Transcendental Numbers

In beginning to read Brian's post about non-equal-tempered, non-just tunings,
I promptly realized that I was missing one very basic piece of information that
perhaps some others of you may also be wondering about:

What the bloody hell is a transcendental number?!

That sort of ignorance of course is difficult for a practicing engineer to
admit, so please forgive the sarcastic tone of this message. It comes from
having to swallow my mathematical pride even after taking twenty-some-odd
heavily mathematical classes after Vector Calculus.

Those included a mysterious class called Automatic Control Theory, the
equations in whose textbook, I was once amused to notice, had more appeal as
abstract visual artforms than as mathematical statements. Then again standards
of amusement drop to all-time lows when you average (including weekends) four
hours of sleep a night for an entire semester in a room located directly above
the central water heater for the entire dormitory complex!

Of course Brian makes a point - in belching out two printed pages of examples
of transcendental and nontranscendal numbers (each of which approximately halves
my estimate of my mathematical prowess) - to explain the concept ever so
concisely by pointing out that "there appears to be NO general criterion for
determining whether a number is transcendental". Gee thanks Brian, that just
about sums it up for me!

So having accepted the embarrassing truth that I'm a complete mathematical
moron, I decided that maybe Grolier's CD-ROM encyclopedia might help out. "A
transcendental number is an irrational number that is not a root of any
polynomial equation with integer coefficients."

Thank you, Grolier.

Maybe some other blithering idiot like me was wondering...

Fortunately, my mathematical ego having been deflated to about the size of a
white pepper corn, I have the gratification of realizing the significance of a
number being the root of a polynomial equation with integer coefficents. If on
the other hand you don't, let me tell you a secret: playing the guitar is more
fun!

End of sarcastic tone. Sorry.


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