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Sitaram · Site Admin Joined: 14 Sep 2005 Posts: 1079

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.

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