Jeez, that was close

On Sep 15, 5:38 pm, John Schutkeker
wrote:

I look at how mathematicians handle astronomical material,no respect
for methods or insights and making things as dull as possible for
everyone.A real astronomer can enjoy the insight of Kepler without
having to call it a 'law' and indeed it was just a proportion he
observed as representative of some geometric harmony he found in
astronomy -

"...if you want the exact time, was conceived mentally on the 8th of
March in this year One Thousand Six Hundred and Eighteen but
unfelicitously submitted to calculation and rejected as false,
finally, summoned back on the 15th of May, with a fresh assault
undertaken, outfought the darkness of my mind by the great proof
afforded by my labor of seventeen years on Brahe's observations and
meditation upon it uniting in one concord, in such fashion that I
first believed I was dreaming and was presupposing the object of my
search among the principles. But it is absolutely certain and exact
that the ratio which exists between the periodic times of any two
planets is precisely the ratio of the 3/2th power of the mean
distances, i.e., of the spheres themselves; provided, however, that
the arithmetic mean between both diameters of the elliptic orbit be
slightly less than the longer diameter. And so if any one take the
period, say, of the Earth, which is one year, and the period of
Saturn, which is thirty years, and extract the cube roots of this
ratio and then square the ensuing ratio by squaring the cube roots, he
will have as his numerical products the most just ratio of the
distances of the Earth and Saturn from the sun. 1 For the cube root of
1 is 1, and the square of it is 1; and the cube root of 30 is greater
than 3, and therefore the square of it is greater than 9. And Saturn,
at its mean distance from the sun, is slightly higher than nine
times
the mean distance of the Earth from the sun." KEPLER

I see nobody enjoys the statement from Kepler -

"The proportion existing between the periodic times of any two planets
is exactly the sesquiplicate proportion of the mean distances of the
orbits, or as generally given,the squares of the periodic times are
proportional to the cubes of the mean distances." Kepler

In the hands of dismal mathematicians,the enjoyable correlation Kepler
made becomes a contrived and convoluted mess -


"PHÆNOMENON IV.
That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun. " Newton

I do not mind that people would make an effort to try and understand
Newton's junk however it leaves the original reasoning
unappreciated.It is one thing to giver Kepler a voice in this
mathematical wasteland that calls itself 'astronomy' but the voice of
Kepler is a gentle and familiar one for those who see how vibrant
astronomy can be.


How many would skip that passage from Kepler because they think it is
'hard',if they did make the small effort they would be repaid a
thousand times.

oriel36 wrote in news:1189881705.486970.18190
@y42g2000hsy.googlegroups.com:

On Sep 15, 5:38 pm, John Schutkeker
wrote:

I look at how mathematicians handle astronomical material,no respect
for methods or insights and making things as dull as possible for
everyone.A real astronomer can enjoy the insight of Kepler without
having to call it a 'law' and indeed it was just a proportion he
observed as representative of some geometric harmony he found in
astronomy -

"...if you want the exact time, was conceived mentally on the 8th of
March in this year One Thousand Six Hundred and Eighteen but
unfelicitously submitted to calculation and rejected as false,
finally, summoned back on the 15th of May, with a fresh assault
undertaken, outfought the darkness of my mind by the great proof
afforded by my labor of seventeen years on Brahe's observations and
meditation upon it uniting in one concord, in such fashion that I
first believed I was dreaming and was presupposing the object of my
search among the principles. But it is absolutely certain and exact
that the ratio which exists between the periodic times of any two
planets is precisely the ratio of the 3/2th power of the mean
distances, i.e., of the spheres themselves; provided, however, that
the arithmetic mean between both diameters of the elliptic orbit be
slightly less than the longer diameter. And so if any one take the
period, say, of the Earth, which is one year, and the period of
Saturn, which is thirty years, and extract the cube roots of this
ratio and then square the ensuing ratio by squaring the cube roots, he
will have as his numerical products the most just ratio of the
distances of the Earth and Saturn from the sun. 1 For the cube root of
1 is 1, and the square of it is 1; and the cube root of 30 is greater
than 3, and therefore the square of it is greater than 9. And Saturn,
at its mean distance from the sun, is slightly higher than nine
times
the mean distance of the Earth from the sun." KEPLER

I see nobody enjoys the statement from Kepler -

"The proportion existing between the periodic times of any two planets
is exactly the sesquiplicate proportion of the mean distances of the
orbits, or as generally given,the squares of the periodic times are
proportional to the cubes of the mean distances." Kepler

In the hands of dismal mathematicians,the enjoyable correlation Kepler
made becomes a contrived and convoluted mess -

The amazing thing about Kepler is that he discovered the Law of
Conservation of Angular Momentum, although it didn't come to be known as
such for two or three more centuries. I still haven't figured out who
coined that phrase, but AFAIK, it's considered to be even more
mathematically profound than Newton's Law(s).

Emmy Noether is considered one of the giants of modern mathematical
physics, but her work is still so abstract that most intelligent people
are unaware of it. By "abstract," I mean that it is not yet refined
into language, both verbal and mathematical, that can be understood by
beginning students. And yet, once you've gotten past the complex
notation and verbiage, it becomes clear how simple, general and powerful
its meaning is. AFAIK, it's one of the few occurrences of the word
"theorem" in physics.

"PHÆNOMENON IV.
That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun. " Newton

I do not mind that people would make an effort to try and understand
Newton's junk however it leaves the original reasoning
unappreciated. It is one thing to giver Kepler a voice in this
mathematical wasteland that calls itself 'astronomy'

Apparently, Newton was deliberately obfuscating his verbiage, to lock
the door to outsiders and preserve savant status of practitioners who
were already members of the insider's club of scientists.

However, it is disappointing to me that so many smart people of today
cannot see the beauty and elegance of mathematics, which, in their most
refined form, give abstraction, precision and comprehensiveness, all at
once.

It is a testimony to the banality of American science education at both
the primary and secondary levels. Teachers seem to prefer to force the
material down the student's throats, rather than inspiring them with its
beauty and wonder.

OTOH, student have no clue as to either the value or the meaning of the
field, but at best, see science as merely a path to a paycheck or tasks
to be performed for their own sakes. Both will take a person forward in
the profession, but neither will make him into a Feynmann.

I suppose that these must be values that are learned from one's family,
at a very young age, before a child even starts going to school.

but the voice of Kepler is a gentle and familiar one for those who
see how vibrant astronomy can be.

How many would skip that passage from Kepler because they think it is
'hard', if they did make the small effort they would be repaid a
thousand times.

I do find it hard reading the run-on sentences generated as musings in
other people's diaries. Kepler was a brilliant scientist, but merely a
bright writer of prose. As far as complex sentence structure is
concerned, he's can't hold a candle to Herman Melville.

Perhaps an appropriate technique for parsing such a difficult passage
would be what I call "active reading," ie. to read it at the same time
as editing it on a word processor. In doing so it can be taken apart
microscopically, while simultaneously translating it into something
readable to the person at the keyboard.

John Schutkeker wrote:
Apparently, Newton was deliberately obfuscating his verbiage, to lock
the door to outsiders and preserve savant status of practitioners who
were already members of the insider's club of scientists.

I would not be so hard on Newton. Of course a phrase like
"sesquiplicate proportion" is meaningless to people in the present
day, but at that time, powers and roots were still novel concepts in
mathematics, so the modern notational conventions had not yet been
established.

The difference between what Kepler wrote, and what Newton wrote, that
makes Kepler right but Newton wrong when saying the same thing,
however, that the former poster sees is truly obscure to me. And both
use the term "sesquiplicate proportion" for the 3/2 power.

John Savard

On Sep 16, 4:12 am, Quadibloc wrote:
John Schutkeker wrote:
Apparently, Newton was deliberately obfuscating his verbiage, to lock
the door to outsiders and preserve savant status of practitioners who
were already members of the insider's club of scientists.

I would not be so hard on Newton. Of course a phrase like
"sesquiplicate proportion" is meaningless to people in the present
day, but at that time, powers and roots were still novel concepts in
mathematics, so the modern notational conventions had not yet been
established.

The difference between what Kepler wrote, and what Newton wrote, that
makes Kepler right but Newton wrong when saying the same thing,
however, that the former poster sees is truly obscure to me. And both
use the term "sesquiplicate proportion" for the 3/2 power.

John Savard

You are like children in this matter,you have no idea what Newton did
but I assure you I do.The creation of the so-called AU was based on
the zodiacal framework hence the ridiculous geocentric/heliocentric
equivalency -

"PHÆNOMENON IV.
That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun. " Newton

The minute Copernicus set the Earth in motion between Venus and
Mars,geocentricity is gone forever,that it was re-introduced as a
principle in the late 17th century via Flamsteed/Newton hardly matters
to pretensious people who have gotten plenty of mileage out of showing
how 'difficult' mathematics is .

At least the illegal maneuver Newton did is interesting if not
destructive,the idea that you can get the right answer by whatever
means seems to be the currency among people since then.