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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
10 Sep 2007 11:33:38 AM |
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Sam Wormley <swormley1@mchsi.com> wrote in
news:jp%Ei.76616$Xa3.56894@attbi_s22:
John Schutkeker wrote:
I came this close :p to sending my letter to the journal with a
mistake in it. But it's all fixed now, and all I have to do is screw
up the nerve to click the 'send' button on arxiv.
Click the 'send' button--You nned the feedback.
I'm thinking of putting in two more graphs. Suddenly I'm insecure about
the small quantity of content.
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
12 Sep 2007 10:15:04 AM |
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Sam Wormley <swormley1@mchsi.com> wrote in
news:jp%Ei.76616$Xa3.56894@attbi_s22:
John Schutkeker wrote:
I came this close :p to sending my letter to the journal with a
mistake in it. But it's all fixed now, and all I have to do is screw
up the nerve to click the 'send' button on arxiv.
Click the 'send' button--You nned the feedback.
It's not gonna see the light of day. It's got an unfixable mistake in it.
;(
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| User: "Sam Wormley" |
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| Title: Re: Jeez, that was close |
12 Sep 2007 10:22:16 AM |
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John Schutkeker wrote:
Sam Wormley <swormley1@mchsi.com> wrote in
news:jp%Ei.76616$Xa3.56894@attbi_s22:
John Schutkeker wrote:
I came this close :p to sending my letter to the journal with a
mistake in it. But it's all fixed now, and all I have to do is screw
up the nerve to click the 'send' button on arxiv.
Click the 'send' button--You nned the feedback.
It's not gonna see the light of day. It's got an unfixable mistake in it.
;(
On the brighter side... it was good you caught the mistake. :-)
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
12 Sep 2007 02:50:21 PM |
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Sam Wormley <swormley1@mchsi.com> wrote in
news:IuTFi.81306$Xa3.73263@attbi_s22:
John Schutkeker wrote:
Sam Wormley <swormley1@mchsi.com> wrote in
news:jp%Ei.76616$Xa3.56894@attbi_s22:
John Schutkeker wrote:
I came this close :p to sending my letter to the journal with a
mistake in it. But it's all fixed now, and all I have to do is
screw up the nerve to click the 'send' button on arxiv.
Click the 'send' button--You nned the feedback.
It's not gonna see the light of day. It's got an unfixable mistake
in it. ;(
On the brighter side... it was good you caught the mistake. :-)
Unfortunately, that's merely a silver lining to a dark cloud, and not
enough to really compensate for the loss of a publication, even if it
was only a letter. This has been sitting on my desk for a many years
now, which means that I've been operating under a misconception for all
that time. :(
Since I'm giving up on it, I think I'll throw it open to the whole
physics community, or at least that part of it that resides here in this
BBS.
I was trying to find an equation for the following succession of powers
of '2', (0,1,2,4,8,16, 32,64,128,256). As you can see, the problem is
with the first two items in the list, '0' and '1', because '0' is not
strictly a power of '2'. I believe that anyone who can do that, will be
able to publish at least a letter, because it's relevant to an important
problem in physics and astronomy.
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| User: "George Dishman" |
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| Title: Re: Jeez, that was close |
12 Sep 2007 03:03:36 PM |
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"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns99A9A127B613Alkajehoriuasldfjknak@207.115.17.102...
...
Since I'm giving up on it, I think I'll throw it open to the whole
physics community, or at least that part of it that resides here in this
BBS.
I was trying to find an equation for the following succession of powers
of '2', (0,1,2,4,8,16, 32,64,128,256). As you can see, the problem is
with the first two items in the list, '0' and '1', because '0' is not
strictly a power of '2'. I believe that anyone who can do that, will be
able to publish at least a letter, because it's relevant to an important
problem in physics and astronomy.
'1' is not a problem but '0' is, in reverse order
the log to the base 2 of your series is
... 8, 7, 6, 5, 4, 3, 2, 1, 0, -infinity.
George
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| User: "dlzc" |
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| Title: Re: Jeez, that was close |
12 Sep 2007 05:05:16 PM |
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Dear John Schutkeker:
On Sep 12, 12:50 pm, John Schutkeker
<jschutke...@sbcglobal.net.nospam> wrote:
....
I was trying to find an equation for the following
succession of powers of '2', (0,1,2,4,8,16, 32,64,
128,256). As you can see, the problem is with
the first two items in the list, '0' and '1', because
'0' is not strictly a power of '2'. I believe that
anyone who can do that, will be able to publish
at least a letter, because it's relevant to an
important problem in physics and astronomy.
Well, it is not continuous, nor differentiable, but
Result = int( 2^n ), for any integer n.
With int( ) returning the "integer portion of" without rounding.
(Might need to add a small bit (like 0.1) inside the int() operation,
since floating point math is always so "goosy".)
But, if you are looking for a computer algorithm, that will work.
What problem would this solve?
David A. Smith
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
13 Sep 2007 06:41:59 AM |
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dlzc <dlzc1@cox.net> wrote in news:1189634716.774606.134360@
57g2000hsv.googlegroups.com:
Dear John Schutkeker:
On Sep 12, 12:50 pm, John Schutkeker
<jschutke...@sbcglobal.net.nospam> wrote:
...
I was trying to find an equation for the following
succession of powers of '2', (0,1,2,4,8,16, 32,64,
128,256). As you can see, the problem is with
the first two items in the list, '0' and '1', because
'0' is not strictly a power of '2'. I believe that
anyone who can do that, will be able to publish
at least a letter, because it's relevant to an
important problem in physics and astronomy.
Well, it is not continuous, nor differentiable, but
Result = int( 2^n ), for any integer n.
With int( ) returning the "integer portion of" without rounding.
(Might need to add a small bit (like 0.1) inside the int() operation,
since floating point math is always so "goosy".)
But, if you are looking for a computer algorithm, that will work.
What problem would this solve?
It's called Bode's Law, the number series which describes the ratios of
the radii of our sun's planetary orbits. You can read about it in
Abel's (old) introductory astronomy text, "Exploration of the
Universe," or in Ivars Peterson's excellent recent book for the general
audience, "Newton's Clock: Chaos in the Solar System." It's clearly a
solution to the dynamical equations, but being unable to express it as
an equation means that you can't put the solution equation into the
starting equations, to see what comes out.
.
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| User: "Margo Schulter" |
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| Title: Re: Jeez, that was close |
13 Sep 2007 07:16:08 PM |
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In sci.astro.amateur John Schutkeker <jschutkeker@sbcglobal.net.nospam> wrote:
It's called Bode's Law, the number series which describes the ratios of
the radii of our sun's planetary orbits. You can read about it in
Abel's (old) introductory astronomy text, "Exploration of the
Universe," or in Ivars Peterson's excellent recent book for the general
audience, "Newton's Clock: Chaos in the Solar System." It's clearly a
solution to the dynamical equations, but being unable to express it as
an equation means that you can't put the solution equation into the
starting equations, to see what comes out.
Hi, John. As I recall, Bode's Law (or maybe better Bode's Model, since
it fits most but not all the data now known for the Solar System), goes
about like this.
Let 10 equal the distance between Sun and Earth -- or, as we now say,
one astronomical unit (1 AU).
To derive the distances to what I might term the macroplanets through
Pluto (excepting Neptune!), those with sufficient mass to attain and
maintain hypostatic equilibrium or a near-spherical shape (apart from
rotational oblation and the like), we start with 4, the distance for
Mercury; note that the series of integers for this and other distances
represent tenths of an AU (e.g. 0.4 AU for Mercury).
Our sequence goes like this:
Mercury 4 + 0 = 4
Venus 4 + 3*2^0 = 7
Earth 4 + 3*2^1 = 10
Mars 4 + 3*2^2 = 16
1 Ceres 4 + 3*2^3 = 28
Jupiter 4 + 3*2^4 = 52
Saturn 4 + 3*2^5 = 100
Uranus 4 + 3*2^6 = 196
[Neptune].............................
Pluto 4 + 3*2^7 = 388
Bode's Model thus quite accurately predicts the orbital distance
for seven of the eight dominant planets (all except Neptune), those
which have "cleared the neighborhood of their orbit[s]" and have
masses far exceeding the total mass of bodies in their orbital
zones not under their gravitational influence; and also notably
for the belt or congregate macroplanet 1 Ceres, in fact discovered
by Giuseffe Piazzi in 1801 in an orbit very close to where Bode's
Model predicted it should be (a discovery also of the first body
in what would would be recognized as the main asteroid belt), and
also 134340 Pluto. also now known to be a belt macroplanet, and
the largest of the Kuiper Belt objects. (While 136199 Eris is
larger, it is a Scattered Disk Object with an orbit beyond that
of the Kuiper Belt.) In IAU terms, these categories are called
respectively "planets" and "dwarf planets."
In other words, with Bode's Model, the series of integers to be
added to 4 to derive the orbital distances of the relevant bodies
starting with Mercury is is (0,3,6,12,24,48,96,192,384).
Most appreciatively,
Margo Schulter
mschulter@calweb.com
Lat. 38.566 Long. -121.430
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
14 Sep 2007 12:42:36 PM |
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Margo Schulter <mschulter@web1.calweb.com> wrote in
news:46e9d2c8$0$30973$d368eab@news.calweb.com:
In sci.astro.amateur John Schutkeker
<jschutkeker@sbcglobal.net.nospam> wrote:
It's called Bode's Law, the number series which describes the ratios
of the radii of our sun's planetary orbits. You can read about it in
Abel's (old) introductory astronomy text, "Exploration of the
Universe," or in Ivars Peterson's excellent recent book for the
general audience, "Newton's Clock: Chaos in the Solar System." It's
clearly a solution to the dynamical equations, but being unable to
express it as an equation means that you can't put the solution
equation into the starting equations, to see what comes out.
Hi, John. As I recall, Bode's Law (or maybe better Bode's Model, since
it fits most but not all the data now known for the Solar System),
goes about like this.
Let 10 equal the distance between Sun and Earth -- or, as we now say,
one astronomical unit (1 AU).
To derive the distances to what I might term the macroplanets through
Pluto (excepting Neptune!), those with sufficient mass to attain and
maintain hypostatic equilibrium or a near-spherical shape (apart from
rotational oblation and the like), we start with 4, the distance for
Mercury; note that the series of integers for this and other distances
represent tenths of an AU (e.g. 0.4 AU for Mercury).
Our sequence goes like this:
Mercury 4 + 0 = 4
Venus 4 + 3*2^0 = 7
Earth 4 + 3*2^1 = 10
Mars 4 + 3*2^2 = 16
1 Ceres 4 + 3*2^3 = 28
Jupiter 4 + 3*2^4 = 52
Saturn 4 + 3*2^5 = 100
Uranus 4 + 3*2^6 = 196
[Neptune].............................
Pluto 4 + 3*2^7 = 388
Bode's Model thus quite accurately predicts the orbital distance
for seven of the eight dominant planets (all except Neptune), those
which have "cleared the neighborhood of their orbit[s]" and have
masses far exceeding the total mass of bodies in their orbital
zones not under their gravitational influence; and also notably
for the belt or congregate macroplanet 1 Ceres, in fact discovered
by Giuseffe Piazzi in 1801 in an orbit very close to where Bode's
Model predicted it should be (a discovery also of the first body
in what would would be recognized as the main asteroid belt), and
also 134340 Pluto. also now known to be a belt macroplanet, and
the largest of the Kuiper Belt objects. (While 136199 Eris is
larger, it is a Scattered Disk Object with an orbit beyond that
of the Kuiper Belt.) In IAU terms, these categories are called
respectively "planets" and "dwarf planets."
In other words, with Bode's Model, the series of integers to be
added to 4 to derive the orbital distances of the relevant bodies
starting with Mercury is is (0,3,6,12,24,48,96,192,384).
Most appreciatively,
Margo Schulter
mschulter@calweb.com
Lat. 38.566 Long. -121.430
Margo, you're the hottest babe in the solar system. I now have the
solution, and you can come over Saturday night to claim your reward. :D
.
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| User: "Quadibloc" |
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| Title: Re: Jeez, that was close |
14 Sep 2007 09:12:03 PM |
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John Schutkeker wrote:
Margo, you're the hottest babe in the solar system. I now have the
solution, and you can come over Saturday night to claim your reward. :D
I'm curious: how was she of assistance?
You, after all, already knew that the sequence of numbers was of
interest to you because of Bode's Law, and all she did was show how
the distances of the planets, in tenths of an A.U., were equal to 4
plus 3 times the numbers in your sequence - which is, of course, what
you started from.
Everyone else presumably thought that since the sequence would have
gone on to infinity, Mercury came about in place of all the tiny
planets it would have predicted. I would think that if you were
looking for a "reason" for the distribution of the planets in the
solar system, you would start by using the exact distances of the
planets (including Neptune instead of Pluto).
But we already know that the planets didn't always have their current
distances from the Sun. At one time, while Jupiter's orbital period
was its present 12 years, that of Saturn was 18 years instead of 30.
This resonance led to Saturn's orbit becoming larger, leading to the
Late Heavy Bombardment. (I just learned about this stuff at the last
astronomy club meeting I attended...)
So that means that the spacing of planets in the Solar System is very
much the result of historical causes, which would seem to mitigate
against any simple regular law. Or the law might be really simple -
planets in adjacent orbits repel one another, until the ratio in
distance from the sun is nearly, but not quite, 2 to 1, and the ratio
in orbital period is therefore something like the 13:8 of Earth and
Venus, or the 5:2 of Saturn and Jupiter.
John Savard
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
15 Sep 2007 11:38:43 AM |
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Quadibloc <jsavard@ecn.ab.ca> wrote in news:1189822323.290526.231200@
50g2000hsm.googlegroups.com:
John Schutkeker wrote:
Margo, you're the hottest babe in the solar system. I now have the
solution, and you can come over Saturday night to claim your reward.
:D
I'm curious: how was she of assistance?
Typing my reply to her helped me organize my thoughts, and I sudden;y
realized that I had had an idea for it that I hadn't tried yet. I tried
it and it didn't work, but a similar function did.
You, after all, already knew that the sequence of numbers was of
interest to you because of Bode's Law, and all she did was show how
the distances of the planets, in tenths of an A.U., were equal to 4
plus 3 times the numbers in your sequence - which is, of course, what
you started from.
Everyone else presumably thought that since the sequence would have
gone on to infinity, Mercury came about in place of all the tiny
planets it would have predicted. I would think that if you were
looking for a "reason" for the distribution of the planets in the
solar system, you would start by using the exact distances of the
planets (including Neptune instead of Pluto).
But we already know that the planets didn't always have their current
distances from the Sun. At one time, while Jupiter's orbital period
was its present 12 years, that of Saturn was 18 years instead of 30.
This resonance led to Saturn's orbit becoming larger, leading to the
Late Heavy Bombardment. (I just learned about this stuff at the last
astronomy club meeting I attended...)
So that means that the spacing of planets in the Solar System is very
much the result of historical causes, which would seem to mitigate
against any simple regular law. Or the law might be really simple -
planets in adjacent orbits repel one another, until the ratio in
distance from the sun is nearly, but not quite, 2 to 1, and the ratio
in orbital period is therefore something like the 13:8 of Earth and
Venus, or the 5:2 of Saturn and Jupiter.
John Savard
As I recall correctly, you're a mathematical whiz, which means that
Danby's book will be useful to you. I'd recommend spending the $35 at
Willmann-Bell for such a well written hardcover, of such mathematical
rigor and such a good price. AFAIK, you can't get current hardcover
texts from any other source, although there are plenty of good used ones
at the usual sources.
Once you've read Danby, you're ready for Laskar's papers, which are the
state of the art. Wisdom's work is useful for everything except
equations, because he's using Hamiltonian rather than Newtonian
mechanics, so his equations are impossible for anybody but a total
genius to decipher. Someday I hope he writes another text on the
Hamiltonian analysis of the problem, because it would be a wonderful
contribution. He had to trade first authorship of his first text to
Jerry Sussman, in exchange for the kick starting his career.
For now, Laskar's work is the only thing us ordinary mathematicians have
to work with. I've looked closely at his equations, and there are a
couple of trivial simplifications possible, but I can't see anything
worth a paper. Since you're good at math, you might be able to spot the
next change of variables that goes somewhere useful.
Or you can be the one to put Bode's Law into the perturbed equations of
n-body motion, and show that it generates a meaningful solution. That's
what I say in the conclusion of this letter I'm working on, although I
haven't yet found out whether the content will be acceptable to whomever
reviews it.
It's not too different from control theory, which is mathematically a
very rich subject.
.
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| User: "oriel36" |
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| Title: Re: Jeez, that was close |
15 Sep 2007 01:41:45 PM |
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On Sep 15, 5:38 pm, John Schutkeker <jschutke...@sbcglobal.net.nospam>
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 -
"=2E..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 -
"PH=C6NOMENON 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.
.
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
15 Sep 2007 08:26:52 PM |
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oriel36 <geraldkelleher@yahoo.com> wrote in news:1189881705.486970.18190
@y42g2000hsy.googlegroups.com:
On Sep 15, 5:38 pm, John Schutkeker <jschutke...@sbcglobal.net.nospam>
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.
.
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| User: "Quadibloc" |
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| Title: Re: Jeez, that was close |
15 Sep 2007 10:12:51 PM |
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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
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| User: "oriel36" |
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| Title: Re: Jeez, that was close |
16 Sep 2007 07:45:11 AM |
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On Sep 16, 4:12 am, Quadibloc <jsav...@ecn.ab.ca> 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 -
"PH=C6NOMENON 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.
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| User: "Margo Schulter" |
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| Title: Re: Jeez, that was close |
12 Sep 2007 03:19:42 PM |
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In sci.astro.amateur John Schutkeker <jschutkeker@sbcglobal.net.nospam> wrote:
Since I'm giving up on it, I think I'll throw it open to the whole
physics community, or at least that part of it that resides here in this
BBS.
Hi, there, John. As someone on the Usenet newsgroup sci.astro.amateur,
please let me clarify that while you may be using a BBS to access the
groups to which you are posting, you are indeed posting to three Usenet
newsgroups. Since Usenet does in some ways resemble, for example,
FidoNet, I can understand how this distinction isn't always so obvious.
As a layperson, I'm curious about your mathematical quandary even if not
so expert at addressing it, so please let me try a question.
I was trying to find an equation for the following succession of powers
of '2', (0,1,2,4,8,16, 32,64,128,256). As you can see, the problem is
with the first two items in the list, '0' and '1', because '0' is not
strictly a power of '2'. I believe that anyone who can do that, will be
able to publish at least a letter, because it's relevant to an important
problem in physics and astronomy.
Please let me ask if I'm right that these numbers represent integers equal
to powers of two, actually starting with 2^0=1, then 2^1=2, 2^2=4, etc.?
If so, then 0 is a problem for the reason that you state: it could be
more and more closely approximated by very high negative powers of 2
(e.g. 2^-100) with very small sizes, but never reached; I guess it might
be the limit of 2^-x when x approaches an infinitely large size.
Apart from the 0, of course, you have a simple power series, 2^x where
n is a nonnegative integer. I'd need to look up the formal notation for
such a series, but it should be pretty straightforward.
I'm curious about the application, and the main mathematical question,
it would seem to me as a layperson, is to how to define a series that
would start with that initial 0, the rest being a straightforward
series of powers of 0 (2^0, 2^1, 2^2, ..., 2^n-1).
Most appreciatively,
Margo Schulter
mschulter@calweb.com
Lat. 38.566 Long. -121.430
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| User: "John Park" |
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| Title: Re: Jeez, that was close |
12 Sep 2007 05:16:32 PM |
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John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
I was trying to find an equation for the following succession of powers
of '2', (0,1,2,4,8,16, 32,64,128,256). As you can see, the problem is
with the first two items in the list, '0' and '1', because '0' is not
strictly a power of '2'. I believe that anyone who can do that, will be
able to publish at least a letter, because it's relevant to an important
problem in physics and astronomy.
Well Bode's law isn't *that* good a fit (assuming that's what you're
hinting at). Maybe you can look for a better one instead?
--John Park
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
13 Sep 2007 06:35:18 AM |
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(John Park) wrote in
news:fc9og0$t1p$1@theodyn.ncf.ca:
John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
I was trying to find an equation for the following succession of
powers of '2', (0,1,2,4,8,16, 32,64,128,256). As you can see, the
problem is with the first two items in the list, '0' and '1', because
'0' is not strictly a power of '2'. I believe that anyone who can do
that, will be able to publish at least a letter, because it's
relevant to an important problem in physics and astronomy.
Well Bode's law isn't *that* good a fit (assuming that's what you're
hinting at). Maybe you can look for a better one instead?
Bode's Law is an *amazing* fit to the data, and without it, Uranus,
Neptune and Pluto would have never been discovered. There is nothing
better, and if you were to discard it, because of a small error in the
2nd decimal place, you would throw the baby out with the bathwater.
Anybody who would do that shows themselves to be a bad astronomer, who
can't tell the difference between a reliable global solution and a small
error in a lower decimal place.
Furthermore, Bode's Law proves that Pluto is a planet, and that the poor
scientists who decided otherwise are not fit to kiss the shoes of
Herschel, Tombaugh and Le Verrier, the patron saints if planetary
science. The only thing that has been proved by Demoting Pluto from the
status of planet is that human arrogance and intellectual vanity knows
no bounds.
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| User: "John Park" |
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| Title: Re: Jeez, that was close |
13 Sep 2007 03:18:22 PM |
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John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
Bode's Law is an *amazing* fit to the data, and without it, Uranus,
Neptune and Pluto would have never been discovered.
Are you sure? I thought observational discrepancies had more to do with it.
There is nothing
better, and if you were to discard it, because of a small error in the
2nd decimal place, you would throw the baby out with the bathwater.
Anybody who would do that shows themselves to be a bad astronomer, who
can't tell the difference between a reliable global solution and a small
error in a lower decimal place.
Furthermore, Bode's Law proves that Pluto is a planet, and that the poor
scientists who decided otherwise are not fit to kiss the shoes of
Herschel, Tombaugh and Le Verrier, the patron saints if planetary
science. The only thing that has been proved by Demoting Pluto from the
status of planet is that human arrogance and intellectual vanity knows
no bounds.
Ignoring the rhetoric, I'm more concerned with the fact that Bode's Law asks
the wisp of stuff in the asteroid belt to be given the same status as Mars and
Jupiter. And that for Neptune it's off by nearly 30%, and for Pluto by
nearly a factor of 2--or if you want to claim Pluto as a hit, it omits
Neptune entirely (a far more serious error than demoting minuscule Pluto).
With only about six degrees of freedom, two or three major errors
among its predictions don't make for a brilliant success--though for such a
simple relation its result are intriguing.
--John Park
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
14 Sep 2007 11:34:29 AM |
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(John Park) wrote in
news:fcc5ue$8kl$1@theodyn.ncf.ca:
John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
Bode's Law is an *amazing* fit to the data, and without it, Uranus,
Neptune and Pluto would have never been discovered.
Are you sure? I thought observational discrepancies had more to do
with it.
There is nothing
better, and if you were to discard it, because of a small error in
the 2nd decimal place, you would throw the baby out with the
bathwater. Anybody who would do that shows themselves to be a bad
astronomer, who can't tell the difference between a reliable global
solution and a small error in a lower decimal place.
Furthermore, Bode's Law proves that Pluto is a planet, and that the
poor scientists who decided otherwise are not fit to kiss the shoes
of Herschel, Tombaugh and Le Verrier, the patron saints if planetary
science. The only thing that has been proved by Demoting Pluto from
the status of planet is that human arrogance and intellectual vanity
knows no bounds.
Ignoring the rhetoric, I'm more concerned with the fact that Bode's
Law asks the wisp of stuff in the asteroid belt to be given the same
status as Mars and Jupiter. And that for Neptune it's off by nearly
30%, and for Pluto by nearly a factor of 2--
That's what makes it so fascinating, because it leads to a second
problem in celestial mechanics that is more subtle. In fact, the error
associated with Uranus is also more severe than that of the six planets
known to the ancients. If you plot the error of those three planets vs.
index number, perhaps including Saturn a reference point, the pattern is
so obvious that it slaps you in the face.
Likewise, putting the asteroid belt into the analysis raise another,
equally interesting question, which is "What specific features of the
system's dynamics prevent the asteroids from having coalesced into a
planet?" I don't know if this problem has been mathematically solved
yet, although, having asked the question, it's easy to predict the
appearance of a pretender with a hand waving argument.
My rhetoric about hand waving arguments vs. mathematical arguments is
the same one I made in my previous post about being unworthy men not
being fit to kiss the boots of giants like Herschel, Tombaugh and Le
Verrier.
or if you want to claim
Pluto as a hit, it omits Neptune entirely (a far more serious error
than demoting minuscule Pluto).
Neptune is not omitted; it's right there, with all the rest of them.
With only about six degrees of freedom, two or three major errors
among its predictions don't make for a brilliant success--though for
such a simple relation its result are intriguing.
There are no major errors; all the errors are minor, and well accounted
for by the mathematics.
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| User: "John Park" |
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| Title: Re: Jeez, that was close |
15 Sep 2007 07:25:32 AM |
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John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
My rhetoric about hand waving arguments vs. mathematical arguments is
the same one I made in my previous post about being unworthy men not
being fit to kiss the boots of giants like Herschel, Tombaugh and Le
Verrier.
Which, as I said, I ignored.
or if you want to claim
Pluto as a hit, it omits Neptune entirely (a far more serious error
than demoting minuscule Pluto).
Neptune is not omitted; it's right there, with all the rest of them.
With only about six degrees of freedom, two or three major errors
among its predictions don't make for a brilliant success--though for
such a simple relation its result are intriguing.
There are no major errors; all the errors are minor, and well accounted
for by the mathematics.
???
The last few predictions of Bode's Law are: 19.6, 38.8, 77.2 AU.
The 19.6 fits Uranus at 19.2. But if you match the next two to Neptune and
Pluto you get deviations of 8.7 and 37.7 AU respectively. Alternatively,
if you match 38.8 to Pluto, Bode's Law has no room for Neptune.
Whichever way you do it, Bode's Law makes at least one major error among the
outer planets.
--John Park
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
15 Sep 2007 07:55:08 PM |
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(John Park) wrote in
news:fcgivs$n5l$1@theodyn.ncf.ca:
John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
My rhetoric about hand waving arguments vs. mathematical arguments is
the same one I made in my previous post about being unworthy men not
being fit to kiss the boots of giants like Herschel, Tombaugh and Le
Verrier.
Which, as I said, I ignored.
This mistake is made by mediocre scientists across the world. You can't
ignore the giants of history, because history is as great a force for
science as science is a force for history. While you're at it, just go
ahead and ignore Newton, Hamilton, Jacobi and Lagrange. Thhen get some
eye of newt and cast some magickal spells, instead of applying Occam's
Razor or Aquinas' Dialectical Method. Just throw Socratic logic out the
window, too.
Dont'cha get it? Solving equations is only half the battle, and the
other half is understanding the great works of the supreme thinkers that
have gone before, which you must learn to quote by name. "The reason we
see so far is because we stand on the shoulders of giants." You can't
just topple that sort of edifice on a whim and expect to be taken
seriously. That's how the Einstein deniers think. ?:(
With only about six degrees of freedom, two or three major errors
among its predictions don't make for a brilliant success--though for
such a simple relation its result are intriguing.
There are no major errors; all the errors are minor, and well
accounted for by the mathematics.
???
The last few predictions of Bode's Law are: 19.6, 38.8, 77.2 AU.
The 19.6 fits Uranus at 19.2. But if you match the next two to Neptune
and Pluto you get deviations of 8.7 and 37.7 AU respectively.
Alternatively, if you match 38.8 to Pluto, Bode's Law has no room for
Neptune.
Whichever way you do it, Bode's Law makes at least one major error
among the outer planets.
You're confused about the distinction between major and minor errors,
because you can't see the forest for the trees. Science is not
primarily about small details, but rather it is about large concepts.
The small details are merely vehicles we use to eliminate the chance of
making mistake in our large concepts. To understand science, you've got
to have both under control, but the two are *not* of equal importance.
One is a great gift, and the other is a necessary evil.
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| User: "John Park" |
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| Title: Re: Jeez, that was close |
16 Sep 2007 11:16:05 AM |
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John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
af250@FreeNet.Carleton.CA (John Park) wrote in
news:fcgivs$n5l$1@theodyn.ncf.ca:
John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
My rhetoric about hand waving arguments vs. mathematical arguments is
the same one I made in my previous post about being unworthy men not
being fit to kiss the boots of giants like Herschel, Tombaugh and Le
Verrier.
Which, as I said, I ignored.
This mistake is made by mediocre scientists across the world. You can't
ignore the giants of history, because history is as great a force for
science as science is a force for history. While you're at it, just go
ahead and ignore Newton, Hamilton, Jacobi and Lagrange. Thhen get some
eye of newt and cast some magickal spells, instead of applying Occam's
Razor or Aquinas' Dialectical Method. Just throw Socratic logic out the
window, too.
Dont'cha get it? Solving equations is only half the battle, and the
other half is understanding the great works of the supreme thinkers that
have gone before, which you must learn to quote by name. "The reason we
see so far is because we stand on the shoulders of giants." You can't
just topple that sort of edifice on a whim and expect to be taken
seriously. That's how the Einstein deniers think. ?:(
With only about six degrees of freedom, two or three major errors
among its predictions don't make for a brilliant success--though for
such a simple relation its result are intriguing.
There are no major errors; all the errors are minor, and well
accounted for by the mathematics.
???
The last few predictions of Bode's Law are: 19.6, 38.8, 77.2 AU.
The 19.6 fits Uranus at 19.2. But if you match the next two to Neptune
and Pluto you get deviations of 8.7 and 37.7 AU respectively.
Alternatively, if you match 38.8 to Pluto, Bode's Law has no room for
Neptune.
Whichever way you do it, Bode's Law makes at least one major error
among the outer planets.
You're confused about the distinction between major and minor errors,
because you can't see the forest for the trees. Science is not
primarily about small details, but rather it is about large concepts.
The small details are merely vehicles we use to eliminate the chance of
making mistake in our large concepts. To understand science, you've got
to have both under control, but the two are *not* of equal importance.
One is a great gift, and the other is a necessary evil.
So are you saying that failing to predict Neptune is a minor error?
--John Park
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
17 Sep 2007 06:31:43 AM |
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(John Park) wrote in
news:fcjks5$d7r$1@theodyn.ncf.ca:
John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
(John Park) wrote in
news:fcgivs$n5l$1@theodyn.ncf.ca:
John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
My rhetoric about hand waving arguments vs. mathematical arguments
is the same one I made in my previous post about being unworthy men
not being fit to kiss the boots of giants like Herschel, Tombaugh
and Le Verrier.
Which, as I said, I ignored.
This mistake is made by mediocre scientists across the world. You
can't ignore the giants of history, because history is as great a
force for science as science is a force for history. While you're at
it, just go ahead and ignore Newton, Hamilton, Jacobi and Lagrange.
Thhen get some eye of newt and cast some magickal spells, instead of
applying Occam's Razor or Aquinas' Dialectical Method. Just throw
Socratic logic out the window, too.
Dont'cha get it? Solving equations is only half the battle, and the
other half is understanding the great works of the supreme thinkers
that have gone before, which you must learn to quote by name. "The
reason we see so far is because we stand on the shoulders of giants."
You can't just topple that sort of edifice on a whim and expect to
be taken seriously. That's how the Einstein deniers think. ?:(
With only about six degrees of freedom, two or three major errors
among its predictions don't make for a brilliant success--though
for such a simple relation its result are intriguing.
There are no major errors; all the errors are minor, and well
accounted for by the mathematics.
???
The last few predictions of Bode's Law are: 19.6, 38.8, 77.2 AU.
The 19.6 fits Uranus at 19.2. But if you match the next two to
Neptune and Pluto you get deviations of 8.7 and 37.7 AU
respectively. Alternatively, if you match 38.8 to Pluto, Bode's Law
has no room for Neptune.
Whichever way you do it, Bode's Law makes at least one major error
among the outer planets.
You're confused about the distinction between major and minor errors,
because you can't see the forest for the trees. Science is not
primarily about small details, but rather it is about large concepts.
The small details are merely vehicles we use to eliminate the chance
of making mistake in our large concepts. To understand science,
you've got to have both under control, but the two are *not* of equal
importance. One is a great gift, and the other is a necessary evil.
So are you saying that failing to predict Neptune is a minor error?
That's the second time you've said it, and I don't know where you get
that from. It successfully predicted Neptune, just fine.
http://en.wikipedia.org/wiki/Le_Verrier
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| User: "John Park" |
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| Title: Re: Jeez, that was close |
17 Sep 2007 10:38:19 AM |
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John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
af250@FreeNet.Carleton.CA (John Park) wrote in
news:fcjks5$d7r$1@theodyn.ncf.ca:
The last few predictions of Bode's Law are: 19.6, 38.8, 77.2 AU.
The 19.6 fits Uranus at 19.2. But if you match the next two to
Neptune and Pluto you get deviations of 8.7 and 37.7 AU
respectively. Alternatively, if you match 38.8 to Pluto, Bode's Law
has no room for Neptune.
Whichever way you do it, Bode's Law makes at least one major error
among the outer planets.
You're confused about the distinction between major and minor errors,
because you can't see the forest for the trees. Science is not
primarily about small details, but rather it is about large concepts.
The small details are merely vehicles we use to eliminate the chance
of making mistake in our large concepts. To understand science,
you've got to have both under control, but the two are *not* of equal
importance. One is a great gift, and the other is a necessary evil.
So are you saying that failing to predict Neptune is a minor error?
That's the second time you've said it, and I don't know where you get
that from. It successfully predicted Neptune, just fine.
Its prediction of the orbital radius is off by nearly 30% and the
corresponding value for Pluto is off by nearly a factor of 2. Or, if you want
good agreement for Pluto, you can't have Neptune.
--John Park
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| User: "John Schutkeker" |
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| Title: Re: Jeez, that was close |
17 Sep 2007 03:38:43 PM |
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(John Park) wrote in
news:fcm71b$q4s$1@theodyn.ncf.ca:
John Schutkeker (jschutkeker@sbcglobal.net.nospam) writes:
(John Park) wrote in
news:fcjks5$d7r$1@theodyn.ncf.ca:
The last few predictions of Bode's Law are: 19.6, 38.8, 77.2 AU.
The 19.6 fits Uranus at 19.2. But if you match the next two to
Neptune and Pluto you get deviations of 8.7 and 37.7 AU
respectively. Alternatively, if you match 38.8 to Pluto, Bode's
Law has no room for Neptune.
Whichever way you do it, Bode's Law makes at least one major error
among the outer planets.
You're confused about the distinction between major and minor
errors, because you can't see the forest for the trees. Science is
not primarily about small details, but rather it is about large
concepts.
The small details are merely vehicles we use to eliminate the
chance
of making mistake in our large concepts. To understand science,
you've got to have both under control, but the two are *not* of
equal importance. One is a great gift, and the other is a
necessary evil.
So are you saying that failing to predict Neptune is a minor error?
That's the second time you've said it, and I don't know where you get
that from. It successfully predicted Neptune, just fine.
Its prediction of the orbital radius is off by nearly 30% and the
corresponding value for Pluto is off by nearly a factor of 2. Or, if
you want good agreement for Pluto, you can't have Neptune.
We're going around in circles, and I've had enough, so this is good-bye.
It's frustrating tlking to people with no vision, but if it weren't for
that it wouldn't be so easy to get good publications.
I'll tell ya, I just don't understand people who are afraid to discuss
their insights in public, for fear if having their ideas stolen. I get
so much resistance from supposed professionals that I lost that fear
long ago.
The only reason to post here is for the privilege of thinking out loud,
because the only replies I ever get are bitter arguments. Have a good
life Mr. Park, and don't darken my doorstep anymore. I can find more
entertaining ways to waste my time.
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| User: "Quadibloc" |
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| Title: Re: Jeez, that was close |
14 Sep 2007 08:59:42 PM |
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John Schutkeker wrote:
I was trying to find an equation for the following succession of powers
of '2', (0,1,2,4,8,16, 32,64,128,256). As you can see, the problem is
with the first two items in the list, '0' and '1', because '0' is not
strictly a power of '2'. I believe that anyone who can do that, will be
able to publish at least a letter, because it's relevant to an important
problem in physics and astronomy.
There are some trivial solutions. Since the real series of powers of
two, for which there is a simple equation, would bt (1/2, 1, 2, 4,
8...), you could have as your equation:
ceil(2^(i-2)-(3/4))
But I'll assume that the use of ceiling and floor functions and the
like is considered "cheating".
You have ten numbers there. That means you can fit a ninth-degree
polynomial to them if you want a real mathematical formula.
If you've found a non-trivial solution, of course, it is indeed a pity
if it has been lost.
John Savard
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