Re: funny creationsist

On 2006-03-16, Jim Spaza <spaza9@xxxxxxxxx> wrote:

Mark VandeWettering wrote:
On 2006-03-03, Jim Spaza <spaza9@xxxxxxxxx> wrote:

Ernest Major wrote:
In message <1139537822.921371.325500@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, Jim
Spaza <spaza9@xxxxxxxxx> writes

Just how is it useful is anything practical other than a theoretical
sense when the scientist needs to get around some roadblock to his
theory?

And my background is in aerospace engineering. We deal in real
numbers, pal. Imaginary numbers are for people who don't have to
produce anything tangible, just white papers and theoretical assertions
for "research" purposes.

Please let me know how imaginary numbers can be used in a real,
practical sense.

Aerospace systems nowadays are chock full of electrical and electronic
systems. Imaginary numbers are extensively used in electrical
engineering. (Don't get hung up on the name.)

In circuit theory, there are sometimes complex roots where the
polynomial equation (created by the practical human trying to create
practical working machines) is part of the model equation for simple
circuits. There is a big difference between theoretical design on a
chalk board or computer screen and the manufacturing of a circuit board
at the transitor level.

I can't imagine why you think this argument might be convincing in the
shallowest measure. Your argument says nothing specific about complex
numbers, and therefore just as obviously must apply to all mathematics.
Since I don't think you'd argue that all mathematics is useless in the
design and manufacture of electronic circuits, I'd ask you to refine
your argument so that it actually says something about complex numbers.

OK. Hmmm...let's try this:

What physical process can be accurated represented by the square root
of a negative number?

Dusting off twenty year old electronics knowledge...

In electrical circuits, the state of a circuit element is often described
by both voltage and current (call them V and I) and elements often possess
resistance and inductance (call the C and L). It's convient to express
both as complex numbers (indeed, really natural) to express both sets of
quantities as single complex numbers, and expressing the normal laws of
electricity as operations over the complex numbers. Ohm's law is simply
V = I R, which is adequate perhaps for the understanding of DC circuits,
but not a whole lot of help in terms of AC circuits. Let's imagine that
we have a time varying voltage, described by the following:

V(t) = amplitude * e^(i w t / (2 pi))

The real component of this function is a sinusoid with angular velocity w.

If you pass the voltage through a system with resistance R, capacitance P
and inductance L, you can derive a quantity called impedence Z which
is defined as the complex value :

Z = R + i w L - i/(w C)

That looks odd, but guess what? Now the formula for AC circuits looks
exactly like the ordinary Ohm's law:

V = I Z

where the multiplication here is complex multiplication.

If, on the other hand, you'd like to argue that mathematical modelling
of all sorts is useless, well, I don't even know how to argue against
that...

No, not at all. Mathematical modeling is a great tool.

So, you're just a snob. Perhaps you trust only positive integers.

BTW, imaginary numbers were originally introduced as an aid in solving
polynomial equations.

No problem here. It's just that the universe doesn't care whether you
need an imaginary number to describe its function. If the polynomial
equation supposedly describing the universe demands imaginary numbers,
then the polynomial equation has only academic qualities.

Because, after all, polynomials aren't useful.

No, they can be. It's just whether or not they're accurate.

This criticism applies equally to all mathematics, and is therefore
irrelevent to the discussion.

Mark

.

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