Fossicking: Musings on an Associative Universe

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Fossicking: Musings on an Associative Universe

Postby zuestorz » Tue Oct 09, 2007 8:39 am

Considering the technology and the era and the individual involved this was one of the weirdest disappearances imaginable. No weirder however, than the rapid descent of silence in the mainstream media and over the Nevada desert as the search for Steve Fossett dwindles. But maybe the Air Force are on to something?

But as Winter looms, no real leads emerge and hopes of a nuts and bolts, linear and logical search - one driven by air patrols, chopper sweeps, satellite imaging, ground parties and even Google's trawler Turk engine - hopes of a good outcome in this search are dwindling.

Now that gets me interested. This vanishing and this affront to our supposed technological mastery of our world. This failure, this breakdown in the mechanistic certainty we impart to our world of reliable machines and intrepid, knowledgeable people operating them. I freely admit to having no great interest in Steve Fossett, adventurer. My understanding of his career as a balloonist, sailor and flyer is limited to brief memories of his triumphs splashed across the TV screen and just as quickly forgotten. But the man was not even a blip on my radar, until I googled a weblink to a (hardly very compelling ) association to another famous vanished individual - Ambrose Bierce.

American writer AMBROSE BIERCE was a famous columnist, critic, novelist and master of the short story in the late 19th century. . .when he was 71 years old he toured the Civil War battlefields of his youth, then set off for Mexico in 1913. Through letters he indicated that he was bidding farewell to his life in the United States, and some believe he was intent on joining the forces of Pancho Villa south of the border.

Bierce was never seen again, and search missions over the years failed to come up with any conclusive answers. There are many rumors: some say he committed suicide in the Grand Canyon; some say he got shot by Pancho Villa because Bierce drank too much tequila; some say he was kidnapped by aliens; and some say he never died at all, which would make him over 160 years old and probably even more cynical than he was a century ago.

Okay, well, cute but so what - then by just using the two word search of Vanishing Ambrose, I was suddenly inundated by a whole set of bizarre associations! Some overtly (and irreverently) referencing Fossett -

but the numerous crazy linkages between Vanishing and Ambrose began to exceed any logical pattern.

There were quotes from Ambrose Bierce's Devil's Dictionary, " Plunder (Def). . .To wrest the wealth of A from B and leave C lamenting a vanishing opportunity."

There were extreme mathematical theories . . .

Ambrose-Singer theorem
The Ambrose-Singer theorem relates the holonomy of a connection with its curvature form. To make this theorem plausible, consider the familiar case of an affine connection (or a connection in the tangent bundle — the Levi-Civita connection, for example). The curvature arises when one travels around an "infinitesimal parallelogram".

In detail, if σ : [0,1] × [0,1] → M is a surface in M parametrized by a pair of variables x and y, then a vector V may be transported around the boundary of σ: first along (x,0), then along (1,y), followed by (x,1) going in the negative direction, and then (0,y) back to the point of origin. This is a special case of a holonomy loop: the vector V is acted upon by the holonomy group element corresponding to the lift of the boundary of σ. The curvature enters explicitly when the parallelogram is shrunk to zero,(vanishing) by traversing the boundary of smaller parallelograms over [0,x] × [0,y]. This corresponds to taking a derivative of the parallel transport maps at x=y=0:

where R is the curvature tensor.[3] So, roughly speaking, the curvature gives the infinitesimal holonomy over a closed loop (the infinitesimal parallelogram). More formally, the curvature is the differential of the holonomy action at the identity of the holonomy group. In other words, R(X,Y) is an element of the Lie algebra of Holp(ω).

In general, let g be the Lie algebra of the Lie group G. Then the curvature form of the connection is a g-valued 2-form Ω on P. The Ambrose-Singer theorem states:[4]

The Lie algebra of Holp(ω) is spanned by all the elements of g of the form Ωq(X,Y) as q ranges over all points which can be joined to p by a horizontal curve (q ~ p), and X and Y are horizontal tangent vectors at q.
Alternatively, the theorem can be restated in terms of the holonomy bundle:[5]

The Lie algebra of Holp(ω) is the subspace of g spanned by elements of the form Ωq(X,Y) where q ∈ H(p) and X and Y are horizontal vectors at q.

But these two 'La Grangian Points' of apparent connection in the anti-logical, associative and synchronous Universe to 'the vanished' and to 'Ambrose' - had a strong , even overwhelmingly randomness, unless there was some third and direct connection to Fossett to provide some triangulation approaching meaning?!?

And then this from Sailing World . . .

Cory Sertl and Steve Fossett Named Rolex Winners
A US SAILING release announces the new Yachtsman and Yachtswoman of the Year for 2001
By The Editors (More articles by this author)

Steve Fossett, age 57, of Chicago, Ill., and Cory Sertl, age 42, of Rochester, N.Y., today were named 2001 Rolex Yachtsman and Yachtswoman of the Year, respectively. A panel of sailing journalists selected the two accomplished sailors for this year’s distinction from a short list of six nominees for the Rolex Yachtsman and five nominees for the Rolex Yachtswoman.

Established in 1961 by US SAILING and sponsored by Rolex Watch, U.S.A. since 1980, the Rolex Yachtsman and Yachtswoman of the Year Awards recognize outstanding on-the-water achievement in the calendar year just concluded. The winners will be honored at a luncheon and press conference at the New York Yacht Club in New York City on February 15, where they will be presented with Rolex timepieces.

Accomplished sailor and celebrated adventure sportsman Steve Fossett was recognized for shattering not one, but five speed sailing records aboard his 125-foot catamaran PlayStation. The records are for the fastest times sailing from Miami to New York; across the Atlantic; around England’s Isle of Wight; and across the English Channel. While shattering the TransAtlantic record, Fossett also posted the fastest time for distance covered in a 24-hour period.

“I’m a happy, happy guy,” said Fossett. “It’s very gratifying to be recognized by my peers in the sport, especially for the kind of sailing I do. Normally sailors measure themselves against others in boats of the same class. My goal is also to be the fastest. Even when in a race, I focus on setting the race record as well as winning my class.” The panel members were most impressed by Fossett’s successful attempt in October to better the west to east TransAtlantic record (Ambrose Light Tower off New York to Lizard Point off Cornwall, England), considered by sailors around the world to be the Holy Grail of distance sailing. . .

Some strange musings on an associative Universe.
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