Chaos theory and the 2023 Tour de France

Jai Hindley is in the yellow jersey, and Jonas Vingegaard now looks like the favourite for the 2023 Tour title, after a chaotic and unpredictable day in the Pyrenees

‘Deterministic non periodic flow’ was the title of a paper by the American mathematician and meterorologist Edward Lorenz written in 1963, which was one of the most influential scientific papers of the 20th century. In it, he described how tiny, insignificant-looking variations in inputs to a nonlinear system could result in vastly different outcomes, as fluctuations magnified and cascaded through. In order to make the dense maths and equations comprehensible to the layperson, he came up with an image of a bird flapping its wings: “One flap of a seagull’s wings would be enough to alter the course of the weather forever,” he said. This was later tweaked into the evocative image of a butterfly flapping its wing and ultimately causing a tornado: the butterfly effect. This is also known as chaos theory.

Lorenz developed his theory after trying to duplicate a sequenced weather pattern on his computer. In order to save time, he started the run halfway through, and rounded down his numbers to the third decimal place. In the time it took him to make a cup of coffee and get back to his computer, the pattern had deviated so much from the original that the outcome had completely changed. Lorenz’s interest as a mathematician was the weather, which is a classic nonlinear system. Other examples of nonlinear systems are fluid dynamics, traffic flow and stock markets. And also: bike races.

The insignificant-looking rounding error that might have cost Tadej Pogačar the 2023 Tour de France came with somewhere around 136 kilometres of stage five between Pau and Laruns to go. A wheel was let go, and the effects cascaded through the day to result in an outcome that not many could have predicted, and would surely have been less dramatic had the stage been run in a more traditional fashion: Jai Hindley in the yellow jersey, Jonas Vingegaard just behind and Pogačar looking out of it already. Laruns has hosted the Tour two times before, and both times there was a Slovenian winner. This time, there was a big Slovenian loser. The organisers of the Tour de France are always in a tricky position. They want exciting things to happen, but the trouble is, exciting things tend to define bike races, and then the race is over. So on paper, this straightforward-looking early mountain stage looked ideal to shake things up a little, and maybe magnify the small gaps that were prised open in the first two stages in the Basque Country.

Instead, bit by bit, a 36-rider break went up the road, including Jai Hindley, who started the race as third favourite with most bookies and has a Giro d’Italia title to his name and, crucially, two very strong teammates in Patrick Konrad and Emanuel Buchmann, who has been quiet in the last few seasons but was fourth in the 2019 Tour de France. It also had three Jumbo-Visma riders in Wout van Aert, Christophe Laporte and Tiesj Benoot, none of whom are going to win the Tour de France, but took any obligation off their team to help UAE in their pursuit of Hindley.

Read more: Can Jai Hindley win the Tour de France?

The break wasn’t entirely cohesive, but there was enough motivation, firepower and teams with numbers there to ensure it steadily built a lead. Mads Pedersen pulled for his Lidl-Trek team-mate Giulio Ciccone, and AG2R’s Aurélien Paret-Peintre and Clément Berthet pulled for their climber Felix Gall, who earned the KOM jersey for their efforts. But even with occasional splits in the lead group, the group was four minutes ahead with just 45km to ride. And though Hindley was without doubt going to be the main beneficiary of the day, AG2R opted to ride for Gall to get mountain points and perhaps the stage win, which benefited Bora, and made life even more difficult for UAE.

There were interesting dynamics at play. The ambush had not been planned, but the race had effectively ganged up on UAE Emirates, who chased alone, and didn’t play their hand well, initially having put two riders – Felix Großschartner and Marc Soler – in the break. Both went back to the peloton eventually, but the team were not up to the task of chasing a motivated and huge break, and spent a lot of energy in failing to catch it.

Having Adam Yates in the yellow jersey meant that they were more or less obliged to take responsibility, and took away from Pogačar the option of getting help from Jumbo-Visma. The Dutch team took a risk in putting riders into the break instead of aiding in the chase – after all, Hindley is a rival to Vingegaard as well as to Pogačar. But instead it worked out perfectly. The bike race had been decidedly chaotic to this point, but with about 1500m to go on the Col de Marie-Blanque, after a textbook Sepp Kuss winnowing-down of the favourites’ group, Jonas Vingegaard attacked and Pogačar couldn’t follow. There was nothing nonlinear about the steadily and inexorably increasing time gap between the defending champion and the Slovenian – by the finish Vingegaard was 64 seconds ahead of his rival, and only a manageable 34 behind Hindley.

Today was a great day for Jai Hindley and Bora-Hansgrohe, who also have Buchmann in fourth overall after he came in just ahead of Vingegaard, It was an even better day for Vingegaard and Jumbo-Visma. Vingegaard struck a signal blow in the 2023 Tour de France, but can still, if he wishes, let Hindley spend a few days or even a week in the yellow jersey and absorbing the stress, interviews and time-sucking podium ceremonies, safe in the knowledge that he put over three minutes into the Australian in the recent Critérium du Dauphiné, and carved a minute out of his lead in just the final kilometre-and-a-bit of the Col de Marie-Blanque. And the fact that Pogačar, still in the white jersey, will have to do the same, is even better.

Edward Lorenz understood that chaos theory and the butterfly effect meant that making predictions in complex systems was fraught with complication. “Our ability to predict astronomical events, earthquakes and weather phenomena with a high degree of accuracy, is still limited,” he said. However, we might now be able to predict that Jonas Vingegaard is going to win the 2023 Tour de France with at least some degree of accuracy.

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