At the beginning of the seventeenth century, Johannes Kepler spent approximately five years grappling with the planet Mars. He possessed the finest astronomical observations ever conducted to that point: those of Tycho Brahe, a Dane who had measured planetary positions with the naked eye, devoid of a telescope, using immense instruments and unparalleled persistence, achieving a precision of one or two arcminutes, a minute fraction of the sky. Kepler sought to fit the orbit of Mars into a circle, as dictated by two millennia of astronomy. He nearly succeeded. He was left with an excess of eight arcminutes.
Eight arcminutes is a negligible quantity, one-sixth of the apparent diameter of the Moon, something no previous astronomer could have even detected. Ptolemy, fourteen centuries earlier, worked with a margin of error of approximately ten minutes: for him, those eight minutes would have been within the tolerable range, invisible, dissolved in the imprecision of his own measurements. Anyone with inferior data would have accepted the circle as correct and considered the problem resolved. Kepler could not, and the reason is what warrants recounting.
He could not because the data were not his own, and they were of exceptional quality. He understood the extent to which Brahe had measured with care; he knew that an error of eight minutes was inconsistent with the capabilities of that observer. If his calculations diverged from the observations by eight minutes, the fault did not lie with Brahe: it lay in the theory. He wrote as much himself: 'If I believed those eight minutes were of no consequence,' he stated, 'I would correct them with a minor adjustment.' Yet he could not disregard them, for they originated from Tycho Brahe, the most diligent of observers, and that gift necessitated that he treat it with gravity. Based on eight arcminutes, Kepler dismantled two thousand years of circles and formulated the first of his laws: planets move in ellipses.
The legend must be dismantled, for the romanticised version misrepresents what is significant. Kepler did not observe the eight minutes and immediately discern the ellipse in a flash of insight. He struggled for years, tested dozens of figures, experimented with ovals, erred repeatedly, corrected the data for atmospheric refraction, and performed endless calculations by hand. The ellipse was not hidden within the data, waiting for someone to interpret it. What the data achieved, through their precision, was to render the comfortable falsehood untenable. They did not provide him with the answer; they deprived him of the ability to settle for the false one.
Brahe’s precision did not serve to confirm what was already believed, which is what we usually desire good data for; it served the opposite purpose: to ensure that a discrepancy which anyone else would have swept under the carpet became impossible to ignore. The quality of a measurement is not judged by how often it confirms our views, but by how often it prevents us from continuing to hold them without merit. Precise data are inherently uncomfortable: they leave no room to conceal one’s own error.
We live surrounded by data, more so than any other era, and we almost invariably utilise them to reaffirm our existing beliefs: we seek the figure that confirms what we already thought and dismiss as noise that which does not fit. Kepler performed the rare, the difficult, the act that almost no one performs: treating the data that did not align not as a nuisance to be eliminated, but as the only portion to be trusted. The eight minutes he was left with were not a defect in his calculations to be obscured. They were the planet informing him that his conception of the heavens was erroneous. He possessed the rare integrity to listen to the planet rather than to tradition, and to trust the work of another more than his own desire to be correct.
He was not the solitary genius of legend. He was a man who inherited the meticulous work of another, fought with that man’s heirs for the right to use it, and instead of bending those data to his theory, he bent his theory to the data. It takes two for that: the one who measures with a patience bordering on obsession, and the one who refuses to ignore the small remainder that such patience lays bare. Neither, alone, would have found the ellipse. Science, when it functions, is typically that kind of debt between someone who observes well and someone who dares to believe what they see.
On the open conversation
This text departs from my usual subjects, but a notebook is also for what one finds marvellous. I recount a verified episode from the history of science, the discovery of the elliptical orbit of Mars, to reflect upon something I find highly relevant today: what we do with data that do not fit. I distinguish the documented fact from the legend surrounding it, which in this case distorts it significantly. If anyone wishes to contribute from the perspective of the history of science, astronomy, or epistemology, this notebook remains open.
Sources
Johannes Kepler, Astronomia nova (1609); on the eight arcminutes and the acknowledgement of Tycho Brahe (trans. William H. Donahue, New Astronomy, Cambridge University Press, 1992).
Owen Gingerich and James R. Voelkel, 'Tycho and Kepler: Solid Myth versus Subtle Truth', Social Research (2005).
Christian C. Carman, 'When Genius Met Data: Kepler’s First Exploration of Tycho’s Observations', Archive for History of Exact Sciences (2025).
James R. Voelkel, 'Publish or Perish: Legal Contingencies and the Publication of Kepler’s Astronomia nova', Science in Context (1999).
On the preservation of Tycho Brahe’s observation protocols: Royal Danish Library (1655 acquisition).