Joseph didn't care much whether he won or lost his bet with Napoleon. He remembered a movie about Napoleon that he'd watched in his previous life, which had shown Napoleon submitting a paper to the French Academy of Sciences. It seemed Napoleon had written an article analyzing social issues, but after he submitted it, it had sunk without a trace. So Joseph felt he was unlikely to lose this bet, at least.
Still, he had to prepare the paper carefully. Under normal circumstances, the first step in research would naturally be to conduct experiments. But for Joseph, who had traveled from another time, that could wait for now. What he needed to do first was prepare some mathematical tools for the arguments and calculations that would come later.
That made things complicated. The two or three decades from the 1770s to the beginning of the nineteenth century were precisely when mathematics—and French mathematics in particular—made a great leap forward. During this period, France produced a succession of mathematicians who still made Joseph draw a sharp breath and tremble with dread whenever he thought of them. Even as a time traveler, just remembering them brought back his fear of being dominated by Fourier, Laplace, and Lagrange. A chill rose from his tailbone and crept all the way to the back of his neck. Fresnel's perfect explanation of double-slit diffraction was also inseparable from the achievements of these great, terrifying men. To copy Fresnel's argument directly, Joseph would first have to come up with several key mathematical breakthroughs.
"This is just like, 'To solve the Korean problem, we have to solve Manchuria; to solve the Manchurian problem, we have to solve China; and to solve the China problem, we have to solve the United States.' When did I start acting like those brainless Showa staff officers who make a bigger problem to solve a smaller one?" Joseph couldn't help mocking himself. But considering the impact this experiment had left on history, and under the influence of his vanity, he still planned to write about it. Of course, if possible, he would use existing mathematical methods to solve the problem as much as he could. In principle, it wasn't impossible; the whole argument would simply be clumsy and cumbersome. It was like taking a problem you could solve with multiplication and insisting on doing it with addition.
After trying for a few days, Joseph realized that if he really wanted to avoid all the mathematical tools that hadn't been invented yet, the paper would have to be much longer.
Some essential mathematical tools still have to be developed. Otherwise, we can't seriously use addition to do multiplication, can we? Joseph thought.
After nearly a month of using relatively clumsy methods to work around some advanced tools—and inventing a few "more elementary" ones along the way—Joseph finally completed his paper. Gazing at the manuscript, which was thick enough to be a book, he nodded with satisfaction. "At last, I've managed to cut the length in half. A paper with breakthroughs in both physics and mathematics—what a bargain. The only pity is that I didn't get any feedback from the real world."
Joseph made another copy of the paper and sent one off. Then he took the other to show Armand.
The moment Armand saw the great mass of mathematical symbols in the paper, he frowned. "Joseph, I was wondering what you'd been so busy with all this time. So this is what you were working on. Well, I can just about follow the first part. You think light is a wave rather than a particle—which isn't quite the same as Sir Newton's view. Your experiment is very interesting, too. As for the rest, I recognize every symbol, but I honestly have no idea what they mean when they're all put together. Of course... you didn't write this for me to read, did you? It's for my uncle, right?"
"Yes," Joseph said. "I'd like to hear Mr. Lavoisier's opinion."
"Right, then. Tomorrow's Sunday. I'll take the paper over and let him have a look."
"Good morning, Mr. Lavoisier. Is there anything you need?" A waiter hurried to open the door and addressed Lavoisier, a member of the French Academy of Sciences and a renowned chemist.
"Ah, Mabeuf, is Mr. Laplace here today?" Lavoisier asked as he handed his cane to the waiter.
"Yes, Mr. Lavoisier. Mr. Laplace is in his office," the waiter replied.
"Excellent. Please bring a pot of black tea to his office in a little while." Lavoisier spoke as he strode down the corridor toward Laplace's office on the left.
"Of course, sir. I'll bring it right over."
Lavoisier reached the door of Laplace's office and gently knocked. There was no sound from within. He smiled faintly and knocked again, just as softly, but still heard nothing.
Lavoisier gently pushed the door, and it swung open. He stepped inside and saw Laplace sitting at his desk, head bowed, working calculations with a quill. Scraps of used paper lay scattered all over the desk.
Lavoisier said nothing. He simply walked over, pulled up a chair, sat down across from Laplace's desk, and waited quietly.
Just then, Mabeuf came in carrying a pot of black tea.
"Ah, Mabeuf, just leave it here and pour me a cup," Lavoisier said.
Mabeuf set the teapot on the table beside them, poured a cup, and handed it to Lavoisier.
"That's all for now. You can go," Lavoisier said with a smile as he took the tea.
Mabeuf bowed slightly and slipped out, leaving the door ajar behind him.
Lavoisier drank his tea as he watched Laplace work. Laplace never looked up; he hadn't even noticed that someone was sitting across from him.
After a while, Laplace dipped his quill into the inkwell again, but when he tried to write down a number, nothing came out. The inkwell had run dry.
"Damn it! I should get a bigger inkwell," Laplace said. He looked up and noticed Lavoisier sitting across the desk.
"Mr. Lavoisier, what are you doing here? How long have you been here?" Laplace asked.
For a long time, Laplace had worked as Lavoisier's assistant, and together they had measured the specific heat of many substances. In 1780, the two men had proved that the heat required to decompose a compound into its constituent elements was equal to the heat released when those elements formed that compound. This could be seen as the beginning of thermochemistry, and it was also another milestone on the road to the law of conservation of energy, following Black's research into latent heat. The two men therefore got along very well.
"Ah, I've been here a while. What is it? It looks like you're checking the calculations for that 'Bonaparte Spot'?"
"Yes, Mr. Lavoisier." Laplace stood up. "Have you read the paper? It goes so much against our intuition. But damn it, you really can observe it in an experiment... Which means that if his entire derivation is sound, then light really must be a wave. Well, Hooke will be spinning in his grave with joy."
"Yes, I've read the paper. I read it yesterday morning. It was written by a classmate of my art-loving nephew—Joseph Bonaparte. You've met him. He gave it to me through Armand. I must say, although the paper's conclusions run counter to common sense, the two experiments are truly impressive. Especially that 'Bonaparte Spot.' I imagine the young man also submitted it to the Academy of Sciences, hoping to win the prize. In any case, just for those two experiments, I think it's worth six hundred francs, perhaps more."
"Those few new mathematical tools he developed for the paper are worth that much on their own," Laplace said. "But many people will find the conclusion that light is a wave hard to accept."
"Hard to accept? Just because Sir Newton said light was made of particles?" Lavoisier said dismissively. "Aristotle made plenty of mistakes. Was Sir Newton an infallible pope? But you know I always have a lot on my plate. There are so many mathematical calculations in this paper. He came up with a few clever shortcuts, but there's still a great deal of work. I have my own research, too, so yesterday I only checked his experiment and skimmed through his argument. I haven't had time to study the mathematical details carefully. You know I'm not as good at mathematics as you, and when it comes to speed of calculation, I doubt anyone in the world is better than you. So I thought I'd ask you to check it thoroughly. I didn't expect you to have already started."
Before you continue