The Clock That Wasn’t

Yesterday, The Independent reported on astronomers discovering the first known disappearing planet.¹ TOI-2535 b, a gas giant orbiting its star every 8.236 days, has been observed by NASA’s TESS space telescope since 2019. In the seven years since, its transits became progressively shorter and shallower, until they stopped appearing altogether. The planet seemed to have vanished.²

»Poincaré had entered the competition to demonstrate mathematical order. His corrected proof became one of the founding texts of chaos theory«

It hadn’t, of course. A neighbouring planet was pulling on its orbit, gradually tilting its orbital plane until, from Earth, it no longer passed in front of its star. It’s expected to become visible again in 30 to 50 years.

Nothing had disappeared but the signal: the small, periodic dip in starlight as the planet passed in front of its star. Mathematician and philosopher Alfred North Whitehead called the confusion of an abstraction with the concrete reality it represents the »fallacy of misplaced concreteness«.³ The planet hadn’t vanished; it had simply ceased to be visible by our method of observation.

But the discovery raises a much older question. Explaining the result, the study’s lead author Samuel Yee remarked: »We think of the universe as resembling clockwork, where everything is regular, but that’s not true.«⁴ The clockwork universe is more than a metaphor.

Newton doubted that gravity alone could keep the planetary system stable indefinitely. He thought gravitational disturbances might accumulate, eventually requiring divine intervention to restore order.⁵ Laplace later showed that the planets’ gravitational pull on one another caused only limited changes to their orbits, rather than disturbances that grew indefinitely. The solar system, it seemed, was self-regulating: the clock no longer needed a clockmaker. Asked by Napoleon where God fitted into this picture, Laplace is said to have replied: »I had no need of that hypothesis.« That may be an apocryphal exchange, but it captures the confidence of the new mechanics.

And then came a Swedish king.

In 1885, King Oscar II established an international mathematical competition, offering 2,500 kronor and a gold medal for solutions to four difficult problems. The most ambitious concerned the gravitational interactions of multiple bodies: could their movements be described by mathematical series that remained valid over arbitrarily long periods? Henri Poincaré, then one of Europe’s most brilliant young mathematicians, submitted a memoir on the problem (the older term for a formal scientific paper). He won.

There was a complication. While his memoir was being prepared for Acta Mathematica, the journal’s sharp editorial assistant, Edvard Phragmén, began questioning the proof, and Poincaré realised he’d made a serious error. On 30 November 1889, he telegraphed the journal’s editor, Gösta Mittag-Leffler, telling him to stop the presses.

The already-distributed copies were recalled and the edition destroyed. Poincaré rewrote the memoir, paying more than the prize money for the reprint.⁶ The correction changed everything. He had assumed that the mathematical surfaces describing the system’s possible motions fitted together neatly, enclosing a bounded region. Instead, he found that they could intersect repeatedly, producing an intricate tangle of trajectories. Even the relatively simple restricted three-body problem could be chaotic, its behaviour sensitive to initial conditions and fundamentally difficult to predict over the long term.

Poincaré had entered the competition to demonstrate mathematical order. His corrected proof became one of the founding texts of chaos theory.

This didn’t mean the solar system was about to fall apart, or Newton’s laws had stopped working. Deterministic laws do not guarantee regular cycles. A system can obey exact equations and still run on several clocks at once.

TOI-2535 b illustrates this. Its eight-day orbit appeared regular, but beneath it lay a much slower cycle: the gradual tilt of its orbital plane. The observations weren’t wrong. They captured one timescale and missed another.

The same geometry explains why solar eclipses don’t occur every month. The Moon’s orbit is tilted about five degrees relative to Earth’s around the Sun. Most months, it passes above or below the Sun from our viewpoint. An eclipse occurs only when the three bodies align.

Poincaré showed that the universe could obey precise laws and still defy prediction. TOI-2535 b shows that even its regularities can escape us. The universe keeps its own time.

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