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Napoleon Bonaparte in Russia
How some mathematical calculations can be crucial for taking strategic decisions in this battle of empires
Regina Goncalves
Chapter 5
I love power. But it is as an artist that I love it. I love it as a musician loves his violin, to draw out its sounds and chords and harmonies.
Napoleon Bonaparte
“I hope this is urgent, Rapid, to be disturbing my dinner this way,” said Napoleon gravely, taking another glass of wine from the table. “Sire, the fires in the city are scattering, and we are not able to stop the culprits as our prisons are full. The residents of Moscow and the allied soldiers are equal suspects of the crime. We have many people with burns, especially children, and all without medical care.” “It is regrettable that my own soldiers are suspects. Tell them that my orders are that they accommodate the victims in houses that are in good condition, and that tomorrow, early, I will personally visit them. Tell them also that I ordered for more paper roubles to be produced and used as money. In this way, the merchants can sell, and soldiers can buy instead of ransacking the shops.” “The men and the merchants know that money is worthless,” Ney immediately regretted his statement when he saw Napoleon’s reaction. “I should have imagined that those Polish, Saxon, Austrian, Bavarian, Prussian, Hungarian, Danish, German of all principalities, Portuguese, Spanish, Swiss, Italian soldiers.... Humph! Have I left any conquered country out? Whatever! I should have foreseen that when they enlisted in my army, they would cause this type of problem. Poor boys! They are weary and hungry. I am feared, but also admired. They are capable of giving their life for their emperor...” Napoleon was interrupted by his sudden violent coughing. Sniffing impatiently, he popped a pill into his mouth. “This cold has been trying to kill me for weeks. I can hardly sense the aroma of my precious wine. What medicine is this that cannot defeat a simple cold?” He looked at the clock on the wall and asked his aide. “Any news of Marshal Murat? “Sire, after days of searching for the Russian army, we learned that he found it and went into battle in Tarutino. It seems he did not do very well. This time, the Russians got the best of him and…” “That news is old!” Napoleon fumed at Rapid. “I do not need to be reminded of the absurdities of war. I have yet to talk to that brother-in-law of mine. How could he have lost track of a huge army, only to then confront them face-to-face and be defeated? A war is not won without mistakes, but in order to not be defeated, we must forcibly err less than our enemy. Without strategy, without calculations, we will not advance in this war, we will conquer nothing! Has he not understood that the progress and improvement of mathematics are connected to the prosperity of the state?” “Not everyone is an excellent strategist like your Majesty,” pondered the marshal. “I am not as good a strategist as they say!” shouted the emperor. “I am only a scholar of battles of the past. I know all the evolution and the decisions taken by notable men who make war an art, like: Attila, King of the Huns; Hannibal, of Carthage; Alexander, the Great; men who essentially counted on mathematics as their ally. Rest assured, like them, I am more efficient than all my marshals put together.” He spun round to face Rapid, and waved his hand as if carrying a sword, making the aide cringe. “Come on, my boy, if you have anything else to say, say it now.” The boy cleared his throat and continued. “Sire, as I was telling your Majesty, we are having problems with the prisons. Marshal Davout requests your permission to execute the rebels.” “How many Russians are imprisoned?” “I do not have that information, sire. I only know what I overheard the marshal say; that six French soldiers are needed to catch six Russians every six hours.” “What is this? Another of Davout’s riddles?” The marshal slammed his glass on the table. “Are you telling me that one Frenchman is needed to catch a single Russian per hour?” Ney divided all numbers by six. “I disagree, Ney.” Napoleon was rubbing his chin and smiling coyly. “I think that it means that the more Russians they must capture, the longer it will take, and that the more French, the less time it will take. So, how long does it take for one Frenchman to capture one Russian?” “I expect a true soldier will take one hour!” “Do you, Ney? Hmm, who else thinks this way?” Silence hung over the room until Napoleon broke it to lean on his young saviour’s shoulder. “So, Caius, what is your opinion on this matter?” he asked. “Well, I don’t know really. The only thing I can say is that it seems reasonable to think it will take one hour.” “No, boy, don’t think. If you have no basis for your affirmation, then you are simply guessing. Without reasoning, you will see that in a battle, this leads to total defeat.” “But, sire,” pleaded the marshal, trying to return to the discussion, “with all due respect, I did not guess. This problem is only a question of proportion.” “Ha! I believe I will have to teach you a small lesson. Think, man! Think like a strategist, if it is at all possible for you.” Napoleon gestured for Rapid to hand him a sheet of paper and a quill from on top of the table next to the fireplace. After the dishes were removed, Napoleon spread the sheet out and, as if standing before a map with his conquests, started to define his calculations. “Let us take one step at a time. “The first step: “The more Russians, the more time it will take! “We have here a case of direct proportion. “So, we must maintain the proportion.
Russians Hours 6 6 — = — 1 X
“I was right then,” Ney beamed victoriously. “I have not finished yet.” Napoleon’s eyes shot at everyone mercilessly. “And I will not be interrupted.” He looked back at the paper. “As I was saying, now I will show you the second step: “The more French, the less time to capture. “We have here a case of inverse proportion. “So, what we must do is invert the proportion that is contrary to the proportion where the X of the matter stands:
From: 6 / 1 = 6 / X
To: 1 / 6 = 6 / X
“If we now join our data:
French Russians Hours
1 1 X
1 /6 . 6/1 = 6/X 1 ∙ 6 ∙ X = 6 ∙ 1 ∙ 6
6 X = 36 ; X = 36 / 6 ; X = 6
“The final result, ladies and gentlemen, is that each Frenchman captures one Russian in six hours.” “Pardon me, sire,” mumbled Rapid, rubbing his forehead, “but I did not fully understand.” “If you have difficulty with this type of reasoning, maybe I should use another way. In fact, the problem is very simple. It would be enough to leave the time constant, and forget it for a moment. We have a direct proportion, I mean, the more French soldiers, the more Russians, and then if six Frenchmen soldiers capture six Russians, it is clear that one French capture one Russian. Coming back now with the time, surely this happens in six hours. I could have done this reasoning since the beginning, but I wanted to show the general solution. Sometimes, the solution is not so clear, for this type of problem may have more than three variables, more inverse proportions, and the numbers and the variables may not be so familiar. Now, as we know the time and the amount of French soldiers engaged in the work, I can say that there are several hundred prisoners.” “Brilliant as always, sire!” said the Marshal, doing a gesture of reverence to his leader. “You bow so that I may not see your eyes,” snapped Napoleon, catching the marshal by surprise. “Words are ways of obfuscating what the eyes truly speak.” “I did not know that the general needs mathematics so much,” intervened the young soldier, saving the marshal from direct confrontation. Napoleon walked away from the marshal, and together with Rapid, contemplated the solution of the problem. “Let it be known, soldier, that I am here as a leader because I was an excellent student. I was amongst the seventeen boys chosen for the great mathematics exam, and that was after only having studied for a year in the École Royale, whilst one usually did the exam after two years.” “Ah, that I know!” asserted the marshal. “Your Excellence was one of the 56 finalists in the entire nation.” “Incredible, sire!” admired Rapid. “I cannot even write properly, much less know anything about mathematics. I suppose I will never be anyone.” “It is never too late, dear Rapid. In the meantime, if you insist on this attitude, you will never reach my greatest triumph, to conquer the unattainable.” “Oui, sire! But, what are your orders in relation to the prisoners?” “Well, before my orders, I will submit another challenge to you. Let’s see if you have really understood direct and inverse proportion.
CHALLENGE If six French soldiers are needed to catch six Russians every six hours, how many French soldiers are needed to catch 100 Russians in 50 hours?
------------------------------------------------------------------------------- Caius
Zip, the Time Traveller, in: Napoleon
Bonaparte in Russia
Caius attends a dinner in which there is a memorable dialogue with Napoleon, of a determined and captivating personality, the faithful Marshal Ney and, on the Russian side, the patriotic princess, Natasha. During the dinner, Caius listens in awe to the narration of Napoleon’s strategies and exploits, up to the moment of the invasion of Moscow. A great lesson of strategy and of a notable human virtue: patience! Caius meets the great Russian commander-in-chief who, resisting the pressures of other officials and even of the tsar himself, persisted with his strategy of avoiding direct combat with Napoleon’s Grande Armeé. Kutuzov retreats and hinders the life of the invaders, cutting their supply lines and constantly beating them with guerrilla tactics, until the arrival of his great ally: General Winter. The participation of Caius will be important in this historical moment, as he solves enigmas and learns with the Russian marshal how some mathematical calculations can be crucial in taking strategic decisions in this battle of empires. After the story, in a very original manner, Napoleon tells us his memories of that time.
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