Newton's inverse-square (1/r2) law

The standard model of particle physics is a self-contained picture of fundamental particles and their interactions. Physicists, on a journey from solid matter to quarks and gluons, via atoms and nuclear matter, may have reached the foundation level of fields and particles. But have we reached bedrock, or is there something deeper? Savas Dimopoulos

While in the post previous to this I gave some indication of the gravity from the cosmological point of view, I then took it down to the particle collisions. I again reiterate this, in this post as well.


Source-detector configuration for the 1-m 1/r² test

Newton's inverse-square (1/r²) law is a cornerstone of General Relativity. However, this law has been challenged by many modern theories of gravity and particle physics. The supergravity and unified field theories often run into a new short-range force, with an accompanying new particle, which should appear as a violation of the 1/r² law. More recently, a possible violation of the 1/r² law in the range below 1 mm was suggested by string theories with extra dimensions.

Gravity: Another Example of a 1/R² Law

Two masses at a given distance place equal and opposite forces of attraction on one another. The magnitude of this force of attraction is given by:




where G is the universal gravitation constant (6.67 X 10^-11 Nm²/kg²), m₁ is the mass of the first object in kilograms, m₂ is the mass of the second object in kilograms, and r is the distance between the centers of the two masses, in meters.

It is not without thinking here that what you thought of the "microstate blackhole," could have found it's relevance in the temperatures reached, when seen at this level?


Fig. 1. In quantum chromodynamics, a confining flux tube forms between distant static charges. This leads to quark confinement - the potential energy between (in this case) a quark and an antiquark increases linearly with the distance between them.

The ideal experimental test of this new feature of QCD would be to study the flux tube of figure 1 directly by anchoring a quark and antiquark several femtometres apart and examining the flux tube between them. In such ideal circumstances, one of the characteristics of the gluonic flux tube would be the model-independent spectrum shown in figure 2. The excitation energy is p/r because the flux tube's mass is entirely due to its stored energy. There are two initially excited longest wavelength vibrations with identical energies because the motion of the flux tube is in the two symmetrical dimensions perpendicular to its length.

You ever hear of the term, "you can't hit the broad side of a barn?" WEll lets think about this when it comes to the measures of femtometres and such. Classically old, it was not witout some direction in thinking that one could be taken down to certain measures for those same considerations. Barn Yard?

Origin of the (classified) barn

In the luminosity lexicon, a picobarn is one trillionth (10-12) of a barn, and a femtobarn is one quadrillionth (10-15) of a barn... but what's a barn? The distinctive and amusing term originated with two Purdue University physicists working on the Manhattan Project in 1942—and it was classified information by the US government until after World War II.

A History of Physics at Purdue (Gartenhaus, Tubis, Cassidy, and Bray) cites the July 1972 issue of Physics Today in which Marshall Halloway and Charles Baker write of tossing around ideas over dinner until arriving at "barn" to describe the typical nuclear cross section of 10-24 cm2, the effective target area that a nuclear particle represents in a collision. Dining in the Purdue Memorial Union, back in Lafayette, Indiana, Halloway and Baker dismissed "Oppenheimer" and "Bethe" as candidates, then considered John Manley, director of the Purdue group at Los Alamos. They decided "Manley" was too long, and then, as the authors put it in the Physics Today article to:

So here we are looking at what the EOT-WASH GROUP is doing? What is "compactification" in line with any thinking, that the world around us from a cosmological point of view is large(large circle), and that amidst it's reality, exists this finer world of particulars that "we'd only imagine" while the measures to it's finest(small circle) was produce and then energies assigned.

It would be as if you looked at the cosmos and never thought about it constituents "bits and pieces," which make up those cosmological processes. Yet, for me, "circles within circles" would have made me wonder which circle represented which part of the views at any one time, whilst we speak about these energies from one perspective to the next.

Savas Dimopoulos:At close encounter the particles can exchange gravitons via the two extra dimensions, which changes the force law at very short distances. Instead of the "Newtonian inverse square law" you’ll have an inverse fourth power law. This signature is being looked for in the ongoing experiments.

.....and more here for how perspectve can change once you give a direction in which to think about.

Savas Dimopoulos:At first we faced denial. We had deliberately used the word "sub-millimeter" in our first paper. Physicists were surprised, to say the least, that such a thing was not already excluded experimentally. I remember a stage in 1998 when colleagues wondered if we had not forgotten some crucial experiment. We were not discouraged. No! We gave talks on the ideas, and by July 1998 had analyzed the laboratory and cosmological constraints. That paper marked a sea-change in opinion: physicists began to think this was an interesting idea. By the fall of 1998 we were showing how to do real physics. Now several study groups are taking us very seriously: the high citation rates speak for themselves.
Personally I am not surprised by the reaction. Revolutionary ideas go through a cycle: denial, followed by "okay it is consistent but can you do anything with it?" and finally, once you show how to do real physics, you may get the third phase where many physicists become interested in the field. The same thing happened to me and Giorgi back in 1981 when we first proposed the supersymmetric extension of the standard model of particle physics. Initially there were the usual skeptics but now it is completely accepted.
Oddly, for me, the major competitor to these proposals for extra dimensions is the supersymmetry extension. But let's recall some of the disadvantages of the standard model. First, it shuts out gravity. Second, it has 18 free parameters, many of them very small. Third, the vacuum energy is 120 orders of magnitude larger than what you would naively guess from the standard model.
Proposing extra dimensions to space is a drastic step. But once you have the extra space you can attribute the smallness of some quantities to the statement that their origin is somewhere far away inside space, just as an astronomer might attribute the faintness of a galaxy to its large distance. For example, maybe the smallness of the electron mass arises because its origin is far away inside the extra dimensions.
My view is that both of the big ideas I have worked on are testable in the next decade by LHC. The two frameworks have complementary features. I'm greatly looking forward to the outcome

Make sure you look at the "compactification" label to the right index

Gravity Free Environment on Earth

It's taken some time from a layman perspective to try and "place this experiment" in a setting that helps orientate views. Well, at least in my case. :)

So here is a "guide below" that may seem trivial to some, yet, directed to the "microperspective" on this experiment, speak to cosmology as well. While it may seem easy from a "cosmological standpoint" gravities "effect" is of some importance in "condense matter views."

A "Top/down approach" pointing you toward LHC and the "anomaly of relativity" in the perfect fluid, seems like going "full circle?"

See:"Cosmic Variance"

Anyway to the essence of what has been instigated by the post of Seans, and what came about from the "Aerogel and Stardust" Post.


Microgravity Science Glove Box-The MSG will enable astronauts on board the ISS to perform a wide variety of materials, combustion, fluids and biotechnology experiments as well as investigations in the microgravity environment. It can also accommodate minor repairs and servicing of hardware requiring a controlled working environment. The facility offers users a wide range of innovative, utilization alternatives from manual control by astronauts via laptop computers to fully automated and remote control from Earth (telescience). A permanent data exchange link with ground stations is also ensured.The MSG will be integrated and used in the US Destiny Laboratory for a projected operational period of ten years.ESA is planning to use the facility for European experiments. The first time MSG will be used by a European astronaut to perform European experiments will be during a Soyuz taxi flight mission in October 2002. ESA's Belgian astronaut Frank De Winne will perform four different experiments in the MSG in the field of protein crystallization, zeolites crystallization, combustion and fluid science.
Frank De Winne works with the Microgravity Science Glovebox(MSG)Credits: ESA

Why is it we cannot create this environment, other then, the method described in terms of the drop tower, or, out in space? What ways do you know that such simulation can be developed to move the ideas of product development "done there in space." To make it feasible to create the condense matter states that are purer free from the effect of gravity on earth.

“On Earth, buoyancy continuously deforms and moves fluids in complex manners, making it difficult to study how materials that solidify from the melt form semiconductors and other products,” said Dr. Aleksandar Ostrogorsky, the SUBSA principal investigator who also teaches and conducts research at the Rensselaer Polytechnic Institute in Troy, N.Y. “In microgravity, the fluids are almost stagnant, resembling solids. The absence of motion makes it easier to observe and mathematically describe what is occurring when the crystals are melted, and how the materials solidify to form a new crystal.”

The idea occurred to me today to find a way in which to "create the environment" that is conducive to perfecting the "purity of alignment of substances" in a gravity free environment. I mentioned the aerogel in the previous article and how developing that product in space gives the product superior qualities, that one might not have here on earth.


Aircraft: A two-engine turbofan aircraft similar to the McDonnell-Douglas DC-9

A typical mission is 2 to 3 hours long and consists of 40 to 50 parabolas. These parabolas can be flown in succession or with short breaks between maneuvers to reconfigure test equipment. The Reduced Gravity Office provides scheduling, test coordination, and in-flight direction for the test programs.

So, we create the conditions for it. Whether it be the Space Shuttle, the Airplane or the Miniature Drop Tower.

NASA's "Weightless Wonder" KC-135a Reduced Gravity Laboratory

By comparing the results from fuel vaporization in a reduced-gravity environment with those under normal conditions, the students aim to gain a better understanding of how fuel droplets behave under different conditions to optimize the fuel injection process. The findings may be used in helping promote changes in engine design while improving efficiency and reducing emissions.

By understanding the process from "space to earth" we see where ingenuity of mind applies the differences of "time clocks" and such.


As one of the fields which obey the general inverse square law, the gravity field can be put in the form shown above, showing that the acceleration of gravity, g, is an expression of the intensity of the gravity field.

In a manner that "it's effects" in relation to gravity may be considered from a cosmological and micro-gravity perspective, in relation to "Inverse Square law( I use sound in the example, but click on the image provided)" and "Inverse Fourth Power Law."


This miniature drop tower is used by Microgravity man and others to demonstrate the effects of reduced gravity on physical and chemical phenomena that are normally masked by Earth's gravity.

So here we are "to the experiment" in a microperspective that is currently being explored.

Eric Adelberger on Aug 12th, 2005 at 2:37 pm

Please don’t get too excited yet about rumors concerning the Eot-Wash test of the 1/r^2 law. We can exclude gravitational strength (|alpha|=1) Yukawa violations of the 1/r^2 law for lambda>80 microns at 95% confidence. It is true that we are seeing an anomaly at shorter length scales but we have to show first that the anomaly is not some experimental artifact. Then, if it holds up, we have to check if the anomaly is due to new fundamental physics or to some subtle electromagnetic effect that penetrates our conducting shield. We are now checking for experimental artifacts by making a small change to our apparatus that causes a big change in the Newtonian signal but should have essentially no effect on a short-range anomaly. Then we will replace our molybdenum detector ring with an aluminum one. This will reduce any signal from interactions coupled to mass, but will have little effect on subtle electromagnetic backgrounds. These experiments are tricky and measure very small forces. It takes time to get them right. We will not be able to say anything definite about the anomaly for several months at least.

Update:

Check out Backreaction's Water in Zero Gravity

Aerogels and Stardust

IN a previous post on "Stardust," I was enamoured with "the product," that could do all the things that it said it could do.

-It is 99.8% Air

-Provides 39 times more insulating than the best fiberglass insulation

-Is 1,000 times less dense than glass

-Was used on the Mars Pathfinder rover

So having understood what "less gravity can do" in organizing of chemicals in space, it is of course of interest when such a chemical can be made into a product in it's "pure form," to have it "almost clear" in it's constitution and strong to hold weight.

It sort of opens the idea for me of manufacturing processes in space, and the construction of and use of those same products to build in space, and on, "planets of the future"

Almost as light as air, capable of withstanding a direct flame or catching speeding comet dust like a baseball mitt stops a hardball, aerogels are some of the strangest solids in the world. This "Space Age Styrofoam" was developed in a chemistry lab decades ago but is now appearing in snowsuits, explosives and even energy storage technology.

Aerogels are the lightest and lowest-density class of materials in the world. Up to 99 percent of the dry, rigid gels are air, while the rest consists of silica, carbon, metals and other substances; it feels like a Styrofoam peanut. Yet, some formulations can support close to two thousand times their weight (if it is lowered onto them slowly). "Enough force to crush a Rice Krispie will crush an aerogel," states Stephen Steiner, a nanomaterials graduate student at the Massachusetts Institute of Technology and aerogel researcher.

<Image: COURTESY OF LAWRENCE BERKELEY NATIONAL NATIONAL LABORATORIES-Aerogels are poor thermal conductors and therefore exceptional insulators for windows, snowsuits and spacecraft


Image: COURTESY OF NASA/JPL-CALTECH-Translucent silica aerogel is mostly air but two grams of the material is strong enough to hold a 2.5 kilogram brick

I was less then kind in my statements about stardust, as the images of dust in the air were given for introspection, about how we might see that dust in the universe.

"Last Sunday, after seven years in space traveling nearly three billion miles, Stardust landed in the Great Salt Lake Desert with a treasure from when the solar system formed 4.6 billion years ago," says astronomer Donald Brownlee of the University of Washington, who led the Stardust team. "We should have more than one million particles larger than one micron in diameter."

Image: D. BROWNLEE / NASA-Collecting of Stardust

Music of Hemispheres

Hearing Colors, Tasting Shapes By Vilayanur S. Ramachandran and Edward M. Hubbard

Modern scientists have known about synesthesia since 1880, when Francis Galton, a cousin of Charles Darwin, published a paper in Nature on the phenomenon. But most have brushed it aside as fakery, an artifact of drug use (LSD and mescaline can produce similar effects) or a mere curiosity. About four years ago, however, we and others began to uncover brain processes that could account for synesthesia. Along the way, we also found new clues to some of the most mysterious aspects of the human mind, such as the emergence of abstract thought, metaphor and perhaps even language.

See here.

Who would have thought to present such an "overlapping of the senses," to think, that our life is much better defined in all that we can become. While we "concretize" our views about the matter states . "IN principle, in our convictions, and no less, then the "what of change" in our human constitutions.


Images courtesy of Vinod Menon (Stanford University)-Images from an experiment to locate the neural regions of the brain involved in listening to music. Daniel Levitin and another scientist scanned the brains of 13 people as they listened to scrambled and unscrambled versions of a tune.

“By the age of 5 we are all musical experts, so this stuff is clearly wired really deeply into us,” said Dr. Levitin, an eerily youthful-looking 49, surrounded by the pianos, guitars and enormous 16-track mixers that make his lab look more like a recording studio.

This summer he published “This Is Your Brain on Music” (Dutton), a layperson’s guide to the emerging neuroscience of music. Dr. Levitin is an unusually deft interpreter, full of striking scientific trivia. For example we learn that babies begin life with synesthesia, the trippy confusion that makes people experience sounds as smells or tastes as colors. Or that the cerebellum, a part of the brain that helps govern movement, is also wired to the ears and produces some of our emotional responses to music. His experiments have even suggested that watching a musician perform affects brain chemistry differently from listening to a recording.

Of course these are "matter states" defined and "of measure."

Synesthesia (Greek, syn = together + aisthesis = perception) is the involuntary physical experience of a cross-modal association. That is, the stimulation of one sensory modality reliably causes a perception in one or more different senses.

But yes indeed, what of a more "quantumly defined view" about what is not seen? Least I say, with "conclusive proof" that all these states of being in our human structure, and without measure are "not true?" Then what use "any method" that I would say and develop of value to "other defines states" of being, other then the "physical?" Emotional, Mental, or spiritual?

Sir Isaac Newton

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.

Babies Begin Life with Synesthesia

It is not without wonder then, that the child in us all, was in a better defined state of existance? Before, the "focus of structure" along with the views of the physical body, could have "pronounced the reality" with "all the things" that make each of us human to our reality now.

Whilst it "may have been" less complicated then "before," we assigned each of our senses accordingly to what stimulai will activate the "different regions of our brain?" These are learnt and developed states, that has "past our meddling", to have now become engrained in our physical makeup? What then, are we to evolve too?

Society with the way it now is, is focused in the "communication era of computers" and such. What attribute of the mind/brain is being developed, as we physically type on the keynoard in front of us, whilst we communicate on a level of mind that is less then the verbal sound communications our mouth's manifest in relations?

Clock Work Universe

Fig 1.4 A two-dimensional coordinate system can be used to locate the position of any point in terms of its x- and y-coordinates

Figure 1.4 shows the two-dimensional case, with a grid extending over part of the page. The grid is calibrated (in centimetres) so the position of any point can be specified by giving its x- and y- coordinates on the grid. For example, the coordinates of point A are x = 3cm and y = 4cm.

This idea becomes more powerful when we consider lines and geometrical shapes. The straight line shown in Figure 1.5 is characterized by the fact that, at each
point along the line, the y-coordinate is half the -coordinate. Thus, the x- and
y- coordinates of each point on the line obey the equation y = 0.5x, and this is
said to be the equation of the line.



This is the beginning of a branch of mathematics, called coordinate geometry, which represents geometrical shapes by equations, and which establishes geometrical truths by combining and rearranging those equations.

Hubble Maps the Cosmic Web of "Clumpy" Dark Matter in 3-D

Three-Dimensional Distribution of Dark Matter in the Universe

This three-dimensional map offers a first look at the web-like large-scale distribution of dark matter, an invisible form of matter that accounts for most of the universe's mass. This milestone takes astronomers from inference to direct observation of dark matter's influence in the universe. Because of the finite speed of light, regions furthest away are also seen as they existed a long time ago. The map stretches halfway back in time to the beginning of the universe.

The map reveals a loose network of dark matter filaments, gradually collapsing under the relentless pull of gravity, and growing clumpier over time. This confirms theories of how structure formed in our evolving universe, which has transitioned from a comparatively smooth distribution of matter at the time of the big bang. The dark matter filaments began to form first and provided an underlying scaffolding for the subsequent construction of stars and galaxies from ordinary matter. Without dark matter, there would have been insufficient mass in the universe for structures to collapse and galaxies to form.

Part of this reporting is the way in which one could look at the Cosmos and see the gravitational relationships, as one might see it in relation to "Lagrangian views" in the Sun Earth Relation.


Diagram of the Lagrange Point gravitational forces associated with the Sun-Earth system.

Make sure you click on the image for further information. Mouseovers as your cursor is placed over images or worded links are equally important. You learn about satellites and the way they travel through these holes.

While one can see "dark matter" in terms of it's constraints, what of "dark energy" as it makes it way through those holes? This reveals the expansionary nature in terms of dark energy being repelled, whether you like to think so or not. This explains the dark energy developing free of the dark matter constraints and explains the state of our universe.


LSST Homepage background image. (Image credit: LSST Corporation, Bryn Feldman) Design of LSST Telescope dome and local facilities, current as of January 2007. Google Inc. has joined with nineteen other organizations to build the Large Synoptic Survey Telescope, scheduled to see first light atop Cerro Pachón in Chile in 2013.

The Large Synoptic Survey Telescope (LSST) is a proposed ground-based 8.4-meter, 10 square-degree-field telescope that will provide digital imaging of faint astronomical objects across the entire sky, night after night. In a relentless campaign of 15 second exposures, LSST will cover the available sky every three nights, opening a movie-like window on objects that change or move on rapid timescales: exploding supernovae, potentially hazardous near-Earth asteroids, and distant Kuiper Belt Objects. The superb images from the LSST will also be used to trace billions of remote galaxies and measure the distortions in their shapes produced by lumps of Dark Matter, providing multiple tests of the mysterious Dark Energy.

Two simulations of strong lensing by a massive cluster of galaxies. In the upper image, all the dark matter is clumped around individual cluster galaxies (orange), causing a particular distortion of the background galaxies (white and blue). In the lower image, the same amount of mass is more smoothly distributed over the cluster, causing a very different distortion pattern.

Here in this post the example of "how one may see" is further expounded upon to show how dark matter and dark energy are in action as a 90% aspect of the cosmos, while the remaining 10% is a discrete measure of what is cosmologically matter orientated. We don't loose sight of these relationships, but are helped to further develope them in terms of this gravitational relationship.

See:

Dark Matter in 3D

COSMOS Reveals the Cosmos

PLATO:Mathematician or Mystic ?

Mathematics, rightly viewed, possesses not only truth, but supreme beauty, a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.--BERTRAND RUSSELL, Study of Mathematics

One should not conclude that such a bloggery as this is not without a heartfelt devotion to learning. That I had made no great claims to what science should be. other then what a layman point of view in learning has become excited about. What may be a natural conclusion to one who has spent a long time in science. Do not think me so wanting to knock on your door to enforce the asking of education that may be sent my way was truly as a student waiting for some teacher to appear.

This did not mean I should not engage the world of science. Not become enamoured with it. Or, that seeing the teachers at their bloggeries, were "as if" that teacher did appear many times. This is what is good about it.

I did not care how young you were, or that I, "too old" to listen to what scientists knew, or were theoretically endowed with in certain model selections.

More from the Heart?


"Let no one destitute of geometry enter my doors."

You know that by the very namesake of Plato used here, that I am indeed interested how Plato thought and his eventual conclusions about what "ideas" mean. So, of course there is this learning that has to take place with mathematics.

If I may, and if I were allowed to fast forward any thought in this regard, it would be to say, that the evolution of the human being is much appreciated in what can transfer very quickly "between minds" while a dialogue takes place. Hence the title of this bloggery.

Science demands clarity, and being deficient in this transference of "pure thought" would be less then ideal speaking amongst those scientists without that mathematics. Yet, I do espouse that such intuitiveness can be gained from the simple experiment, by distilling information, from the "general concepts" which have been mention many times now by scientists.

So it is of interest to me that the roads to mathematical understanding through it's development would be quick to point out this immediate working in the "world of the abstract imaging" is to know that such methods are deduced by it's numbers and their greater meaning.

That such meaning can be assign to a "natural objector function" and still unbeknownst to the thinking and learning individual "a numerical pattern that lies underneath it. A "schematics" if you like, of what can become the form in reality.

No reader of Plato can fail to recognize the important role which mathematics plays in his writing, as would indeed be expected for an author about whom the ancient tradition maintains that he had hung over the entry to his school the words "Let No One Un-versed in Geometry Enter". Presumably it was the level of ability to work with abstract concepts that Plato was interested in primarily, but if the student really had never studied Greek geometric materials there would be many passages in the lectures which would be scarcely intelligible to him. Modern readers, versed in a much higher level of mathematical abstraction which our society can offer, have sometimes felt that Plato's famous "mathematical examples'" were illustrations rather than central to his arguments, and some of Plato's mathematical excursuses have remained obscure to the present time.

A Musical Interlude



Plato's Academy-Academy was a suburb of Athens, named after the hero Academos or Ecademos.

I can't help but say that I am indeed affected by the views of our universe. In a way that encompasses some very intriguing nodal points about our universe in the way that I see it.

While I may not have shown the distinct lines of the Platonic solids, it is within context of a balloon with dye around it, that it could be so expressive of the Chaldni plate, that I couldn't resist that "harmonics flavour" as to how one might see the patterns underneath reality. How some gaussian coordinates interpretation of the "uv" lines, that were distinctive of an image in abstract spaces.

Mersenne Prime: One < the Power of two

It looks as though primes tend to concentrate in certain curves that swoop away to the northwest and southwest, like the curve marked by the blue arrow. (The numbers on that curve are of the form x(x+1) + 41, the famous prime-generating formula discovered by Euler in 1774.)

This is part of the education of my learning to understand the implications of the work of Riemann in context of the Riemann Hypothesis. Part of understanding what this application can do in terms helping us to see what has developed "from abstractions of mathematics," to have us now engaged in the "real world" of computation.

In mathematics, a power of two is any of the nonnegative integer powers of the number two; in other words, two multiplied by itself a certain number of times. Note that one is a power (the zeroth power) of two. Written in binary, a power of two always has the form 10000...0, just like a power of ten in the decimal system.

Because two is the base of the binary system, powers of two are important to computer science. Specifically, two to the power of n is the number of ways the bits in a binary integer of length n can be arranged, and thus numbers that are one less than a power of two denote the upper bounds of integers in binary computers (one less because 0, not 1, is used as the lower bound). As a consequence, numbers of this form show up frequently in computer software. As an example, a video game running on an 8-bit system, might limit the score or the number of items the player can hold to 255 — the result of a byte, which is 8 bits long, being used to store the number, giving a maximum value of 28−1 = 255.

I look forward to the help in terms of learning to understand this "ability of the mind" to envision the dynamical nature of the abstract. To help us develop, "the models of physics" in our thinking. To learn, about what is natural in our world, and the "mathematical patterns" that lie underneath them.

What use the mind's attempt to see mathematics in such models?

"Brane world thinking" that has a basis in Ramanujan modular forms, as a depiction of those brane surface workings? That such a diversion would "force the mind" into other "abstract realms" to ask, "what curvatures could do" in terms of a "negative expressive" state in that abstract world.

Are our minds forced to cope with the "quantum dynamical world of cosmology" while we think about what was plain in Einstein's world of GR, while we witness the large scale "curvature parameters" being demonstrated for us, on such gravitational look to the cosmological scale.

Mersenne Prime


Marin Mersenne, 1588 - 1648

In mathematics, a Mersenne number is a number that is one less than a power of two.

Mn = 2n − 1.
A Mersenne prime is a Mersenne number that is a prime number. It is necessary for n to be prime for 2n − 1 to be prime, but the converse is not true. Many mathematicians prefer the definition that n has to be a prime number.

For example, 31 = 25 − 1, and 5 is a prime number, so 31 is a Mersenne number; and 31 is also a Mersenne prime because it is a prime number. But the Mersenne number 2047 = 211 − 1 is not a prime because it is divisible by 89 and 23. And 24 -1 = 15 can be shown to be composite because 4 is not prime.

Throughout modern times, the largest known prime number has very often been a Mersenne prime. Most sources restrict the term Mersenne number to where n is prime, as all Mersenne primes must be of this form as seen below.

Mersenne primes have a close connection to perfect numbers, which are numbers equal to the sum of their proper divisors. Historically, the study of Mersenne primes was motivated by this connection; in the 4th century BC Euclid demonstrated that if M is a Mersenne prime then M(M+1)/2 is a perfect number. In the 18th century, Leonhard Euler proved that all even perfect numbers have this form. No odd perfect numbers are known, and it is suspected that none exist (any that do have to belong to a significant number of special forms).

It is currently unknown whether there is an infinite number of Mersenne primes.

The binary representation of 2n − 1 is n repetitions of the digit 1, making it a base-2 repunit. For example, 25 − 1 = 11111 in binary

So while we have learnt from Ulam's Spiral, that the discussion could lead too a greater comprehension. It is by dialogue, that one can move forward, and that lack of direction seems to hold one's world to limits, not seen and known beyond what's it like apart from the safe and security of home.

Images or Numbers By Themself

“Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate” (cited by Ivars Peterson in Science News, 5/4/2002).

I have an idea in mind here that will be slow to show because I am not sure how it is supposed to be laid out. So maybe by showing these numbers by them self? What use, if one did not, or was not able to see in another way?


Figure 22.10: Double slit diffraction


I looked at the "straight lines" of Thomas Young's trajectories of photon emission and while quite understandably shown to be of consequence in this post "Interference." I was more interested in how something could start off in one place and do this rotation of sorts, and then come back for examination again in the real world. The Spectrum

Plato:

What a novel idea to have the methods used by the predecessors like Maxwell, to have been united from Faraday's principals? To have Maxwell's equation Gaussian in interpretation of Riemann geometry, somehow, united by the geometries of Einstein and defined as gravity?

But it is also in mind "that the image" has to be put here also before the numbers can show them self. What use these numbers if I do not transcend them to what they can imply in images, to know that the thinking here has to be orientated in such a way that what was simple and straight forward, could have non-euclidean orientations about it?


Michael Faraday (September 22, 1791 – August 25, 1867) was a British scientist (a physicist and chemist) who contributed significantly to the fields of electromagnetism and electrochemistry.

So one reads history in a lot of ways to learn of what has manifested into todays thinking. What lead from "Gaussian coordinates in an "non-euclidean way" to know that it had it's relation in today's physics. To have it included in how we see the consequences of GR in the world. It had been brought together for our eyes in what the photon can do in the gravitational field.

Our Evolution to Images


The Albrecht Durer's Magic Square


Ulam's Spiral


Pascal's Triangle

Evolve to What?

Who was to know what Leonard Susskind was thinking when his mathematical mind was engaged in seeing this "rubber band" had some other comparative abstraction, as something of consequence in our world. Yet, people focus on what they like to focus on, other then what "lead the mind" to think the way they do?


Poincaré Conjecture

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut......

I have to rest now.

Latex Rendering

Andrew Roberts:Here are some tutorials I have written for getting up to speed with this excellent document processing system. If you are not sure why Latex is any good, find out the benefits. I wouldn't consider myself an expert, but I'm learning all the time. I recall finding it quite taxing when I start to learn Latex, which is why I have started these tutorials. However, I hope that my experiences plays to your advantage, since I hope I can let you into the sort of questions and problems I had when I first learning Latex.

While preparing myself for the intricacies of PDF or science documents, which is a requirement of science people, I went back of course to what Robert and Clifford had found in the science community.

I am of course least in terms of the science education as I go through these bloggeries, yet the message has not fallen on a deaf ear in my case. So working toward helping others in science, is no less important then being given the skill to express myself/yourself properly.

So this is a beginning for me then, of what I had said I would do for the coming year.

Latex Symbol      Latex language
{times}             \times
{div}               \div
{diamond}           \diamond
{pm}                \mp
{ominus}            \ominus   \Big oplus
{otimes}            \otimes
{oslash}            \oslash
{odot}              \odot
{bigcirc}           \bigcirc
{circ}              \circ
{bullet}            \bullet
{asymp}             \asymp
{}....and so on.... \                  

[tex]{times}[/tex]= Latex symbology examples

In the "above link" to John Forkosh Associates, I used the pre "enclosed html brackets and /pre to finish article link even though it had been redone, as a demonstration to illustrate the symbolizations in latex rendering.

Click on Image for a larger size


Click on Image for a larger size


Click on Image for a larger size

Above, Clifford has laid it out for demonstration within his Sandbox to help others within his bloggery. Hope people use it. I am a little shy when it comes to demonstrating my ignorance, so having my "own sand box" would be nice without polluting someone else.

Imaging in Latex

Clifford:This is a space, easily accessible from the front page, where you can practice your LaTeX/MimeTeX commands for writing equations for adding to discussions, etc. You can see several people’s experiments at the earlier post here.

1st generation plotted according to weak hypercharge and weak isospin. Suggestive that the antiparticles are defined rather arbitrarily, and that the structure of idempotents of Clifford algebras (hypercubes) be used to model internal symmetries.

So having the understanding of what is necessary in the language development of latex, I am still far beneath those who I have linked in terms of that development. But, what ever the case, anything that can help, should not be so far beneath us that we ignore what had been found wanting in those who live the life as a scientist.