Thursday, October 22, 2009

Artifacts in the Exploration of Geometry



Ashmolean Museum, Oxford, UK

It should not be lost on individuals who have followed this blog, that there is a range of connection to Platonic Forms idealization, that such an artifact in Ashmolean Museum although modeled to represent a reality and constituent forming basis, it is by this choice,  that I exercised a" foundational attitude"  about what I can use to push my own perspective forward in science. What others were using.


"The Artist and his Museum"

The first public showing of the mastodon (also known as the "Mammoth", the American incognitum and the "animal de l'Ohio") took place next door to Independence Hall, the building in which both the Declaration of Independence and Constitution were finalized. The venue, known variously as Peale's Museum, the American Museum or simply as The Museum, was the remarkable product of a resourceful, versatile and passionate artist and showman, Charles Wilson Peale.

Peale (1741-1827) was born and raised in Maryland. A vocal opponent of the Stamp Act, he was effectively driven from his first trade, saddle making, when loyalist merchants cut off his credit. He turned to a traveling life of a self-taught, itinerant portrait painter. After a short apprenticeship with Benjamin West in London, Peale returned to Maryland in 1769 to paint wealthy patrons throughout the Chesapeake region.
In 1776 he moved to the largest city of the colonies, Philadelphia, in the hopes of further developing his career. Through his contacts made while serving as a captain of the Continental Army, Peale painted a remarkable assemblage of Revolutionary War figures, including the most comprehensive portrait series ever painted of George Washington
. See:Charles Willson Peale's Museum

After doing quite a bit of reading over the years it is surprising what one can come across as they look at the historical perspective with artifacts which sat on shelves to curious onlookers as they examine these items.

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




So you have in fact "forerunners of museums today" revealed in pursuits by individuals to catalog items according to the range of professions and undertakings. In this case, I was interested on geometrical forms as it was some interest to me that we could move our minds around in abstract spaces . I followed the surfaces of "dynamic movement"  issued forth by theoretical application. These would be,  modular forms or Genus figures of string theory, that raised my interest about the space we are working in.


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.

Now you must know that I do not have the education of the universities but this did not stop me from trying to understand what these artifacts in geometry actually represented. Where they were placed by theoreticians to represent the figurative evolution of what actual begins in this universe, from beyond time and space and arrived to a direction of expressions unfolding in the arrow of time. This was a recognition of the times in microseconds that had been "used in minutes" of Steven Weinberg.


A giddy craze was sweeping across Europe at the turn of the 17th century. The wealthy and the well-connected were hoarding things—strange things—into obsessive personal collections. Starfish, forked carrots, monkey teeth, alligator skins, phosphorescent minerals, Indian canoes, and unicorn tails were acquired eagerly and indiscriminately. Associations among these objects, if they were made at all, often reflected a collector's personal vision of an underlying natural "order". Critical taxonomy was rarely in evidence.

So this historical perspective of the artifacts moved my perspective to today and what is going on in mathematical abstraction. What are these shapes actually representing in reality? Is there such a thing once perception has been granted of the close correlative function of the description of that microscopic reality?

It would be that the mind has become capable of moving into the realm of the microscopic, that by measure of energy used, details the plethora of particle and constituents of that energy, that each artifact is leading toward ever finer issues of what began in the formation of the matter, to allow us to see it's constitutions as they are revealed today macroscopically.