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ary orbits from the very beginning he didn t revert to it because he discovered that his model gave less successful predictions when compared against ptolemy s enter tycho brahe in the decades following copernicus others took interest in the solar system tycho brahe for example constructed the best naked eye astronomy setup in history measuring the planets as precisely as human vision allows to within one arc minute 1 60th of a degree during every night that planets were visible toward the end of the 1500s while tycho s models fell out of favor almost immediately offering no improvement over copernicus or ptolemy his data was top notch we get no explanation of tycho s geo heliocentric model whatsoever why waste words explaining a system that was never adopted i come across this and similar claims about tycho s system fairly often always from people who have never bothered to research the history of seventeenth century astronomy in reality following the collapse of a pure geocentric model following the telescopic discoveries at the beginning of the second decade of the seventeenth century tycho s model rose to become the dominant model of the cosmos and remained so until about 1670 not really almost immediately enter johannes kepler taking advantage of it his assistant johannes kepler attempted to make a glorious beautiful model that fit the data more precisely than ever given that there were six known planets if you included the earth as one of them and exactly five and only five perfect polyhedral solids the tetrahedron cube octahedron icosahedron and dodecahedron kepler constructed a system of nested spheres that supported the solar system a model he called the mysterium cosmographicum source wikimedia commons kepler s mysterium cosmographicum was written and published four years before he moved to prague to work with tycho and so was not in any way based on tycho s data it was not a model of the orbits at all and so did not fit the data more precisely than ever it was an explanation of why there were only six planets in god s mathematical cosmos which merely gave the relative distances between the planets in that it was only an approximate fit in fact he went to prague to attempt to get the data to determine the exact sizes of the orbits in order to fine tune his model ethen now tells his readers kepler formulated this model in the 1590s and brahe boasted about the quality of his own work that only his observations could put such a model to the test but no matter how kepler did his calculations not only did disagreements with observation remain but ptolemy s geocentric model still made superior predictions kepler s model made no predictions whatsoever so ptolemy s couldn t be superior ethan again in the face of this unsuccessful confrontation with the data what do you think kepler did did he tweak his model attempting to save it did he distrust the critical observations demanding new superior ones did he make additional postulates that could explain what was truly occurring even if it was unseen in the context of his model kepler s model made no predictions so none of the above was in any way relevant however ethan continues to spin his fairy tale that s what most of us when we find ourselves in a similar situation typically resort to by default but much to his credit kepler did none of these instead he did something revolutionary he put his own ideas and his own favored model aside and looked at the data to see if there was a better explanation that could be derived while demanding that any model needed to agree and agree better than ptolemy s prevailing model did with the full suite of observational data as we know kepler did not put his own ideas and own favoured model aside but instead took up a task to which tycho had appointed him to determine for the first time the dimensions and shape a of a planet s orbit namely mars ethan waxing poetically if only we could all be so brave so brilliant and at the same time so humble before the universe itself kepler calculated that ellipses not circles would better fit the data that brahe had so painstakingly acquired although it defied his intuition his common sense and even his personal preferences for how he felt the universe ought to have behaved indeed he had previously stated that the mysterium cosmographicum was a divine epiphany that had revealed god s geometrical plan for the universe to him kepler was successfully able to abandon his notion of circles and spheres and instead used what seemed to him to be an imperfect solution ellipses however according to ethan we can still criticise the saintly johannes it cannot be emphasized enough what an achievement this is for the good of science yes there are many reasons to be critical of kepler he continued to promote his mysterium cosmographicum we even though it was clear ellipses fit the data better he continued to mix astronomy with astrology becoming the most famous astrologer of his time and he continued the long tradition of apologetics claiming that ancient texts meant the opposite of what they literally said in order to reconcile the acceptability of the new knowledge that had emerged but it was through this revolutionary action of abandoning his model for a new one that he himself devised to explain the observations more successfully than ever before that kepler s laws of motion became elevated to scientific canon as we will see he did a lot more that continuing to promote his mysterium cosmographicum and his discovery of the elliptical had no effect on it for a very good reason the mysterium cosmographicum assumes circular orbits because that was the norm but they don t play any form of significant role in the book and he doesn t determine them in any meaningful way the practice of astrology is a stick that all presentists such as ethan use to beat the early modern astronomer all astronomers at the beginning of the seventeenth century including galileo were practicing astrologers and i don t think kepler was regarded as the most famous astrologer of his times i have absolutely no idea what ethan is trying to say with his last point ethan now closes with great pathos but the greatest achievement of all came on the day kepler threw out his own idea of a mysterium cosmographicum my emphasis an idea that he was arguably more emotionally attached to than any other in order to follow the data no matter how far from his preferred solution it led him that brought him to elliptical orbits for the planets which kicked off a revolution in our understanding of the physical universe around us the revolution of the modern sciences of physics and astronomy which continue to the present day like all scientific heroes kepler certainly had his faults but the ability to admit when you re wrong to reject your insufficient ideas my emphasis and to follow the data wherever it leads are traits we should all aspire to it s one lesson that we should take to heart not only in the realm of science but in all aspects of our lives let us examine all that ethan gets wrong to reiterate mysterium cosmographicum is not a new astronomical model to replace either ptolemaeus or copernicus and contains no models of planetary orbits in the first instance it explain why the cosmos created by kepler s god who is not just mathematical but is mathematics incarnate only has six planets secondly by placing the platonic solids in between the orbits it explains the relative distances between those orbits the mysterium cosmographicum was an introduction to kepler s to our modern way of thinking bizarre cosmology constructed out of astronomy astrology music mathematics and theology when kepler using tycho s data determined the orbit of the planet mars and in doing so established the first two of his laws of planetary motion he wasn t producing a replacement for his mysterium cosmographicum but rather creating what would eventually become an addition to it kepler s work on the orbit of mars took him six years and it was first published in his astronomia nova in 1609 one of the things that delayed this work was the production and publication of the work in which he revolutionised optic his astronomia pars optica published in 1604 in the period following the publication of his astronomia nova he became embroiled in the power struggles for the control of the holy roman empire the emperor rudolf ii was his employer it ended with him moving to linz as district mathematicus where he would remain until 1626 all of this time his actual official work was construction the rudolphine tables completed in 1623 but first published in 1627 throughout all of this kepler was plagued by problems financial domestic and not least the trial for witch craft of his mother to return to 1596 and the mysterium cosmographicum its full title is prodromus dissertationum cosmographicarum continens mysterium cosmographicum de admirabili proportione orbium coelestium de que causis coelorum numeri magnitudinis motuumque periodicorum genuinis proprijs demonstratum per quinque regularia corpora geometrica forerunner of the cosmological essays which contains the secret of the universe on the marvelous proportion of the celestial spheres and on the true and particular causes of the number magnitude and periodic motions of the heavens established by means of the five regular geometric solids the important word here is prodromus forerunner this is merely the introduction the main work was to follow in 1599 kepler stated his intention to write that main work his move to prague was to gain access to tycho s data which he needed to fine tune his cosmology as i have sketched above life and work got in the way and it was first in 1619 that he finally published that intended sequel to the mysterium cosmographicum his opus magnum harmonices mundi libri v the five books of the harmony of the world the original title from 1599 was de harmonia mundi books i ii deal with the two and three dimensional geometry of regular and semi regular polygons and polyhedra book iii is the application of his geometrical theories to music in book iv sees the application of his geometry to astrology and finally in book v he combines his geometry his music theory and his astronomy to show how the planets in their orbits create the celestial harmony those orbits of course obey his first two laws of planetary motion and here he discovers his third law the harmony law kepler didn t abandon his mysterium cosmographicum for his elliptical astronomy but rather built his elliptical astronomy into his mysterium cosmographicum if anyone still had doubts that the harmonice mundi was the perfection of the mysterium cosmographicum in 1621 kepler published an expanded second edition of mysterium half as long again as the first detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication at the very latest at this point ethan s central thesis explaining why johannes kepler was the greatest scientist of all crumbles to dust let us examine ethan s achievements as a wanna be historian of early modern astronomy he gets copernicus use of the deferent epicycle model for his planetary orbits totally wrong his almost non existent analysis of tycho s geo heliocentric model is horribly wrong his explanation of the purpose and content of the mysterium cosmographicum is total bullshit and he even claims that it is based on tycho s data although it was written and published four years before kepler even met tycho finally his grand central claim that kepler abandoned the mysterium cosmographicum to develop his elliptical astronomy is one hundred percent ahistorical hogwash ethan is all too typical of a certain type of scientist who think that they can do history of science without doing the necessary ground work and research he seems to think that his passing obviously superficial knowledge of early modern astronomy qualifies him to pontificate knowledgeably on the subject whereas in reality all he does is to display an almost total ignorance 3 comments filed under history of astronomy july 30 2026 8 58 am take it to the limit one more time a history of calculus ii according to legend the pythagoreans were devastated when they discovered that the diagonal of a unit square is an irrational number because they believed that the natural numbers were the building bricks of the cosmos it is even said that they murdered the man who made the discovery it wasn t just the pythagoreans who had difficulties with the existence of irrational numbers or incommensurable numbers as the greeks called them in their geometry taking our example of the diagonal of a square one can t measure it with a given fixed length so if the side of the square is 1 cm the diagonal cannot be measured by any rational multiple of 1 cm lengths one can t measure the one against the other the mathematician whose was credited with supplying a solution to this problem was eudoxus of cnidus c 390 c 340 bce he was born and died in cnidus on the southwest coast of anatolia none of his original works have survived although some fragments are preserved in the commentaries on the phenomena of aratus and eudoxus by hipparchus c 190 c 120 bce which is the only one of hipparchus works to survive according to diogenes laertius fl third century ce eudoxus was an astronomer mathematician doctor and lawmaker one should note that what little information we have about eudoxus as with most early greek mathematicians comes from sources written centuries after he lived he studied mathematics with archytas 435 410 360 350 bce a pythagorean and medicine with philiston of locri 4 th century bce both of whom lived in magna graecia i e southern italy at the age of twenty three he travelled to athens and spent two months attending the lectures of the sophists next he spent sixteen months in egypt studying mathematics and astronomy following further travels he returned to athens and is said to have he assumed headship of the academy during plato s absence later he returned to cnidus and became a politician in the history of science eudoxus is best known as the originator of the homocentric spheres model of the cosmos to explain the seemingly erratic observed motion of the planets further developed by callippus c 370 c 300 bce one of his students and then by aristotle 384 322 who is also said to have studied under eudoxus in the academy when it became together with aristotle s cosmology the standard greek model of the cosmos until replaced by the deferent epicycle model of ptolemaeus fl 2 nd century ce however what interests us here is eudoxus contribution to mathematics to find eudoxus contributions to mathematics we must turn to euclid s elements starting with book v the most of which is thought to be attributable to eudoxus here he helps the greek mathematicians to avoid the problem of irrational or incommensurable numbers early greek mathematicians did n...
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