為什麼世界紀錄似乎越來越難打破——從數學角度來看

World records in sports capture the imagination of fans around the world. Some records seem to fall regularly, while others stand for decades. Recently, Swedish pole vaulter Armand Duplantis amazed the world by breaking his own world record for the 14th time, clearing an incredible 6. 3 meters at the Athletics World Championships in Tokyo. The crowd erupted as he soared above the bar, showing once again that he is pushing the limits of what is possible in his sport.

In many sports, improvements in diet, training techniques, and equipment have led to sudden bursts of new records. This is especially true in technical events like pole vaulting and cycling, where even small changes can make a big difference. Running events have also seen new records thanks to better shoes and training methods. However, not all sports see records broken so often. For example, the men's long jump world record has only been broken once since 1968. This could mean that athletes have reached the peak of what is possible in the long jump, and breaking the record now depends on factors like wind or how well the athlete feels on the day of the event.

Mathematics can help explain why records become harder to break over time. If we look at something like annual rainfall in different cities, the first year is always a record. The second year, about half the cities will have more rain than the first year. The third year, only a third of the cities will have more rain than the previous two years. This pattern continues, and the sum of these fractions is called the Harmonic series. Even though the numbers we add get smaller, the total keeps growing, but very slowly. This means that as time goes on, new records become much less common. For example, after 100 years, we might expect only five records, and after 1,000 years, just seven.

Scientists use this idea to study climate change. If records are broken more often than expected, it means the system is changing. For example, hot weather records are being broken much more often now, which shows that the climate is warming. In sports, it is hard to know if we have reached the limit in every event. Some studies suggest that we are getting close to the peak in many track and field events, so records will be broken less often. Others believe that human performance will keep improving. The fact that Duplantis has broken so many records suggests that pole vaulting has not yet reached its limit, while the long jump might have.

Swimming is another example. When special swimsuits were allowed, many records were broken, but after they were banned, the rate of new records slowed down. This shows that technology can have a big impact on sports. Sometimes, it is extraordinary athletes like Duplantis or swimmer Katie Ledecky who break many records because of their talent and hard work. However, as the world gets hotter, it might become even harder to break records in the future. At the recent World Championships in Tokyo, only one world record was broken, and many athletes said that the heat affected their performance. This shows that climate change could make it even more difficult to set new records.

In the end, breaking a world record is a rare and special achievement. As records become harder to beat, we should appreciate the athletes who manage to do it. They have overcome many challenges and shown what humans are capable of achieving.