The Fox of France

The design of the Fort of Calais and its associated calculations were not particularly difficult, and Montreuil had entrusted this task to Joseph more as a means for him to earn some extra money. However, Montreuil soon realized that Joseph was gaining much more than just a few coins from this endeavor.

One day in July, while Montreuil was on a business trip to Nice, he received a thick letter from Joseph. The envelope was hefty and, had it not been sent through military channels, it would have cost Joseph a significant amount in postage. Montreuil opened the letter to find a stack of papers covered with various numbers and symbols.

Montreuil glanced briefly at the contents and understood that the letter discussed problems related to the limits of mathematical functions. However, he was about to head out and had no time to thoroughly examine the letter. So, he slipped it into the pocket of his coat and left.

After finishing his work, it was already past four in the afternoon. Some colleagues invited Montreuil to join them for dinner in the evening. He declined, citing personal matters that required his attention. The colleagues did not press him further and left on their own.

According to Christian beliefs, there are seven sins that can lead a person's soul to hell: pride, envy, wrath, sloth, greed, gluttony, and lust. If this were true, then in Europe, the French, particularly the nobility, had the highest probability of descending into hell due to their gluttony. Like the great eating nations of the East, the French, especially the French nobility, were renowned for their extravagant feasts that extended well into the night. Compared to Paris, Nice had relatively lower prices, and its seafood offerings were abundant. A group of friends indulged in an eating and drinking spree from the afternoon until deep into the night, with their stomachs and throats fully satisfied. As they returned to their accommodations, they noticed that Montreuil's room, which was usually well-disciplined, had a lit lamp.

"What is Montreuil doing?" one of them mumbled.

"Who cares? That stiff guy doesn't seem like a real Frenchman," another intoxicated fellow replied.

These inebriated companions weren't genuinely interested in what Montreuil was doing, so they merely muttered some comments and went to sleep.

Montreuil, oblivious to the speculations outside his door, sat at his desk with a stack of draft papers, meticulously filled with various mathematical calculations. He furrowed his brow and continued his work, even after one candle burned out and the sky outside began to lighten.

"Joseph's research is quite impressive. I haven't found any issues with it so far. Well, he must have been inspired while working on the construction of the fort. Ah, youth is truly a wonderful thing. In my younger days, my thoughts flowed much more swiftly," Montreuil sighed as he put down his quill.

"Joseph probably submitted this paper to the Academy of Sciences. I wonder how those folks at the Academy will evaluate it," Montreuil pondered.

Indeed, Joseph had submitted the paper to the Academy of Sciences. However, what Montreuil had not anticipated was that, within a week, Joseph would send another paper to the Academy, in which he derived a significant inequality. This inequality, originally known as Cauchy's inequality in history, might need a new name now.

But this was just the beginning. Six months later, Joseph published a physics paper titled "Research on Frictional Heat." In this paper, Joseph conducted an experiment where he placed two ice blocks of equal mass and temperature in a glass container submerged in water. The ice blocks were rubbed against each other, causing them to melt. In contrast, another set of ice blocks, also of equal mass and temperature but left untouched, naturally melted as well. Joseph recorded the temperature changes of the water in both cases. Surprisingly, the water in the frictional heat group did not cool as rapidly as expected. Instead, its temperature decrease was more gradual and gentle. Joseph pointed out that this phenomenon contradicted the predictions of the traditional caloric theory, a concept widely accepted in Europe.

Caloric theory posited that heat was a substance called "caloric" - an immaterial, non-spatial substance. When an object absorbed caloric, its temperature would rise, and caloric would flow from a warmer object to a cooler one or through the pores of solids and liquids.

Caloric theory successfully explained many physical phenomena, including the cooling of hot tea at room temperature: the tea's high temperature indicated a higher caloric concentration, causing caloric to flow to the cooler surrounding air. It could also account for the expansion of heated air, as air molecules absorbed caloric, increasing their volume. Despite some challenges, caloric theory remained the dominant scientific hypothesis until the mid-19th century.

However, caloric theory had its flaws. It required that caloric could neither be created nor destroyed but only transferred between objects. Therefore, if one object's temperature rose, another's had to fall by an equivalent amount, and this posed difficulties in explaining phenomena like frictional heat. In Joseph's experiment, there was no clear source of caloric to melt the ice into water.

Unlike Humphry Davy, the scientist who initially conducted the experiment, Joseph fully grasped its significance. He accompanied the experiment with rigorous mathematical analysis and showed that, in this context, caloric theory and the kinetic theory of heat were not equivalent.

"To be honest, this paper almost spells doom for caloric theory!" Laplace said to Carnot, his face contorted in anguish. "This Joseph, he's such a headache! There are so many fascinating things to explore in this world, but he seems to derive joy from demolishing others' theories. He... he's just..."

"Yeah, I remember your distress when he first introduced the wave theory of light," Carnot replied, his face equally troubled. "Actually, I've just completed a study based on caloric theory."

"Me too," Laplace replied. "I had an idea recently. Perhaps by considering changes in caloric, I can refine some aspects of Newton's formula for the speed of sound. However, right now, the research has only just started, and I might have to pause it for a while."

"That's not a big problem," Carnot said. "Your research is still in its early stages, and now you can consider it from the perspective of kinetic theory instead. According to Joseph's arguments, although caloric theory and kinetic theory are not entirely equivalent, in most cases, they can be considered interchangeable. So, the changes you need to make should be minimal. But my research is already complete..."

"Well then, Teacher, how do you view Joseph's paper?" Laplace asked.

"What can I say?" Carnot replied. "Just like last time, I haven't found any problems with his paper, at least not yet. Of course, his viewpoint surely has some issues, but how can caloric theory be wrong? At most, it might need some adjustments, some supplements. He also acknowledges that there may be alternative explanations besides his. Currently, caloric theory does have its shortcomings when it comes to explaining frictional heat, but that doesn't mean it's entirely finished. It merely indicates that for it to remain valid, we need to make further modifications. However, at the moment, I haven't found a way to do that... This Joseph, he always enjoys causing trouble for us."

Laplace noticed that despite the trouble Joseph's research had caused Carnot and the numerous conflicts with Carnot's own work, Carnot's attitude toward Joseph was unexpectedly lenient. While Carnot complained aloud, his tone conveyed more a sense of "this child is mischievous" than any genuine malice.

"This teacher is surprisingly magnanimous, isn't he? It's so unlike him!" Laplace couldn't help but think. "And he doesn't even fully agree with Joseph's views. If someone else had proposed such ideas, maybe even myself, the teacher might have been furious. Why, then, is he so tolerant this time?"

"That lad, he's truly intelligent, but he enjoys stirring up trouble. Imagine if he could channel his cleverness into something more productive, rather than exclusively unsettling our theories. Well, when he returns, I'll have a good talk with him," Carnot remarked, still smiling and oblivious to Laplace's thoughts.