kottke.org posts about Albert Einstein
Steven Strogatz walks us through the first mathematical proof Albert Einstein did when he was a boy: a proof of the Pythagorean theorem.
Einstein, unfortunately, left no such record of his childhood proof. In his Saturday Review essay, he described it in general terms, mentioning only that it relied on "the similarity of triangles." The consensus among Einstein's biographers is that he probably discovered, on his own, a standard textbook proof in which similar triangles (meaning triangles that are like photographic reductions or enlargements of one another) do indeed play a starring role. Walter Isaacson, Jeremy Bernstein, and Banesh Hoffman all come to this deflating conclusion, and each of them describes the steps that Einstein would have followed as he unwittingly reinvented a well-known proof.
Twenty-four years ago, however, an alternative contender for the lost proof emerged. In his book "Fractals, Chaos, Power Laws," the physicist Manfred Schroeder presented a breathtakingly simple proof of the Pythagorean theorem whose provenance he traced to Einstein.
Of course, that breathtaking simplicity later became a hallmark of Einstein's work in physics. See also this brilliant visualization of the Pythagorean theorem
P.S. I love that two of the top three most popular articles on the New Yorker's web site right now are about Albert Einstein.
Randall Munroe has a new book coming out called Thing Explainer: Complicated Stuff in Simple Words in which he uses the 1000 most common English words to explain interesting mostly scientific stuff. In a preview of the book, Munroe has a piece in the New Yorker explaining Einstein's theory of relativity using the same constraint.
The problem was light. A few dozen years before the space doctor's time, someone explained with numbers how waves of light and radio move through space. Everyone checked those numbers every way they could, and they seemed to be right. But there was trouble. The numbers said that the wave moved through space a certain distance every second. (The distance is about seven times around Earth.) They didn't say what was sitting still. They just said a certain distance every second.
It took people a while to realize what a huge problem this was. The numbers said that everyone will see light going that same distance every second, but what happens if you go really fast in the same direction as the light? If someone drove next to a light wave in a really fast car, wouldn't they see the light going past them slowly? The numbers said no-they would see the light going past them just as fast as if they were standing still.
It's a fun read, but as Bill Gates observed in his review of Thing Explainer, sometimes the limited vocabulary gets in the way of true understanding:1
If I have a criticism of Thing Explainer, it's that the clever concept sometimes gets in the way of clarity. Occasionally I found myself wishing that Munroe had allowed himself a few more terms -- "Mars" instead of "red world," or "helium" instead of "funny voice air."
See also Albert Einstein's Theory of Relativity In Words of Four Letters or Less. You might prefer this explanation instead, in the form of a video by high school senior Ryan Chester:
This video recently won Chester a $250,000 Breakthrough Prize college scholarship.2 Nice work!
Astronomers have been able to view the same supernova in a distant part of the Universe several times due to the gravitational lensing effect of a cluster of galaxies in-between here and there. From Dennis Overbye in the NY Times:
Supernovas are among the most violent and rare events in the universe, occurring perhaps once per century in a typical galaxy. They outshine entire galaxies, spewing elemental particles like oxygen and gold out into space to form the foundations of new worlds, and leaving behind crushed remnants called neutron stars or black holes.
Because of the galaxy cluster standing between this star and the Hubble, "basically, we got to see the supernova four times," Dr. Kelly said. And the explosion is expected to appear again in another part of the sky in the next 10 years. Timing the delays between its appearances, he explained, will allow astronomers to refine measurements of how fast the universe is expanding and to map the mysterious dark matter that supplies the bulk of the mass and gravitational oomph of the universe.
Scientists expect the supernova to reappear in the next few years. Gravitational lensing was predicted by Einstein's general theory of relativity and as Overbye writes, "the heavens continue to light candles for Albert Einstein."
Here's a photograph of Albert Einstein's Princeton desk taken only a few hours after he died in 1955.
It's from a slideshow of photos taken at the time of Einstein's death but never published before last week. (via clusterflock)
In 1905, Einstein came up with the concept of special relativity, published his paper on the photoelectric effect, finished his doctoral dissertation, devised the E=mc^2 concept, published a paper on Brownian motion, was approved for his doctorate, and turned 26.
So......what have you guys been up to?
Among the watches being auctioned at a sale in October is a watch once owned by Albert Einstein.
For the Einstein fan, we have a Longines that was owned by the scientist himself. It is a unique and historically important wristwatch, made in 1930.The watch was presented to Professor Albert Einstein on February 16, 1931 in Los Angeles. It is a fine, tonneau-shaped, 14K yellow gold wristwatch accompanied by various photos showing Prof. Einstein wearing the watch. Estimate: $25,000 - $35,000
You'd think that the price for timepiece once owned by the man who changed our conceptions about time and space would be substantial, but it's one of the lower priced featured watches. And the price is not even close to the world record:
In 2002, Antiquorum established the all-time world record price for a wristwatch at auction when it sold a platinum Patek Philippe World Time Ref. 1415 from 1939 for an astounding CHF 6,603,500 (US$ 4,026,524). This record-breaking price more than doubled the previous world record price for a wristwatch at auction. Another record price for a modern watch was achieved in 2004, the unique white gold Calibre 89, also by Patek Philippe, was sold for SFr. 6,603,500 (US$ 5,002,652).
A moving mass has been shown to generate a gravitomagnetic field (just like a moving electrical charge creates a magnetic field) and "the measured field is a surprising one hundred million trillion times larger than Einstein's General Relativity predicts". (via rw)
Brian Greene on Einstein's most famous equation, E =mc^2. When he finally gets around to it in the middle of the article, Greene's got a pretty good layman's explanation of what the formula actually means.
PBS has put up a companion web site to the Nova program on Einstein airing in October. Features include audio clips of several physicists describing e=mc^2 to non-physicists.
The importance of narrative in science. "Science and stories are not only compatible, they're inseparable, as shown by Einstein's classic 1905 paper on the photoelectric effect".
A near perfect Einstein Ring found. Close galaxies can act as a lens for farther galaxies, focusing the distant light with an "Einstein Ring".