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Monday, March 31, 2008

Numerical Relativity and the Human Experience?

"I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Donald (H. S. M.) Coxeter


I contrast the nature of Numerical Relativity to the computer and the way we would think human consciousness could have been linked in it's various ways. Who hasn't thought that the ingenuity of the thinking mind could not have been considered the Synapse and the Portal to the thinking Mind?:)

Also think about what can be thought here as Gerardus t" Hooft asked as to think about in the limitations of what can be thought in relation to computerizations.

There is something to be said here about what conscious is not limited too. It is by it's very nature "leading perspective" that we would like to have all these variables included in or assertions of what we can see while providing experimental data to the mind set of those same computerization techniques?

Numerical Relativity Mind Map

So we of course like to see the mind's ingenuity( computerized or otherwise) when it comes to how it shall interpret what is the road to understanding that gravity is seen in Relativities explanation.

Source:Numerical Relativity Code and Machine Timeline


It is a process by which the world of blackholes come into viewing in it's most "technical means providing the amount of speed and memory" that would allow us to interpret events in the way we have.

The information has to be mapped to computational methodology in order for us to know what scientific value scan be enshrined in the descriptions of the Blackhole. Imagine that with current technologies we can never go any further then what we can currently for see given the circumstances of this technology?


Source:Expo/Information Center/Directory-Spacetime Wrinkles Map

So on the one hand there is an "realistic version" being mapped according to how we develop the means to visualize of what nature has bestowed upon us in the according to understanding Blackhole's and their Singularities.

Numerical Relativity and Math Transferance

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.

Scientists are watching two supermassive black holes spiral towards each other near the center of a galaxy cluster named Abell 400. Shown in this X-ray/radio composite image are the multi-million degree radio jets emanating from the black holes. Click on image to view large resolution. Credit: X-ray: NASA/CXC/AIfA/D.Hudson & T.Reiprich et al.; Radio: NRAO/VLA/NRL

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.


Quantum Gravity

Now their is a strange set of circumstance here that would leave me to believe, that the area of quantum gravity has lead Numerical Relativity to it's conclusion? Has the technology made itself feasible enough to explore new experimental data that would allow us to further interpret nature in the way it shows itself? What about at the source of the singularity?

See: Dealing with a 5D World

I would not be fully honest if I did not give you part of the nature of abstract knowledge being imparted to us, if I did not include the "areas of abstractness" to include people who help us draw the dimensional significance to experience in these mathematical ways. It is always good to listen to what they have to say so that we can further developed the understanding of what becomes a deeper recognition of the way nature unfolds of itself.

There are two reasons that having mapped E8 is so important. The practical one is that E8 has major applications: mathematical analysis of the most recent versions of string theory and supergravity theories all keep revealing structure based on E8. E8 seems to be part of the structure of our universe.

The other reason is just that the complete mapping of E8 is the largest mathematical structure ever mapped out in full detail by human beings. It takes 60 gigabytes to store the map of E8. If you were to write it out on paper in 6-point print (that's really small print), you'd need a piece of paper bigger than the island of Manhattan. This thing is huge.
Emphasis and underlined, my addition.

Computer Language and Math Joined from Artistic Impressionism?

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."- Lisa Randall



THOMAS BANCHOFF has been a professor of mathematics at Brown University in Providence, Rhode Island, since 1967. He has written two books and fifty articles on geometric topics, frequently incorporating interactive computer graphics techniques in the study of phenomena in the fourth and higher dimensions


The marriage between computer and math language(Banchoff) I would say would be important from the prospective of displaying imaging, seen in the development of abstract language as used in numerical relativity? Accummalated data gained from LIGO operations. Time variable measures?

See:Computer Graphics In Mathematical Research

6 comments:

Bee said...

Interesting post, Plato. The value of numerical simulations lies very much in the question of what conclusions can be drawn from such doing. If one doesn't know better what the code is doing than one knows what nature does then what good is it? But in most cases a computer simulation has the advantage of being controllable, and repeatable. It is necessarily some reduction of the full system, but one hopes it is one that captures the important features. Things become awkward if people start making assumptions for their code because it makes them 'work better', or add additional parameters to 'fit the data better'. With each such step, the value of the model decreases - though the outcome might be nicer.

The appendix of the book that I wrote about today has a nice summary of the traps one can run into with numerical codes (like e.g. the temptation to add more and more details and features to make the situation more 'realistic').

Best,

B.

Plato said...

Bee:The value of numerical simulations lies very much in the question of what conclusions can be drawn from such doing. If one doesn't know better what the code is doing than one knows what nature does then what good is it?

For sure, and where our language leaves off what shall begin? New post on tscan today was brought up for consideration in this respect.

Consistency of measure. Yes, people do like to fit what they see to the data.

Regards,

Jérôme CHAUVET said...

Hi Plato,

In fact I would consider myself a Platonist too as I believe mathematical structures to be the primitive of all phenomenon.

Following this line, and corroborating Bee's argument, simulation are to me idealized natural systems, i.e., natural systems tested ceteris paribus.

The fact is that simulated simulation can help you test the effect of the open values of a theory (control parameters), and compensate the lack of integral functions.

Everyone is aware of the fact that logic is the deepest structure in the Universe, which is what makes the link between computing and reality.

Should one simply believe in the latter, i.e. admit it, or can one demonstrate it? I do not know whether or not logic can prove its own existence.

Best,

Plato said...

Jérôme:In fact I would consider myself a Platonist too as I believe mathematical structures to be the primitive of all phenomenon.

I never considered being a Platonist as being primitive.

Can this be surmised from your statement above?

Donald (H. S. M.) Coxeter

One of Coxeter’s major contributions to geometry was in the area of dimensional analogy, the process of stretching geometrical shapes into higher dimensions. He is also famous for “Coxeter groups,” the inversive distance between two disjoint circles (or spheres).

Historically in regards to "Plato's time as being primitive" we can say that this is so, but if one is to consider the "Cave and the light" that shines from behind to cast shadows, it is not unlike "for me" that the fire/sun represents the beginning of the process for the thinking process too, and probable outcomes.

The brain is not hot then is it? Yet, it is quite capable of firing neurons at a tremendous rate? What does it look like under imaging?

Best,

Plato said...

Corrected link for wording

dimensional analogy, the process of stretching geometrical shapes into higher dimensions.

Best,

Plato said...

"...underwriting the form languages of ever more domains of mathematics is a set of deep patterns which not only offer access to a kind of ideality that Plato claimed to see the universe as created with in the Timaeus; more than this, the realm of Platonic forms is itself subsumed in this new set of design elements-- and their most general instances are not the regular solids, but crystallographic reflection groups. You know, those things the non-professionals call . . . kaleidoscopes! * (In the next exciting episode, we'll see how Derrida claims mathematics is the key to freeing us from 'logocentrism'-- then ask him why, then, he jettisoned the deepest structures of mathematical patterning just to make his name...)

* H. S. M. Coxeter, Regular Polytopes (New York: Dover, 1973) is the great classic text by a great creative force in this beautiful area of geometry (A polytope is an n-dimensional analog of a polygon or polyhedron. Chapter V of this book is entitled 'The Kaleidoscope'....)"


(bold added by me for emphasis)

also below for consideration...

The crystalline state is the simplest known example of a quantum , a stable state of matter whose generic low-energy properties are determined by a higher organizing principle and nothing else. Robert Laughlin (again bold added by me for emphasis.)

Does any of this help?

Best,