Tag: Albert Einstein

The Simple Problem Einstein Couldn’t Solve … At First

Albert Einstein and Max Wertheimer were close friends. Both found themselves in exile in the United States after fleeing the Nazis in the early 1930s, Einstein at Princeton and Wertheimer in New York.

They communicated by exchanging letters in which Wertheimer would entertain Einstein with thought problems.

In 1934 Wertheimer sent the following problem in a letter.

An old clattery auto is to drive a stretch of 2 miles, up and down a hill, /\. Because it is so old, it cannot drive the first mile— the ascent —faster than with an average speed of 15 miles per hour. Question: How fast does it have to drive the second mile— on going down, it can, of course, go faster—in order to obtain an average speed (for the whole distance) of 30 miles an hour?

Einstein fell for this teaser
Einstein fell for this teaser

Wertheimer’s thought problem suggests the answer might be 45 or even 60 miles an hour. But that is not the case. Even if the car broke the sound barrier on the way down, it would not achieve an average speed of 30 miles an hour. Don’t be worried if you were fooled, Einstein was at first too. Replying “Not until calculating did I notice that there is no time left for the way down!”

Gerd Gigerenzer explains the answer in his book Risk Savvy: How to Make Good Decisions:

Gestalt psychologists’ way to solve problems is to reformulate the question until the answer becomes clear. Here’s how it works. How long does it take the old car to reach the top of the hill? The road up is one mile long. The car travels fifteen miles per hour, so it takes four minutes (one hour divided by fifteen) to reach the top. How long does it take the car to drive up and down the hill, with an average speed of thirty miles per hour? The road up and down is two miles long. Thirty miles per hour translates into two miles per four minutes. Thus, the car needs four minutes to drive the entire distance. But these four minutes were already used up by the time the car reached the top.

Einstein: The World As I See It

"The most beautiful experience we can have is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. Whoever does not know it and can no longer wonder, no longer marvel, is as good as dead, and his eyes are dimmed."
“The most beautiful experience we can have is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. Whoever does not know it and can no longer wonder, no longer marvel, is as good as dead, and his eyes are dimmed.”

Originally published in Forum and Century, Vol. 84, in 1931 and now found in the powerful collection Ideas and Opinions, Einstein’s essay speaks to our creative child, our search for wonder, and our curiosity.

How strange is the lot of us mortals! Each of us is here for a brief sojourn; for what purpose he knows not, though he sometimes thinks he senses it. But without deeper reflection one knows from daily life that one exists for other people—first of all for those upon whose smiles and well-being our own happiness is wholly dependent, and then for the many, unknown to us, to whose destinies we are bound by the ties of sympathy. A hundred times every day I remind myself that my inner and outer life are based on the labors of other men, living and dead, and that I must exert myself in order to give in the same measure as I have received and am still receiving. I am strongly drawn to a frugal life and am often oppressively aware that I am engrossing an undue amount of the labor of my fellow-men. I regard class distinctions as unjustified and, in the last resort, based on force. I also believe that a simple and unassuming life is good for everybody, physically and mentally.

I do not at all believe in human freedom in the philosophical sense. Everybody acts not only under external compulsion but also in accordance with inner necessity. Schopenhauer’s saying, “A man can do what he wants, but not want what he wants,” has been a very real inspiration to me since my youth; it has been a continual consolation in the face of life’s hardships, my own and others’, and an unfailing well-spring of tolerance. This realization mercifully mitigates the easily paralyzing sense of responsibility and prevents us from taking ourselves and other people all too seriously; it is conducive to a view of life which, in particular, gives humor its due.

To inquire after the meaning or object of one’s own existence or that of all creatures has always seemed to me absurd from an objective point of view. And yet everybody has certain ideals which determine the direction of his endeavors and his judgments. In this sense I have never looked upon ease and happiness as ends in themselves—this ethical basis I call the ideal of a pigsty. The ideals which have lighted my way, and time after time have given me new courage to face life cheerfully, have been Kindness, Beauty, and Truth. Without the sense of kinship with men of like mind, without the occupation with the objective world, the eternally unattainable in the field of art and scientific endeavors, life would have seemed to me empty. The trite objects of human efforts—possessions, outward success, luxury—have always seemed to me contemptible.

My passionate sense of social justice and social responsibility has always contrasted oddly with my pronounced lack of need for direct contact with other human beings and human communities. I am truly a “lone traveler” and have never belonged to my country, my home, my friends, or even my immediate family, with my whole heart; in the face of all these ties, I have never lost a sense of distance and a need for solitude—feelings which increase with the years. One becomes sharply aware, but without regret, of the limits of mutual understanding and consonance with other people. No doubt, such a person loses some of his innocence and unconcern; on the other hand, he is largely independent of the opinions, habits, and judgments of his fellows and avoids the temptation to build his inner equilibrium upon such insecure foundations.

My political ideal is democracy. Let every man be respected as an individual and no man idolized. It is an irony of fate that I myself have been the recipient of excessive admiration and reverence from my fellow-beings, through no fault, and no merit, of my own. The cause of this may well be the desire, unattainable for many, to understand the few ideas to which I have with my feeble powers attained through ceaseless struggle. I am quite aware that it is necessary for the achievement of the objective of an organization that one man should do the thinking and directing and generally bear the responsibility. But the led must not be coerced, they must be able to choose their leader. An autocratic system of coercion, in my opinion, soon degenerates. For force always attracts men of low morality, and I believe it to be an invariable rule that tyrants of genius are succeeded by scoundrels. For this reason I have always been passionately opposed to systems such as we see in Italy and Russia today. The thing that has brought discredit upon the form of democracy as it exists in Europe today is not to be laid to the door of the democratic principle as such, but to the lack of stability of governments and to the impersonal character of the electoral system. I believe that in this respect the United States of America have found the right way. They have a President who is elected for a sufficiently long period and has sufficient powers really to exercise his responsibility. What I value, on the other hand, in the German political system is the more extensive provision that it makes for the individual in case of illness or need. The really valuable thing in the pageant of human life seems to me not the political state, but the creative, sentient individual, the personality; it alone creates the noble and the sublime, while the herd as such remains dull in thought and dull in feeling.

This topic brings me to that worst outcrop of herd life, the military system, which I abhor. That a man can take pleasure in marching in fours to the strains of a band is enough to make me despise him. He has only been given his big brain by mistake; unprotected spinal marrow was all he needed. This plague-spot of civilization ought to be abolished with all possible speed. Heroism on command, senseless violence, and all the loathsome nonsense that goes by the name of patriotism—how passionately I hate them! How vile and despicable seems war to me! I would rather be hacked in pieces than take part in such an abominable business. My opinion of the human race is high enough that I believe this bogey would have disappeared long ago, had the sound sense of the peoples not been systematically corrupted by commercial and political interests acting through the schools and the Press.

The most beautiful experience we can have is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. Whoever does not know it and can no longer wonder, no longer marvel, is as good as dead, and his eyes are dimmed. It was the experience of mystery—even if mixed with fear—that engendered religion. A knowledge of the existence of something we cannot penetrate, our perceptions of the profoundest reason and the most radiant beauty, which only in their most primitive forms are accessible to our minds—it is this knowledge and this emotion that constitute true religiosity; in this sense, and in this alone, I am a deeply religious man. I cannot conceive of a God who rewards and punishes his creatures, or has a will of the kind that we experience in ourselves. Neither can I nor would I want to conceive of an individual that survives his physical death; let feeble souls, from fear or absurd egoism, cherish such thoughts. I am satisfied with the mystery of the eternity of life and with the awareness and a glimpse of the marvelous structure of the existing world, together with the devoted striving to comprehend a portion, be it ever so tiny, of the Reason that manifests itself in nature.

Ideas and Opinions is a necessary addition to your anti-library.

Einstein on The Essential Feature of Productive Thought

“Combinatory play seems to be the essential feature in productive thought.”
“Combinatory play seems to be the essential feature in productive thought.”

There is a view, to which I subscribe, that a lot of innovation and creativity comes from the combination of worldly wisdom, perspective, accumulating existing ideas, failures from multiple disciplines, amongst other things. These ideas — sometimes consciously and sometimes unconsciously tossed around in our head — combine into something new. This is part of the reason that creativity and innovation is hard. You can’t just pick up a single book or thread of knowledge and have it deliver results.

This beautiful Steve Jobs quote sums it up nicely.

“Creativity is just connecting things. When you ask creative people how they did something, they feel a little guilty because they didn’t really do it, they just saw something. It seemed obvious to them after a while.”

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In 1945 Jacques S. Hadamard surveyed mathematicians to determine their mental processes at work by posing a series of questions to them and later published his results in An Essay on the Psychology of Invention in the Mathematical Field.

It would be very helpful for the purpose of psychological investigation to know what internal or mental images, what kind of “internal words” mathematicians make use of; whether they are motor, auditory, visual, or mixed, depending on the subject which they are studying.

Especially in research thought, do the mental pictures or internal words present themselves in the full consciousness or in the fringe-consciousness …?

Einstein‘s response to the French mathematician, found in his Ideas and Opinions, shows the physicist’s mind at work and the value of “combinatory play.”

My Dear Colleague:

In the following, I am trying to answer in brief your questions as well as I am able. I am not satisfied myself with those answers and I am willing to answer more questions if you believe this could be of any advantage for the very interesting and difficult work you have undertaken.

(A) The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be “voluntarily” reproduced and combined.

There is, of course, a certain connection between those elements and relevant logical concepts. It is also clear that the desire to arrive finally at logically connected concepts is the emotional basis of this rather vague play with the above-mentioned elements. But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought — before there is any connection with logical construction in words or other kinds of signs which can be communicated to others.

(B) The above-mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will.

(C) According to what has been said, the play with the mentioned elements is aimed to be analogous to certain logical connections one is searching for.

(D) Visual and motor. In a stage when words intervene at all, they are, in my case, purely auditive, but they interfere only in a secondary stage, as already mentioned.

(E) It seems to me that what you call full consciousness is a limit case which can never be fully accomplished. This seems to me connected with the fact called the narrowness of consciousness (Enge des Bewusstseins).

Remark: Professor Max Wertheimer has tried to investigate the distinction between mere associating or combining of reproducible elements and between understanding (organisches Begreifen); I cannot judge how far his psychological analysis catches the essential point.

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Still curious? Combinatory play is one of the principles of Farnam Street. It’s so important I’ve incorporated it into the Re:Think Workshops.

How a Scientist Gets Things Wrong

Albert Einstein, writing to fellow physicist Hendrik Lorentz in 1915, describes how a scientist gets things wrong:

1. The devil leads him by the nose with a false hypothesis. (For this he deserves our pity.)

2. His arguments are erroneous and sloppy. (For this he deserves a beating.)

“Einstein himself certainly committed errors of both types,” the astrophysicist Mario Livio writes in, Brilliant Blunders: From Darwin to Einstein – Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe.

“More than 20 percent of Einstein’s original papers contain mistakes of some sort,” Livio writes. “In several cases, even though he made mistakes along the way, the final result is still correct. This is often the hallmark of great theorists: They are guided by intuition more than by formalism.”

Carl Zimmer, in his New York Times review of Brilliant Blunders, describes some of Charles Darwins “mistakes:”

When Charles Darwin presented his theory of evolution in 1859, he built a foundation for all of modern biology. Crucial to his theory was the fact that animals and plants inherited traits from their ancestors. Natural selection favored some traits over others, giving rise to long-term change. But Darwin didn’t know how heredity worked. He devoted a lot of time to developing ideas that, in hindsight, seem daft. “Darwin had been educated according to the then widely held belief that the characteristics of the two parents become physically blended in their offspring,” Livio writes, “as in the mixing of paints.” By this logic, each ancestor’s genetic contribution would be halved in each generation.

This idea wasn’t just wrong. It undermined Darwin’s own theory of evolution. If our traits are just a result of blended particles, it shouldn’t be possible for natural selection to change traits over the generations. But try as he might, Darwin couldn’t figure out a better explanation.

Yet right around the time that Darwin published “On the Origin of Species,” the Czech monk Gregor Mendel was discovering genetics. Crossing pea plants in his garden, he got a glimpse at how heredity actually does work. Darwin apparently never became aware of Mendel’s work, nor did he discover Mendel’s results for himself.

Still curious? Read the book

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