Saturday, July 13, 2019

STEVEN WEINBERG ON GRAVITY WAVES

On Friday night, July 12, Nobel laureate Steven Weinberg was the guest speaker at the monthly Austin Astronomy Club meeting. His topic was gravitational waves. 

(The grammar can be important. A “gravity wave” is actually a weather event here on Earth. Waves on the ocean are gravity waves. But we call gravitation waves “gravity waves” just as we sometimes are careless with “speed” and “velocity”.)

Dr. Steven Weinberg
(UT Austin)
Dr. Weinberg said that the LIGO (Laser Interferometer Gravitational-Wave Observatory) apparatus was an advance in the technology of perception as significant as Galileo’s use of the telescope. According to the LIGO website, gravitation waves are as different from electro-magnetic radiation (“light waves “) as light is from sound. 

Dr. Weinberg credited A. A. Michelson with the development of the kind of interferometer used for these investigations. Reading websites before the lecture, it was apparent to me that these arrangements are extensions of the Michelson-Morley experiment. Long paths of light set at right angles and placed far apart (Hanford, Washington; Livingston, Louisiana; and Pisa, Tuscany), are superimposed so that the smallest variation is revealed by an interference pattern. 

Entropy is real. The Moon will collide with the Earth – eventually. When neutron stars and black holes orbit each other, the losses of energy are (what else?) astronomically immense, collisions and collapses are recorded as “chips” of about a half a second. 
 
https://www.ligo.caltech.edu/page/ligo-gw-interferometer
It is also true that as they rotate on their individual axes, massive bodies produce gravitation waves.* Any acceleration does, even when you turn the corner on your bike or in your car. But gravity is extremely weak. At shoulder height, place a golf ball next to a bowling ball and let go of the golf ball. They don’t stick. Now, try it with magnets. I was once told that machine shop gauge blocks are finished so fine that if they touch they cannot be separated because the molecular forces are insuperable: the two blocks become one. Gravity is not like that. 

So, even though gravitation waves were argued by Newton, Leibniz, Kant, and Berkeley, it was 300 years before they were first detected on 14 September 2015. Dr. Weinberg also praised the intellectual honesty of the previous attempts by Joseph Weber and others which meticulously ruled out false positives until nothing was left.

*The gravitation waves produced by a massive superdense rotating body are caused by minor variations within or on the surface of the body. A perfect sphere, rotating on its axis produces no gravitation waves.

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Sunday, June 30, 2019

Birth of a Theorem by Cédric Villani

I gave up after 30 pages. The difficult mathematics was the largest but not the only barrier. 
 
Birth of a Theorem:
A Mathematical Adventure

by Cédric Villani, 
translated by
Malcom DeBevoise,

Farrar, Straus and Giroux,
2011. 
The story follows the “Save the Cat” format. As the author says in the Preface: 
“This book tells the story of a mathematical journey, a quest, from the moment when the decision is made to venture forth into the unknown until the moment when the article announcing a new result—a new theorem—is accepted for publication in an international journal.
“Far from moving swiftly between these two points, in a straight line, the mathematician moves forward haltingly, along a long and winding road. He meets with obstacles, suffers setbacks, sometimes loses his way. As we all do from time to time.”


But if you do not know what a “cat” is (or the nuance in "save"), then saving him lacks context. 

"Ah! The Boltzmann, the most beautiful equation in the world, as
I once described it to a journalist." (page 4)
For his work, Villani was recognized with a Fermat Prize, the Henri Poincaré Prize, and, ultimately, on August 19, 2010, a Fields Medal. At the ceremony he heard the announcer: “A Fields Medal is awarded to Cédric Villani for his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation.” (Page 231) One thing I will give Villani is that he was clearly focused on winning the Fields medal (pages 61-62).

 I once read that publishers feel that every equation costs 100,000 readers. If that is so, then this book was read by one person. Pages 144-155 consist entirely of a section of a paper from Acta Mathematica. 

The same truth can be spoken in different words.
Well, OK, you speak French, but how is your Italian? I mean, they are close right? Read one, read the other? I ask because pages 129-130 consist of an email with passages of HTML code to display mathematics in the presentation layer. Villani writes: ">>therefore you are left with
\int_0 ^t \int_ v F[h^(n+1)] \cdot < ( (\nabla_v f^n) \circ \Omega^n > (x-v(t-\tau),v) \ d\tau \, dv "

Those are not just two egregious examples. The whole book is like that. 

It is not just the equations. The vocabulary is highly technical. "Yes, a Moser-style scheme. The key is that the Boltzmann operator... true, the operator is bilinear, it's not local, but even so, it's basically in divergence form--that's what makes the Moser scheme work. You make a non-linear function change, you raise the power...You need a little more than temperature, of course, there's a matrix of moments of order 2 that have to be controlled. But the positivity is the main thing." [ellipses in the original] 

You know all the words. What you do not know is their mathematical meaning. The "Boltzmann operator" is the collision operator. I had to look that up and read three links to get the meaning. But I already knew that Boltzmann's work was a statement of thermodynamics.  "Divergence" has a common meaning close the mathematical use of the Nabla operator. The Nabla is the upside down Delta. It is used to express changes in vectors. (Look for Div-Grad-Curl).  "... a matrix of moments..." is not a grid of small times. In common engineering, a moment measures force times distance to express rotation. A moment is like a lever arm, why on a teeter-totter or see-saw, 40-lb child six feet from the center can lift a 160-lb man only one foot from the fulcum. In statistics, the first, second, third, and fourth moments express mean, variance, skewness, and kurtosis. So, now, it is somewhat clearer why the matrix of second moments is related to the divergence. But not knowing the language, I have stop to look up every word.

By comparison, like any American boy, I know “something” about cars and have worked on my own over the years. I was employed by Kawasaki. I have been on projects at GM, Ford, and Honda. So, when I read that in 1998 Honda developed an experimental Formula One car, the RA099 3-liter V-10, I can say “That’s nice.” The stuff that excites motorheads is beyond me. And, so, too, here, were the plot turns lost in the dense shoptalk among specialists. 

The detours were also problematic. The author loves Manga. It is his escape from mathematics. I know the genre a little bit. Long ago, I even read some in Japanese. But rather than an inclusion, it was an exclusion. An editor warned me about that: when you write for two different audiences, you do not get the union of the sets, you get the intersection. Here, the audience is the set of mathematicians whose published works bring them to the attention of prize judges.
  
Previously on Necessary Facts


Thursday, June 27, 2019

A Simple Truth

A picture is worth a thousand words, so I will not say much. I just thought that it is interesting that when something is true, it can be demonstrated by many methods.





































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From Texas to the Moon with John Leonard Riddell
Nerd Nation: 4.5
Integrating Criminologies
Why a Level Playing Field?

Monday, June 24, 2019

Number Theory as an Adventure

Number theory can be taught to children. It all begins with integers. First year algebra (at least) is required to prove these conjectures. But the facts can be presented and tested by a nine-year old who is comfortable with long division. Even a first grader can understand, appreciate, and test many of them. 

Multiplying odds and evens always yields: odd X odd = odd; even X even = even; odd X even = even. A child learning arithmetic can test examples until she is tired and at least get a lot of practice. It is not a proof, of course, but it can remain a challenge for a child who wants to learn algebra. The algebra is easy to show. 
 
An Adventurer's Guide to Number Theory
by Richard Friedberg, Dover, 1968, 1994
(This Dover edition contains corrections
and appendices not in the McGraw-Hill
printing of 1968.)
A child who is comfortable with first year algebra can get lost in the Pythagorean theorem and many of the truths that can be derived from it. Among the Pythagorean Triples are some such as 3-4-5 and 5-12-13 and 15-112-113 for which the hypotenuse is one unit longer than the longer of the two other sides. And there is an easy formula for generating them. It can be coded up as a computer program or a spreadsheet. 

This second edition was released soon after Andrew Wiles announced his proof of Fermat’s Last Theorem. Richard Friedberg cautions that the proof was not yet accepted. It was not. A second proof was. Friedberg discusses Fermat’s Last Theorem as an extension of other explorations, principally the Pythagorean Theorem. That venerable truth is the crux of this work though Friedberg brings the reader into many other fields: infinite descent, perfect numbers, modulo arithmetic, and prime numbers. Along the way, he cites the discoveries made by Fermat, Euler, Lagrange, Gauss, and, of course, Diophantus, among others. 

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Thursday, May 30, 2019

General Henri Guisan and Swiss Neutrality

Switzerland was surrounded and divided. Germany had annexed Austria. Italy was Germany’s ally. France had fallen. Denmark, Norway, Yugoslavia, and Greece also fell. Many Swiss were aligned to the German Nazi  party. About 12,000 Germans of military age were in Switzerland in 1941; and they were organized under the German High Command. Germans and their agents carried out acts of sabotage. (Fifteen Swiss and two foreigners were executed for their crimes.) Others adopted an unsurprising and seemingly realistic and pragmatic attitude, accepting Germany’s domination of Europe. The central government of Switzerland was granted emergency powers to make laws without legislation. Any criticism of Germany by any newspaper was considered “unneutral conduct.” Independent journalism ceased.
  
Inside book cover text showing title, author, and publisher: Spying for Peace:  General Guisan and Swiss Neutrality  by Jon Kimche  (London: Weidenfeld and Nicolson, 1961).
Spying for Peace:
General Guisan and Swiss Neutrality

by Jon Kimche
(London: Weidenfeld and Nicolson, 1961).
 

The meaning of “neutrality” evolved over 400 years. The oldest and easiest definition is that a state (and they were mostly small) did not take sides in a dispute between two other states. In the 16thcentury, the standard was not actively helping one side or the other. By the 18thcentury, it was merely being inactive. (Consider the inactions of Spain and France in the early years of our War for Independence, despite their granting various helps or not enacting hindrances to our conduct.) By 1899, the Hague Conference, which was reconvened in 1915, set 47 articles of neutrality. (The Hague and Geneva Conventions are archived at the Yale Law School’s “Avalon Project” here.) The rules included protections for non-combatants and civilians in general.

Gen. Henri Guisan wanted those rules suspended. All male Swiss citizens age 20 to 60 serve in their armed forces. And they were mobilized to meet the German threat. Eventually, many were released back to civilian life, but all remained available. Meanwhile, over four years, from 1939 to 1943, Gen. Guisan issued a series of orders to create first a line of defense facing Germany, and then, ultimately, an interior “redoubt” (reduit), a fortified central command in the middle of Switzerland, which could hold out against the Wehrmacht and the Luftwaffe. Tunnels and bridges were armed to collapse, sealing the center of the nation. 

Gen. Guisan understood that however it was defined Switzerland's neutrality would be meaningless--in fact, it would be impossible--without Swiss independence.  Therefore, on July 25, 1940, he addressed his officers in speech known as the Rütli Rapport. Nascent nationalism in the 18th century established a historiography to explain Rütli as the site of the first Swiss Confederation. The Rütlischwur (lit: Rütli Swear = the Oath of Rütli) brought the cantons of Uri, Schwyz and Unterwalden into a common league traditionally dated to 1307. It was also associated with the legend of Wilhelm Tell, certainly as told by Friedrich Schiller.

"Everywhere, where the order is to hold, it is the duty of conscience of each fighter, even if he depends on himself alone, to fight at his assigned position. The riflemen, if overtaken or surrounded, fight in their position until no more ammunition exists. The cold steel is next. ... The machine-gunners, the cannoneers of heavy weapons, the artillerymen, if in the bunker or on the field, do not abandon or destroy their weapons, or allow the enemy to seize them. Then the crews fight further like riflemen. As long as a man has another cartridge or hand weapon to use, he does not yield. " -- from General Henri Guisan's order to Swiss troops, July 25, 1940. (http://www.swissworld.org) 

Germany held off. On the one hand, obviously, Switzerland would be a tough nut to crack. This is a nation of soldiers who hold shooting contests for fun and prizes firing everything from crossbows to the most modern sniper rifles. On the other hand, Germany’s own fifth column assured them that rather than a tough nut, Switzerland was a ripe fruit, ready to fall into their hands. 
Swiss shooting Thaler - silver dollar sized coin celebrating a shooting match
"Swiss Shooting Thaler"
commemorative coin
1872 Shooting Festival Zuerich
(Some local issues are rare,
but there is no shortage of the kind.)
Civitas Galleries, Calgary.

Then came Allen Dulles. For Dulles, espionage and counter-espionage were more important than guns. By 1943,. Hitler had lost the confidence of his military command and an agent known as “Viking Line” provided intelligence to the Swiss, and through them to the Allies. As Victor Davis Hanson argued in The Second World Wars this was not a simple matter of Three of Us versus Three of Them. Some Germans held back-channel communications with the USSR, the UK, and the USA. In Yugoslavia, Marshall Tito, acting in accordance with Stalin’s instructions, was willing to throw in with the Germans in order to prevent an Allied landing across the Adriatic. Heinrich Himmler’s SS was willing to write off most of Italy, if they could hold the Alps as the ramparts of Festung Europa. To that end German agents in Switzerland negotiated through Swiss contacts with the Americans and British. Eventually, the American point of view was made clear and the German army in Italy surrendered unconditionally. Switzerland was safe and secure.

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Tuesday, May 28, 2019

At Oryana Co-op I Took my Change in Bay Bucks

Over the weekend of May 18, we were in Traverse City. After shopping on Front Street, we went to Oryana Community Co-op to buy snacks. We were members when we lived in TC. And at that time, I worked with the Bay Bucks planning committee. So, I took my change in community currency. 
Early Stage Concepts
  
A local currency provides an economic “cul-de-sac” that keeps wealth within a community. Local money tends to stay close to home. This means that profits do not get exported via chain stores and multinational corporations. Instead, people buy and sell goods and services among themselves, with the currency being an accounting tool. About 30 towns have tried the experiment, some with more success than others. 
[Portions of this article first appeared in the Michigan State Numismatic Society MichMatist where it can be found online here]

Late Stage Concept
10BB Pre-Production Proof 
In the summer of 2003, I heard a radio interview on WIAA-FM, Interlochen, in which two Traverse City community activists, Chris Grobbel and Natasha Lapinski, explained their plans for a hometown money. They sounded competent and intelligent and the project was compelling to me as a numismatist. I tracked them down by asking around at the Oryana Natural Food Co-op. I interviewed them (and others) for an article that ran in the November 13, 2003 issue of Northern Express hereI wrote a follow-up article for the June 9, 2004 issue here. 

For me, the rewards were in managing the design team. I found three design students at Northwestern Michigan College. Brendan O’Brien, Pauline Viall, and Thomas Loomis launched a model company (OVL Design) and signed off on a Statement of Work. I gave them samples of world currencies, a copy of Standish’s The Art of Money and links to websites for the International Banknote Society and the Paper Money Collectors. 

20BB as Pre-Production Proof
Seeking a printer, I found Deep Wood Press and Chad Pastotnik. (There was another alternative but now I cannot find her name.) Chad did everything he could to help them with their insufficient production budget. We abandoned intaglio printing, hemp paper, die cut corners to facilitate telling by touch, and other craft elements. The final version does have a foil security appliqué. Each note was to carry its own motto: “Regional Community Currency” (BB1); “Traverse Area Community Currency” (BB5); “Bread for Your Watershed” (BB10); and “In Community We Trust” (BB20). Instead all of the backs say "Trustworthy Tools for Local Exchange."

Patty Fabian, a designer with Peninsula Partners in Traverse City, developed a set of proposed logos to support the imaging and branding of Bay Bucks in store windows, on bumper stickers, and on the notes themselves.
5BB (Face) and 1BB (Face and Back)

The final version of the series consists of four notes: BB1, BB5, BB10 and BB20. Each represents an eco-system: Dunes (Dune Lily and Piping Plover); Wetland (Morrell Mushroom and Ringtail Raccoon); Farm (Cherry Blossom and Barn Owl); and Forest (Lady Slipper and Whitetail Deer). The Petoskey Stone pattern supplied the border of all four faces.  

The planning committee identified about 100 local businesses that could benefit from participating in “Bay Bucks.”  About 30 of them were considered early adopters. Oryana Community Co-op was central to the success of Bay Bucks. Among the other participants was the State Theatre, home of the Traverse City Film Festival, a joint effort of Michael Moore and the Chamber of Commerce.

RESOURCES AND READING
  • Bay Bucks here: http://www.baybucks.org
  • Launching Bay Bucks “Local Money Plan for Homegrown Currency has a Rich Past” Northern ExpressNovember 12, 2003, here.
  • “Passing the Bay Bucks: Local Currency Could Hit the Streets This Summer,” (Northern Express, 2004) here. 
  • Traverse Ticker (2018) “Yes, Traverse City Still has its own Currency” here.
  • Traverse Ticker (2019) “Could Bay Bucks go Digital?” here
  • “I Took My Change in Bay Bucks” on CoinTalk here.
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Monday, May 27, 2019

Enerdyne and Brain Storm in Suttons Bay

While visiting family May 17-20, I stopped in at Enerdyne to shop for an optical adapter for my telescope. They were very helpful. They found the part that I needed. I also bought two pairs of small forceps (“tweezers”) and four bar magnets.

Enerdyne sells Petoskey stones, but I did not see any out on display. So, I went next door to Brain Storm and found one there. While at Brain Storm, I bought a game, "Word A Round," for Laurel and me.

Elaine and Stu were working the store on Saturday.
Dick Cookman, formerly a science instructor
at Northwestern College, is the owner.


















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