Showing posts with label Dirac. Show all posts
Showing posts with label Dirac. Show all posts

Tuesday, August 27, 2013

What Dirac And Feynman Had in Common?

"The adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing" -- Richard Feynman
Should I be so bold to change the word in Feynman's quote as to suggest that "perpetual" be changed to "perceptual?" Conceptually, to be able to explain the Diagrams,  as a process unfolding?

"When I see equations, I see the letters in colors – I don't know why. As I'm talking, I see vague pictures of Bessel functions from Jahnke and Emde's book, with light-tan j's, slightly violet-bluish n's, and dark brown x's flying around. And I wonder what the hell it must look like to the students." Feynman, Richard. 1988. What Do You Care What Other People Think? New York: Norton. P. 59.

A Conformal Diagram of a Minkowski Spacetime

The question I raised in the Blog Post title is one that has to do with perception and how we can see in different ways. How did such a view of the natural world bring to light....anti-matter? Was it a conceptualization about time?

While Dirac spoke about projective geometry I could not but help to see that Feynman thought to use his diagrams to help see in "that kind of space."  As a layman, I could definitely be wrong.

You can picture all the directions in Minkowski space as the points in a three-dimensional projective space. The relationships between vectors, null-vectors and so on - - and you get at once just the relationships between points in a three-dimensional vector space. I always used these geometrical ideas for getting clear notions about relationships in relativity although I didn’t refer to them in my published works.Oral History Transcript — Dr. P. A. M. Dirac


Word Picture

Thursday, February 02, 2012

Word Picture

 Undoubtedly we have no questions to ask which are unanswerable . We must trust the perfection of the creation so far, as to believe that whatever curiosity the order of things has awakened in our minds, the order of things can satisfy. Every man's condition is a solution in hieroglyphic to those inquiries he would put. He acts it as life, before he apprehends it as truth. In like manner, nature is already, in its forms and tendencies, describing its own design. Let us interrogate the great apparition, that shines so peacefully around us. Let us inquire, to what end is nature? See: Nature by Emerson

I have this idea brewing for sometime in my mind and I am sure it fits with some who believe a comic strip while it can show it's humor can also show the discussion in science as well. But this is something quite subtle for what I had found in sciences developing mind that could at the same time speak about it's mathematics,  as well as unfolding in pictures who form as a continuous line of geometrical thinking. I might of in the past called it the Royal Road to Geometry, it was always the question of where all these lines of thinking could have evolved too.

It always brings me back to the success of Einsteins to have realize that his freedom came when the geometry of Riemann was used to help move beyond the Euclidean frame of Reference:) While that success took to a malleable form of line bending(greater or less than the perfect line interferometer)(LIGO laser or GRACE), of course it's success was built on the successes of those before him. That's just the way of it.

We see the earth much differently now. Much more then when it was first looked at from space, yet, there was individual peoples who dreamed of the earth from such a lofty ideal. Stepping out from the space capsule was an important step in moving beyond the fields of expression of an agricultural age.

The importance of what I am saying is to understand the very act of "tracing back toward inside" where this line emerged from. So as to ask,  what is it that such emergence could encompass that we would say that the driving force of this manifestation?  It is to become ever the selection of matter constituents that will form the basis of the reality? So is it matter choosing or some deeper understanding of our having chosen to become partners in the reality we exist in? Where did this line lead too,  having traced it back to where it began?

So the "word picture idea" is to understand that a universal language exists in each of us as a partner in the reality with which we participate? While one could have said that the math is revealing of the very schematics underlying this reality how does such math branch "outward" as it takes on the forms of what we find in nature? How are these mathematical terms "layered over" as to form the very conceptual basis of the words spoken? The word picture is a result then, but individual we shall choose it's covering, yet science must be very exact in this description.

 Paul Dirac

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

So one traces back the development of our for-bearers of geometrical inquisition as to ask how to break free of the thoughts that we had been restricted too(Poincaré conjecture). This then is why our thrust to expression is the success based on the developing line of  geometry? Ask yourself.....shall Dali be your respite from what is sought in XY painting,  to have understood the Crucifix was leading even though Salvador's religion some vast question of a ideal based on the developing frame. It was the question of the association in mind as an artist? Where was this geometry leading then, as if leading to the ideal of what leads us all to our religion?

Tuesday, September 20, 2011

The Universe, as an Expression of the Geometry

A new movie from NASA's Chandra X-ray Observatory shows a sequence of Chandra images of the Crab Nebula, taken over an interval of seven months. Dramatic variations are seen, including the expansion of a ring of X-ray emission around the pulsar (white dot near center) and changes in the knots within this ring.

Mathematically, it has to make sense.To visualize the universe then such scenarios must allow the potential of information to help form perspectives which show dynamical activities toward identifying the shape of the universe. This has to be able to be done in the now, and what of it is becoming in any moment?

I have opened with Dirac's comments before, but I thought at this point I should show Sir Roger Penrose comment  in contrast so you sort of get the idea.
The following is a quote from Dr. Roger Penrose's closing remarks.
"One particular thing that struck me... [LAUGHTER] the fact that he found it necessary to translate all the results that he had achieved with such methods into
algebraic notation. It struck me particularly, because remember I am told of Newton, when he wrote up his work, it was always exactly the opposite, in that he obtained so much of his results, so many of his results using analytical techniques and because of the general way in which things at that time had to be explained to people, he found it necessary to translate his results into the language of geometry, so his contemporaries could understand him. Well, I guess geometry… [INAUDIBLE] not quite the same topic as to whether one thinks theoretically or analytically, algebraically perhaps. This rule is perhaps touched upon at the beginning of Professor Dirac's talk, and I think it is a very interesting topic." See: Paul Dirac Talk: Projective Geometry, Origin of Quantum Equations

See Also:

Monday, May 30, 2011

TED Talk-Leonard Susskind: My friend Richard Feynman

I decided when I was asked to do this that what I really wanted to talk about was my friend Richard Feynman. I was one of the fortunate few that really did get to know him and enjoyed his presence. And I'm going to tell you the Richard Feynman that I knew. I'm sure there are other people here who could tell you about the Richard Feynman they knew, and it would probably be a different Richard Feynman.
Richard Feynman was a very complex man. He was a man of many, many parts. He was, of course, foremost a very, very, very great scientist. He was an actor. You saw him act. I also had the good fortune to be in those lectures, up in the balcony. They were fantastic. He was a philosopher; he was a drum player; he was a teacher par excellence. Richard Feynman was also a showman, an enormous showman. He was brash, irreverent -- he was full of macho, a kind of macho one-upsmanship. He loved intellectual battle. He had a gargantuan ego. But the man had somehow a lot of room at the bottom. And what I mean by that is a lot of room, in my case -- I can't speak for anybody else -- but in my case, a lot of room for another big ego. Well, not as big as his, but fairly big. I always felt good with Dick Feynman.
See Also: Leonard Susskind: My friend Richard Feynman


At 9:16 AM, June 01, 2011 Plato said

Listening to this talk with regard to Susskind's opinion about his friend Dick, he too would have thought about, "irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience." Albert Einstein

Pure thought(what does this linguistic representation actually mean) would have to lead you there and be most understandable as to leaving no doubt as to what has been derived.

I have often wondered where Feynman actually deduced his diagrams from and for me I think seeing how Dirac worked, this was suffice to me to actually see how "i" in for matrices was derived.

This again is my opinion. I am searching for answers.

For me it was about where one set them self in terms of their observation of the place "this simplicity" might have been realized.

Coxeter might have said circle when looking at a round table from above, while standing to the side, he would say ellipse

At 10:10 AM, June 03, 2011 Plato said...
Nothing worse then having to quote oneself in order to press the point. Carry on with life indeed as if nothing missed.:)
Pure thought(what does this linguistic representation actually mean) would have to lead you there and be most understandable as to leaving no doubt as to what has been derived.

Algorithmically, the HTML language is representative of the order in which we might represent an is done mathematically...that it is conceptually enriched(
put a cloud around it) that by such representation it would include historical understandings. These encapsulated by that rhetorical past is "inclusive."

You just take that for granted/assumption as long as the interpretation actually speaks to the historical development and proceeds forward toward an phenomenological order.

Most had to go through the historical development in order to understand where we are today. For the layman in my "seeing choice of method of production" toward falsifying, the choice of structure of phenomenological order is displayed as to demonstrate the thinking's involved scientifically that demonstrates the logic of approach toward a culmination of models of apprehension.

This display's the approach for myself. Might it be an example then of the whole development toward phenomenological order?


Friday, December 18, 2009

What the "i" represents, is Natural?

A Conformal Diagram of a Minkowski Spacetime
John D. Norton

First, here is the conformal diagram of a Minkowski spacetime. This is the complete spacetime. It includes all of the infinity of space and the infinity of time through which things persist.

This diagram gives the simplest case in which we consider just one dimension of space.

Note the three types of infinities: timelike, lightlike and spacelike. They correspond to the different vanishing points in an ordinary perspective drawing.

The Quantum Theory of the Electron

Paul Dirac

Projective Geometry
When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

In mathematical physics, the gamma matrices, {γ0123}, also known as the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cℓ(1,3). It is also possible to define higher-dimensional Gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of space time acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate space-time computations in general, and in particular are fundamental to the Dirac equation for relativistic spin-½ particles.

In Dirac representation, the four contravariant gamma matrices are
 \gamma^0 = 
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\ 
0 & 0 & -1 & 0 \\
0 & 0 & 0 & -1 \end{pmatrix},\quad
\gamma^1 \!=\! \begin{pmatrix}
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 \\
0 & -1 & 0 & 0 \\
-1 & 0 & 0 & 0 \end{pmatrix}
\gamma^2 \!=\! \begin{pmatrix}
0 & 0 & 0 & -i \\
0 & 0 & i & 0 \\
0 & i & 0 & 0 \\
-i & 0 & 0 & 0 \end{pmatrix},\quad
\gamma^3 \!=\! \begin{pmatrix}
0 & 0 & 1 & 0 \\
0 & 0 & 0 & -1 \\
-1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \end{pmatrix}.
Analogue sets of gamma matrices can be defined in any dimension and signature of the metric. For example the Pauli matrices are a set of "gamma" matrices in dimension 3 with metric of Euclidean signature (3,0).


Can we hope to use antimatter as a source of energy? Do you feel antimatter could power vehicles in the future, or would it just be used for major power sources?

There is no possibility to use antimatter as energy "source". Unlike solar energy, coal or oil, antimatter does not occur in nature: we have to make every particle at the expense of much more energy than it can give back during annihilation.

You might imagine antimatter as a possible temporary storage medium for energy, much like you store electricity in rechargeable batteries. The process of charging the battery is reversible with relatively small loss. Still, it takes more energy to charge the battery than what you get back out of it. For antimatter the loss factors are so enormous that it will never be practical.

If we could assemble all the antimatter we've ever made at CERN and annihilate it with matter, we would have enough energy to light a single electric light bulb for a few minutes.


Thoughts on Angel and Demons Plot

``For me, the most attractive way ... would be to capture the antihydrogen in a neutral particle trap ... The objective would be to then study the properties of a small number of [antihydrogen] atoms confined in the neutral trap for a long time."Gerald Gabrielse, 1986 Erice Lecture (shortly after first trapping of antiprotons)
"Penning Traps, Masses and Antiprotons", in Fundamental Symmetries,
edited by P. Bloch, P. Paulopoulos and R. Klapisch, p. 59 (Plenum, New York, 1987). See:Goals for ATRAP

Physics at this high energy scale describes the universe as it existed during the first moments of the Big Bang. These high energy scales are completely beyond the range which can be created in the particle accelerators we currently have (or will have in the foreseeable future.) Most of the physical theories that we use to understand the universe that we live in also break down at the Planck scale. However, string theory shows unique promise in being able to describe the physics of the Planck scale and the Big Bang.

Friday, May 15, 2009

The Cross Over Point and Time Travel

One of the issues that is evoked by any faster-than-light transport is time paradoxes: causality violations and implications of time travel. As if the faster than light issue wasn’t tough enough, it is possible to construct elaborate scenarios where faster-than-light travel results in time travel. Time travel is considered far more impossible than light travel.

I mean sure how is it one can measure time in energy particulate views when it appears all smeared out? It is the collision process itself and what I see in nature as Cascading particles as microscopic blackholes created and then quickly dissipated as decay in those particle showers.

Seeing muon detections that tunnel, and find their way across the globe is something that is interesting, as we can now use them in measure, as to what passes through to what is fabricated there in the LHC, becomes an interesting new tool of climate change or even gravitational inclination in relativistic approaches.

Length contractions is a key word here in microscopic measure.


Juan Martín Maldacena and Joseph Polchinski

Dr. Maldacena and Dr. Polchinski each gave brief lectures related to their work. Both included broad overviews of string theory basics, with Dr. Polchinski noting the importance of "thought experiments" to help physicists make advances in the field. He said that physicists are excited about future experiments using particle accelerators such as the Large Hadron Collider at CERN, where some of these "thought experiments" could be validated.

Dr. Maldacena, who was born in Buenos Aires, also spoke about ICTP's important influence on physics in Argentina, noting that many of his professors had spent time at the Centre. Dr. Maldacena himself has participated in ICTP training programmes and was a director of the Spring School on String Theory for four years.

The Dirac Medal is given in honour of P.A.M. Dirac, one of the greatest physicists of the 20th century and a staunch friend of ICTP, to scientists who have made significant contributions to physics. Recipients are announced annually on Dirac's birthday, 8 August. The Medallists also receive a prize of US $5,000.
Noted physicists awarded Dirac Medal


Juan Martín Maldacena, Institute for Advanced Study, Princeton
Joseph Polchinski, Kavli Institute for Theoretical Physics, University of California at Santa Barbara
Cumrun Vafa, Harvard University

Professors Maldacena, Polchinski and Vafa are being honored for their fundamental contributions to superstring theory. Their studies range from early work on orbifold compactifications, physics and mathematics of mirror symmetry, D-branes and black hole physics, as well as gauge theory-gravity correspondence. Their contributions in uncovering the strong-weak dualities between seemingly different string theories have enabled us to learn about regimes of quantum field theory which are not accessible to perturbative analysis. These profound achievements have helped us to address outstanding questions like confinement of quarks and QCD mass spectrum from a new perspective and have found applications in practical calculations in the fluid dynamics of quark gluon plasma.

The dualities have also led string theorists to conjecture that the five different superstring theories in ten space-time dimensions are manifestations of one underlying theory, yet undiscovered, which has been named the M-theory.
See:Dirac Medalists 2008


Another deep quantum mystery for which physicists have no answer has to do with "tunneling" -- the bizarre ability of particles to sometimes penetrate impenetrable barriers. This effect is not only well demonstrated; it is the basis of tunnel diodes and similar devices vital to modern electronic systems.

Tunneling is based on the fact that quantum theory is statistical in nature and deals with probabilities rather than specific predictions; there is no way to know in advance when a single radioactive atom will decay, for example.

The probabilistic nature of quantum events means that if a stream of particles encounters an obstacle, most of the particles will be stopped in their tracks but a few, conveyed by probability alone, will magically appear on the other side of the barrier. The process is called "tunneling," although the word in itself explains nothing.

Chiao's group at Berkeley, Dr. Aephraim M. Steinberg at the University of Toronto and others are investigating the strange properties of tunneling, which was one of the subjects explored last month by scientists attending the Nobel Symposium on quantum physics in Sweden.

"We find," Chiao said, "that a barrier placed in the path of a tunnelling particle does not slow it down. In fact, we detect particles on the other side of the barrier that have made the trip in less time than it would take the particle to traverse an equal distance without a barrier -- in other words, the tunnelling speed apparently greatly exceeds the speed of light. Moreover, if you increase the thickness of the barrier the tunnelling speed increases, as high as you please.

"This is another great mystery of quantum mechanics."
Signal Travels Farther and Faster Than Light By MALCOLM W. BROWNE

You and I know it as a time machine. Physicists, on the other hand, call it a "closed timelike curve." Below, feast on the concepts and conjectures, the dialects and definitions that physicists rely on when musing about the possibility of time travel. If this list only whets your appetite for more, we recommend you have a gander at the book from which we excerpted this glossary: Black Holes and Time Warps: Einstein's Outrageous Legacy, by Kip S. Thorne (Norton, 1994).


See Also:
  • Tunnelling in Faster then Light
  • Status of "Warp Drive"
  • Result of Effective Changes in the Cosmos
  • TimeSpeak
  • Tuesday, May 12, 2009

    Thoughts on Angel and Demons Plot

    ``For me, the most attractive way ... would be to capture the antihydrogen in a neutral particle trap ... The objective would be to then study the properties of a small number of [antihydrogen] atoms confined in the neutral trap for a long time."Gerald Gabrielse, 1986 Erice Lecture (shortly after first trapping of antiprotons)
    "Penning Traps, Masses and Antiprotons", in Fundamental Symmetries,
    edited by P. Bloch, P. Paulopoulos and R. Klapisch, p. 59 (Plenum, New York, 1987). See:Goals for ATRAP

    Perhaps you may see some familiarities with research material that may insight some correlative recognitions of events as they are portrayed in the science fiction scenario portrayed in the plot? So of course you do your homework first, and then you write about it?

    The techniques for slowing, cooling and storing cold antiprotons make it possible for ATRAP and its competitors to pursue the production of antihydrogen that is cold enough to trap for precise laser spectroscopy. TRAP got extremely close to cold antihydrogen with our simultaneous confinement of 4.2 K antiprotons and positrons reported in 1999.

    All the initial cold antiproton experiments were carried out at the CERN Laboratory with antiprotons coming from its Low Energy Antiproton Ring (LEAR), a unique facility that then closed. Antihydrogen experiments in 2000 and beyond will be pursued at the new Antiproton Decelerator ring of CERN which was constructed for this purpose. Using the techniques developed by TRAP, antiprotons will be accumulated within traps rather than in storage rings, thereby reducing the operating expenses to CERN.

    I finished the book Angel and Demons a couple of days ago. I've had the book for sometime, but just hadn't bothered. I needed a little break from the reporting here so thought to immerse myself in some reading, knowing the movie is out there now.

    A single solar flare might hold enough antimatter to power humanity's needs for millions of years. Credit: NASA/Goddard Space Flight Center/SOHO Project

    As in any crucial "blackhole calamities reported" some of our science advisers are speaking out to ward off "conspiracy theories" with some factual information, seems to be the jest at allaying fears about what energy released could happen in relation to the plot of the book.

    High Energy Solar Spectroscopic Imager (RHESSI).

    At even higher energies, we find gamma rays produced, not from the flare electrons, but from nuclear interactions of the protons and heavier ions accelerated in the flare. These high energy particles interact with the nuclei of the different elements in the ambient solar atmosphere to produce a far more complicated emission spectrum than the relatively smooth continuum bremsstrahlung spectrum. Many individual gamma-ray lines from a wide variety of different elements in the solar atmosphere have been detected. They result from the decay of such relatively abundant elements as carbon, nitrogen, oxygen, etc. that are excited to high energy states in the various nuclear interactions. The relative intensities of the various lines provide information about the composition of both the accelerated particles and the target nuclei.

    Furthermore, the lines are Doppler broadened and shifted because of the high velocities of the nuclei as they decay and emit the gamma rays. Consequently, the widths and detailed shapes of the lines can reveal the distribution of velocities of the emitting particles and hence also impose severe constraints on the acceleration mechanism itself. Despite the wealth of information believed to be available from observations of these gamma-ray lines, no gamma-ray spectrometer with the resolution necessary to reveal anything other than the intensities of the strongest lines has ever been flown.

    See:Overview of Solar Flares


    See Also:
  • Angels and Demons
  • Angels and Demons on a Pinhead
  • Tuesday, April 08, 2008

    Richard Feynman

    "The adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing" -- Richard Feynman Richard Feynman: Cover of The Feynman Lectures on Physics See also: The Feynman Lectures on Physics

    Tuesday, March 25, 2008

    Dennis William Sciama

    Dennis William Siahou Sciama FRS (November 18, 1926–December 18, 1999) was a British physicist who, through his own work and that of his students, played a major role in developing British physics after the Second World War.

    Sciama also strongly influenced Roger Penrose, who dedicated his The Road to Reality to Sciama's memory. The 1960s group he led in Cambridge (which included Ellis, Hawking, Rees, and Carter), has proved of lasting influence.

    Sciama was elected a Fellow of the Royal Society in 1982. He was also an honorary member of the American Academy of Arts and Sciences, the American Philosophical Society and the Academia Lincei of Rome. He served as president of the International Society of General Relativity and Gravitation, 1980-84.

    In 1959 he married Lidia Dina, a social anthropologist, who survived him, along with their two daughters.

    Alma mater
    University of Cambridge

    Doctoral advisor
    Paul Dirac

    Doctoral students

    John D. Barrow
    George Ellis
    Gary Gibbons
    Stephen Hawking
    Martin Rees
    David Deutsch
    Brandon Carter

    It was important that I understood the context of the entry by Phil Warnell.

    However, if the second is taken as truth and all is remembering, then what can the force of gravity do to a memory that is not in any, yet of all? So if all were to collapse would the memory not persist, since it is not of what vanished. Strangely, Hawking proved it so and yet he still denies his mentor who advised not only that it would be so, yet why

    Saturday, February 24, 2007

    Newton's Space was the Sensorium

    Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher who is generally regarded as one of the greatest scientists and mathematicians in history. See here for further information.

    While reading the responses to Aaron on the Cosmic Variance section, Lee Smolin made a comment there in his writing which triggered some recognition as I was doing some research on what he had proposed in previous work. So of course I am interested in how people form their ideas, so I went to have a look.

    Lee Smolin:
    I suspect this reflects the expectation many people have that time is not fundamental, but rather emerges only at a semiclassical approximation in quantum cosmology. If you believe this then you believe that the fundamental quantities a quantum cosmology should compute are timeless. This in turn reflects a very old and ultimately religious prejudice that deeper truths are timeless. This has been traced by scholars to the theology of Newton and contemporaries who saw space as “the sensorium” of an eternal and all seeing god. Perhaps the BB paradox is telling us it is time to give up the search for timeless probability distributions, and recognize that since Darwin the deep truths about nature cannot be divorced from time.

    The alternative is to disbelieve the arguments that time is emergent-which were never very convincing- and instead formulate quantum cosmology in such a way that time is always real. I would suggest that the Boltzman Brain’s paradox is the reducto ad absurdum of the notion that time is emergent and that rather than play with little fixes to it we should try to take seriously the opposite idea: that time is real.

    The key word here is "Sensorium."

    The Life of the Cosmos By Lee Smolin Oxford University Press; New York, N.Y.: 1997

    The critic is very harsh toward Lee Smolin, and I am very sensitive to these kinds of responses, so trust me when I tell you that these are not my views. My views are still forming.

    Lee Smolin:
    For Newton the universe lived in an infinite and featureless space.There was no boundary, ad no possibility of conceiving anything outside of it. This was no problem for God, as he was everywhere. For Newton, space was the "sensorium" of God-the medium of his presence in and attachment to the world. The infinity of space was then a necessary reflection of the infinite capacity of God.The Life of the Cosmos By Lee Smolin Oxford University Press; New York, N.Y.: 1997, Page 91

    The term "Sensorium" is compelling for reasons that I am still not quite aware of, yet, it holds a fascination to me. It is colourful to me, yet, it had a nice ring to it as well.

    Okay. :) I think it is the "relationship pointed out" and describing this relationship of Newton that is interesting. Most who have been reading my site will have some inkling of why.

    It is not in what may be assumed of Newton and his religion towards the relationship to science? But some of the ways in which such "thought processes" may have been compelling. The way in which one can look at the world, gives new meaning to what was not so transparent before, now one included these aspects of the sensorium as "one."

    That all of the senses had been "crossed wire to give perspective" in the way it did. How would you know this?

    But lets move on with this here for a minute and I'll tell you why. But first some part of it's Definition from Wikipedia.

    This interplay of various ways of conceiving the world could be compared to the experience of synesthesia, where stimulus of one sense causes a perception by another, seemingly unrelated sense, as in musicians who can taste the intervals between notes they hear (Beeli et. al., 2005), or artists who can smell colours. Many individuals who have one or more senses restricted or lost develop a sensorium with a ratio of sense which favours those they possess more fully. Frequently the blind or deaf speak of a compensating effect, whereby their touch or smell become more acute, changing the ways they perceive and reason about the world; especially telling examples are found in the cases of 'wild children,' whose early childhoods were spent in abusive, neglected or non-human environments, both intensifying and minimizing perceptual abilities (Classen 1991).

    Part of the developing scientific view can come forth with new propositions if it has a foundation that is different then what was thought to be "it's basis of normalcy."

    But imagine if you were a little different in your wiring that as a scientist you had difficult relating to the world, and you want to be consistent with your approach? Develope new methods, Calculus, to explain a process in nature? What may I ask will be forth coming form such a position, not to have thought, "hey this guy is nuts or just a broken flower pot?"

    The track record so far seems to indicate that if such views are crossed wired in some ways, the interactive features of developing perspective will give model apprehension a new meaning that it did not have before?

    Feynman in his concepts of a toy model approach? He may of seen what was of use from Dirac's geometrical thinking.

    NASA's Hubble Telescope Celebrates SN 1987A's 20th Anniversary

    A String of 'Cosmic Pearls' Surrounds an Exploding Star-NASA, ESA, P. Challis, and R. Kirshner (Harvard-Smithsonian Center for Astrophysics)
    Twenty years ago, astronomers witnessed one of the brightest stellar explosions in more than 400 years. The titanic supernova, called SN 1987A, blazed with the power of 100 million suns for several months following its discovery on Feb. 23, 1987.

    Observations of SN 1987A, made over the past 20 years by NASA's Hubble Space Telescope and many other major ground- and space-based telescopes, have significantly changed astronomers' views of how massive stars end their lives. Astronomers credit Hubble's sharp vision with yielding important clues about the massive star's demise.

    "The sharp pictures from the Hubble telescope help us ask and answer new questions about Supernova 1987A," said Robert Kirshner, of the Harvard-Smithsonian Center for Astrophysics in Cambridge, Mass. "In fact, without Hubble we wouldn't even know what to ask."

    Kirshner is the lead investigator of an international collaboration to study the doomed star. Studying supernovae like SN 1987A is important because the exploding stars create elements, such as carbon and iron, that make up new stars, galaxies, and even humans. The iron in a person's blood, for example, was manufactured in supernova explosions. SN 1987A ejected 20,000 Earth masses of radioactive iron. The core of the shredded star is now glowing because of radioactive titanium that was cooked up in the explosion.

    The star is 163,000 light-years away in the Large Magellanic Cloud. It actually blew up about 161,000 B.C., but its light arrived here in 1987.

    If you get the chance take a look over at the post "Supernova 1987A" done by Stefan of Backreaction in regards to this issue. It is nice to be able to reflect where one was when such a event took place. Maybe you remember where you were and can comment?

    About the event itself I must say it has not triggered any remembrances other then what I choose to reflect on my own life, and that's something different.

    What is of interest to be is how these events unfold and what geometrics play within the design of this unfoldment. I do speak on that in various posts.

    Kepler's Supernova

    Four hundred years ago, sky watchers, including the famous astronomer Johannes Kepler, were startled by the sudden appearance of a "new star" in the western sky, rivaling the brilliance of the nearby planets. Now, astronomers using NASA's three Great Observatories are unraveling the mysteries of the expanding remains of Kepler's supernova, the last such object seen to explode in our Milky Way galaxy.

    See here for link to this story.

    This combined image -- from NASA's Spitzer Space Telescope, Hubble Space Telescope, and e Chandra X-ray Observatory -- unveils a bubble-shaped shroud of gas and dust that is 14 light-years wide and is expanding at 4 million miles per hour (2,000 kilometers per second). Observations from each telescope highlight distinct features of the supernova remnant, a fast-moving shell of iron-rich material from the exploded star, surrounded by an expanding shock wave that is sweeping up interstellar gas and dust.

    By designing the types of satellites we wish to use to measure, we create the image of the events as beautiful pictures of unfoldment within our universe as seen above. Maybe you can see something in "the theory proposed of SN1987a pictures" that will help understand what I mean?

    When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way. Paul Dirac

    This universe has events at a time in space, which allows us to construct this event as as geometrical function. Some of the values seen in the microscopic world have placed an interesting role for me in how I see this relationship of what unfolds within our microperspective views, as to what is on display in our cosmos.

    The Bohr model is a primitive model of the hydrogen atom. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics, and thus may be considered to be an obsolete scientific theory. However, because of its simplicity, and its correct results for selected systems (see below for application), the Bohr model is still commonly taught to introduce students to quantum mechanics.

    While I appreciate these events in the cosmos I also needed to understand how such microperspective were motivating the geometry within that event, so it is not possible for me not to include the arrangements of the physics of reductionism and not compare it to these motivations that create these beautiful events

    Update: It's 9:20 am and I was just over at Quasar9's blog and notice this entry in relation to SN1987a as well.

    Monday, September 11, 2006

    Donald Coxeter: The Man Who Saved Geometry

    "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."Harold Scott Macdonald (H. S. M.) Coxeter

    Some would stop those from continuing on, and sharing the world behind the advancements in geometry. I am very glad that I can move from the Salvador Dali image of the crucifixtion, to know, that minds engaged in the "pursuites of ideas" as they may "descend from heaven," may see in a man like Donald Coxeter, the way and means to have ideas enter his mind and explode in sociological functions? Hmmmm. what does that mean?

    Geometry is a branch of mathematics that deals with points, lines, angles, surfaces and solids. 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).

    It is not often we see where our views are shared with other people?

    I was doing some reading over at Lubos Motl's blog besides just getting the link for Michio Kaku article, I noticed this one too.

    You might think the loss of geometry | like the loss of, say, Latin would pass virtually unnoticed. This is the thing about geometry: we no more notice it than we notice the curve of the earth. To most people, geometry is a grade school memory of fumbling with protractors and memorizing the Pythagorean theorem. Yet geometry is everywhere. Coxeter sees it in honeycombs, sun°owers, froth and sponges. It's in the molecules of our food (the spearmint molecule is the exact geometric reaction of the caraway molecule), and in the computer-designed curves of a Mercedes-Benz. Its loss would be immeasurable, especially to the cognoscenti at the Budapest conference, who forfeit the summer sun for the somnolent glow of an overhead projector. They credit Coxeter with rescuing an art form as important as poetry or opera. Without Coxeter's geometry | as without Mozart's symphonies or Shakespeare's plays | our culture, our understanding of the universe,would be incomplete.

    Now you know what fascination I have with the geometries, as they have moved us towards the comprehension of GR and Reimann? Could Einstein have ever succeeded without him?

    Michael Atiyah:
    At this point in the development, although geometry provided a common framework for all the forces, there was still no way to complete the unification by combining quantum theory and general relativity. Since quantum theory deals with the very small and general relativity with the very large, many physicists feel that, for all practical purposes, there is no need to attempt such an ultimate unification. Others however disagree, arguing that physicists should never give up on this ultimate search, and for these the hunt for this final unification is the ‘holy grail’.

    Without stealing the limelight from Donald, I wanted to put the thinking of Michael Atiyah along side of him too. So you understand that those who speak about the "physics" have things underlying this process which help hold them to the very fabric of thinking.

    Some do not know of "this geometric process" I speak, where such manifestation arise from the very essence of the thinking soul. If you began to learn about yourself you would know that such abstractions are much closer to the "pure thought" then any would have realized.

    Some meditate to get to this essence. Some know, that in having gone through a journey of discovery that they will find the very patterns sealed within each of the souls.

    How does it arise? You had to follow this journey through the "muddle maze" of the dreaming mind to know that patterns in you can direct the vision of things according to what you yourself already do inherently.

    Now some of you "know," don't you, with regards to what I am saying? I spoke often of "Liminocetric structures" just to help you along, and help you realize that the sociological standing of exchange houses many forms of thinking that we had gained previously. Why as a soul of the "thinking mind" should you loose this part of yourself?

    So you begin with the "Platonic Forms" and look for the soccer ball/football? THis process resides at many levels and Dirac was very instrumental in speaking about the basis of the geometer and his vision of things. Along side of course the algebraic way.

    (Picture credit: AIP Emilio Sergè Visual Archives)

    This is very real, and not so abstract that you may have departed form the real world to say, you have lost touch? Do you think only "in a square box" and cannot percieve anything beyond the "condensive thoughts and model apprehensions" which hold you to your own design?

    Maybe? :)

    But the world is vast in terms of discovery, that the question of mathematics again draws us back too, was "Mathematics invented or discovered?" So "this premise" as a question formed and with it "the roads" that lead to inquiry?

    Al these forms of geometrics leading to question about "Quantum geometry" and how would such a cosmological world reveal to the thinkingmind "the microscopic" as part of the dynamical world of our everyday living?

    Only a cynic casts the diversions and illusions to what is real. Because they cannot inherently deal with the "strange language of geometrics" that issues forth in model apprehensions. This is the basis from which Einstein solved the problems of his day.

    But the question is what geometrics could ever reside at such a microscopic level?

    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?

    Tuesday, August 15, 2006

    Newton the Alchemist

    Newton's Translation of the Emerald Tablet

    It is true without lying, certain and most true. That which is Below is like that which is Above and that which is Above is like that which is Below to do the miracles of the Only Thing. And as all things have been and arose from One by the mediation of One, so all things have their birth from this One Thing by adaptation. The Sun is its father; the Moon its mother; the Wind hath carried it in its belly; the Earth is its nurse. The father of all perfection in the whole world is here. Its force or power is entire if it be converted into Earth. Separate the Earth from the Fire, the subtle from the gross, sweetly with great industry. It ascends from the Earth to the Heavens and again it descends to the Earth and receives the force of things superior and inferior. By this means you shall have the glory of the whole world and thereby all obscurity shall fly from you. Its force is above all force, for it vanquishes every subtle thing and penetrates every solid thing. So was the world created. From this are and do come admirable adaptations, whereof the process is here in this. Hence am I called Hermes Trismegistus, having the three parts of the philosophy of the whole world. That which I have said of the operation of the Sun is accomplished and ended.

    The earliest version, written in Middle German, is dated 1532-1535 and is housed at the Prussian State Museum in Berlin. It is illuminated on vellum, with decorative borders like a book of hours, beautifully painted and heightened with gold. The later copies in London, Kassel, Paris and Nuremberg are equally fine. In all twenty copies exist worldwide.

    The original of Splendor Solis which contained seven chapters appeared in Augsburg. In miniatures the works of Albrecht Dürer, Hans Holbein and Lucas Cranach were used. The author of the manuscript was considered to be a legendary Salomon Trismosin, allegedly the teacher of Paracelsus. The work itself consists of a sequence of 22 elaborate images, set in ornamental borders and niches. The symbolic process shows the classical alchemical death and rebirth of the king, and incorporates a series of seven flasks, each associated with one of the planets. Within the flasks a process is shown involving the transformation of bird and animal symbols into the Queen and King, the white and the red tincture. Although the style of the Splendor Solis illuminations suggest an earlier date, they are quite clearly of the 16th century

    Of course the ideas I have about Alchemy are really thwarted by comments I may think arise in todays world, by what we may of called rational thinking. Skeptics/self, a many, might say, listen, like any model of perception, how can you have trusted such outdated thinking?

    Well imagine then, the quote taken here from 2002 of mine and how is it Newton could have been allowed percpetion in science areas, if he was not given to such model making, to assume a investigation, like use of language might help him see the issues differently?

    It would be a Alchemist who would sit with the Crucible to burn the substance within that crucible, to determine the inherent nature contained. Now in holding such a view how is it he could give himself to such a pursuite and to have found such a process of ditilliation to have cleared away the face of that substance to have discovered the deeper aspects of their makeup?

    If we have taken this comparison in a metaphorical sense how is it such a alchemist could have looked at his life and found such substances contained within his psyche. That to have burned away the substance of his nature to discover the inherent possibilities of design from such a process?

    Without some active force within ones consciousness how could any impetus to substance exploration be taken? Something is needed in which to discern the very nature and structure of such pursuites to chemical analysis to have determine the state such a soul could have occupied.

    So a way must be established in which such a person could sift the day to day living and discover the deeper aspects of self. We know that given any experience that reaity has us reflecting on the nature of such experiences, so how is it we change the future but recognize the changes of attitude that must be met those experiences. This could not have been done without some reflective journeys, so what is it we can see, and what is it that determines the meditative qualities to the understanding of those inherent patterns?

    I had mention "time variable measure" many times here and in context of "climate" and the "distilliation process" that I see, it was important that the developmental attitude be seen in context of the "ole ways" in order to understand what I am saying.

    Opticks is a book written by English physicist Isaac Newton that was released to the public in 1704. It is about optics and the refraction of light, and is considered one of the great works of science in history.

    Opticks was Newton's second major book on physical science. Even if he had not made his better-known discoveries concerning gravity and the invention of the calculus, Opticks would have given him the reputation as one of the greatest scientists of his time.

    This work represents a major contribution to science, different from—but in some ways rivaling—the Principia. The Opticks is largely a record of experiments and the deductions made from them, covering a wide range of topics in what was later to be known as physical optics. That is, this work is not a geometric discussion of catoptrics or dioptrics, the traditional subjects of reflection of light by mirrors of different shapes and the exploration of how light is "bent" as it passes from one medium, such as air, into another, such as water or glass. Rather, the Opticks is a study of the nature of light and colour and the various phenomena of diffraction, which Newton called the "inflexion" of light.

    In this book Newton sets forth in full his experiments, first reported in 1672, on dispersion, or the separation of light into a spectrum of its component colours. He shows how colours arise from selective absorption, reflection, or transmission of the various component parts of the incident light. His experiments on these subjects and on the problems of diffraction (which he never fully mastered) set the subject of optics on a new level.

    So in looking back it was a much greater effort then to see "experimental processes" engaged, that would allow us to look at the world in a interesting and viable context of such measures.

    How did Newton look at it in context of the Optics? Maybe, as Mendeleev did? Time spend in the lab, much different then 7 A.M. to 7 P.M and quite relaxed really, since thealchemist labs were not just physical things, but also manifested in "how" they could become better human beings.

    Time variable measures "exist" and in the "climate category" if no such process exists sociologically, then I am going to give you one. I am going to give you a view here about how gravity is percieved, on what we have taken to mean as spherical and encapsulated, is indeed now bumpy.

    Conclusion:The state of mind of the observer plays a crucial role in the perception of time.

    You as the "observer" had to be able to "see" differently. It was more then just "the geometry." Dirac was explicit about this. So he said "develope the algebraic equations."

    A comparison perhaps to Smolin's analogy of hills and valleys, in relation to the people and their qualification as to the work they must do??

    When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.