How Einstein
Learned Physics
Einstein was a student long before
he became a celebrity. There is a lot to glean from his education and unique
approach to learning.
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Wanting to understand how Einstein learned physics may, at first, seem as pointless as trying to fly by watching birds and flapping your arms really hard. How do you emulate someone who is synonymous with genius? However, I think the investigation can still bear fruits, even if you or I might not have the intellectual gifts to revolutionize physics. Whatever Einstein did to learn, he clearly did something right, so there’s merit in trying to figure out what that was.
How Smart Was Einstein? (Did He
Really Fail Elementary Mathematics?)
One of the most common stories about
Einstein is that he failed grade school math. I think this is one of those
ideas that sounds so good it has to get repeated, regardless of whether it is
true or not.
Unfortunately, it’s not true.
Einstein was a strong math student from a very young age. He himself admits:
“I never failed in mathematics.
Before I was fifteen I had mastered differential and
integral calculus.”
While the story about Einstein being
an early dullard is certainly false, it’s not the case that he was universally
regarded as a genius, either.
Einstein’s grades (highest grade =
6).
In college, Einstein often struggled
in math, getting 5s and 6s (out of a possible 6) in physics, but getting only
4s in most of his math courses (barely a passing grade). His mathematics
professor, and future collaborator, Hermann Minkowski called him a “lazy dog”
and physics professor, Jean Pernet, even flunked Einstein with a score of 1 in
an experimental physics course.
At the end of college, Einstein had
the dubious distinction of graduating as the second-to-worst student in the
class.
The difficulty Einstein had was
undoubtedly due in part to his non-conformist streak and rebellious attitude,
which didn’t sit well in an academic environment. This would follow him in his
future academic career, when he was struggling to find teaching jobs at
universities, even after he had already done the work which would later win him
the Nobel prize.
Einstein’s discoveries in physics
were truly revolutionary, which certainly earns him the title of “genius” by
any reasonable standard. However, the early picture of Einstein is more
complicated than that. All of this indicates to me, at least, that it can often
be very easy to judge the genius of someone after the fact, but perhaps harder
to predict in advance.
How Did Einstein Learn Math and
Physics?
Given Einstein’s enormous
contributions to physics, I think it’s now worthwhile to ask how he learned it.
Throughout the biography, I took
notes whenever his methods of learning and discovery were mentioned. Then, I
tried to synthesize these observations into several methods or behaviors that
appeared to have enabled both Einstein’s revolutionary discoveries and his deep
understanding of the subject matter.
1. Learning comes from solving hard
problems, not attending classes.
One thing that becomes apparent when
looking at Einstein’s early schooling was both his distaste for rote
memorization and attending classes. The physics professor that flunked him, did
so, in no small part, because Einstein often skipped class. As he claims, “I
played hooky a lot and studied the masters of theoretical physics with a holy
zeal at home.”
Einstein as a boy.
This habit of skipping classes to
focus on solving hard problems in his spare time was one cultivated by his
uncle, Jakob Einstein, who first introduced him to algebra. By the time he was
12, Einstein already had a, “predilection for solving complicated problems in
arithmetic,” and his parents bought him an advanced mathematical textbook he
could study from during the summer.
Einstein learned physics, not by
dutifully attending classes, but by obsessively playing with the ideas and
equations on his own. Doing, not listening, was the starting point for how he
learned physics.
2. You really know something when
you can prove it yourself.
How do you know when you really
understand something? Einstein’s method was to try prove the proposition
himself! This began at an early age, when Uncle Jakob, challenged him to prove
Pythagoras’s Theorem:
“After much effort, I succeeded in
‘proving’ this theorem on the basis of the similarity of triangles,” Einstein
recalled.
Isaacson explains that Einstein,
“tackled new theories by trying to prove them on his own.” This approach to
learning physics, which came naturally to Einstein, was driven by a strong
curiosity both to know how things actually work, and a belief that, “nature
could be understood as a relatively simple mathematical structure.”
What’s important to note here is not
only the method of proving propositions to learn physics, but also the drive to
do so. It’s clear that Einstein’s curiosity wasn’t merely to perform
adequately, but to develop a deep understanding and intuition about physical
concepts.
Einstein was a better intuitive
physicist than he was a mathematician. In fact, it was only when he struggled
for years in developing general relativity, that he became more enamored with
mathematical formalisms as a way of doing physics.
An early influence which encouraged
this intuitive approach to physics was a series of science books by Aaron
Bernstein. These books presented imaginative pictures to understand physical
phenomenon, such as, “an imaginary trip through space,” to understand an
electrical signal and even discussing the constancy of the speed of light, a
matter which would later underpin Einstein’s discovery of special relativity.
Swiss education reformer Pestalozzi
emphasized learning through images, not by rote.
Einstein’s later education in Aarau,
Switzerland, was heavily influenced by the philosophy of Swiss educational
reformer, Johann Heinrich Pestalozzi. Pestalozzi claimed, “Visual understanding
is the essential and only true means of teaching how to judge things
correctly,” adding, “the learning of numbers and language must definitely be
subordinated.”
Were these early influences causal
factors in Einstein’s later preferred style of visualization to solve physics
problems, or were they merely a welcome encouragement for a mind that was
already predisposed to reasoning in this way? It’s hard to tell. Whatever the
case, I think it can be argued that developing intuitions of ideas,
particularly visual intuitions, has an invaluable role in physics.
How does one develop those
intuitions? Einstein’s own thoughts were that “intuition is nothing but the outcome
of earlier intellectual experience.” Einstein’s hard work building
understanding through proofs and solving problems undoubtedly supported his
ability to visualize as much as it benefited from it.
4. Thinking requires a quiet space
and deep focus.
Einstein was a master of deep work. He had an
incredible ability to focus, his son reporting:
“Even the loudest baby-crying didn’t
seem to disturb Father,” adding, “He could go on with his work completely
impervious to noise.”
Although overlooked for academic
positions, it was his intellectually unstimulating job at the Bern patent
office, which gave him time and privacy to unravel the mysteries of relativity.
Einstein remarks:
“I was able to do a full day’s work
in only two or three hours. The remaining part of the day, I would work out my
own ideas.”
Einstein in his home office.
The obsessive focus Einstein applied
to solving problems as a young boy, eventually served him well in cracking
general relativity, culminating in an “exhausting four-week frenzy.” This
intensity sometimes impacted his health, with him developing stomach problems
in his strain to unravel the difficult mathematics of tensor field equations.
Einstein’s ability to focus,
combined with a reverence for solitude, allowed him to do some of his best work
in physics. Even as he aged, he still spent many hours on his boat, idly
pushing the rudder seemingly lost in thought, interrupted by bursts of
scribbling equations in his notebook.
5. Understand ideas through thought
experiments.
Einstein’s most famous method for
learning and discovering physics has to be the thought experiment.
Books such as this were Einstein’s
first introduction to the power of thought experiments.
One of his most famous was imagining
riding on a beam of light. What would happen to the light beam as he rode
alongside it at the same speed? Well, it would have to freeze. This, to
Einstein, seemed impossible by his faith in Maxwell’s electromagnetic
equations. But if the light doesn’t freeze, what must happen?
These thought experiments were built
on his intuitive understanding of physics, which in turn was built on his
experience with working through theories and problems. Their strength, however,
was to draw attention to contradictions or confusions that may have been missed
by a less intuitive physicist.
His ability to engage in thought
experiments even served him when he ended up being wrong about the underlying
physics. It was exactly this type of thought experiment that he suggested to
refute the current understanding of quantum physics in what is now known as the
ERP paper, which showed that quantum mechanics could create changes in a system
instantaneously, violating the speed of light. In this case, however,
Einstein’s intuition was wrong—quantum mechanical systems do behave in such
bizarre ways—which is now known as quantum entanglement.
6. Overturn common sense … with more
common sense.
Special and general relativity stand
out as being some of the most mind-bending scientific discoveries of all time.
With special relativity, Einstein discovered that there is no absolute
time—that two people moving at different speeds can disagree about the passage
of time—with neither being right or wrong. With general relativity, Einstein
went further, showing that gravity bends space and time.
Einstein at age 42, the year he won
the Nobel prize.
It would be reasonable to assume,
therefore, that to overturn such commonsense principles would require some
departure from common sense. However, Einstein’s genius was to reconcile two
commonsense principles—relativity and the constancy of the speed of light—by
discarding a third (the idea of absolute measurements of space and time).
Einstein’s talent, it would seem,
lay in his ability to defend what he thought were the most reasonable ideas,
even if that meant discarding ones which had a longer tradition of being
thought to be correct.
This skill of overturning
commonsense with other intuitions may have also eventually been behind his
inability to accept quantum mechanics, a very successful theory of physics that
he himself helped create. His intuitions about strict determinism, led him to
champion an unsuccessful and quixotic quest to overturn the theory for much of
his life.
This practice also suggests a method
for learning the many, counter-intuitive principles of math and physics—start
by building off of a different commonsense premise.
7. Insights come from friendly
walks.
While solitude and focus were
essential components of how Einstein learned and did physics, it was often
conversations with other people that provided his breakthroughs.
Albert Einstein with Michele Besso.
The most famous example of this was
a walk with longtime friend Michele Besso. During his struggles with special
relativity, he walked with his friend trying to explain his theory. Frustrated,
he declared that, “he was going to give up,” working on the theory. Suddenly,
however, the correct insight came to him and the next day he told Besso that he
had, “completely solved the problem.”
Discussing ideas aloud, sharing them
with others, can often put together insights that were previously unconnected.
Einstein made great use of this technique of discussing tricky problems with
friends and colleagues, even if they were merely a sounding board rather than
an active participant in the discussion.
8. Be rebellious.
Einstein was never much of a
conformist. While his rebellious streak probably hurt his earlier academic
career when he was struggling to find work in physics, it is also probably what
enabled his greatest discoveries and accentuated his later celebrity.
This rebelliousness likely helped
him in learning physics as he pushed against the traditions and orthodoxy he
didn’t agree with. He hated the German educational system, finding in
Isaacson’s words, “the style of teaching—rote drills, impatience with
questioning—to be repugnant.” This rejection of the common educational method
encouraged him to learn physics on his own through textbooks and practice.
Later, the same rebelliousness would
be essential in revolutionizing physics. His research on the quantization of
light, for instance, had been first discovered by Max Planck. However, unlike
the older Planck, Einstein saw the quantization as being a physical
reality—photons—rather than a mathematical contrivance. He was less attached to
the predominant theory of the time that light was a wave in the ether.
Where many students would have been
happy to conform to predominant educational and theoretical orthodoxies,
Einstein wasn’t satisfied unless something made sense to him personally.
9. All knowledge starts with
curiosity.
“Curiosity has its own reason for
existing,” Einstein explains. “One cannot help but be in awe when one
contemplates the mysteries of eternity, of life, of the marvelous structure of
reality.”
Einstein, curious until the end.
This curiosity is probably
Einstein’s most defining quality, after his intelligence. His love of physics
started as a boy when he was given a compass and fascinated by the idea that
the needle moved because of an unseen force.
Curiosity was his motivation for
learning physics. Einstein, who could be quite lazy and obstinate when a matter
didn’t interest him, nonetheless had an intense passion for understanding the
things, “the ordinary adult never bothers his head about.” Curiosity was also,
in his own mind, the greatest reason for his accomplishments.
Einstein believed that, “love is a
better teacher than a sense of duty.” Love of learning and knowledge is,
perhaps, a more important skill to cultivate than discipline.
Learning as Einstein Did
Einstein’s approach towards learning
cannot be entirely separated from who he was. Was his obsessive focus a result
of his intelligence or his curiosity? Did his ability to easily visualize
thought experiments come from encouragement in an unusual Swiss education
system, extensive practice or natural ability? Was his revolution in physics a
product of genius, rebelliousness, luck or maybe all three? I’m not sure there
are clear answers to any of those questions.
What is clear, however, was
Einstein’s reverence for nature and the humbled attitude to which he approached
investigating it. As he wrote:
“A spirit is manifest in the laws of
the universe—a spirit vastly superior to that of man, and one in the face of
which we with our modest powers must feel humble.”
And, so even if Einstein’s genius
may lay outside the reach of most of us, his curiosity, humility and tenacity
are still worth emulating.