At the beginning of the seventeenth century, Johannes Kepler spent some five years grappling with the planet Mars. He held the finest astronomical observations recorded until that time: those of Tycho Brahe, a Dane who had measured planetary positions with the naked eye, without a telescope, using immense instruments and unparalleled persistence, achieving a precision of one or two arcminutes—a minuscule fraction of the sky. Kepler sought to fit the orbit of Mars into a circle, as two millennia of astronomy dictated. He almost succeeded. He was left with 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 about ten minutes: to 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 I find worthy of recounting.

He could not because the data were not his own, and they were too precise. He knew the extent to which Brahe had measured with care; he knew that an error of eight minutes was not possible for that observer. If his calculations diverged from the observations by eight minutes, the failure did not lie with Brahe: it lay in the theory. He wrote it himself: if he believed those eight minutes did not matter, he said, he would fix them with a minor adjustment. But he could not disregard them, because they came from Tycho Brahe, the most diligent of observers, and that gift compelled him to take them seriously. Over eight arcminutes, Kepler dismantled two thousand years of circles and constructed the first of his laws: planets move in ellipses.

The legend must be dismantled because the romanticised version distorts what is significant. Kepler did not see the eight minutes and leap to the ellipse in a flash. He struggled for years, tested dozens of figures, experimented with ovals, erred repeatedly, corrected the data for atmospheric refraction, and performed endless manual calculations. The ellipse was not hidden in the data, waiting for someone to read it. What the data did, through their precision, was to prevent the convenient falsehood from standing. They did not provide him with the answer; they removed the possibility of settling 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 always use them to reaffirm ourselves: we seek the figure that confirms what we already thought and discard as noise that which does not fit. Kepler did the rare, the difficult, what almost no one does: he treated the data that did not align not as a nuisance to be eliminated, but as the only part to be trusted. The eight minutes he was left with were not a defect in his calculations that needed to be masked. They were the planet telling him that his conception of the heavens was mistaken. He possessed the rare honesty to listen to the planet rather than to tradition, and to trust another’s work more than his own desire to be right.

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 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).