Happy (Summer) Solstice!

At 5:26am PDT today, the Earth's Northern Hemisphere was tilted directly towards the sun. That was the Solstice moment. Northern Hemisphere inhabitants experience this day in several ways - the sun travels the sky higher and spends more time above the horizon than on any other day of the year - a full 14 hours and 25 minutes in Los Angeles. If you're standing on the Tropic of Cancer, the sun will pass directly overhead at noon. If you're standing at the North Pole, the sun will circle the sky higher than any other day, 23 degrees above the horizon.

Another Tri

With my son at the startThis past Sunday, I competed in my third triathlon. Held in Redondo Beach, this one was a bit short, even by "sprint" standards: 1/2 mile in the Pacific next to King Harbor, 6 miles down Catalina Ave. and The Esplanade on the bike, and a 2-mile wrap-up run through King Harbor. With a 7:30 start time, I was up at 5:00 to eat a light breakfast and start battling the butterflies. At these distances, I wasn't really stressed, but competition is competition and in the back of my mind lurked the ugly truth - I'd not trained as hard as I had for previous events.

Feynman Illuminates Newton


Authors:

David L. Goodstein, Judith R. Goodstein


Publisher:

W. W. Norton & Co.


ISBN:

0-393-31995-4 (paperback)


Pages:

191


Price:

$19.95


Rating:

8


Review:

In 1684, the great English astronomer Edmond Halley journeyed to Cambridge to speak with Isaac Newton about the motion of the planets. At that time, Kepler's law stating that a planet travels around the sun in an elliptical orbit with the sun at a focus of the ellipse was well-known and accepted in scientific circles. Kepler had deduced it 70 years prior from careful analysis of Tycho Brahe's exquisite observations of the planets, particularly Mars. While nobody really knew why the planets behaved this way, an idea was floating about that the observed planetary motion might result from a force towards the sun that diminished as the inverse square of the distance between the sun and the planet.

Mr. Halley was keen to discuss these issues with the celebrated mathematician Mr. Newton, in the hopes that an analytical solution could be found that would describe the mechanics behind Kepler's Laws. To Halley's surprise and delight, Mr. Newton claimed to have already worked out a proof of the connection between an inverse-square force and the observed elliptical motion of planets. However, he was unable to put his hands on it immediately and promised to re-create it for Halley shortly. Sure enough, a short time later, Halley received a treatise containing the promised proof. It was brilliant - and it changed the world.

Now leap forward 280 years to March 13th, 1964. On that day, the great 20th-century physicist Richard Feynman presented a lecture to a freshman audience at the California Institute of Technology (CalTech) in which he re-created that very same proof of Kepler's laws of planetary motion. The lecture was recorded and Feyman's notes archived, but somehow they were lost until Judith Goodstein, a CalTech archivist, discovered them in the 1980s. Unfortunately, the records were incomplete, requiring the re-creation of some of Feynman's work by David Goodstein, another CalTech physicist. The book is the result of the Goodsteins' efforts and the circuitous turn of events that culminated in its publication are as interesting as the proof, itself. For those details, do not skip the preface and introduction.

Beyond the details of the proof, the book spins out a personal drama that I found most interesting. Here is one of the most creative scientific geniuses of the 20th century speaking frankly of his own struggles with a proof that for him was "elementary but very hard". In this case, what Feynman means by "elementary" is that the proof does not require any exceptional or arcane knowledge to understand. A simple facility with high school geometry is sufficient. Nonetheless, the proof is "hard" because it demands the creative application of geometry through a protracted series of connected steps. Indeed, the book dedicates 80 pages to carefully elaborate it, complete with dozens of detailed figures. Overall, I found it required a concerted effort to fully grasp the sweep of it. I found myself returning to sections several times to work it all out.

Feynman himself admits that he struggled to follow Newton's original arguments, since Newton approached the problem using obscure properties and theorems of conic sections that are not often used in contemporary mathematics. Undaunted, Feynman successfully developed his own solution to several parts of the proof, simultaneously demonstrating his own creative brilliance, as well as that of Isaac Newton. There are modern solutions to the planetary motion problem that are far easier to construct using higher-order mathematics. But it is Feynman's determination to re-create Newton's proof using only geometric concepts that makes the entire story compelling - and such a fitting glimpse into the inner workings of a legendary modern-day physicist.

The detailed proof itself is accompanied by introductory chapters which describe the relevant history leading up to Newton's great achievement, a brief and poignantly personal biography of Feynman and, finally, the complete transcript of his CalTech lecture - as reproduced on the companion CD.

It's not often we're privileged to witness one genius illuminating the pivotal work of another. So I consider myself lucky to have stumbled across this delightful book. Hats off to the Goodsteins for their personal commitment (and considerable effort) to bring this fascinating story to the rest of us.


Astronomy Night, May 2006

On Friday, May 5th, I held the third Astronomy Night of the year at Rolling Hills Country Day School (RHCDS). I'd planned to start the evening with a presentation in the school's auditorium, using slides and animations driven by my laptop through the excellent audio-video system installed there this year. Unfortunately, in my haste to get to the school with all the necessary components, I managed to leave the laptop at home. Without enough time to retrieve it, I was forced to "wing it".

Luckily, I did manage to remember printed sky charts. So, I gathered those in attendance in the science lab for a little "whiteboard" talk before going out to view. I explained how to use a full-sky star chart and pointed out the objects of primary interest for the evening - Saturn, Jupiter, The Moon and the Schwassmann-Wachmann (73P) comet gracing our skies this month.

The Cherry Orchard

The latest production at The Mark Taper Forum is Anton Chekhov's classic "The Cherry Orchard". As a portrait of late-nineteenth-century Russia, the play captures the contradictory comedy and tragedy of that chaotic period. Unlike most Taper productions, this one included two well-known actors in its unusually large cast. Annette Bening plays a believable Ranyeskaya, the matriarch of an aristocratic family facing financial ruin. Opposite her, Alfred Molina's Lopakhin has emerged from peasant ancestry to become a successful businessman who, in a delightful twist of irony, winds up purchasing Ranyeskaya's estate at auction - the same estate on which his father and grandfather worked their entire lives as serf slaves. The owned becomes the owner, and vice versa.

The Known Balloon

The great science fiction author Frank Herbert once said:

"The beginning of knowledge is the discovery of something we do not understand"

One must pose a question before one can explore for its answer. Luckily, the pursuit of answers to known questions invariably leads to a multitude of new questions. Science is therefore self-sustaining. The pursuit of knowledge through scientific theorizing and experimentation guarantees an endless supply of new problems to solve. This may discourage some, in that every answered question leads to many more questions. However, this is discouraging only if one focuses upon the answers. I prefer to focus on the ever-unfolding questions, for the pursuit of knowledge is significantly more important than the attainment of it.

Dark As Day?

We astronomers, professionals and amateurs alike who depend upon dark night skies for the pursuit of our celestial passions, have long been lamenting their slow demise. In fact, the International Dark-Sky Association (IDA) was founded specifically to promote the preservation of dark skies in general and advocate for the use of public lighting systems that minimize light pollution.

So I had a mixed reaction to a February 27th, 2006 article in The Orange County Register describing recent evidence that light pollution is having detrimental ecological effects on Southern California flora and fauna. On the one hand, it's discouraging to learn that the wasteful artificial lighting in our sprawling suburbs is having a significant negative impact on animals and plants whose survival depends upon night-time darkness. On the other hand, I was encouraged to see this growing problem reported in a major newspaper. As the IDA has learned, raising awareness is the first step to making changes that will benefit everyone - astronomers, stargazers and (increasingly) nocturnal critters in and around our cities.


UpWord Informs & Inspires

Today, the sea of internet blogs is vast and deep, sometimes difficult to navigate and often featureless in all directions. Luckily, there are noteworthy gems - islands of inspiration that serve as welcome sights to all of us sailing about. One of my favorites is UpWord, the intellectual home on the internet of my good friend, Tom Chatt. I've known Tom for over 20 years and have always found his ideas and opinions cogent, thought-provoking, often inspiring and always worth considering. His writing inspires me to pursue my own. I invite you to check out UpWord and enjoy Tom's unique perspectives.


American Voices

At the opening of the first StoryCorps recording booth in Grand Central Station, Studs Terkel said:

"...we shall begin celebrating the lives of the uncelebrated, those men and women ... the working men and women of this country ... who have made all the wheels go 'round..."

And with that, he helped launch an ambitious project to collect audio snapshots of the lives of ordinary Americans. Spend some time with a sampling from the current collection and I suspect you will be moved by the power of extraordinary words from ordinary people.

A Challenge To Science & Religion

Fundamentalism is the theme of Parabola's Winter 2005 issue. In it, William Ventimiglia writes:

"Ours, of course, is a culture dominated by rationality where the non-rational is given short-shrift. This is the collective prejudice of our time, our incomplete ... world-view. What can neither be seen, nor touched, nor subjected to experimental verifiability is often held in intellectual contempt."

In the past 400 years, our secular ethic has greatly advanced human knowledge. Quite simply, it's the foundation upon which modern society has been built. However, at the dawn of the 21st century, we, the proponents of rational, scientific thought, find ourselves unmoored. It's as if we've rushed into a dark room unprepared. Sure, some lights have been lit along the way and some of the territories so illuminated have been explored. But in our head-long pursuit of knowledge, we've ignored the unknowable, the dark corners that will perhaps, by their very nature, remain forever so. We dismiss the numinous. We have come to reject mystery and myth - not just casually, but with contempt. We discount experiential truth.

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