Relative Time and Swiss Clocks

The recent books on Einstein by Isaacson and Neffe (see reviews) cover the development of special relativity in great depth, with special attention to the development of an operational definition of time duration that vanquishes the prior notion of simultaneity. Indeed, simultaneity is now accepted as observer-dependent, thanks to Einstein's Special Theory.

Both books do refer to the role played by Poincaré- although "role" is not necessarily the operative term here. No doubt Poincaré was thinking deeply about time, but did not make Einstein's leap to codify the relative nature of time duration.

An excellent book on the Einstein/Poincare connection is Einstein's Clocks, Poincaré's Maps: Empires of Time, by Peter Galison. Here Galison tries to relate Einstein's experience as patent clerk who most likely saw patent proposals for clock synchronization between different Swiss cities to his ongoing thought -experiments in the foundations of physics. ( In a generally very favorable review by R. Wald for Physics Today, this idea is called into question.)

But the Poincaré connection is fascinating because it is not clear to what extent, if any, Poincaré's writings on time were even seen by Einstein. (And the title of the book is itself a play on words, because a Poincaré Map is a fundamental analysis/visualization tool of chaos and fractals.)

The new Einstein bios have really opened up new avenues of thought on how Einstein came to be Einstein. The Poincare connection is fascinating, and a potentially important piece of the answer.

Most amazing of all is the pictures these books paint of the intellectual ferment taking place in Europe at the end of the 19th and beginning of the 20th century. It is hard to imagine a similarly exhilarating time of new, earth-shattering theories that can possibly duplicate these years for excitement and creative brilliance.

Woodstock and Superconductivity

Physicist lowers body temperature to achieve a superconducting state.

I came upon a child of god
He was walking along the road
And I asked him, where are you going
And this he told me
I'm going on down to Yasgur's farm
- Joni Mitchell

I never made it to Yasgur's farm - I was just too young in 1969 to head to New York to catch all of the acts that I loved. Later that summer I did make it to the Atlantic City Pop Festival , which was a much-sanitized version. No rain, no mud slides, no babies born...and there was certainly no one making movies or disclaiming about the AC Pop Festival Generation.

Many years later I finally made amends for my serious cultural lapse in '69 and attended the next Woodstock - the Woodstock of Physics. This 1987 event was a wild affair as the news of high-temperature superconductivity was just breaking, along with promises of a Jetson-like future soon to be commonplace. There were thousands at the session in NYC, with most (including this author) watching the presentations via monitors in the corridors, straining to hear every word, to make out every blurred overhead with a hastily sketched graph, waiting to hear what would be the next latest (and higher) superconducting temperature...

We are stardust
We are golden
And we've got to get ourselves
Back to the garden

A surprising fact about HTSC is that discovers  Karl Müller and Johannes Bednorz received the Nobel Prize that same year -an amazingly short time for the Nobel committee to name an award winner. (They had first noticed the effect only a year earlier.) Typically it is many years between discovery and award, with other experimenters and theorists demonstrating that the original discovery was both true, and truly significant for physics. More amazing, there was no consensus on why HTSC occurs.

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Visualizing The Core of the Blogosphere

Interactive map of blogosphere. From Hurst. Click to enlargeThere's been a recent flurry of articles concerning visualization of the web itself, and what such visualization might say about the social networks that live and breathe because of the abilities of the net.  This topic is a necessary follow-up, then, to my previous posts on new visualization techniques in web searching.

A conference at UPenn in June 2006 titled The Hyperlinked Society focused on "the effects of digital links on people’s ability to understand and care about their larger society. " The following blurb is from the intro page; the program was quite ambitious:

Most internet users know hyperlinks as highlighted words on a web page that take them to certain other sites. But hyperlinks today are quite complex forms of instant connection—for example, tags, API mashups, and RSS feeds. Moreover, media convergence has led to increased instant linking among desktop computers, cell phones, PDAs, MP3 players, digital video recorders, and even billboards.

Through these activities and far more, “links” are becoming the basic forces that relate creative works to one another. Links nominate what ideas and actors have the right to be heard and with what priority. Various stakeholders in society recognize the political and economic value of these connections. Governments, corporations, non-profits and individual media users often work to digitally privilege certain ideas over others.

Do links encourage people to see beyond their personal situations and know the broad world in diverse ways? Or, instead, do links encourage people to drill into their own territories and not learn about social concerns that seem irrelevant to their personal interests? What roles do economic and political considerations play in creating links that nudge people in one or the other direction?

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Chaos and Compatibilism

Chaos Theory is often cited as a way out of the determinsim-free will paradox. The explanation usually goes like this: OK, everything is determined by physical law, but the laws themselves are non-linear and the output of a particular equation that codifies a law often leads to a pseudo-random process and/or sensitive dependence on initial conditions. Ergo while we are governed by strict physical laws, our behavior - and by implication our decisions - do not give the appearance of being constrained in any way.

The philosophical position that free will can co-exist with determinism pre-dates chaos theory, with Hume and Hobbes early proponents. Known as compatibilism, it stands on its own without chaos theory. Much of the compatibilist argument rests on a careful definition of what it means to act freely, leading to a so-called category error.

The compatibilist definition of free will states that free will is not the ability to choose as an agent independent of prior cause, but as an agent who is not forced to make a certain choice. Determinists argue that all acts that take place are predetermined by prior causes. Because human decision is an act that is not exempt from prior cause, by this definition, some determinists known as hard determinists believe that free will thus becomes an illusion.

A compatibilist, or soft determinist, in contrast, will define a free act in a way that does not hinge on causal necessitation. For them, an act is free unless it involves compulsion by another person. Since the physical universe and the laws of nature are not persons, they argue that it is a category error to speak of our actions being forced on us by the laws of nature, and therefore it is wrong to conclude that universal determinism would mean we are never free.

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Turbulence in Space

Turbulence in SpaceTrying to model and understand turbulence is one of the main thrusts of chaos theory. So it may be a good thing or bad, depending on where you are chaotically, that more turbulence has been found - this time in deep space.

As reported in APS Physics News for 2006:

If you think chaos is complicated in the case of simple objects (such as our inability to predict the long-term velocities and positions of planets owing to their nonlinear interactions with the sun and other planets) it's far worse for systems with essentially an infinite number of degrees of freedom such as fluids or plasmas under the stress of nonlinear forces. Then the word turbulence is fully justified. Turbulence can be studied on Earth easily by mapping such things as the density or velocity of fluids in a tank. In space, however, where we expect turbulence to occur in such settings as solar wind, interstellar space, and the accretion disks around black holes, it's not so easy to measure fluids in time and space. Now, a suite of four plasma-watching satellites, referred to as Cluster, has provided the first definitive study of turbulence in space. The fluid in question is the wind of particles streaming toward the Earth from the sun, while the location in question is the region just upstream of Earth's bow shock, the place where the solar wind gets disturbed and passes by the Earth's magnetosphere. The waves in the shock-upstream plasma, pushed around by complex magnetic fields, are observed to behave a lot like fluid turbulence on Earth. One of the Cluster researchers, Yasuhito Narita (y.narita@tu-bs.de) of the Institute of Geophysics and Extraterrestrial Physics in Braunschweig, Germany, says that the data is primarily in accord with the leading theory of fluid turbulence, the so called Kolmogorov's model of turbulence. (Narita et al., Physical Review Letters, 10 November)

Kolmogorov is one of the famous trio Kolmogorov - Arnold - Moser. after whom the KAM theorem is named. Ironically, the KAM theorem shows the existence of quasi-periodic orbits in a chaotic solar system. The idea of stability within turbulence is an archetypal chaos construct.

Modeling Pandemic Strategies

Spanish Flu in SpokaneModeling how a disease progresses in a pandemic, and the related modeling of the effects of different strategies on stopping the pandemic, are, next to perhaps nuclear attack modeling, some of the most sensitive mathematics being done today.

Consider the difficulties of determining pandemic-containment strategies by looking to past pandemics.

Efforts of several cities to halt the spread of the 1918 Spanish flu have now been analyzed and modeled by several research teams. One technique that appears promising is "social distancing" - referred to a s a non-pharmaceutical intervention (NPI) - a fairly obvious strategy of reducing the potential contact between members of the community by closing schools, churches, stores, etc.

I wrote "fairly obvious" - but is it? There are so many contingencies that affected each city that it is hard to draw conclusions. Consider the report of the studies as described by Maryn McKenna of the Center for Infectious Disease Research & Policy at U. Minnesota

But while NPIs make intuitive sense, actual evidence for their ability to block or slow flu transmission has been limited. An Institute of Medicine report released last December concluded that the measures might help in a pandemic but should not be oversold.

"It is almost impossible to say that any of the community interventions have been proven ineffective," the report said. "However, it is also almost impossible to say that the interventions, either individually or in combination, will be effective in mitigating an influenza pandemic."

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The Art of Biography - Einstein and Goethe

I recently read an interesting review by J. Parini in the May 11, 2007 Chronicle of Love, Life, Goethe: Lessons of the Imagination From the Great German Poet by John Armstrong. According to Parini, Armstong's approach is non-chronological, instead focusing on different thematic "nodes" in Goethe's life. This style of biography is remarkably similar to that of Jürgen Neffe in his recently translated Einstein: An Autobiography. Unlike Isaacson's best-seller Einstein: His Life and Universe, Neffe presents Einsteins's life prismatically in chapters that go over the same events, but with different emphases. (See my review of Isaacson and Neffe)

Here's Panini writing about Armstrong's Goethe:

In the case of Goethe, there were many observers, and the factual record is not much in doubt. Hardly anyone crossed his path who did not feel compelled to record an impression. And so biographers have a wealth of material, some of it quite marvelous. Armstrong plucks the choicest bits from that vast record, but refuses to narrate the life in conventional terms. Instead, he picks 10 key words and gathers his work around those nodes: Luck, Love, Power, Art, War, Friendship, Nature, Peace, Happiness, Death. There is an underpinning of chronology here, as one might expect; but the timeline is folded back upon itself, even discarded for long stretches as Armstrong lunges into meditations on the meaning of the life itself in the context of those seminal words.

The image of "timeline folding back upon itself" is a wonderful way of describing this biography of connected "nodes."  Panini goes on to describe the effect of reading such a biography...

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Mathematics Reveals the Artistry

Brueghel's Fall of IcarusDaniel Rockmore writes about the mathematical analysis of art in the June 2006 Chronicle (The Style of Numbers Behind a Number of Styles). In the essay Rockmore describes Richard Taylor's work in analyzing Jackson Pollock pieces, which may be forgeries. ( See my post on this topic)

The Pollock intro is a lead in to a description of stylometry - the mathematical/scientific analysis of literary texts that attempts to address issues of authorship. (See Bookish Math, an excellent intro to stylometry by Erica Klarreich for Science News Online.) Rockmore than describes a method he developed with co-workers Siwei Lyu and Hany Farid that uses wavelet analysis to determine unique "signatures" of different artists - in effect a stylometry for visual images.

The actual mathematics of the wavelet approach can be found in A Digital Technique for Art Authentication. Here the authors use examples of Pieter Bruegel and Perugino to test their model. They claim that their "techniques, in collaboration with existing physical authentication, to play an important role in the field of art forensics."

The wavelet technique is different from Taylor's fractal analysis of Pollock's works, but both are examples of stylometry applied to visual information. Both Taylor and Rockmore are attempting to quantify art, an activity that Rockmore admits is unsettling/impossible to some. According to Taylor, this quantification should be expected: "Both mathematics and art are all about pattern...it would be unusual that you would not apply mathematical analysis to the question."

Rockmore is more explicit about what mathematical categorization of art analysis does not do: "Fractal analysis doesn't diminish Pollock's athleticism and movement, nature and turbulence, chaos and beauty; it reveals and amplifies it."

For more on this topic, see Can Mathematical Tools Illuminate Artistic Style?, by Sara Robinson for SIAM.

How to read a REAL Climate Modeling article

Diagram of General Circulatin ModelBolstered by the anti-climate-modeling stance of Michael Crichton, there are many out there who claim that climate modeling that predicts global warming is somehow "bad science." I'm not sure many of these folks have ever read a real climate modeling paper (or any who believe that climate change is occurring, for that matter)

It is instructive to try to wade through a serious paper that points out the difficulties of modeling on the one hand, but also presents very confident predictions of the model described in the paper..

By chance I recently came across a paper written almost 2 years ago by Jian Yuan, Qiang Fu (Department of Atmospheric Sciences, University of Washington) and Norman McFarlane (Canadian Centre for Climate Modeling and Analysis, Victoria, British Columbia). The name of the article is forbidding: Tests and improvements of GCM cloud parameterizations using the CCCMA SCM with the SHEBA data set.

(Note: GCM is General Circulation Model, or Global Climate Model - the bellwether of climate modeling)

The article describes the wide variability of different models of the Arctic, and how the authors re-formulated cloud interactions, yielding a model whose output is much closer to actual recorded data.

For the uninitiated, trying to read this type of paper seems impossible. You can get a lot from it, though, by reading the abstract, intro, and conclusion. (This is something I do in the Chaos and Fractals course - i.e. have students read and dense papers in areas outside of their majors - an essential activity for all scientists).

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Poetry, Space-time, and Entropy

Plotkin's Entropy by Donna Bellas. See text for info. With the amazing success of Isaacson's bio of Einstein, and the translation and release in the US of Neffe's uniquely-German bio, Einstein is certainly in the air. Not as much as 100 years ago, when he was perhaps the most famous person in the world, but nevertheless many are reading, and writing poetic about Albert.

From Bernhardt Blumenthal, a colleague at La Salle who is a Rilke scholar and poet (and in his spare time chair of the Dept. of Foreign Languages & Literatures and the Master's Program in Central & Eastern European Studies) describes Einstein's influence on his latest work:

...my latest poem, Schwere Seelen, (Heavy Souls), which just appeared last week in a German literary periodical plays on Einstein's General Relativity. The souls, heavy with love and suffering, warp reality and pass over the space-time curve through hyper-space into another universe--one without entropy. The female lover, incidentally, transits space escaping on a light beam exiting a black hole (thus faster than our conventional absolute speed of light) and rescues the beloved from his entropic situation.

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