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In my freshman year at St. Johns, I heard a story about the education of young Isaac Newton. I have no idea of the source for this story or whether it is factual or apocryphal, but it had a tremendous inspirational impact on my young mind. If the story is mythical, yet still it has a power to inspire real, living people to do something actual and historical. Such a story may serve as justification or apology for the notion of a noble lie in Plato’s Republic.
Young Newton desired to learn the Elements of Euclid’s geometry. He opened Euclid’s Elements, Book I, and studied the first theorem until he knew it by heart and could demonstrate it from memory unaided by the text or diagrams. Having mastered the first theorem, he proceeded to memorize the second theorem in the same complete fashion. Then, he demonstrated from memory both the first and second theorem, to prove to himself that he had not forgotten the first theorem. He then undertook to learn the third theorem by heart, and when he had accomplished this, once again, he demonstrated and proved from memory the three theorems which he had now mastered. He proceeded in this fashion through the entire thirteen books of Euclid’s elements, memorizing the next theorem, and then demonstrating all the preceding theorems from memory. When Isaac Newton had finally finished the entire thirteen books of Euclid’s elements, he “knew” them in a way that few people know something. He had internalized them. They had become part of him.
I was so inspired by this story that I resolved to follow the same strategy as Newton followed in learning Euclid’s elements. I labored for hours each day and each evening, alone, standing at a blackboard with my copy of Euclid and chalk covered hands. Although such an enterprise sounds like it would be near impossible, I found that it was quite possible to learn and memorize in such a fashion. I eventually arrived at a point where I could stand at a blackboard and demonstrate from memory the first five books of Euclid.
Any such learning experience as this is truly transformational. Whenever we study anything in such a fashion as this, we internalize it and make it a second nature, as part of our own nature. Such a learning feat is truly a spectacle, but furthermore the framework mastered in such a fashion becomes a pair of spectacles or looking glass through which we see the world and ourselves in a new way.
There is one drawback. How shall I put this to you delicately? I suppose I shall paraphrase to you from Newton himself and you will get my drift.
Newton describes himself as a small child wandering along the seashore, picking up curious shells and marveling at them, unconscious of the vast ocean of reality is swelling and crashing before him. Newton says that if he has seen further than other men, it is only because he has stood upon the shoulders of giants. It has been said that no man is an island. Yet, when we undertake a transformational learning experience, we become isolated in the sense that what we come to understand cannot easily be shared with others who have not accompanied us on our journey of learning. When we stand upon the shoulders of giants, there is little room for an observation deck or elevator or souvenir stand with postcard panoramas.
I tried to emulate the labor of a Newton, and succeeded in some measure. But I do not possess the genius of a Newton, so such labor will never bear fruit.
There are people who immerse themselves in various areas with the lifetime intensity of a Newton. Religious students master the Torah, or the Talmud, or the Gospels. Musicians devote their life to Chopin or Mozart. Military historians study every battle from Alexander the Great to the American Civil War. They come to see and understand certain things from a vantage point which is inaccessible to us. They may tell us of the fruits of their understanding and their conclusions and we may choose to accept their word or ignore them, but we can never see for ourselves because we have not paid the precious price of the ticket which admits them to embark upon their lifelong journey.
Moses Maimonides does not address everyone, but only that one righteous person who is perplexed.
Knowledge is not a democracy but an oligarchy, an aristocracy. Somehow things do filter down to the street-level. Einstein’s famous E=MC2 has the greatest street recognition of any equation in mathematical history. If you don a tee-shirt emblazoned with that equation and walk through Harlem, everyone will recognize it after a fashion, but few understand its implications.
I was so thrilled during my study of chemistry when it was demonstrated to me that the sum of the weights of the protons, neutrons and electrons of an atom does not add up to the weight of the atom but falls slightly short of the actual weight. That missing mass is the mass which has been converted to the energy necessary to bind the particles together. Einstein’s formula exactly accounts for that missing mass. If that atom were to be smashed, and that binding energy released, then that is the tremendous energy of a nuclear explosion. Yet this understanding which I have gained, which goes well beyond the mere street-level recognition of a tee-shirt and a buzzword, merely scratches the surface of the understanding which a mathematical physicist possesses.
It is said that only a small minority of mathematicians ever succeed in mastering Kurt Gödel’s Incompleteness Theorem. Those who do master it experience a wonder of realization which is akin to religious awe.
When we dwell as pedestrians in a land, we behold the scenery from the most intimate detail and perspective, but that very closeness and intimacy in perspective prevents us from seeing symmetry, intention and design on a grander scale, bearing profounder implications. If we ascend to a mountain peak, we lose discernment of much of the finer details, but we can begin to recognize the "lay of the land" and its geography. From an orbiting space station, we can perceive global structure. And from vantage point of another galaxy, we may comprehend cosmic design.
Young Newton desired to learn the Elements of Euclid’s geometry. He opened Euclid’s Elements, Book I, and studied the first theorem until he knew it by heart and could demonstrate it from memory unaided by the text or diagrams. Having mastered the first theorem, he proceeded to memorize the second theorem in the same complete fashion. Then, he demonstrated from memory both the first and second theorem, to prove to himself that he had not forgotten the first theorem. He then undertook to learn the third theorem by heart, and when he had accomplished this, once again, he demonstrated and proved from memory the three theorems which he had now mastered. He proceeded in this fashion through the entire thirteen books of Euclid’s elements, memorizing the next theorem, and then demonstrating all the preceding theorems from memory. When Isaac Newton had finally finished the entire thirteen books of Euclid’s elements, he “knew” them in a way that few people know something. He had internalized them. They had become part of him.
I was so inspired by this story that I resolved to follow the same strategy as Newton followed in learning Euclid’s elements. I labored for hours each day and each evening, alone, standing at a blackboard with my copy of Euclid and chalk covered hands. Although such an enterprise sounds like it would be near impossible, I found that it was quite possible to learn and memorize in such a fashion. I eventually arrived at a point where I could stand at a blackboard and demonstrate from memory the first five books of Euclid.
Any such learning experience as this is truly transformational. Whenever we study anything in such a fashion as this, we internalize it and make it a second nature, as part of our own nature. Such a learning feat is truly a spectacle, but furthermore the framework mastered in such a fashion becomes a pair of spectacles or looking glass through which we see the world and ourselves in a new way.
There is one drawback. How shall I put this to you delicately? I suppose I shall paraphrase to you from Newton himself and you will get my drift.
Newton describes himself as a small child wandering along the seashore, picking up curious shells and marveling at them, unconscious of the vast ocean of reality is swelling and crashing before him. Newton says that if he has seen further than other men, it is only because he has stood upon the shoulders of giants. It has been said that no man is an island. Yet, when we undertake a transformational learning experience, we become isolated in the sense that what we come to understand cannot easily be shared with others who have not accompanied us on our journey of learning. When we stand upon the shoulders of giants, there is little room for an observation deck or elevator or souvenir stand with postcard panoramas.
I tried to emulate the labor of a Newton, and succeeded in some measure. But I do not possess the genius of a Newton, so such labor will never bear fruit.
There are people who immerse themselves in various areas with the lifetime intensity of a Newton. Religious students master the Torah, or the Talmud, or the Gospels. Musicians devote their life to Chopin or Mozart. Military historians study every battle from Alexander the Great to the American Civil War. They come to see and understand certain things from a vantage point which is inaccessible to us. They may tell us of the fruits of their understanding and their conclusions and we may choose to accept their word or ignore them, but we can never see for ourselves because we have not paid the precious price of the ticket which admits them to embark upon their lifelong journey.
Moses Maimonides does not address everyone, but only that one righteous person who is perplexed.
Knowledge is not a democracy but an oligarchy, an aristocracy. Somehow things do filter down to the street-level. Einstein’s famous E=MC2 has the greatest street recognition of any equation in mathematical history. If you don a tee-shirt emblazoned with that equation and walk through Harlem, everyone will recognize it after a fashion, but few understand its implications.
I was so thrilled during my study of chemistry when it was demonstrated to me that the sum of the weights of the protons, neutrons and electrons of an atom does not add up to the weight of the atom but falls slightly short of the actual weight. That missing mass is the mass which has been converted to the energy necessary to bind the particles together. Einstein’s formula exactly accounts for that missing mass. If that atom were to be smashed, and that binding energy released, then that is the tremendous energy of a nuclear explosion. Yet this understanding which I have gained, which goes well beyond the mere street-level recognition of a tee-shirt and a buzzword, merely scratches the surface of the understanding which a mathematical physicist possesses.
It is said that only a small minority of mathematicians ever succeed in mastering Kurt Gödel’s Incompleteness Theorem. Those who do master it experience a wonder of realization which is akin to religious awe.
When we dwell as pedestrians in a land, we behold the scenery from the most intimate detail and perspective, but that very closeness and intimacy in perspective prevents us from seeing symmetry, intention and design on a grander scale, bearing profounder implications. If we ascend to a mountain peak, we lose discernment of much of the finer details, but we can begin to recognize the "lay of the land" and its geography. From an orbiting space station, we can perceive global structure. And from vantage point of another galaxy, we may comprehend cosmic design.