Bonaparte in Russia
How some mathematical
calculations can be crucial
for taking strategic
decisions in this battle of empires
I love power. But it is as an artist that I love it.
I love it as a musician loves his violin,
draw out its sounds and chords and harmonies.
young man, not older than fifteen, Napoleon’s aide, appeared at the
door and marched straight to his superior, saluting diligently.
“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
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
“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
“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.
more Russians, the more time it will take!
have here a case of direct proportion.
we must maintain the proportion.
— = —
was right then,” Ney beamed victoriously.
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:
more French, the less time to capture.
have here a case of inverse proportion.
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
1 / 6 = 6 / X
we now join our data:
French Russians Hours
1 1 X
. 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
“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.”
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.
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?
Zip, the Time Traveller, in:
Bonaparte in Russia
Caius Zip takes part
in the invasion of the French army in the city of Moscow, commanded by the
legendary Napoleon. He also meets the Russian marshal, Kutuzov, the man
with the mission to block the huge Napoleonic army.
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
The participation of Caius will be important in this
historical moment, as he solves enigmas and learns with the Russian
marshal how some mathematical
can be crucial in taking strategic decisions in this battle of
After the story, in a very original manner, Napoleon tells
us his memories of that time.