Saturday, December 27, 2014

Johannes Kepler: an anniversary

Johannes Kepler was born prematurely near Stuttgart on 12/27/1571. His grandfather was a mayor of their town but once Johannes was born, the family's fortunes were already dropping. His father was a mercenary and left the family when Johannes was five. His mother was a healer and a witch which has also led to some legal problems.

Johannes was a brilliant child with early inclinations to astronomy. In Graz (1594-1600), he was defending the Copernican heliocentric system. At that time, there was no clear difference between astronomy and astrology. Therefore, Kepler also invented the ADE classification of planets orbiting the Sun. ;-) This attempt resembled, but was not identical to, Garrett Lisi's hopeless attempt to unify. Kepler also wrote that the Universe had to be stationary.

In 1600, Kepler finally met Tycho Brahe in Benátky nad Jizerou (see the picture), a central Bohemian town where Brahe built an observatory. Brahe quickly recognized Kepler's magic theoretical powers.

Their negotiations about the new Kepler's job in Prague were accompanied by arguments and tension. Fortunately for the Czech capital, Kepler had more serious problems with Graz where they expected him to convert to Catholicism. Finally, Kepler moved to Prague, including his family.

He became the imperial mathematician of our monarchy, an advisor to Emperor Rudolph II, a predecessor of Václav Klaus and a great sponsor of arts and sciences pictured above, and 11 most productive years of Kepler's life were just getting started. Kepler was also giving his political recommendations to the empire although his common sense was more instrumental than the stars.

In Prague, Kepler established modern optics (he understood geometry of lunar shadows, the inverse-square law controlling the light intensity, and other things). In 1604, he started to observe SN 1604, a supernova also known as Kepler's star, in the constellation Serpentarius, the 13th sign of the zodiac in which your humble correspondent was born. Click at the link and see Kepler's beautiful drawing of Ophiuchus, as the constellation should now be called. It started to be clear to him that the heavens were not as constant as Aristotle used to think.

Kepler's laws

In 1602, Kepler discovered the law that we derive from the conservation of the angular momentum these days. He had a somewhat strange, non-Newtonian interpretation of it: the Sun provides the planets with motive power that decreases as they get further from the Sun which means that when the planets are far away from the Sun, they move more slowly. ;-)

Tycho's very accurate data about Mars were very important for Kepler.

After 40 years of failed attempts, Kepler finally got the right idea about the shape of the orbit in 1605. Why didn't he think about the ellipse - the shape dictated by his first law - earlier? Because it was too simple and Kepler thought that the astronomers would have figured out such a solution a long time ago if it were correct. This story hides at least two general lessons.

The first lesson is that it is sometimes easier to learn important insights from examples that are not the simplest ones because their patterns are sharper, more visible, and more characteristic and they cannot be confused with others. The simplest cases and solutions often look too singular and their modest internal structure is a bad starting point for generalizations. More complex examples typically "pinpoint" the right general law or algorithm uniquely or almost uniquely.

The second lesson is a sociological one. While it may be more likely that a simple solution should have already been found by others, they may have overlooked it, too. And if they did, such a simple solution might be much more valuable. I think it follows that scientists shouldn't ignore a topic just because it was found uninteresting or unrealistic by many others.

On the other hand, you are never guaranteed to succeed. If you attempt to do something simple that has been tried by many others, you are less likely to find something new, especially if you are less gifted than Kepler.

Kepler realized that the Mars data agreed with the ellipse beautifully and he has abruptly and correctly deduced that all planets had elliptical orbits even though he couldn't have done the numerical calculations for all the planets (he had no postdocs and grad students). In 1610, Kepler also had a healthy and friendly exchange with Galileo Galilei, supporting his discovery of the moons and helping him and others to improve the telescope.

The last law of planetary motion I didn't mention was the third one: the orbital times squared are proportional to the distances cubed. Kepler included this law as an example of the harmonies that the Creator used to decorate the heavens.

Religious tension in Prague

Unfortunately, politics slowed the progress down in 1611. Rudolph II became seriously ill - and died in 1612 - and his brother Matthias who was 5 years younger and who was already controlling Austria, Hungary, and Moravia was able to grab the kingdom of Bohemia, too. This, of course, meant a dramatic decrease of the influence of so-far-dominant Bohemia within the Holy Roman Empire. It also meant a dramatic weakening of the conditions to do research in Prague (and elsewhere, for that matter). While Matthias confirmed Kepler's job and salary, he allowed him to leave for Linz, Austria. In Linz, Kepler was teaching at the district school and he was calculating the year of Christ's birth.

That was a pretty bad development for science. At least, Kepler's second marriage was much happier than the first. However, his writing got much less quantitative than during the golden years in Prague. It became somewhat astrological and similar to his early years. A monument to Brahe and Kepler at the picture above is in Prague 6, Pohořelec, a former place of another observatory of Brahe near the Prague Castle.

Vladimir Fock died on December 27th, 1974.

Jacob Bernoulli

Another guy who was born on December 27th was Jacob Bernoulli, namely in 1654. His parents wanted him to do theology but he preferred mathematics and astronomy. The Bernoulli numbers that appear in Martin Schnabl's solution to string field theory and elsewhere belong among his discoveries. However, you should be careful: there were 8 good mathematicians and physicists in his family. For example, the laws of hydrodynamics and aerodynamics are due to Daniel Bernoulli.

Deja vu.


  1. Teflon tape wrapping screw threads prevents galling (metal-metal bonding at friction-cleaned surfaces). Mount and dismount are easy, threads stay smooth. Screw couplings need compliant thread fill against leaks. Silver plated Swagelok VCR female nuts are lubricious, self-aligning, and exert no torque. Teflon in aluminum couplings can explode when tightened, ΔHf AlF3.

    The ellipse story is illustrative. Falsify GR spacetime geometry with geometry. Solid single crystal test masses, right-handed space group P3(1)21 versus left-handed space group P3(2)21 alpha-quartz, violate the Equivalence Principle by ~0.5 ×10^(-12) relative (Eötvös experiment, 100X signal/noise). No prior observation is contradicted. String theory is updated, then triumphs. Do it.

  2. Bullshot CrummondDec 27, 2014, 5:49:00 PM


    The seasons greetings, revellers! :)

    A Fun(?) Question For The Instinctive Physicist, AKA The Vulgar Mechanick, e.g. the physicist who is still suitably seasonally sozzled.

    A cable drum consists of a central cylinder with two discs of the same size attached coaxially, one at each end. The radius the cylinder is less than the radii of the discs. For the sake of argument say the radii of the discs is twice that of the drum. The precise dimensions are unimportant so this could just as well be a simple cotton reel. A light thread or whatever is wound around the cylinder a few times and the drum is placed stationary on a horizontal plane with some length of the thread laying flat on the plane. The coefficient of friction between the drum and plane is nonzero.

    The end of the thread is then gently pulled in a horizontal direction (as it comes off the drum). There are two cases: the thread unwinds from (a) the top of the cylinder, and (b) from underneath.

    Your task, should you wish to accept it, is: describe the motion in each case.

    It is strictly verboten to use the higher parts of your brain in answering this. Anyone caught doing so will be sold as a galley slave and doomed to spend eternity oaring and whoring on a Green Piss trireme where the wimmin are extraordinarily plug fucking ugly. OK, just kidding. But please try this with your layman's hat on first. That is, don't start jiggling mentally with force diagrams etc; just do it instinctively.

    Then do it with your pens out if necessary. Experimentalists may wish to repair to their benches for a final check. :)

    Do your answers differ? I'd be interested to know.

    Of course, it doesn't take much to work out what the motion should be, but that's not the point.

    For what it's worth I noticed this by pure fluke with an actual toy when I was winding my dog up. It surprised me on two levels. Firstly the simple fact of its motion, and secondly it surprised me that I could be surprised by such a simple thing. I thought I'd just about seen everything (e.g. as a boy I was always making things) or rather I thought I should just know instinctively what would happen at this super-simple level. Well, clearly I hadn't, and didn't. I screwed up!

    By the way, you can see me in action here:

    Tally ho!

  3. " . . . an example of the harmonies that the Creator used to decorate the heavens."

    Nice turn of phrase.

  4. Right. Teflon tape enables reproducible mating pressure of the two sealing surfaces and it works irrespective of the materials chosen for the male and female threads.

  5. Standard bronze and brass are highly resistant to galling already, though more exotic stainless steel is not.

  6. In other words, it's not really needed. Just tighten it with a normal wrench and you are good to go since you are not strong enough to over tighten it. If you needed "reproducible mating pressure" you'd use some grease and a torque wrench, but you don't need that.

  7. Really? Between Kepler writing the first science fiction novel, his ideas about the Sun radiating energy pushing the planets and marrying 20 something when he was 40 something, all that comes to minds here is screws, threads and wrenches?
    Disappointing lack of imagination!

  8. Also, I'm still confused by how nearly macroscopic chemical chirality that exists only due to the several angstrom wide geometry of the overall molecule or crystal would be a valid probe of spacetime geometry, even though it can affect how circularly polarized light interacts with it. A very large molecule can be chiral by merely twisting over itself over a large drawn out area and if extended outwards at the edges it could become as big as your hand and I'm not sure if my hand will test spacetime geometric asymmetry or if spacetime asymmetry is really 3D geometric is the same sense as my hand or a molecule is. Much of this is because I'm not a physicist by training nor by temperament. Suggesting

    Eötvös merely invokes a torsion balance being used to equate gravitational mass with inertial mass, and I don't see why even in theory the tinkertoy geometry of atoms would affect that. With an overall chiral crystal, I mean what direction would you orient it for maximum theoretical affect? Is there really any theoretical affect at all or do you need a better physical probe like a chiral neutron star or something? Your ongoing suggestion of an effect is usually overly cryptic.

  9. The sun pushing the planets, affected by the stars I was recently exposed to from a free audiobook of Pliny the Elder who wrote of it two thousand years ago, but I note he expressed a consensus that the Earth was a sphere, albeit at the center of things based on some hand waiving. His prose wanders widely and abruptly between what logic was able to divine from observation and truly bizarre sounding hypotheses to explain what could not be figured out, including dramatic human fate. He also added many observations that were just anecdotal superstition.

    About screw threads, my point was a psychological one, about how having a rebellious instead of presumptive temperament is good for science to encourage, lest it continue to take decades for Scotch Tape to be used to discover graphene all the while transmission electron microscopes have been common since the 1950s. I know since I found an old copy of a volume of Encyclopedia Britannica on the street and was shocked at how advanced it was, and though the Internet *should* have it beat, it actually puts Wikipedia to shame with over twenty pages of equations and very detailed optical diagrams! The "designed by committee" nature of Wikipedia ruins it.

  10. Lubos, you've delivered one of the best and succinct accounts of Kepler's astronomy/physics I've seen to date.

    Slightly, but only just, OT: Kepler, Galilei, Newton, Jacob Bernouilly, John von Neumann, and more than a handful of other mathematical geniuses are winter babies whose DOB's frame the NH winter solstice. I've always felt that people born in December-January share quite a few personality traits. I won't go into these aspects here, tempting as it may be, but I bet I can identify winter solsticers quite easily when I see them or even when I get to know them from a physical distance in space and time.

    I always felt (but couldn't prove, of course) that these traits would probably be related to season-driven environmental effects that the mothers of December-January babies are exposed to during pregnancy. And these astronomy-driven Northern Hemispherical personality differences appear to be able to balance off genetically driven behavioral and physical features to some not unimportant degree, as well. NH winter babies seem to grow up to at least partially identifiable adults. ;-) And some of them apparently turn out to be mathematical wizards and sporting bigger heads as well... The corollary of all this would be that summer babies could be expected to exhibit other characteristics.

    And apparently people have been studying this astronomy-cum-uterus phenomenon in a rational way as reported here on an ancient (pre-2006) study from Harvard:

    If nothing else will ever come out of this but anecdotal observations of Capricorns and their ilk, it's alway fun to observe winter solsticers. ;-)

    Let me add, for the sake of completeness, that both the man behind TRF and the writer of these lines are winter babies - born 5 December and 9 January, respectively. ;-)

  11. It is interesting to note that even with Kepler's and Galilei's achievements geocentrism did not die in the mainstream scientific community until 18th century with its triumph of Newtonian planetary mechanics and new observations of stellar abberation. Besides the problem of star parallax was resolved only in 1838 when it was finally observed by Bessel (yeah, Bessel of Bessel functions)
    Also there was opinion (though I'm afraid I can't say right now who it was exactly) that Tychonic type models and heliocentrism give the same astronomical predictions. So they are observationally indistinguishable and there is no issue to discuss. If you are not interested in dynamics it is a fair point. But not if you understand "observers at rest" as "inertial observers".
    That reminds me a bit of Bohmian mechanics proponents. They reach similar predictions in the specific case and claim that it is as good as proper quantum mechanics. However any step from that specific case is fighting with their construction and renders it meaningless. And similarly they don't want drop it because of prejudices of classical thinking.

  12. Overall, the fact that Lumo was not mentioned in Huffington Post list of 34 physicists to follow on Twitter is probably a good thing.

    Surprisingly, Wikipedia entry on Kepler second marriage : "He eventually returned to Reuttinger (the fifth match) who, he wrote, "won me over with love, humble loyalty, economy of household, diligence, and the love she gave the stepchildren"

    hasn't attracted feminist ire yet.

    I mean, if I were single, 23 year old with such qualities, I would propose her in a heartbeat.

  13. Are you talking about the tapered threads below the stop valve where it threads into the tank?

  14. Interesting. Thanks for your thoughts and link.

  15. So Kepler discovered the Holographic Principle because he found out the inverse-square law of light intensity.

  16. Newton was big on astrology, too, so give Kepler a break. Also, surveys have repeatedly shown that 40% of the members of the US National Academy of Sciences believe in some sort of God, probably of the deist kind, like Einstein (?). This reportedly falls to 4% among biologists, so Darwin is the great enemy of superstition.

    Speaking of Darwin, while almost every biologist accepts his theories of natural, sexual and kin selection (but note Margulis and Gould), a significant fraction of other scientists do not. They get hung up on the probablistic aspect and don't see the selection aspect.

    Of course, essentially no one in the humanities and pseudo-sciences accepts human evolution by natural selection.

  17. I suspect at least the biologist numbers suffer from US-centricism. Anti-Darwin views are less common among religious people elsewhere, so there is less reason for biologists to scoff at religion.

  18. Sad. I am used to encountering the Educated lawyer and other non-scientist who are so ignorant. But more troubling numerous physicians here are fundamentalist Christians
    If they had studied the sciences instead of praying And listening to their God delusion and his illegitimate son as savior,perhaps they would save some real lives instead of imaginary souls.

    Of course, what do you call the student who graduated at the bottom of his medical school class?
    The situation won't likely be fixed even though. After all we can't throw them in jail for their stupidity and incompetence. Probably because what we call those that graduated at the bottom of the law school class.
    Your honor

  19. Every quartz atom is in an "infinite" threefold helix parallel to the crystallographic c-axis along the entire crystal's length. The helices are two-fold intertwined in a trigonal grid when viewed normal to c. Quantitative geometric chirality is calculated CHI = 1, DSI = 0, COR = 1, that being maximal in any number of dimensions,

    J. Math. Phys. 43(8) 4147 (2002), DOI: 10.1063/1.1484559

    J. Math. Phys. 40(9), 4587 (1999), DOI: 10.1063/1.532988

    If spacetime has trace chiral anisotropy (a left foot), sourcing all Standard Model curve fits, then opposite shoes fit with different energies. They vacuum free fall along non-identical minimum action trajectories, exhibiting EP violation. That is what torques the torsion pendulum. There is no preferred direction. They fall at trace different speeds as the Earth inertially spins and gravitationally orbits the sun,

    Class. Quantum Grav. 29, 184002 (2012); doi:10.1088/0264-9381/29/18/184002, arXiv:1207.2442

    Trace breaking perfect spatial isotropy allows Noether's theorems to leak conservation of angular momentum. "Dark matter" is Milgrom acceleration. Chiral geometric experiments are wholly outside physics' founding postulates. There is no defense against them. As with Euclid vs. Bolyai or Dirac vs. Stern, what is obvious and necessary need not be complete. When "anomalies" arise (cartography for Euclid), ya gotta look. Stern demonstrated the Dirac equation failed, big time. surprise

  20. I think you are talking about the situation in the USA. I think you will find that most physicians elsewhere more or less replicate the situation amongst most scientists about religion. The majority are either non-believers or indifferent. You are in Germany? It must be similar there. Even in France, the churches are mostly empty except for music events.

  21. Both Lynn Margulis and Steve Gould were ardent supporters of Natural Selection. Lynn Margulis criticised aspects of Neo-Darwinism, and Gould had his theory of punctuated equilibrium as a mechanism OF natural selection and Darwinism. The idea that they rejected natural selection was hyped by creationists and misguided journalists.

  22. Hmmm "US-centrism"---hey, what else is there? :)

  23. Thing is, I started to note this weird winter baby-summer baby thing already in high school. My then girlfriend said she thought I was a "Capricorn" after speaking to me for a couple minutes, first time we met. But she also knew that astrology was a no-brainer and low-brow stuff so I had no problem with her views. (Well, she was a really smart sweetie pie so it wouldn't have mattered anyway...)

    Since she was able to identify lots of people unknown to her in this way I understood that there could be some "seasonal-nutrional foetus-stage factor" at work here to create these possibly systematic differences between people. And the Harvard data seem to bear this kiddie "theory" out. :)

  24. Thing is if she got your astrological sign wrong she would have said that your ascendant is stronger or that your ascendant cancels your main astrological sign ;-). Anything to get you to buy her a drink right ? ;-D

  25. According to:

    24% are Catholics, while according to:

    "In the 1950encyclical Humani generis, Pope Pius XII confirmed that there is no intrinsic conflict between Christianity and the theory of evolution, provided that Christians believe that the individual soul is a direct creation by God and not the product of purely material forces."

    It would follow that mostly Protestants (41%) are responsible for the situation in the US?

  26. Catholic Church view of evolution, ahem, evolved, while Protestants need a Pope, hehe.

  27. :-D
    But please note that I said she was a sweet, sexy, smart chick who knew that astrology is BS. She knew just as little about "the zodiak" as I did. ;-)
    But still was able to identify me as a winter baby. This is low precision ID but quite enough if we are to believe the Harvard data.
    PS: She got much more than a drink from me.

  28. You could not be more wrong. Margulis clearly thought natural selection was secondary. See her interview here:

    She thought that symbiosis was the major driver. Moreover, she rejected the modern taxonomic classification system based solely on 16/18S RNA and preferred to use Whitaker's Five Kingdom system enhanced modiified by RNA data.

    And much of Gould's writing was aimed at undermining natural selection. His (and Eldridge's) theory of punctuated equilibrium has been interpreted as meaning that natural selection prevents evolution, that evolution occurs when selective pressures are minimized after mass extinctions.

    Gould ended his career in bad odor among biologists. He is also convicted of outright scientific fraud in the case of "The Mismeasure of Man." In that book, he castigates an earlier scientist for using the standard error of the mean when comparing means and claimed that the sample standard deviations should be used instead. An outright lie. Moreover, the skulls in question were remeasured recently by another group of biologists, and they concluded that the earlier scientist criticized by Gould got it right, and Gould's own measurements were fabrications.

    Gould, like his friend and colleague Lewontin, was a Marxist who let his ideology determine his science.

    Margulis was and is (now deceased) a respected scientist who is famous for resurrecting the symbiosis theory of cellular evolution. Her de-emphasis of natural selection as a source of biological innovation is defensible if not the current consensus. Ah, that word again.

    Neither person denied evolution, but also neither person supported the idea that natural selection drives it.

    Creationists and Intelligent Design advocates are part of New Age anti-science and superstition and can be ignored.

  29. Creationism is just one aspect of the religous delusion. I have a problem with cognitive dissonance not precluding attention to some sexually maladjusted old man in Italy who may pronounce that one can reconcile fantasy and truth as you describe. The same and more of course for evangelicals who teach their children that earth is 6k years old and that dinosaurs walked aside man.

  30. Kepler, like all his other contemporaries, 'knew' that the heavens were only made of perfect circles. To think outside this box - which looks trivial today is the reason that he did not consider ellipses. Ref:, etc. Its not easy to see outside the box - except in hindsight.

  31. So, in what century will we have a President who dares declare himself at least agnostic?

    I think we will have a practicing Muslim sooner than that.

  32. Pope is also supposed to go big on Climate Change:

    More modern witch hunt.

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