Tag: Physics

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.

Richard Feynman: The Universe in a Glass of Wine

A poet once said, “The whole universe is in a glass of wine.” We will probably never know in what sense he meant that, for poets do not write to be understood. But it is true that if we look at a glass of wine closely enough we see the entire universe. There are the things of physics: the twisting liquid which evaporates depending on the wind and weather, the reflections in the glass, and our imagination adds the atoms. The glass is a distillation of the earth’s rocks, and in its composition we see the secrets of the universe’s age, and the evolution of stars. What strange array of chemicals are in the wine? How did they come to be? There are the ferments, the enzymes, the substrates, and the products. There in wine is found the great generalization: all life is fermentation. Nobody can discover the chemistry of wine without discovering, as did Louis Pasteur, the cause of much disease. How vivid is the claret, pressing its existence into the consciousness that watches it! If our small minds, for some convenience, divide this glass of wine, this universe, into parts—physics, biology, geology, astronomy, psychology, and so on—remember that nature does not know it! So let us put it all back together, not forgetting ultimately what it is for. Let it give us one more final pleasure: drink it and forget it all!

From the lecture titled “The Relation of Physics to Other Sciences,” in which Richard Feynman highlights the connectedness of everything to everything else. Feynman’s lectures are collected in The Feynman Lectures on Physics.

Science, Religion, and The Universe

I could listen to Neil deGrasse Tyson talk all day. His argument that persuading with facts is not enough, offers some fantastic insight.

Here he talks to Bill Moyers about our mysterious universe and whether faith and science can be reconciled. This is part two of a three part series. The first part is on the new cosmos and the second on science literacy.

In an interesting moment he touches on why, despite the invention of Google street view and online tours, there is no substitute for the real thing.

If you tour the air and space museum in Washington, which has the history of flight, including space flight … (The) museum people could have made an exact replica of the Apollo 11 command module that went to the moon. And then we’d say, here is an exact replica.. so that’s ok. But if I now say this actual thing went to the moon, intellectually that means something different to you. Your eyes see exactly the same thing. You can make a replica … with all the blemishes and the heat shield damage but if you know it is the real thing the meaning is magnified.

The Feynman Lectures on Physics


“The whole thing was basically an experiment,” Richard Feynman said late in his career, looking back on the origins of his lectures. The experiment turned out to be hugely successful, spawning a book that has remained a definitive introduction to physics for decades. Ranging from the most basic principles of Newtonian physics through such formidable theories as general relativity and quantum mechanics, Feynman’s lectures stand as a monument of clear exposition and deep insight. (Feynman Lectures)

The timeless lectures are now being put online for free, these are “not just for students of physics but for anyone seeking an introduction to the field from the inimitable Feynman.”

An iconoclastic and influential theoretical physicist, not to mention Nobel Laureate, Richard Feynman(1918-1988) touched the lives of many.

Feynman is best known for his role in Los Alamos and the challenger investigation, but he was also an amazing teacher.

Now, at long last, his famous physics lectures, thanks to Caltech and The Feynman Lectures website, are being put online. Starting with the 52 chapters of volume one. Of course, you can always watch a few of them in video.

These are the lectures in physics that I gave last year and the year before to the freshman and sophomore classes at Caltech. The lectures are, of course, not verbatim—they have been edited, sometimes extensively and sometimes less so. The lectures form only part of the complete course.

See: Volume I: mainly mechanics, radiation and heat.

It’s impossible to learn very much by simply sitting in a lecture, or even by simply doing problems that are assigned. But in our modern times we have so many students to teach that we have to try to find some substitute for the ideal. Perhaps my lectures can make some contribution. Perhaps in some small place where there are individual teachers and students, they may get some inspiration or some ideas from the lectures. Perhaps they will have fun thinking them through—or going on to develop some of the ideas further.

This is all a work in progress, volumes II and II “will be posted as time and funds permit.” If you can’t wait, or you don’t want to kill your printer, you can always buy the paperbound set.