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Showing posts with label Sylvestor surfaces. Show all posts
Showing posts with label Sylvestor surfaces. Show all posts

Monday, February 26, 2007

Artifacts of the Geometrical WunderKammern

As one visits the mathematical puzzles and conjectures, what value these insights to the physics or our universe if we did not see things in this way? As artifacts of some other kind of geometrical thinking that we could then apply it to how we see the micro-perspective and macro-perspective working within the Quantum or cosmological realms?

So abstract and foreign to our eyes that we let it escape our attention while we talk about all our theoretical points of view and divergences from what is symmetrical?

In the past, new scientific discoveries, strange finds, and striking pieces of original artwork were greeted with awe and wonder. It became popular during the Renaissance to build a "cabinet of curiosities" to display a private collection of art and natural objects of which the owner was extremely proud. These groups of objects were at first housed in an actual cabinet or ornate piece of furniture, known as Wunderkammern or Wunderkabinetts. They are simultaneously pieces of furniture and the collections of items within them.

In the exhibits of these early Wunderkammern, owners might display strange, beautiful, mysterious, and precious marvels like starfish, monkey teeth, alligator skins, phosphorescent minerals, Indian canoes, Egyptian figurines, and “unicorn tails.” Rich art patrons would display their new art acquisitions in the intimate backdrop of a prized spot in an ornate carved cabinet. At Kensington castle, Sir Walter Cope is said to have displayed, “holy relics from a Spanish ship; earthen pitchers and porcelain from China; a Madonna made of feathers; a back-scratcher; a Javanese costume, Arabian coats; the horn and tail of a rhinoceros; the baubles and bells of Henry VIII's fool; and a Turkish emperor's golden seal.” The collections demonstrated manmade wonders and the diversity of God’s creations as well as a fascination with new scientific approaches to the study of natural phenomena. Each collection’s commitment to miscellany dependended on the idiosyncratic interests of the collector.


So it was again important to bring people back to the ways of geometry working in spaces, that although seemingly detached from our reality is the underlying basis of the physics involved.

Mine is a layman's perspective so I cannot say for certain that all I write here will be of value. It is up to you whether you think it important or not.

Figure 2. Clebsch's Diagonal Surface: Wonderful.

Sylvester's models lay hidden away for a long time, but recently the Mathematical Institute received a donation to rescue some of them. Four of these were carefully restored by Catherine Kimber of the Ashmolean Museum and now sit in an illuminated glass cabinet in the Institute Common Room.


The Museum when thought in context of "Platonic solids" was some what of a contention when I showed it's location in early historical context as a artifact.

Shown here are the models in the mathematical wunderkammer located in the Department of Mathematics at the University of Arizona. Like those in most modern mathematics departments, the collection is a combination of locally-made student and faculty projects together with a variety of commercially produced models. Sadly, a century since their Golden Age, many of the models are in disrepair and much of their documentation has been lost. However, some recent detective work, with the help of the Smithsonian Institution in Washington, has helped the department identify models by the American educators W. W. Ross and R. P. Baker in the collection.

Also see here for further thoughts on this

I thought it important to quickly post this so that people understand that "a glass case" can hold many things for inspection, but in this case ,I was referring to the geometrical forms. If any of these form were to show symmetry in action which of these would do so? Sylvestor surfaces?

An attempt in Latex to map these functions from a layman's perspective. What use if I cannot understand the mathematical language as it is written, yet, I can see "acrobatically" the way geometry works in space?

Saturday, April 15, 2006

On Gauss's Day of Reckoning

A famous story about the boy wonder of mathematics has taken on a life of its own -Brian Hayes



Illustration by Theoni Pappas

In a fanciful drawing done in the manner of a woodcut, the young Carl Friedrich Gauss receives instruction in arithmetic from the schoolmaster J. G. Büttner. As the story goes, Gauss was about to give Büttner a lesson in mathematical creativity.


To me the historical significance of this research is important to me. People could chastise me for saying that the research I do has no quality, then what should be assumed with scientific credentials? Still the romance I have for such abstractions and development of thinking is important just the same. It is about creativity to me, and looking back to the ingenuity of thought, is something I can see in everyone. One doesn't have to consider them self less then, just by being the student that would solve the problem, while insight and acute perception, might have been revealed in one who could throw down the slate the quickest.

The story is fascinating tome on a lot of different levels and to tracking down the essence of what we see passed from one hand to another, and how this ambiguity might creep in and additions make there way for added material.

I understand this in our response to writing science, with what language is supposed to be. Sure talk about chinese , Italian, Latin of ole, and we want to know what the truest expression of the language should be?

Of course this is the responsibility of math, that a common basis be found, between all languages, that the source would have described it so abstract/yet closest to the center of the circle) that all would understand and could work the abstract nature of this math.

I feel guilty, that I cannot contribute so well to this math language, that I strive to listen very good to the concepts espoused, as close as possible to the development of this Algebraic way of seeing.

Yes, it is as important, as the geometrical seeing that it be inherent in the way things abstractly can be seen. That both would have supported the continued work fo science.

Mine then is the student's plight in a vast world that I exist away from, yet, try and stay as close as I can to learn.

Do I sanction everyones abilities away from this in character, is no less then the character I assume, and has been treated. That respect be given, might have found the truer calling of sharing the insights, be as truthful as possible. We should all strive to this of course.

What is Swirling in my Mind

As I lay there many things float through my mind about how we are seeing things now.

So the article above sparked some thoughts here about Sylvestor surfaces and B field understandings, that also included Lagrangian perspective along with WMAP polarization mapping. All these things seem so disconnected?

I keep finding myself trying to wrap all of this in a gravitational perspective as it should , no less important then gauss contributions, hidden for a time, while the student of his brings the perspective for us all to see. So how familiar is protege as Riemann that his Hypothesis is so much the like of the numbers apparent, as in the youthful gaze of the student challenged.

Sunday, November 20, 2005

Music of the Spheres

Strange Geometriesby Helen Joyce


Both spherical and hyperbolic geometries are examples of curved geometries, unlike Euclidean geometry, which is flat. In spherical geometry, the curvature is positive, in hyperbolic geometry, it is negative.




I thought I should add the "ascoustic variation" of the struggle for music in the world of "good and evil" as well.

That such "chaos created" in the minds of our youth, would have been frowned upon in Plato's academy.

By such reasonings and understandings of how such sound valuation may have been taken to spherical proportions? Should be no less then the consolidation points, as poincares distribution of eschers angel and demons pictures describe?

What avenues had been less then discribed on those chaldni plates that they had been reduced to dimensional avenues discriptive of the chaldni plates, as a fifth dimensional understanding? Langrangian discription of points L1 or L2, and a visionary context of Sylvestor surfaces as proponents of B field manifestations as part of genus figures with holes?

See:

  • Angels and Demons