Conquering Math

So there I was, trying to drill some smattering of math into this obsessed child.  “Leon!” I called.  “Leon!  Stop playing conquistador and come back to your studies!  Look here, see this problem?  You got it all wrong!  68 out of 88 is not 110%!”

“But ma’am, you have always told me to give 110%!  When I am older, that is what I will demand from my soldiers!  Why would I put 77%?”

“And there you go again!  What is this soldier thing?  We are doing math!  Math is precise and exact…”

“So will my soldiers be,” Leon interrupted in a very definite tone.  “They will be precise!  There will be no disregarding my orders.  Everything will be exact!  No one out of line.  No one a minute late!”

“Then look!  Before you can command, you must be able to obey.  See, I am telling you.  You must divide…”

“Yes!  Divide and conquer!  That will be my maxim.  Keep the enemy separate.  Don’t let their armies unite against me.  Never fear, I have learned!”

“Well, then.  In this case, your enemies are the 68 and the 88.  Divide them.”

“That is simple.  I will divide the 68 into 68 pieces.  I will kill 22 of those pieces and the other 46 I will draft into my own army.  I will divide the 88 into 88 pieces.  Then, I will kill 15 of those pieces and draft the other 73 into my army.  That makes my army grow from 46 to 109.  Then of course, you must add me, which makes 110!”

“My goodness, Leon!  What will you come to?  You must divide the 68 by 88.”

“That does not make any sense.  How can you divide one enemy by another?  No, wait!  I see what you mean!  If I put the peasants of Portugal against the leaders of Spain – and then perhaps, we can get the English in there too, they are sure not to get along with the Spaniards – ha!  Madam Louise, you are a genius!”

“I am glad you think so,” I interjected drily.  “Well, you are incorrigible.  Forget that problem.  Look at the next one.  54.  What does that little letter up toward the corner mean?”

“It means,” Leon began grandly, “that the five must rise to power!  It must take hold of its true place among its fellows!  It may be a mere whole number, it may be short, it may have quite a tummy, but it can rise!  See there?  I have written it, bigger than ever before, with the four bowing down to the dust beneath it!”

“It is all the same with you!  Divide and conquer.  Add and conquer.  Multiply and conquer!  What is next?  It is not rising to power, but it must be raised to a power.”

“What is the difference?  I do not see one.”

“The difference is, that while yours remains a five trampling on a four, mine becomes six hundred twenty five!”

“My!  That is a great difference!  I am not sure I like it.  Are you saying that I must wait to be raised to power, rather than try to rise myself?”

“Something of the sort,” I replied knowingly.  “Else you may very likely end up all alone, stranded on some island perhaps!”

“Me, stranded on an island?  Ha!  If anyone thinks to stop me by such methods, they simply do not know who they are dealing with!  I will return!  I will take anything and anyone they throw at me!  It will be just like the 68 and the 88.  They will become mine, part of my army!  I will rise to power once again!”

“And what,” I asked matter-of-factly, “what if you are put on a very small island, very far away?”

Leon looked at me soberly.  I decided to continue up on my advantage.  “Look at this.  Is eight prime, or is it composite?”

“It is my age, ma’am.  Of course it is a prime number.  Somehow though,” Leon added meditatively, “I think Prime Minister does not sound as good as Emperor.”

I sighed.  Why was this boy so ambitious?  “Look,” I resumed, “You want to be emperor.  That’s as it may be.  To be an emperor, as you surely know, there must be order.  That order must be followed.  Do you not think so?”

“Yes, ma’am.  Of course, all men must follow my orders, especially my soldiers.  They must be ready to follow me anywhere – down to the deserts of Egypt or up through the snows of Russia!  It is true that I do not like snow though.  It is too cold and gloomy.  But what is worse, it just keeps falling!  I do not like the thought of falling.”  The boy looked at me, his eyes flashing under his dark brown knots of hair.

“Then, before you fall down another rabbit hole with this snow thing, let me draw your attention to this problem.  4 x (6 + 9).  We were speaking of order, were we not?  What order should you follow in working through this problem?”

“You told me before that the parenthesis is your first enemy, that is, Russia, and should be taken care of first.  The easiest way to do that is to erase the little curve at the top of the 6 and the little curve at the bottom of the 9.  That makes it o + o.  That, of course, is 0.  Then 4 x 0 is also 0, just as no soldiers, even with 4 generals, is still no soldiers.  So, the Czar ends up with no soldiers!”

“A little bit of stratagem goes a long way with you I perceive!  But suppose you were reduced to the necessity of fighting and could not just erase the annoying little curves.  Before you fought, you would need to know how big the Czar’s army was, would you not?”

“Yes.  I see what you mean.  Well, if I could not erase the lines, then 6 plus 9 is 15.  That is not such a big army!”

“Perhaps not, but you surely know that even a small army, under good leadership, can do amazing things!”

“Aha!  It is those four generals again!  They were worth nothing before, but now that they have soldiers, they are beginning to mess things up!”  Leon struck his favorite commanding pose and looked indignant.

“Is your stomach hurting you, Leon?” I asked.  “Why do you have your hand inside your jacket?”

“It has nothing to do with my stomach, of course, ma’am!  It is my thoughts that are bothering me.  Those four generals simply cannot be that clever!  How can they make an army of 15 be worth an army of 60?  Once I have my troops in Moscow, what can the Czar do to stop me?”

“Well,” I answered with relief, “you have solved the problem in any case, so we may as well as go on.”

“Solved the problem!  On the contrary, the problem has just begun!  The Czar’s army is multiplying and in this case, I do not know what enemy to divide him with!”

“Then, you can meditate on that while we take a break for a minute.  All this talking has made me very thirsty.”  I rose to leave, when Leon’s mother entered the room.

“Would you like a drink, Leon?  And did you say wanted water, Lou?”

“Oh!” Leon exclaimed.  “Please do not say that, Mother!  I do not know why, but it sends shivers down my spine!”

We both looked at him in surprise.  We were used to fancying his dreams of being Emperor as childish aspirations.  But perhaps, I thought, perhaps there was something to them after all!  Who knew what worldwide impact these math lessons with little Napoleon Bonaparte might have?

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