The Joy of Mathematical Proofs

I just received a new physics textbook that I ordered online - yes, I know, I don't need any more physics textbooks - and, as usual, no matter how familiar the material, I can always find something to learn that I didn't know.

This book is Matter in Motion: The Spirit and Evolution of Physics, by Ernest S. Abers and Charles F. Kennel, two UCLA professors. I was a students in Abers's quantum mechanics classes, and Kennel was in the plasma physics group, so I knew them both, although I hadn't known that they had written a book in 1977 for their "Physics for Non-Science Majors" class. I discovered the book while perusing the July 1977 issue of Physics Today while looking for another article (but that is another story, perhaps to be written about in a future post).

The review praised the book for not trying to do too much, and successfully dispelling "the widely held misapprehension that science consists of little more than a vast collection of uncontestable facts meticulously gathered and catalogued by individuals distinguished primarily by their ability to repress their emotions completely." They extend their discussion of the history of physics to the pre-Galileo period, where "Greek and medieval science finally get their day in court." That is, Abers and Kennel show how the Greeks obtained their results, rather than simply telling you.

My two favorites (that I have come across so far) are a simple proof of the Pythagorean theorem (one that they claim is essentially the same as the original) and a neat proof that there are only five regular solids. I've already posted about Euler's formula

F + V - E = 2

in August 2014 when I discussed Zometools. I mentioned then that there were at least 20 different proofs. Now, I don't have a classical math background. In fact, I'm one of the physicists that avoid as much math as possible, not because I don't love it, but because I like to use it rather than play around with it for its own sake. However, the latter is sometimes lots of fun. Back in 2014 I learned one of those proofs. And Abers & Kennel use Euler's formula to prove that there are only 5 regular solids (also known as Platonic solids: tetrahedron, cube, octahedron, dodecahedron, icosahedron).

So, now that I can prove some things, does that make me a mathematician?

Walter Elsasser "Memoirs of a Physicist in the Atomic Age"

Memoirs of a Physicist in the Atomic Age by Walter M. Elsasser
My rating: 4 of 5 stars

Elsasser was the founder of the dynamo theory of the Earth's magnetic field, and also had a successful career in other areas of physics, nuclear physics in Paris with the Joliot-Curies, for example, as well as meteorology. He was prolific, and published many journal articles in these areas. In his later life he turned to biology, and wrote three books on biophysics that never were quite accepted by the biological community.

In this book, he gives a more personal view of famous physicists of the early 20th century (Curie, Born, Oppenheimer, Wigner, Schroedinger, etc) than the well-known histories by Gamow and Segre - i.e., less physics - but interesting and enjoyable. His philosophical ideas I sometimes could not follow (or agree with), but the fact that he interacted professionally with so many famous physicists made for an interesting life - and an interesting read.

One scene that depicted 1922 Germany was especially eye-opening. While I knew that Philipp Lenard (Nobel Prize Physics 1905) was a strong supporter of the Nazi party, I didn't realize the extent to which this permeated his lectures, and the extent to which anti-Semitism had quickly escalated after World War I. Elsasser describes his first physics lecture at the University of Heidelberg like this:

“Every seat in the hall was taken. In walked Professor Lenard wearing an impeccably tailored suit; to his left breast there was fastened a silver swastika of gigantic proportions, perhaps ten centimeters square. This was most unusual, if one remembers that in spite of war and revolution, Germany had then still remained a place of law and order. A distinguished senior professor was most certainly not expected to brandish symbols of political extremism in class. But the students thought otherwise. They applauded intensely. They clapped, and then they shouted; they kept on clapping and shouting, on and on and on. How long this continued I cannot say precisely, but it was certainly the most dedicated and loudest ovation I ever witnessed in my life, before or after."

The recent (2017) biography on Einstein on the National Geographic channel, "Genius," depicts a similar scene in one of Lenard's lectures. There, he refuses to cancel class for the funeral of the assassinated Jewish politician, Walther Rathenau, and instead lectures to supportive students about the need to abolish the "Jewish physics of relativity" and return to "pure German physics."

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UPDATE: In Jeremy Bernstein's biography Einstein, he describes anti-Semitic (and anti-Einstein) activity even earlier, in 1920:

"In 1920 an anti-Einstein League was formed in Germany, and it offered substantial sums of money to anyone who would write refutations of Einstein's work. On August 24, 1920, the League sponsored a meeting in the Berlin Philharmonic Hall, which Einstein himself attended, where swastikas and anti-Semitic pamphlets were on sale, at which Einstein and his work were attacked. A few of his colleges respond in a letter to the 'Berliner Tageblatt' and a few days later Einstein himself wrote an angry letter, also published by the 'Berliner Tageblatt' --- which deeply shocked Ehrenfest, who seemed to feel that Einstein should have ignored the matter as unworthy of his attention. From this time on, until he finally left Germany in 1932, Einstein and his work were the targets of a steadily mounting campaign."

Lola Montez

This lady has one of the craziest stories around. Everywhere in Munich and Bavaria you hear stories about "crazy King Ludwig," and they are usually referring to Ludwig II, the young king who built not one but three fairy tale castles, the most famous of which is Neuschwanstein.

However, his grandfather, Ludwig I, had his own set of interesting problems. Who knows if he was crazy, but he was certainly crazy in love with Lola, who was not his wife. The wife of Ludwig I was Therese of Saxe-Hildburghausen. She is famous because the party after their wedding in 1810 turned out to be the first Oktoberfest. And they liked it so much, they've held it every year since then at a large field in the south of Munich called the Theresienwiese.

Now, Ludwig I ended up abdicating the Bavarian throne in 1848 (a time of much unrest in Germany, but that story is for another day) twenty years before his death, partly due to the scandal of his affair with Lola Montez. She purported to be a "Spanish dancer," but in fact she was Irish. Ludwig I made her a Countess, and she had some influence on his political decisions (this was part of the scandal). However, what I found interesting is what she did after she was forced to flee Bavaria in 1848.

She went to many parts of the world (France, London, Australia), but she spent a fair amount of time in, of all places, Grass Valley, California, just outside of Sacramento. Her home is California Historical Landmark No. 292. And among other things, the highest point in Nevada County is Mount Lola, named after her.

Ulm

While my students went off to Prague for the weekend, I went to Ulm on Saturday. It's a very old city - founded around 850 CE - and is situated on the Donau (Danube) River. For some reason I am drawn to the Donau, not only because of the song. There are several cities on the Danube that I'd like to visit, not least of which is BudaPest, and also Bratislava. But they are too far to go for this trip. For now, I'll content myself with visiting the Bavarian cities on the Donau: Ulm, Ingolstadt, Regensburg. Yes, I know that Ulm is in Baden-Württemburg. But it used to be in Bavaria, and, being that Neu-Ulm across the river is in Bavaria, and noting that you are allowed to travel by train to Ulm using your Bayern ticket, I contend that it should count as Bavaria.

Here is a nice view of Ulm from 1572, in which you can see its most outstanding feature, the Ulmer Münster! This is a church that has the highest steeple in the world, measuring 161 m. You can climb to the top, which I did; well, almost the top. The stairs reach 143 m in 768 steps. And it takes about 20 minutes, unless you're very fit, but still you have to contend with people coming down. The first two thirds are "one way" stairs, so you can effectively go as fast as you wish.

However, the top third is a single stairwell climbing up the center of the the spire. As you can see from the photo below, there is a nice superstructure for the spire, with a column in the center, and a spiral staircase in the center of the column. There's not much room to pass, and some young children were a little frightened. And everyone had to take it slow.

Most of the city center was bombed by the RAF in 1944, but amazingly the Münster was essentially untouched. This was fortunate, because it's construction began in 1377, so it is a "cathedral" with much history. It wasn't completed until 1890 (talk about patience), and it also isn't technically a cathedral, since Ulm went Protestant in 1530 (it's now a Lutheran church).

When I got up to the top, the view, of course, was great. The red roofs of the city buildings spread out along the Donau were quite the sight.

In the photo on the left, from lower down (far below the top) you can clearly see the flying buttresses, as in Notre Dame. In the photo on the right, from the top, you can see the entire church, with the two steeples toward the east. I need to learn my cathedral architecture: chapel, nave, altar, etc. Here's one place to learn it.

Finally, the inside was incredibly large, and no pictures would do it justice. They did have beautiful stained glass windows, and I tried to give a feeling for them below. There were several along the sides of the church.

The Pullach Deutsch - Französisches Freundschaftsfest

Yesterday, Freitag 24 Juni, was the start of the 23rd Freundschaftsfest on the Kirchplatz in Pullach im Iasartal, just south of Munich, on the Isar river. The square was closed off for food, drink (lots of bier und wein), and music. My favorite Weissbier (Franziskaner) was served, along with Rotbratwurst (chili hot) and much else. As you can see from the schedule, the fun will continue all weekend.

However, the weather may not cooperate. It's supposed to rain starting tonight, and also on Sunday. Hopefully that won't put too much of a damper on things.

There were plenty of cute kids playing festival games (ring toss, etc), and winning prizes, like stuffed animals and roses.

And there was even a marching band! (Note: below is a 6MB Quicktime Movie)

Prost from Pullach!

Germany II

Tomorrow will be the 6th time I will travel to Europe. Summer 1973 to Madrid to live in my uncle's house for one month. Summer 1983 to live in Vitoria with a family for 5 weeks. Thanksgiving 1999 to Brussels to collaborate with J. Lemaire for one week. Fall 2002 to Maastricht for a conference for one week. Winter 2014-2015 to Munich to teach at Hochschule München for 4 months while on sabbatical. And now Summer 2016 to Munich to lead 9 students on a Summer B study abroad. I feel very lucky to have had these opportunities in my life, and I think the perspective that one gains (at least that I have gained) by interacting with people from other countries and cultures is invaluable.

The last time I went to Munich I arrived in the morning, took the S-Bahn to Pullach, just south of the city on the edge of the Isar river, joined some people (who I'd never met) who were visiting for Oktoberfest, and went to the WaWi for lunch (sausages and bier).

So this is now my "Munich routine." The first thing I'll do on Thursday morning when I arrive at the München Flughafen is to take the S-Bahn to Pullach, and have lunch and excellent Bavarian bier at the WaWi.

The best popular science books

I just ran across this post by Steven Weinberg listing the best science books for the general reader. For the most part, I like the list (see below). I own 6 of the books, and have read most of 4 of them. There are some that I think are excellent, like Gamow's The Birth and Death of the Sun, although I prefer One, Two, Three...Infinity by the same author better. Feynman's The Character of Physical Law I think is excellent. But my favorite book, although it's probably best for someone with a technical bent, not a general reader, is Weinberg's own The First Three Minutes. I first read that book between my junior and senior years as a physics major at UC Santa Cruz, and was literally blown away. It had a huge impact on me. Although I had already decided to lead a life in physics, that was at a point where I found everything having to do with physics incredibly cool and interesting.

I was led to Weinberg's article (which is an interesting and well-written article, completely separate from his list of books) by this article by Chad Orzel. To be honest, I wasn't very impressed by Orzel's book on 'how to teach your dog physics.' It may play to the general reader who doesn't know anything about physics, but I'm more interested in books that are geared toward intelligent readers that know something about physics. Along this vein, I hand out such books to students in my introductory (and advanced) physics classes who score well on exams. Especially freshman students taking university-level physics for the first time, I want to expand their knowledge about different kinds of physics and astronomy, and how to actually use the physics that we're learning. Along this line are the three books listed above, or Weinberg's Dreams of a Final Theory, or books by Isaac Asimov, or Lawrence Krauss's The Physics of Star Trek. Given the wide interest among students in string theory, the recent book by Jim Baggot, Farewell to Reality, gives a level-headed picture of what physics (and science) is, and how to think about cutting-edge physics when you are a freshman. I also pointedly do not give out any books by Michio Kaku, because he is definitely part of the problem. I've already mentioned in a previous post one of the best books for clearly stating which physical ideas are speculative, and which have lots of observational evidence.

Orzel gives his own list here, and chides Weinberg for being "in the Whig history mode," whatever that means. His first book is probably the worst science book every for the general reader - defined as someone who is not an expert in any of the science in the book, but hopefully will take away a realistic picture of what the important issues are. This bad book is Bill Bryson's A Short History of Nearly Everything. First of all, Bryson is not a scientist. This is not necessarily a bad thing, but in Bryson's case it is. He has no understanding of what science is all about, and hence he conveys many wrong things. I've read pieces of the book, and what I read seemed OK, even enlightening. This is probably true because Bryson is such a great writer. (In fact his comedy writing, like A Walk in the Woods, is top notch.) However, then I read an interesting review of the book by a scientist. They said that everything looked pretty good, but when he covered the reviewer's own field of expertise, Bryson got things wrong. So the reviewer asked other scientsist their opinion. They said essentially the same thing: "It's a great book, but when he talks about X [my field of expertise] he doesn't know what he's talking about." This means that the reader thinks he's getting an understanding of some technical issue, but he's getting the wrong understanding. And that's the worst kind of science writing because it's masquerading as good writing.

The only other books on Orzel's list that I've heard of before are Richard Feynman's QED: The Strange Theory of Light and Matter, Kip Thorne's Black Holes and Time Warps, and George Gamow's Mr Thompkins in Wonderland. All three are excellent, but I think the first two are not really for the general reader at all, and would require at least some formal education in physics at the university level, if not an undergraduate degree.

As I said, I give away books to my physics students, and over the past 10-15 years I've given away approximately 150 books. I get them from used book stores, and I often give away duplicate copies of the same book, for example, Steven Hawking's A Brief History of Time. Below I give Weinberg's list of 13 books, and then I give all the books I've given away. There's not much overlap, mostly because I try to give away books that deal with physics and astronomy, either directly or indirectly.

Here is Weinberg's list:

Philosophical Letters (1733) Voltaire

The Origin of Species (1859) Charles Darwin

On a Piece of Chalk (1868) Thomas Huxley

The Mysterious Universe (1930) James Jeans

The Birth and Death of the Sun (1940) George Gamow

The Character of Physical Law (1965) Richard Feynman

The Elegant Universe (1999) Brian Greene

The Selfish Gene (1976) Richard Dawkins

The Making of the Atomic Bomb (1986) Richard Rhodes

The Inflationary Universe (1997) Alan Guth

The Whole Shebang (1997) Timothy Ferris

Hiding in the Mirror (2005) Lawrence Krauss

Warped Passages (2005) Lisa Randall

And here is my list:

Abbott	Flatland: A romance of many dimensions
Andrade	Quanta
Andrade	Sir Isaac Newton: His life and work
Andrade	Rutherford and the nature of the atom
Asimov	Quasar, Quasar, Burning Bright
Asimov	Understanding Physics: Motion, Sound, and Heat
Asimov	Atom: Journey across the subatomic cosmos
Asimov	The Collapsing Universe
Aveni	Conversing with the planets
Barrow	Theories of Everything
Barrow	The origin of the universe
Bergreen	Voyage to Mars: NASA's Search for Life Beyond Earth
Bodanis	E=mc2: A biography of the world's most famous equation
Bruce	Schrodinger's Rabbits
Calder	Einstein's Universe
Carter	Latitude: How American astronomers solved the mystery of variation
Chaikin	A Man on the Moon
Collins	Carrying the Fire
Coveney	The arrow of time
Crease	The second creation: Makers of the revolution in 20th-century physics
Davies	The Last Three Minutes
Davies	About Time: Einstein's unfinished revolution
Ehrlich	The cosmological milkshake
Einstein	Relativity: The special and the general theory
Einstein	Einstein's Miraculous Year
Ferris	The Whole Shebang
Feynman	Surely You're Joking, Mr. Feynman
Fritz	Understanding Cosmology
Galileo	Discoveries and Opinions of Galileo
Gamov	The Great Physicists from Galileo to Einstein
Gamow	Mr Tompkins in paperback
Gamow	One Two Three … Infinity
Gleick	Chaos
Gleick	Isaac Newton
Glenn	We Seven
Gray	Angle of Attack
Greene	The elegant universe
Gribbin	Spacewarps: A book about Black Holes, White Holes, Quasars, and our violent Universe
Gribbin	Schrodinger's Kittens and the Search for Reality
Gribbin	Stardust
Gribbin	Quantum Physics
Guth	The Inflationary Universe
Hawking	Black holes and baby universes
Hawking	A brief history of time
Hawking	A brief history of time: A reader's companion
Helmholtz	On the sensations of tone
Herbert	Faster than light
Jastrow	Red Giants and White Dwarfs
Jones	Physics for the rest of us
Kane	The Particle Garden
Krauss	Fear of Physics
Krauss	The Physics of Star Trek
Levin	How the universe got its spots
Lightman	Ancient Light: Our changing view of the universe
Lindley	The end of physics
Lloyd	Programming the Universe
Magueijo	Faster than the speed of light
Marshall	Who's Afraid of Schrodinger's Cat?
McPhee	The curve of binding energy
Nahin	An imaginary tale: The story of i
Nasar	A beautiful mind
Pagels	The cosmic code
Parker	The vindication of the Big Bang
Peat	Superstrings and the search for the theory of everything
Petroski	To Engineer is Human
Pullman	The atom in the history of human thought
Randall	Warped passages
Reichenbach	From Copernicus to Einstein
Reid	Marie Curie
Rhodes	The Making of the Atomic Bomb
Segre	From falling bodies to radio waves
Shipman	Black holes, quasars, and the universe
Singh	Big Bang: The origin of the universe
Smolin	The trouble with physics
Smoot	Wrinkles in Time
Sobel	Longitude
Stewart	Nature's Numbers
Thorne	Black holes and time warps
Time-Life	The Far Planets
Trefil	The Unexpected Vista
Tufte	Visual Explanations
von Baeyer	Taming the Atom
von Baeyer	The Fermi Solution
Watson	The double helix
Weinberg	Dreams of a Final Theory
Weinberg	The First Three Minutes
Weinberg	The Discovery of Subatomic Particles
Will	Was Einstein Right?
Zee	Fearful symmetry: The search for beauty in modern physics