The Journey to Mt. CalculusPublished January 24, 2017
The Journey to Mt. Calculus
Life seems to be many things when we are born. But a force that few really understand is going to shape our lives.
We are all born onto the continent of mathematics. Forces are at work that will determine our whole lives. And no one was going to clearly explain the situation to you….until now.
We all spend our early lives on the vast plains of Arithmetic. A happy place where our fingers and toes are out numeric friends. They help us to do sums and takeaways. Things make number sense. Money made is added, money spent is subtracted. Given a choice, few of us would ever choose to leave this world of numerical reality.
But we are not given a choice. We are forced to set for on a quest. No one tells us that is what is happening, no one explains the goals, the point or the reasons. We are just told we are going to school. You must go. It is the law.
And so we go. And for a time our toes and fingers are enough. Later, we start using blocks and coins for numbers larger than 20. But this is pretty comfortable and all seem at ease. Slowly as the years goo by, we are introduced to multiplication and division. Although it is a stretch for some, everyone is eventually Okay and we continue to be confident and content.
‘Suddenly’, we confront fractions, decimals and percentages. Things are slightly confused and confusing now. We so rarely multiply or divide pieces of things in the real world. Yet in the world of Arithmetic it is assumed. Some of our friends stumble and fall here and turn back. We don’t see them again.
As we enter the teen years, a time of inherent stress and confusion, a change occurs. Our teachers begin to speak of a land called Algebra. A highland place where we must go. We are not told why we must go. We are not told that it is not even the real goal. We are all going so we go.
Algebra is a strange world. We learn to talk of things that are not there as if they were. We call them unknowns and we spend a year trying to find these unknowns. It is a hard year for some. Drawing pictures of a two-dimensional worlds controlled by mysterious “X”s and “Y”s. Some of our friends are just mesmerized by this process. Their eyes glaze over and they seem to go away. We try to reach them, help them, but many don’t seem to hear us or understand us. After many years and much suffering, they turn back from the quest. The foothills of Algebra take an enormous toll on the human spirit. Some will never recover.
But the rest of us seem fine. Algebra is a strange world, but it is exciting and interesting. With a good teacher, we have mastered the unknowns. The pictures that were once like hieroglyphics, now make sense. We have completed the journey through the foothills of Algebra and all is well with us. This is about to change.
Oracles meet with us and tell us that our journey is not over. Algebra is not the goal! We are shocked.
It gets worse!
We are told by the oracles that we must leave our beloved continent. The place where we learned to count our blessings must be abandoned.
We must travel out from our continent to an island far off shore. The island is called Geometry. The Oracles don’t tell us why we must go there. They say it has always been so. The ancient ones, the Greeks, created this great place. We must go there to live for 15 months. From June to June and on to September. If we survive on the island and are successful we can return.
Since we are dutiful children we trust the Oracles. We go.
If Algebra is a strange world, than Geometry is beyond words.
We start with axioms that make no sense. We are told that every ‘thing’ starts from a point that has no dimension but still ‘is’. Where is it we ask? We are told to believe that such a thing can be. Then we are told that a line is a succession of these things that have no dimension. But how, we ask, can we put them side to side and they have length but no width? Distance is made up of these non-things. Area becomes even more bizarre.
We talk of circles, triangles,and squares, of angles, tangents, and arcs. We are to see them in our minds. We are to be able to turn them in our minds and still make sense of them. This is called rotation.
Many of us, often times the girls, find this place much more difficult than Algebra ever was. Those who want things explained just get more pictures. The explanations never made much sense and the pictures are worse. Those who are struggling grow frustrated, angry and confused. They had been so strong at Algebra, often better than the boys. Yet this Geometry is so strange. What does this have to do with Algebra they ask? No answer is given. “It is important, you must learn it.”
A story is told to us that ever since the Middle Ages or ancient time, a person was not considered educated unless they had learned Geometry. That once it was the only Mathematics. It is old, venerable and required. If you can not do well here we are repeatedly told, then maybe you are not ready for….
It is never said clearly, but the message is still sent. If you can not do well here, then you don’t have what it takes to go on! This is a hard message. Many among us, whom we trust and respect as bright and hardworking, are doubting themselves. We try to boost their spirits but serious damage has been done. Their confidence has been shaken. These cracks are very hard to repair.
Finally the 15 months pass and we return to the mainland of the continent of mathematics. Some among us turn back to return to our homeland. There they are received with some respect, but they have failed in their quest. Those who never were even able to go to the island of Geometry hold them in some respect, but that is little comfort.
Those of us who “did well” on the Island of Geometry meet again with the Oracles. They tell us that now the real journey begins. And now the real climbing starts. Next to the Plateau of Algebra 1 begins the low mountains of Algebra 2. We must continue our journey, our quest.
Since we are dutiful. we must go on. Some question why, but now the oracleThe world is again three dimensionals are again silent.
We quickly find that the mountains of Algebra 2 are not so bad. Much that we learned in the foothills of Algebra 1 is very useful. We wonder at times what use our Geometry is on this part of our journey. We think of our friends who turned back and realize that if we hadn’t gone out to the Island of Geometry, they would still be with us.
But there is so much work to do that we don’t dwell on this long. Besides, The Oracles must know what is best for us.
Some among us falter as we climb higher in the mountains of Algebra 2. Their confidence has not recovered from the difficulties in Geometry. They doubt that they can go on. And one by one, we lose other of our friends. And many of these were good students of Algebra 1. They were confident then, but now they are broken spirits.
We pass on without them.
The mountains of Algebra 2 turn out to be mountains in name only. For we now face even tougher climbs. Before us loom the craggy peaks of of Trigonometry.
The Oracles just point and most of us trudge on. Others return home to receive the lesser rewards of those who tried hard but failed.
Trigonometry is a powerful and wonderful world of rarefied heights. The world is again three dimensional. The language of the natives is different but we soon learn it. Much of what we learned in Algebra 1 and 2 is useful to us. By continuing to work hard and believing in ourselves, we press on.The year of climbing pass and we journey through this land. Some of us are slightly injured, all of us are weary of all the years of effort. But many feel strong with all they have accomplished.
That night we pitch camp. Out of the darkness, into the light of our campfire, the Oracles again appear. They look at us and are not smiling. Have we not done well? Have we not done all that they asked?
Yes, they tell us. You have accomplished much. But you are not done. And if you do not accomplish this final task, it will have all been for almost nothing.
The words are like burning swords thrust into our sides. The torment is beyond words.
Slowly we recover our senses. The inevitable question is asked. “What must we do next?” The Oracles tell us that sunrise all will be clear.
We have a fitful night of nightmare dreams. We think of all who have turned back. We dream of our homes and how nice it would be to go there. To be done with all this work and suffering that seems to have no point. Was this the secret message of Geometry.
We awaken to the sun rising. It would be a glorious day if we where just there for the view. But we are not enjoying THIS view! Before us stands a mountain that makes all we have done before seem like so little. It is Mt. Calculus.
The Oracles tell us that this is the goal. This is the culmination of our quest. If we can climb mount Calculus then we can return to our homeland as conquering heroes.
We speak among ourselves. “How can we continue to trust the Oracles?” “What if there is more after this?” Some can not face the task before us. Our ranks are thinned again!
Nothing can fully prepare a person for this task. The Oracles tell us that many will fail. That this is as it must be. Our homeland can not use too many conquering heroes.
We begin the climl.
The air is thin and it is hard to breathe. Even at rest, one seems to use energy just being on this mountain. We are light headed and unsure of ourselves. Derivatives and Integrations swim in our minds.
The guides that have been assigned to us by the Oracles seem to know the way but they won’t make it clear. They jeer at us, if we question this madness. They challenge us to turn back. Go home if you are not tough enough. We don’t really want you here. The women among us took an unmerciful mental beating. They were repeatedly told that they belonged somewhere else. That they weren’t tough enough. That they didn’t have the talent for such a task. Some broke under this relentless pressure. But others took to the task with a resolve that was chilling to observe.
Their eyes said, “Nothing will stop me!” And so we struggled on. Some were better equipped for this climb than others. For those lucky ones, the directions of the guides actually made sense. Many of these would later become guides themselves. Just as merciless to the later generations.
But for most of us the climb was just brutalizing work. Never sure of what was to come next or why. The mountain became our life. We helped each other as we could. Puzzling over the strange explanations the guides gave us, we made some sense out of their words. Teaching ourselves as we went, we passed the tests the guides gave us. We rarely got the answers completely correct. But in their condescending way, we learned to love the words, ” partial credit will be given.” They allowed us to continue. For they held our destinies in their hands. They told us it was a privilege to suffer like this. They had to endure this pain and so must we. Their eyes held no solace. If we could not take the pain, they were more than willing to let us fail and turn back.
For months we toiled, making what seemed to be progress. Our guides continued their never ending harangues of “explanation.” Occasionally one of us would have the temerity to ask why we must we make this climb? Why must we learn these hard lessons?
The retribution was swift! Such questions were greeted with a tirade of invective that would wither even the hardiest among us. Those who looked back at Sodom and Gomorrah faired better those who asked our guides WHY! These questions were asked less and less.
On we toiled.
Then one day, a miracle happened! The guides smiled at us. We looked at each other and assumed that our fates must be sealed. Something truly horrific must be about to happen.
Just then, the Oracles walked out of the mist. The mountain had been shrouded in this cloud cover every day. The Oracles gathered us together. Some of us could barely move. Bleeding and battered, this had been no beauty contest. Many of us had only made progress these last few weeks by crawling. We had long since ceased begging for mercy.
Now the Oracles spoke gently, almost reverently, to us. “You have finished your task!”
Just then the sun broke through the clouds. What we had assumed to be just another shoulder on this endless mountain was actually the summit.
When the sun broke upon us, it was as if the Heavens had opened. We glorified in the wonderful warmth. The Oracles now told us many wonderful things.
“You have all harbored dreams for your lives. These dreams will now come to pass.”
“Some of you have wanted to be doctors. It will be allowed. Some of you wanted to be architects, engineers, scientists,veterinarians and other professions, it will be allowed.”
“For you have proven your worth. When you return to your homeland it will be different for you few. You will be given respect like no others. You will be allowed to live in glorious homes and receive all the most wonderful things your country offers, that others will not. This is the reason that you set forth on this quest. You had to prove that you were worthy of receiving all of the societies rewards.
Although we didn’t all see how conquering Mt. Calculus should allow us all these wonderful things, we surely didn’t want to argue. And those of us who actually enjoyed the climbing were returning as guides. They already had that terrible look in their eyes. As guardians of the summit, they too would be merciless.
Only the truly worthy would achieve the peak under their leadership. For Mt. Calculus is the academic Holy Grail!
Note: Our society does use math as a filter. If you can not complete college level Calculus, the door remains closed on many of the most profound and rewarding life paths. It might not seem fair or relevant to decide who pursues medicine, optometry, veterinary and other professions based on a skill that they will rarely if ever use. But it is a fact and students need to know it and be mentally toughened to face the task ahead. Many math teachers unfortunately see themselves as ‘guardians of the summit’ and whose task is to “weed out those who are not truly worthy”, not truly math gifted!
Until the situation in our society changes, this story will remain very relevant.