How low can you orbit?

From Scott Hedrick:
"Kevin Willoughby" wrote in message
...
Ok, now what is your excuse for calling 1"x1"x5" a *cube*?

Depends on your topography, of course :P It becomes a cube in the vicinity
of a Klein Bottle.

Ok, now what is your excuse for calling topology *topography*?

Hee hee.


~ CT

From Mary Pegg:
Stuf4 wrote:

From Jan Philips:

[musical scales]

I see it to have everything to do with harmonious divisibility. It is
not mere coincidence that powers of the 12th root of 2 mesh well with
Pythagorean ratios. It is a quality inherent in numbers themselves,
regardless of base.

The 12 note equal-tempered scale is just one of many. The gamelan
slendro and pelog scales consist of five and seven tones respectively:
http://w1.570.telia.com/~u57011259/pelog_main.htm

Indian music traditionally uses a 22-note scale:
http://www.musicalnirvana.com/introd...an_scales.html
And so on.

Frequencies can be divided *any* way we like. There is no need to
even base a scale on an octave.

But octaves are used because division by two is so resonant. The
question then becomes finding resonant subdivisions of the octave.
The decimal/metric answer is division by 10. Your Indian example
gives division by 22.

Mathematical formulas for harmony can be written explicitly. The
argument here is that metric is standing on an Achilles heel of
non-harmonious division by 10.

Mary, I would be glad to consider the potential advantages of division
by 22, but my expectation is that I wouldn't get through too many
seconds worth of traditional division-by-22 mp3 music before my ears
will be begging me for metric music.

Pythagoras was all over this consonance/dissonance stuff, as he and
his followers found applications in the fields of mathematics, music,
astronomy, astrology and psychology.

If Pythagoras were alive today and he were to learn about how global
cultures have entrenched their economies on Base-10, I expect he would
think that someone is playing a cruel joke on him.


~ CT

From Jan Philips:
That's because the moon goes through the cycle of phases 12+ times in
a year. The month was originally the "moonth".

This is precisely my point, Jud. The laws of physics that govern
orbital mechanics of the Moon have resolved a solution approaching 12
(look at the gaps in Saturns rings for more beautifully visible signs
of harmonic resonance in action).

Division by 12 happens all throughout nature. I am puzzled as to why
the French gave so much emphasis to mammalian phalanges. Even more
puzzling is that the rest of the world followed suit, save a few
countries.

And why are there 7 days in a week, and not 12 (if 12 is so good)?
That's because the days are named after the 7 things in the sky that
the ancients saw move against the stars (and the corresponding gods).
Sun-day, Moon-day, and Saturn-day. The others used other set of
names, like Thor's-day (now Thursday).

If the ancients had known about Uranus, Neptune, and Pluto then
perhaps we would have 10 days per week now.

I am not so quick to buy off on explanations that get promulgated
through textbooks. Many historical facts have been long forgotten and
those who have played detective don't always come up with accurate
answers.

After spending a lot of time studying the argument for a causal
relationship from visible wanderers (planets, Sun and Moon) to days of
the week, I don't find anything compelling.

I am open to the possibility that certain groups of high priests
(astronomer/astrologers) decided on 7 days because of divisibility
limitations of 365 (.24) and then the mythology followed subsequently
(the popular text of Genesis, for example).

And, as with measuring systems, 7 days to the week is only one of many
solutions. The fundamental problem facing the calendar is
rationalizing an irrational quantity. (That's "irrational" in the
mathematical sense of infinite fractionalization.)


~ CT

From Jan Philips:
I don't see many metric advocates
protesting the Babylonian system of chopping up a circle by degrees.

Have you heard of radians and grads (gradians)? Radians are the
natural way to measure angles, and there are 100 grads in a right
angle.

Your point about grads hints at another irony built into the metric
system. From the word go, the ideal meter was based on a measurement
of 1/4th of the circumference of the Earth. How silly to have a goal
of getting rid of fractions while *starting* with a fraction.

Some of the other things you mention are hangovers from the Babylonian
base 60 system because they were convenient in base 60 and they aren't
convenient now.

I see our clocks to be very convenient. Again the basis is harmony.
Hour angles match up to constellations which were subdivisions paced
by lunations. All rooted on the harmony of 12.

Once again, this is a property of numbers irrespective of the concept
of base.

If you have a string vibrate, and you start to play that string, your
ear will find divisions of 12 because they sound good. If you have an
accretion disk, the particles within that disk will settle into
natural harmonies as well.

Nothing resembling metric by any stretch.


~ CT

Stuf4 wrote:

Frequencies can be divided *any* way we like. There is no need to
even base a scale on an octave.

A scale is by definition the method of dividing the octave.

From Mary Pegg:
Stuf4 wrote:

Frequencies can be divided *any* way we like. There is no need to
even base a scale on an octave.

A scale is by definition the method of dividing the octave.

I was offering a less restrictive definition of a musical scale, as
with the one provided he

http://dictionary.reference.com/search?q=scale&r=67

"7. Music. An ascending or descending collection of pitches proceeding
by a specified scheme of intervals."

Note the origins:

"...from Latin sc lae, ladder."


~ CT

The fundamental problem facing the calendar is
rationalizing an irrational quantity. (That's "irrational" in the
mathematical sense of infinite fractionalization.)

More accurately...

The fundamental problem facing the calendar is rationalizing irrational ratios.

(The ratios btwn natural oscillations: Earth rotation, lunation, Earth orbit, etc)


~ CT

Stuf4 wrote...

snippage
I am puzzled as to why
the French gave so much emphasis to mammalian phalanges. Even
more puzzling is that the rest of the world followed suit, save
a few countries.

AIUI France and England agreed that 0deg longitude would be through
Greenwich, and SI would be the accepted scientific system.

We nearly had 0deg longitude through Paris!

- Peter

On Wed, 01 Oct 2003 07:55:30 GMT, "Peter Smith"
wrote:


Stuf4 wrote...

snippage
I am puzzled as to why
the French gave so much emphasis to mammalian phalanges. Even
more puzzling is that the rest of the world followed suit, save
a few countries.

AIUI France and England agreed that 0deg longitude would be through
Greenwich, and SI would be the accepted scientific system.

SI didn't exist until 1960, and wasn't arrived at through an agreement
between England and France. The metric system was already the
accepted scientific system before there was an SI.

We nearly had 0deg longitude through Paris!

We did have 0° longitude through Paris. No "nearly" about it. And
through Oslo. And through Washington, DC. And through lots of other
places.

Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/

From Peter Smith:
Stuf4 wrote...

snippage
I am puzzled as to why
the French gave so much emphasis to mammalian phalanges. Even
more puzzling is that the rest of the world followed suit, save
a few countries.

AIUI France and England agreed that 0deg longitude would be through
Greenwich, and SI would be the accepted scientific system.

We nearly had 0deg longitude through Paris!

The story I remember is that the French absolutely refused to adopt a
meridian based on Greenwich (or anywhere outside of France, for that
matter). When the Greenwich meridian was finally adopted, the
legislative wording was along the lines of "The prime meridian shall
be the meridian [however many] degrees west of Paris".

But it was America that set the stage for worldwide adoption of the
Greenwich meridian. And it was the railroad that forced that change.

(Very interesting story behind that.)


~ CT