Sunday, August 27, 2006

Numerical Relativity and Math Transference

Part of the advantage of looking at computer animations is knowing that the basis of this vision that is being created, is based on computerized methods and codes, devised, to help us see what Einstein's equations imply.

Now that's part of the effort isn't it, when we see the structure of math, may have also embued a Dirac, to see in ways that ony a good imagination may have that is tied to the abstractions of the math, and allows us to enter into "their portal" of the mind.

NASA scientists have reached a breakthrough in computer modeling that allows them to simulate what gravitational waves from merging black holes look like. The three-dimensional simulations, the largest astrophysical calculations ever performed on a NASA supercomputer, provide the foundation to explore the universe in an entirely new way.

According to Einstein's math, when two massive black holes merge, all of space jiggles like a bowl of Jell-O as gravitational waves race out from the collision at light speed.

Previous simulations had been plagued by computer crashes. The necessary equations, based on Einstein's theory of general relativity, were far too complex. But scientists at NASA's Goddard Space Flight Center in Greenbelt, Md., have found a method to translate Einstein's math in a way that computers can understand.

Already having this basis of knowledge availiable, it was important to see what present day research has done for us, as we look at these images and allow them to take us into the deep space as we construct measures to the basis of what GR has done for us in a our assumptions of the events in the cosmo.

But it is more then this for me, as I asked the question, on the basis of math? I have enough links here to show the diversity of experience created from mathematical structures to have one wonder how indeed is th efinite idealization of imagination as a endless resource? You can think about livers if you likeor look at the fractorialization of the beginning of anythng and wonder I am sure.

That has been the question of min in regards to a condense matter theorist who tells us about the bulding blocks of matter can be anything. Well, in this case we are using "computer codes" to simulate GR from a mathematical experience.

So you see now don't you?:)

Is Math Invented or Discovered?

The question here was one of some consideration, as I wondered, how anyone could have delved into the nature of things and come out with some mathematcial model? Taken us along with the predecessors of endowwment thinking(imagination). To develope new roads. They didn't have to be 6 0r 7 roads Lubos, just a assumation. Sort of like, taking stock of things.

So I may ask, "what are the schematics of nature" and the build up starts from some place. Way back, before the computer modeling and such. A means, by which we will give imagination the tools to carry on.

So the journey began way back and the way in which such models lead our perspectives is the "overlay" of what began here in the postulates and moved on into other worldy abstractions?

This first postulate says that given any two points such as A and B, there is a line AB which has them as endpoints. This is one of the constructions that may be done with a straightedge (the other being described in the next postulate).

Although it doesn't explicitly say so, there is a unique line between the two points. Since Euclid uses this postulate as if it includes the uniqueness as part of it, he really ought to have stated the uniqueness explicitly.

The last three books of the Elements cover solid geometry, and for those, the two points mentioned in the postulate may be any two points in space. Proposition XI.1 claims that if part of a line is contained in a plane, then the whole line is. In the books on plane geometry, it is implicitly assumed that the line AB joining A to B lies in the plane of discussion.

One would have to know that the history had been followed here to what it is today.

Where Non-euclidean geometry began, and who were the instigators of imaginitive spaces now that were to become very dynamic in the xyzt direction.

All those who have written histories bring to this point their account of the development of this science. Not long after these men came Euclid, who brought together the Elements, systematizing many of the theorems of Eudoxus, perfecting many of those of Theatetus, and putting in irrefutable demonstrable form propositions that had been rather loosely established by his predecessors. He lived in the time of Ptolemy the First, for Archimedes, who lived after the time of the first Ptolemy, mentions Euclid. It is also reported that Ptolemy once asked Euclid if there was not a shorter road to geometry that through the Elements, and Euclid replied that there was no royal road to geometry. He was therefore later than Plato's group but earlier than Eratosthenes and Archimedes, for these two men were contemporaries, as Eratosthenes somewhere says. Euclid belonged to the persuasion of Plato and was at home in this philosophy; and this is why he thought the goal of the Elements as a whole to be the construction of the so-called Platonic figures. (Proclus, ed. Friedlein, p. 68, tr. Morrow)

These picture above, belongs to a much larger picture housed in the Raphael rooms in Rome. This particular picture many are familiar with as I use part of it as my profile picture. It is called the "Room of the Segnatura."

The point is, that if you did not know of the "whole picture" you would have never recognized it's parts?