more useful than 1 ;))) . But while the square root of -5
is an imaginary number (like every square root of a negative real number),
the fourth root of -1 is not imaginary but complex, as it has both a real
part and an imaginary part. the idea is that while you put real numbers on
a line, you need to put complex numbers on a plane, with the horizontal
coordinate being the real part of a complex number, and the vertical
coordinate the imaginary part. "i", as such, is just the unit length of the
vertical coordinate.

>[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 I've had to
use complex numbers nearly everyday. They are vital for modern science.


>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 ;))) .

Christophe Grandsire.

http://rainbow.conlang.free.fr

You need a straight mind to invent a twisted conlang.

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