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Lying on his deathbed in 1601, Tycho Brahe, the preeminent astronomer of his time, pleaded with his young mentee Johannes Kepler not to let his life’s work go to waste. At the dawn of the new century, the scientific community was torn between Ptolemaic geocentrism and Copernican heliocentrism, and Brahe had dedicated much of his career to reconciling the two in his eponymous astronomical model. In the Tychonic system, Brahe depicted the known planets revolving around the Sun which in turn revolves around a stationary Earth. Despite their disagreements over the role of the Earth as the centre of the Universe, all three models postulated that celestial bodies move along perfect circular orbits, in accordance with Aristotelian ideals.
The elaborate contraptions that ensued failed to impress Kepler. So, equipped with Brahe’s state-of-the-art observations of Mars and with no theoretical framework to tie him down, Kepler set out to discover a simpler way to describe the red planet’s orbit. Nearly a decade of persistent inquiry and countless wrong turns later, Astronomia Nova was published. In this monumental treatise, Kepler demonstrated that the three competing models were fundamentally flawed. Not only was the Earth just another planet orbiting the Sun (as Copernicus had suggested), but in a further blemish to the divinely ordained Universe, the orbits turned out to be elliptical.
Kepler’s discovery, neatly summarised in his three laws of planetary motion, stands as an unprecedented feat of distilling mathematical relations from data. Starting with Newton’s invention of calculus later in the century, the mathematical foundations of physics have been laid down, providing an ever-more extensive toolbox for describing experimental results. But even within the framework of modern physics, regression à la Kepler is no trivial task as it often involves considerable guesswork and intellectual leaps of faith, not to mention dead ends.
In his own words, Kepler went through no fewer than seventy repetitions of his calculations “at a very great loss of time”. However, the days of number-crunching and head-scratching may soon be over, thanks to a slew of recent advances in symbolic regression – a sub-field of machine learning. Where classical regression analysis seeks the optimal parameters in a given mathematical equation (such as the slope and intercept of a straight line) to fit a set of data, symbolic regression aims to create both the equation and parameters from scratch. By sifting through a vast catalogue of mathematical expressions and combining them to its artificial heart’s content, the algorithm eventually settles on an equation that best matches the data. One need not spend decades juggling equations to appreciate the implications for scientific discovery.
…To read the full article, head over to Issue 31: Science in the 22nd Century
Written by Mika Kontainen (he/him), a fourth-year MPhys Astrophysics student and the ex-head copy editor of EUSci.
