Showing posts with label Numerical Relativity. Show all posts
Showing posts with label Numerical Relativity. Show all posts

Saturday, April 14, 2012

Mega Mind?


Source:Numerical Relativity Code and Machine Timeline

In 2005 in "Lightening," as Strings, Strike?" I could see where certain issues were developing in terms of using computerized techniques in order establish a numerical correlations. Computations with how one might look and see the universe. Albeit, the brain in the end always came to my mind too.

 
DEUS consortium is developping the largest cosmological Dark Matter simulations to date with realistic Dark Energy component, involving billions of particules, with highest spatial resolution for the largest set of simulated Universe. Our challenge is to reproduce with unprecedented details the cosmic structure formation process and answer to the fundamental questions: what can we learn on Dark Energy from Large Scale Structure Formation (LSS) ? and How LSS formation process is affected by the presence of Dark Energy ? and then to understand the nature of the Dark Energy. www.deus-consortium.org, Contact: jean-michel.alimi@obspm.fr


Sort of like:  Mapping the Internet Brain and Consciousness

Thursday, December 29, 2011

Computational Science


Discussion from UC-HiPACC on VimeoAlso See: Bolshoi Simulation: WMAP Explorer

 As Richard Feynman put it:[13]
"It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypotheses that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities".


Computational science (or scientific computing) is the field of study concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems.[1] In practical use, it is typically the application of computer simulation and other forms of computation to problems in various scientific disciplines.

The field is distinct from computer science (the study of computation, computers and information processing). It is also different from theory and experiment which are the traditional forms of science and engineering. The scientific computing approach is to gain understanding, mainly through the analysis of mathematical models implemented on computers.

Scientists and engineers develop computer programs, application software, that model systems being studied and run these programs with various sets of input parameters. Typically, these models require massive amounts of calculations (usually floating-point) and are often executed on supercomputers or distributed computing platforms.

Numerical analysis is an important underpinning for techniques used in computational science.

Contents

  

  

Applications of computational science

Problem domains for computational science/scientific computing include:

  

Numerical simulations

Numerical simulations have different objectives depending on the nature of the task being simulated:
  • Reconstruct and understand known events (e.g., earthquake, tsunamis and other natural disasters).
  • Predict future or unobserved situations (e.g., weather, sub-atomic particle behaviour).

     Model fitting and data analysis

    • Appropriately tune models or solve equations to reflect observations, subject to model constraints (e.g. oil exploration geophysics, computational linguistics).
    • Use graph theory to model networks, especially those connecting individuals, organizations, and websites.

     

    Computational optimization

    • Optimize known scenarios (e.g., technical and manufacturing processes, front-end engineering).

      

    Methods and algorithms

    Algorithms and mathematical methods used in computational science are varied. Commonly applied methods include:

    Programming languages commonly used for the more mathematical aspects of scientific computing applications include R (programming language), MATLAB, Mathematica,[2] SciLab, GNU Octave, COMSOL Multiphysics, Python (programming language) with SciPy, and PDL.[citation needed] The more computationally intensive aspects of scientific computing will often utilize some variation of C or Fortran and optimized algebra libraries such as BLAS or LAPACK.

    Computational science application programs often model real-world changing conditions, such as weather, air flow around a plane, automobile body distortions in a crash, the motion of stars in a galaxy, an explosive device, etc. Such programs might create a 'logical mesh' in computer memory where each item corresponds to an area in space and contains information about that space relevant to the model. For example in weather models, each item might be a square kilometer; with land elevation, current wind direction, humidity, temperature, pressure, etc. The program would calculate the likely next state based on the current state, in simulated time steps, solving equations that describe how the system operates; and then repeat the process to calculate the next state.

    The term computational scientist is used to describe someone skilled in scientific computing. This person is usually a scientist, an engineer or an applied mathematician who applies high-performance computers in different ways to advance the state-of-the-art in their respective applied disciplines in physics, chemistry or engineering. Scientific computing has increasingly also impacted on other areas including economics, biology and medicine.

    Computational science is now commonly considered a third mode of science, complementing and adding to experimentation/observation and theory.[3] The essence of computational science is numerical algorithm[4] and/or computational mathematics.[5] In fact, substantial effort in computational sciences has been devoted to the development of algorithms, the efficient implementation in programming languages, and validation of computational results. A collection of problems and solutions in computational science can be found in Steeb, Hardy, Hardy and Stoop, 2004.[6]

     Education

    Scientific computation is most often studied through an applied mathematics or computer science program, or within a standard mathematics, sciences, or engineering program. At some institutions a specialization in scientific computation can be earned as a "minor" within another program (which may be at varying levels). However, there are increasingly many bachelor's and master's programs in computational science. Some schools also offer the Ph.D. in computational science, computational engineering, computational science and engineering, or scientific computation.

    There are also programs in areas such as computational physics, computational chemistry, etc.

     Related fields

      

    See also

     

     References

    1. ^ National Center for Computational Science
    2. ^ Mathematica 6 Scientific Computing World, May 2007
    3. ^ Siam.org
    4. ^ Nonweiler T. R., 1986. Computational Mathematics: An Introduction to Numerical Approximation, John Wiley and Sons
    5. ^ Yang X. S., 2008. Introduction to Computational Mathematics, World Scientific Publishing
    6. ^ Steeb W.-H., Hardy Y., Hardy A. and Stoop R., 2004. Problems and Solutions in Scientific Computing with C++ and Java Simulations, World Scientific Publishing. ISBN 981-256-112-9

     

    External links

    Wednesday, December 28, 2011

    The mechanism that explains why our universe was born with 3 dimensions: a 40-year-old puzzle of superstring theory solved by supercomputer


    A group of three researchers from KEK, Shizuoka University and Osaka University has for the first time revealed the way our universe was born with 3 spatial dimensions from 10-dimensional superstring theory1 in which spacetime has 9 spatial directions and 1 temporal direction. This result was obtained by numerical simulation on a supercomputer. .....

    .....Furthermore, the establishment of a new method to analyze superstring theory using computers opens up the possibility of applying this theory to various problems. For instance, it should now be possible to provide a theoretical understanding of the inflation5 that is believed to have taken place in the early universe, and also the accelerating expansion of the universe6, whose discovery earned the Nobel Prize in Physics this year. It is expected that superstring theory will develop further and play an important role in solving such puzzles in particle physics as the existence of the dark matter that is suggested by cosmological observations, and the Higgs particle, which is expected to be discovered by LHC experiments7.See:The mechanism that explains why our universe was born with 3 dimensions:a 40-year-old puzzle of superstring theory solved by supercomputer

    Thursday, December 08, 2011

    Bolshoi Simulation: WMAP Explorer


    Bolshoi Simulation Visualization from UC-HPACC on Vimeo. Watch With Music.

      Visualization of the dark matter in 1/1000 of the gigantic Bolshoi cosmological simulation, zooming in on a region centered on the dark matter halo of a very large cluster of galaxies.  Visualized by Chris Henze, NASA Ames Research Center. This visualization was narrated in the National Geographic TV special "Inside the Milky Way".  It was used with the piece "Dark Matter" in Bjork's Biophilia concert. 

     The Bolshoi simulation is the most accurate cosmological simulation of the evolution of the large-scale structure of the universe yet made (“bolshoi” is the Russian word for “great” or “grand”).  The first two of a series of research papers describing Bolshoi and its implications have been accepted for publication in the Astrophysical Journal. The first data release of Bolshoi outputs, including output from Bolshoi and also the BigBolshoi or MultiDark simulation of a volume 64 times bigger than Bolshoi, has just been made publicly available to the world’s astronomers and astrophysicists. See: Introduction: The Bolshoi Simulation

    See Also:

    Saturday, January 22, 2011

    The Edge World Question Center:

    Evidently, something powerful had happened in my brain.FRANK WILCZEK


    So this year.....

    WHAT SCIENTIFIC CONCEPT WOULD IMPROVE EVERYBODY'S COGNITIVE TOOLKIT?

    The term 'scientific"is to be understood in a broad sense as the most reliable way of gaining knowledge about anything, whether it be the human spirit, the role of great people in history, or the structure of DNA. A "scientific concept" may come from philosophy, logic, economics, jurisprudence, or other analytic enterprises, as long as it is a rigorous conceptual tool that may be summed up succinctly (or "in a phrase") but has broad application to understanding the world. The Edge Question 2011

    ***


    FRANK WILCZEK

    Physicist, MIT; Recipient, 2004 Nobel Prize in Physics; Author, The Lightness of Being



    In this picture, the flow of information runs from top to bottom. Sensory neurons — the eyeballs at the top — take input from the external world and encode it into a convenient form (which is typically electrical pulse trains for biological neurons, and numerical data for the computer "neurons" of artificial neural networks). They distribute this encoded information to other neurons, in the next layer below. Effector neurons — the stars at the bottom — send their signals to output devices (which are typically muscles for biological neurons, and computer terminals for artificial neurons). In between are neurons that neither see nor act upon the outside world directly. These inter-neurons communicate only with other neurons. They are the hidden layers.WHAT SCIENTIFIC CONCEPT WOULD IMPROVE EVERYBODY'S COGNITIVE TOOLKIT?

    ***


    Pathways

    Can we say that no two pathways are ever the same, then to what value "applying constraints on communication, then are they not the idea of limiting the potential, through connection of "other hidden layer neurons," in other people, are also activated? What is "the link" between this communication?



    ....finally, having the ability to dream:) See:Creating the Perfect Human Being or Maybe.....


    Expository on one level to realize that such diversity could create in the person the ability to dream, and actualize image creation according to the information at hand, how illusionist indeed that "such shapes" can come out of such communications within that that hidden layer? How would such application be realized according to computerized development?

    STEPHEN M. KOSSLYN

    We had an old headboard, which was so rickety that it had to be leaned against a wall. This requirement was a constraint on the positioning of the headboard. The other pieces of furniture also had requirements (constraints) on where they could be placed.Constraint Satisfaction

    How "large" the point/synapse, how large the room, how the large the universe? It's just a word. But it's culpability of "dimensional significance" is the ultimate picture that comes out of the resulting fabrication from the hidden layers? Just as one might think of string theory and the real world?

    Tuesday, January 04, 2011

    Sonification

    The lessons of history are clear. The more exotic, the more abstract the knowledge, the more profound will be its consequences." Leon Lederman, from an address to the Franklin Institute, 1995

    BBC article-Click on Image
    See Also: LHC sound

    ***

    Sonification is the use of non-speech audio to convey information or perceptualize data. Due to the specifics of auditory perception, such as temporal and pressure resolution, it forms an interesting alternative or complement to visualization techniques, gaining importance in various disciplines. It has been well established for a long time already as Auditory Display in situations that require a constant awareness of some information (e.g. vital body functions during an operation). Sonification as a method for exploration of data and scientific modeling is a current and ongoing research desideratum.

    One of the first successful applications of sonification is the well-known Geiger counter, a device measuring ionizing radiation. The number and frequency of audible clicks are directly dependent on the radiation level in the immediate vicinity of the device.

    Contents

    Fields

    Sonification is an interdisciplinary field combining:

    Some existing applications and projects

    Sonification techniques

    Many different components can be altered to change the user's perception of the sound, and in turn, their perception of the underlying information being portrayed. Often, an increase or decrease in some level in this information is indicated by an increase or decrease in pitch, amplitude or tempo, but could also be indicated by varying other less commonly used components. For example, a stock market price could be portrayed by rising pitch as the stock price rose, and lowering pitch as it fell. To allow the user to determine that more than one stock was being portrayed, different timbres or brightnesses might be used for the different stocks, or they may be played to the user from different points in space, for example, through different sides of their headphones.

    Many studies have been undertaken to try to find the best techniques for various types of information to be presented, and as yet, no conclusive set of techniques to be used has been formulated. As the area of sonification is still considered to be in its infancy, current studies are working towards determining the best set of sound components to vary in different situations.

    Several different techniques for rendering auditory data representations can be categorized:

    References

    1. ^ Thomas Hermann, Andy Hunt, and Sandra Pauletto. Interacting with Sonification Systems: Closing the Loop. Eighth International Conference on Information Visualisation (IV'04) : 879-884. Available: [1]. DOI= http://doi.ieeecomputersociety.org/10.1109/IV.2004.1320244.
    2. ^ Thomas Hermann, and Andy Hunt. The Importance of Interaction in Sonification. Proceedings of ICAD Tenth Meeting of the International Conference on Auditory Display, Sydney, Australia, July 6–9, 2004. Available: [2]
    3. ^ Sandra Pauletto and Andy Hunt. A Toolkit for Interactive Sonification. Proceedings of ICAD Tenth Meeting of the International Conference on Auditory Display, Sydney, Australia, July 6–9, 2004. Available: [3].

    See also

    External links


    ***

    Radar echos from Titan's surface

    This recording was produced by converting into audible sounds some of the radar echoes received by Huygens during the last few kilometers of its descent onto Titan. As the probe approaches the ground, both the pitch and intensity increase. Scientists will use intensity of the echoes to speculate about the nature of the surface.

    ***




    Gravity is talking. LISA will listen.

    The Cosmos sings with many strong gravitational voices, causing ripples in the fabric of space and time that carry the message of tremendous astronomical events: the rapid dances of closely orbiting stellar remnants, the mergers of massive black holes millions of times heavier than the Sun, the aftermath of the Big Bang. These ripples are the gravitational waves predicted by Albert Einstein's 1915 general relativity; nearly one century later, it is now possible to detect them. Gravitational waves will give us an entirely new way to observe and understand the Universe, enhancing and complementing the insights of conventional astronomy.
    See:What Does Gravity Sound Like?

    See Also: Gravitational Wave Detectors are Best Described as "Sounds.

    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

    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?

    Wednesday, April 12, 2006

    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




    Cubist Art: Picasso's painting 'Portrait of Dora Maar'
    Cubist art revolted against the restrictions that perspective imposed. Picasso's art shows a clear rejection of the perspective, with women's faces viewed simultaneously from several angles. Picasso's paintings show multiple perspectives, as though they were painted by someone from the 4th dimension, able to see all perspectives simultaneously.


    Sean from Cosmic Variance writes his opening post by including the title, "The language of Science".


    I would have said maths as well, yet, as a Layman there is much for me to learn.


    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?



    My first demonstration was with a Calabi Yau model of the torso. Visually seeing this way, helped to progress understanding. The transferance from the math structure to imaging in computer, to me, seemed very hard thing to do.


    Alain Connes

    Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition.



    If the math is right, the "concepts spoken," will be right also?



    How such reductionism is held to the values of science, is seen in the work of the calorimeters. Glast and LHC designs give introspective views of how fine our perspective is being shaped. Can we see the underlying imaging as a toll, respective of reductionism as seeing the dynamical and geoemtrical background to all events measured? LIGO in data accumulation, describing the infomration released into the bulk perspective.

    Toroidal_LHC_ApparatuS

    In the theory of relativity, momentum is not proportional to velocity at such speeds.) Thus high-momentum particles will curve very little, while low-momentum particles will curve significantly; the amount of curvature can be quantified and the particle momentum can be determined from this value.