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.

The Sun's Before Us

The Cosmic Ray of Creation

We are "shadows" of the Sun's creations.

Sometimes it good to go back to "the beginning" so that one can see the context of what exists in reality, has a much "greater story to tell" then what we of the real world live under.

Those of science, have been focused in their own worlds. We just had to understand why they were so absorbed.

"String theory and other possibilities can distort the relative numbers of 'down' and 'up' neutrinos," said Jonathan Feng, associate professor in the Department of Physics and Astronomy at UC Irvine. "For example, extra dimensions may cause neutrinos to create microscopic black holes, which instantly evaporate and create spectacular showers of particles in the Earth's atmosphere and in the Antarctic ice cap. This increases the number of 'down' neutrinos detected. At the same time, the creation of black holes causes 'up' neutrinos to be caught in the Earth's crust, reducing the number of 'up' neutrinos. The relative 'up' and 'down' rates provide evidence for distortions in neutrino properties that are predicted by new theories."

Who is to know of what is sent to earth, and not understand, that what happens above us, also happens within the LHC?


Jacque Distler:

Travis Stewart reports that the LHC’s ATLAS detector has seen cosmic ray events, an excellent sign that things are working as they should.

One does not have to think, or be insulted by "such stories" that have captured minds in our history. The "ideas of cultures" are pervaded by such religious practises and context, by the fascination of some greater being? Having worked with them long enough?

As a scientist, you know your place in the world. Yet, you dream of such "fantastical stories." About things travelling through the little towns in Europe, as if, seeing the "Overlords of Science." Like some futuristic God making it's way through the town of some primitive era on earth. "Shocked people" looking from windows, as this enormous object in the "war of the worlds," has finally come upon us.

The article traces in non-technical language the historical development of our understanding of nuclear fusion reactions as the source of stellar energy, beginning with the controversy over the age of the sun and earth between Darwin and Kelvin, and including the discovery of radioactivity, the experimental demonstration that four hydrogen nuclei are heavier than a helium nucleus, and the theoretical insights provided by Einstein, Gamow, and Bethe. The concluding sections concern solar neutrino experiments that were designed to test the theory of stellar evolution and which, in the process, apparently revealed new aspects of microscopic physics.

It is important that one understands that such a thing having been studied by our scientists, is still a "noble thing." Where we learn to understand what these things could represent symbolically? Enlightenment possibly? When all the understanding of the "Neutrino overlords" are understood in their place and time.



The winged sun was an ancient (3rd millennium BC) symbol of Horus, later identified with Ra.

A solar deity is a god or goddess who represents the sun, or an aspect of it. People have worshipped the sun and solar deities for all of recorded history; sun worship is also known as heliolatry. Hence, many beliefs and legends have been formed around this worship, most notably the various myths containing the "missing sun" motif from around the world. Although many sources contend that solar deities are generally male, and the brother, father, husband and/or enemy of the lunar deity (usually female), this is not cross-culturally upheld, as sun goddesses are found on every continent. Some mythologists, such as Brian Branston, therefore contend that sun goddesses are more common worldwide than their male counterparts. They also claim that the belief that solar deities are primarily male is linked to the fact that a few better known mythologies (such as those of ancient Greece and Egypt) sometimes break from this rule. The dualism of sun/male/light and moon/female/darkness is found in many (but not all) European traditions that derive from Orphic and Gnostic philosophies, with a notable exception being Germanic mythology, where the Sun is female and the Moon is male.

Sun worship is a possible origin of henotheism and ultimately monotheism. In ancient Egypt's Eighteenth Dynasty, Akhenaten's heretical Atenism used the old Aten solar deity as a symbol of a single god. The neolithic concept of a solar barge, the sun as traversing the sky in a boat, is found in ancient Egypt, with Ra and Horus. Proto-Indo-European religion has a solar chariot, the sun as traversing the sky in a chariot. At Roman Empire, a festival of the birth of the Unconquered Sun (or Dies Natalis Solis Invicti) was celebrated when the duration of daylight first begins to increase after the winter solstice, — the "rebirth" of the sun. In Germanic mythology this is Sol, in Vedic Surya and in Greek Helios and (sometimes) Apollo. Mesopotamian Shamash plays an important role during the Bronze Age, and "my Sun" is eventually used as an address to royalty. Similarly, South American cultures have emphatic Sun worship, see Inti. See also Sol Invictus.

Symmetries Can be Chaotically Complex

Imagine in an "action of a kind" you start off from one place. A photon travelling through a slit of Thomas Young's, to get through "a world" to the other side. Sounds like some fairy tale doesn't it? Yet, "the backdrop" is where you started?


Thomas Young (June 14, 1773 – †May 10,1829)

was an English scientist, researcher, physician and polymath. He is sometimes considered to be "the last person to know everything": that is, he was familiar with virtually all the contemporary Western academic knowledge at that point in history. Clearly this can never be verified, and other claimants to this title are Gottfried Leibniz, Leonardo da Vinci, Samuel Taylor Coleridge, Johann Wolfgang Goethe and Francis Bacon, among others. Young also wrote about various subjects to contemporary editions of the Encyclopedia Britannica. His learning was so prodigious in scope and breadth that he was popularly known as "Phenomenon Young."

Simplistically this "massless entity" is affected by the "geometrics of gravity?" Is affected from it's "first light." All the way to some "other point in reality" to some image, called the spectrum.

I am dreaming. I am walking down the street and there is this "N category cafe."

Imagine walking off the street into this very public venue and seeing the philosophy shared is also held to certain constraints. :)Philosophy? Yes, we all have our "points of view."

Travelling the Good Life with Ease

So in this travel how is one to see this "curve of light" or "slide" and we get this sense of what gravity can do.

Imagine indeed, "a hole cosmological related" in the three body problem, it has to travel through, and we get this sense of "lensing and distortion," abstractually gravitationally induced?



So as we look at the cosmos what illusion is perpetrated on our minds as we look into the "great distance of measure" that somehow looking to the journey of "an event local," from our place on and about earth, has not been "chaotically entrained in some way, as we look deep into space?


The Magic Square

Plato:Like Pascal, one finds Albrecht has a unique trick, used by mathematicians to hide information and help, to exemplify greater contextual meaning. Now you have to remember I am a junior here in pre-established halls of learning, so later life does not allow me to venture into, and only allows intuitive trials poining to this solid understanding. I hope I am doing justice to learning.

Moving in abstract spaces

It was necessary to explain why I added "the image" to the right in my index.

Some would think me so "esoteric" that I had somehow lost touch with the realities of science? That to follow any further discussion here "has to be announced" to save one's dignity? What ever?:)I am esoteric in that my views of the world come from a different place, not unlike your expression of where you had come from living your life. How would I come to know all that you are in a "single sentence." A single and very short equation? It's really not that easy is it?:)

So I read you from all the things that you say and get the sense of who you are no different then what is implied in the language of poetic art implied carefully from choosing your words?

Artistically Inclined?

I tried to give some hint of the "ideas floating" around in my head. I understand quite well that my challenge has been to get those "images in my head" transmitted onto paper, in a way that one would not become confused as to what is being implied.

So a good writer I may not be, a "not so good scientist" whose mathematics very ill equipped.

Thus I am faced with these challenges in the new year? A "recognition" of trying to produce that clarity. Whether in "latex" the symbols of mathematics, it is quite a challenge for me, whilst all these things are still engaged in abstract views of reality.

So someone like Clifford, may look at Robert by what he has written and say, "hey, my fellow scientists are indeed in trouble" from what Robert has learnt. So I Clifford will provide "the latex sandbox" for you to play in?

It "appears" I am not alone. My struggle, are to be many a struggle.

Art and the Abstract

But to my amazement this morning in checking up the links associated of Clifford's, I was amazed to see the article of, Hooking Up Manifolds

Now how interesting that what is being displayed there in terms of fun, mathematics, art, could have been so abstractly appealing? "Moving over these surfaces" in ways that one might never appreciated, had you not known about how one can look at the universe in the "two ways mentioned previously," and by simple experiment, transcend such things to art.

N category and the Hydrogen spectrum

Picture of the 1913 Bohr model of the atom showing the Balmer transition from n=3 to n=2. The electronic orbitals (shown as dashed black circles) are drawn to scale, with 1 inch = 1 Angstrom; note that the radius of the orbital increases quadratically with n. The electron is shown in blue, the nucleus in green, and the photon in red. The frequency ν of the photon can be determined from Planck's constant h and the change in energy ΔE between the two orbitals. For the 3-2 Balmer transition depicted here, the wavelength of the emitted photon is 656 nm.

In atomic physics, the Bohr model depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus — similar in structure to the solar system, but with electrostatic forces providing attraction, rather than gravity.

Introduced by Niels Bohr in 1913, the model's key success was in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen; while the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced.

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.

For one to picture events in the cosmos, it is important that the spectral understanding of the events as they reveal themselves. So you look at these beautiful pictures and information taken from them allow us to see the elemental considerations of let's say the blue giants demise. What was that blue giant made up of in term sof it's elemental structure

The quantum leaps are explained on the basis of Bohr's theory of atomic structure. From the Lyman series to the Brackett series, it can be seen that the energy applied forces the hydrogen electrons to a higher energy level by a quantum leap. They remain at this level very briefly and, after about 10-8s, they return to their initial or a lower level, emitting the excess energy in the form of photons (once again by a quantum leap).


Lyman series
Hydrogen atoms excited to luminescence emit characteristic spectra. On excitation, the electron of the hydrogen atom reaches a higher energy level. In this case, the electron is excited from the base state, with a principal quantum number of n = 1, to a level with a principal quantum number of n = 4. After an average dwell time of only about 10-8s, the electron returns to its initial state, releasing the excess energy in the form of a photon.
The various transitions result in characteristic spectral lines with frequencies which can be calculated by f=R( 1/n2 - 1/m2 ) R = Rydberg constant.
The lines of the Lyman series (n = 1) are located in the ultraviolet range of the spectrum. In this example, m can reach values of 2, 3 and 4 in succession.


Balmer series
Hydrogen atoms excited to luminescence emit characteristic spectra. On excitation, the electron of the hydrogen atom reaches a higher energy level. In this case, the electron is excited from the base state, with a principal quantum number of n = 1, to a level with a principal quantum number of n = 4. The Balmer series becomes visible if the electron first falls to an excited state with the principal quantum number of n = 2 before returning to its initial state.
The various transitions result in characteristic spectral lines with frequencies which can be calculated by f=R( 1/n2 - 1/m2 ) R = Rydberg constant.
The lines of the Balmer series (n = 2) are located in the visible range of the spectrum. In this example, m can reach values of 3, 4, 5, 6 and 7 in succession.


Paschen series
Hydrogen atoms excited to luminescence emit characteristic spectra. On excitation, the electron of the hydrogen atom reaches a higher energy level. In this case, the electron is excited from the base state, with a principal quantum number of n = 1, to a level with a principal quantum number of n = 7. The Paschen series becomes visible if the electron first falls to an excited state with the principal quantum number of n = 3 before returning to its initial state.
The various transitions result in characteristic spectral lines with frequencies which can be calculated by f=R( 1/n2 - 1/m2 ) R = Rydberg constant.
The lines of the Paschen series (n = 3) are located in the near infrared range of the spectrum. In this example, m can reach values of 4, 5, 6 and 7 in succession.


Brackett series
Hydrogen atoms excited to luminescence emit characteristic spectra. On excitation, the electron of the hydrogen atom reaches a higher energy level. In this case, the electron is excited from the base state, with a principal quantum number of n = 1, to a level with a principal quantum number of n = 8. The Brackett series becomes visible if the electron first falls to an excited state with the principal quantum number of n = 4 before returning to its initial state.
The lines of the Brackett series (n = 4) are located in the infrared range of the spectrum. In this example, m can reach values of 5, 6, 7 and 8 in succession.

Wolf-Rayet star

While I have started off with the definition of the Wolf-Rayet star, the post ends in understanding the aspects of gravity and it's affects, as we look at what has become of these Wolf-Rayet stars in their desimination of it's constituent properties.

Similar, "in my thinking" to the expansion of our universe?


Artist's impression of a Wolf-Rayet star

About 150 Wolf-Rayets are known in our own Milky Way Galaxy, about 100 are known in the Large Magellanic Cloud, while only 12 have been identified in the Small Magellanic Cloud. Wolf-Rayet stars were discovered spectroscopically in 1867 by the French astronomers Charles Wolf and Georges Rayet using visual spectrometery at Paris Observatory.

There are some thoughts manifesting about how one may have see this energy of the Blue giant. It's as if the examples of what began with great force can loose it's momentum and dissipate very quickly(cosmic winds that blow the dust to different places)?


Illustration of Cosmic Forces-Credit: NASA, ESA, and A. Feild (STScI)

Scientists using NASA's Hubble Space Telescope have discovered that dark energy is not a new constituent of space, but rather has been present for most of the universe's history. Dark energy is a mysterious repulsive force that causes the universe to expand at an increasing rate.

What if the Wolf-Rayet star does not produce the jets that are exemplified in the ideas which begin blackhole creation. Is this part of blackhole development somehow in it's demise, that we may see examples of the 150 Wolf-Rayets known in our own Milky Way as example of what they can become as blackholes, or not.

Quark to quark Distance and the Metric

If on such a grand scale how is it thoughts are held in my mind to microscopic proportions may not dominate as well within the periods of time the geometrics develop in the stars now known as Wolf-Rayet. So you use this cosmological model to exemplify micro perspective views in relation to high energy cosmological geometrics.



Plato:

"Lagrangian views" in relation may have been one result that comes quickly to my mind. Taking that chaldni plate and applying it to the universe today.

While I had in the previous post talked about how Lagrangian views could dominate "two aspects of the universe," it is not without linking the idea of what begins as a strong gravitational force to hold the universe together, that over time, as the universe became dominated by the dark energy that the speeding up of inflation could have become pronounced by discovering the holes created in the distances between the planets and their moons. Between galaxies.



I make fun above with the understanding of satellites travelling in our current universe in relation to planets and moons, as well as galaxies. To have taken this view down to WMAP proportions is just part of what I am trying to convey using very simplistic examples of how one may look at the universe, when gravity dominated the universe's expansion versus what has happened to the universe today in terms of speeding up.


LOOP-DE-LOOP. The Genesis spacecraft's superhighway path took it to the Earth-sun gravitational-equilibrium point L1, where it made five "halo" orbits before swinging around L2 and heading home.Ross

If the distances between galaxies have become greater, then what saids that that the ease with which the speeding up occurs is not without understanding that an equilibrium has been attained, from what was once dominate in gravity, to what becomes rapid expansion?

This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel.

Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed. Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions.

Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.

First Stars Behind the Scene

There are several recognized processes from the early universe that leave relic effects setting the stage for galaxy formation and evolution. We deal here with the first generarion of stars, primordial nucleosynthesis, the epoch of recombination, and the thermal history of various cosmic backgrounds.

Part of understanding the time line is first knowing where the Pregalactic Universe exists in that time line.

Plato:

So given the standard information one would have to postulate something different then what is currently classified?

A new Type III (what ever one shall attribute this to definition), versus Type I, Type IIa?

The idea is to place the distant measure in relation to what is assumed of TYPE I, TypeIIa. It assumes all these things, but has to been defined further, to be a Type III. That's the point of setting the values of where this measure can be taken from.

I wrote someplace else the thought generated above. It is nice that the world of scientists are not so arrogant in some places, while some have been willing to allow the speculation to continue. Even amidst their understanding, that I was less then the scientist that they are, yet recognizing, I am deeply motivated to understanding this strange world of cosmology and it's physics.

When I wrote this title above I was actually thinking of two scenarios that are challenging the way I am seeing it.


Credit: NASA/WMAP Science Team

WMAP has produced a new, more detailed picture of the infant universe. Colors indicate "warmer" (red) and "cooler" (blue) spots. The white bars show the "polarization" direction of the oldest light. This new information helps to pinpoint when the first stars formed and provides new clues about events that transpired in the first trillionth of a second of the universe.

First of these, was in terms of the time line and what we know of the WMAP demonstration given to us of that early universe. I of course inject some of what I know by past research to help the general public understand what is being demonstrated from another perspective.

This is what happens as you move through different scientists(Wayne Hu) thoughts to see the world in the way they may see it. This concept can be quite revealing sometimes giving a profound effect to moving the mind to consider the universe in new ways.



"Lagrangian views" in relation may have been one result that comes quickly to my mind. Taking that chaldni plate and applying it to the universe today.



Even though in the context of this post, we may see the universe in a "simple experiment" not just demonstrating the "early universe," but the universe in it's "gravitational effect" from that evolution to matter defined now.

The Time Line


Credit: NASA/WMAP Science Team

The expansion of the universe over most of its history has been relatively gradual. The notion that a rapid period "inflation" preceded the Big Bang expansion was first put forth 25 years ago. The new WMAP observations favor specific inflation scenarios over other long held ideas.

Looking to the "far left" of the image we see the place where the cosmic background is being demonstrated, while to the "far right" we see the satellite which has helped measure what we know of the early universe. So this "distant measure" has allowed us to understand what is behind the scene of what we know of cosmology today of events, galaxies and such.

Second, what comes to mind is the Massive Blue Star of 100 Solar masses that would have been further out in terms of the billions of years that we may of sought in terms of our measures. So this would be of value I would assume in relation to model perspective and measures?

So the distance measure has been defined then by understanding the location of the cosmic background and the place where the Blue giants will have unfolded in their demise, to the creation of blackholes.


The processes in the Universe after the Big Bang. The radio waves are much older than the light of galaxies. From the distortion of the images (curved lines) - caused by the gravitation of material between us and the light sources - it is possible to calculate and map the entire foreground mass.Image: Max Planck Institute of Astrophysics

We don't have to wait for the giant telescope to get unparalleled results from this technique, however. One of the most pressing issues in current physics is to gain a better understanding of the mysterious Dark Energy which currently drives the accelerated expansion of the Universe. Metcalf and White show that mass maps of a large fraction of the sky made with an instrument like SKA could measure the properties of Dark Energy more precisely than any previously suggested method, more than 10 times as accurately as mass maps of similar size based on gravitational distortions of the optical images of galaxies.

The Geometrics Behind the Supernova and it's History

It is not always easy for people to see what lies behind the wonderful beauty of images that we take from the satellite measures of space, and it's dynamical events illustrated in Cassiopeia A. There before you is this majestic image of beauty, as we wonder about it's dynamics.


These Spitzer Space Telescope images, taken one year apart, show the supernova remnant Cassiopeia A (yellow ball) and surrounding clouds of dust (reddish orange). The pictures illustrate that a blast of light from Cassiopeia A is waltzing outward through the dusty skies. This dance, called an "infrared echo," began when the remnant erupted about 50 years ago. Image credit: NASA/JPL-Caltech/Univ. of Ariz.

An enormous light echo etched in the sky by a fitful dead star was spotted by the infrared eyes of NASA's Spitzer Space Telescope.

The surprising finding indicates Cassiopeia A, the remnant of a star that died in a supernova explosion 325 years ago, is not resting peacefully. Instead, this dead star likely shot out at least one burst of energy as recently as 50 years ago.

How is it such information arrives to us, and we would have to consider the impulse's behind such geometrical explanations. Which we are lucky to see in other ways. So, of course we needed to see the impulse as dynamically driven by the geometrical inclinations of that collapse, and all it's information spread outward by the description in images painted.


Credit: Weiqun Zhang and Stan Woosley

This image is from a computer simulation of the beginning of a gamma-ray burst. Here we see the jet 9 seconds after its creation at the center of a Wolf Rayet star by the newly formed, accreting black hole within. The jet is now just erupting through the surface of the Wolf Rayet star, which has a radius comparable to that of the sun. Blue represents regions of low mass concentration, red is denser, and yellow denser still. Note the blue and red striations behind the head of the jet. These are bounded by internal shocks.

If I had approached you early on and suggested that you look at "bubble geometrodynamics" would it have seemed so real that I would have presented a experiment to you, that would help "by analogies" to see what is happening? Might I then be called the one spreading such information that it was not of value to scientists to consider, that I was seeing in ways that I can only now give to you as example? What science has done so far with using the physics with cosmological views?


Image Credit: NASA/JPL-Caltech/STScI/CXC/SAO

This stunning false-color picture shows off the many sides of the supernova remnant Cassiopeia A, which is made up of images taken by three of NASA's Great Observatories, using three different wavebands of light. Infrared data from the Spitzer Space Telescope are colored red; visible data from the Hubble Space Telescope are yellow; and X-ray data from the Chandra X-ray Observatory are green and blue.

Located 10,000 light-years away in the northern constellation Cassiopeia, Cassiopeia A is the remnant of a once massive star that died in a violent supernova explosion 325 years ago. It consists of a dead star, called a neutron star, and a surrounding shell of material that was blasted off as the star died. The neutron star can be seen in the Chandra data as a sharp turquoise dot in the center of the shimmering shell.

In this image above we learn of what manifests in "jet production lines," and such examples are beautiful examples to me of what the geometrics are doing. You needed some way to be able to explain this within context of the universe's incidences "as events." We say this action is one with which we may speak to this "corner of the universe." Yet it is very dynamical in it's expression as we see it multiplied from various perspectives.


The structure of Model J32 as the jet nears the surface 7820 seconds after core collapse.

So by experiment(?) I saw such relations, but what use such analogies if they are laid waste to speculation that what was initiated such ideas had been the inclination of geometrics detailed as underlying the basis of all expression as an example of some non euclidean views of Riemann perspectives leading shapes and dynamics of our universe by comparison within the local actions of stars and galaxies?

Gamma Rays?



So we get this information in one way or another and it was from such geometrical impulse that such examples are spread throughout the universe in ways that were not understood to well.


X-ray image of the gamma-ray burst GRB 060614 taken by the XRT instrument on Swift. The burst glowed in X-ray light for more than a week following the gamma-ray burst. This so-called "afterglow" gave an accurate position of the burst on the sky and enabled the deep optical observations made by ground-based observatories and the Hubble Space Telescope. Credit: NASA/Swift Team

A year ago scientists thought they had figured out the nature of gamma-ray bursts. They signal the birth of black holes and traditionally, fall into one of two categories: long or short. A newly discovered hybrid burst has properties of both known classes of gamma-ray bursts yet possesses features that remain unexplained.

The long bursts are those that last more than two seconds. It is believed that they are ejected by massive stars at the furthest edge of the universe as they collapse to form black holes.

So looking back to this timeline it is important to locate the ideas spread out before us. Have "some place" inclusive in the reality of that distance from the origins of the stars of our earliest times. 13.7 billions years imagine!


Fig. 1: Sketchy supernova classification scheme

A supernova is the most luminous event known. Its luminosity matches those of whole galaxies. The name derives from the works of Walter Baade and Fritz Zwicky who studied supernovae intensively in the early 1930s and used the term supernova therein.
Nowadays supernova is a collective term for different classes of objects, that exhibit a sudden rise in luminosity that drops again on a timescale of weeks.
Those objects are subdivided into two classes, supernovae of type I or II (SNe I and SNe II). The distinguishing feature is the absence or the presence of spectral lines of hydrogen. SNe I show no such lines as SNe II do. The class of SNe I is further subdivided in the classes a, b and c. This time the distinguishing feature are spectral features of helium and silicon. SN Ia show silicon features, SN Ib show helium but no silicon features and SN Ic show both no silicon and no helium spectral features.
The class of SN II is further subdivided in two classes. Those are distinguished by the decline of the lightcurve. Those SN II that show a linear decline are named SN II-L and those that pass through a plateau-phase are referred to as SN II-P.

So given the standard information one would have to postulate something different then what is currently classified?

A new Type III (what ever one shall attribute this to definition, versus Type I, Type IIa?


ssc2006-22b: Brief History of the Universe
Credit: NASA/JPL-Caltech/A. Kashlinsky (GSFC)

This artist's timeline chronicles the history of the universe, from its explosive beginning to its mature, present-day state.

Our universe began in a tremendous explosion known as the Big Bang about 13.7 billion years ago (left side of strip). Observations by NASA's Cosmic Background Explorer and Wilkinson Anisotropy Microwave Probe revealed microwave light from this very early epoch, about 400,000 years after the Big Bang, providing strong evidence that our universe did blast into existence. Results from the Cosmic Background Explorer were honored with the 2006 Nobel Prize for Physics.

A period of darkness ensued, until about a few hundred million years later, when the first objects flooded the universe with light. This first light is believed to have been captured in data from NASA's Spitzer Space Telescope. The light detected by Spitzer would have originated as visible and ultraviolet light, then stretched, or redshifted, to lower-energy infrared wavelengths during its long voyage to reach us across expanding space. The light detected by the Cosmic Background Explorer and the Wilkinson Anisotropy Microwave Probe from our very young universe traveled farther to reach us, and stretched to even lower-energy microwave wavelengths.

Astronomers do not know if the very first objects were either stars or quasars. The first stars, called Population III stars (our star is a Population I star), were much bigger and brighter than any in our nearby universe, with masses about 1,000 times that of our sun. These stars first grouped together into mini-galaxies. By about a few billion years after the Big Bang, the mini-galaxies had merged to form mature galaxies, including spiral galaxies like our own Milky Way. The first quasars ultimately became the centers of powerful galaxies that are more common in the distant universe.

NASA's Hubble Space Telescope has captured stunning pictures of earlier galaxies, as far back as ten billion light-years away.

Would sort of set up the challenge?

Hubble Finds Evidence for Dark Energy in the Young Universe

I had to go back to the article for some further reading.


These snapshots, taken by NASA's Hubble Space Telescope, reveal five supernovae, or exploding stars, and their host galaxies.

The arrows in the top row of images point to the supernovae. The bottom row shows the host galaxies before or after the stars exploded. The supernovae exploded between 3.5 and 10 billion years ago.

Astronomers used the supernovae to measure the expansion rate of the universe and determine how the expansion rate is affected by the repulsive push of dark energy, a mysterious energy force that pervades space. Supernovae provide reliable measurements because their intrinsic brightness is well understood. They are therefore reliable distance markers, allowing astronomers to determine how far away they are from Earth.

Pinpointing supernovae in the faraway universe is similar to watching fireflies in your back yard. All fireflies glow with about the same brightness. So, you can judge how the fireflies are distributed in your back yard by noting their comparative faintness or brightness, depending on their distance from you.

Only Hubble can measure these supernovae because they are too distant, and therefore too faint, to be studied by the largest ground-based telescopes.

These Hubble observations show for the first time that dark energy has been a present force for most of the universe's history. A spectral analysis also shows that the supernovae used to measure the universe's expansion rate today look remarkably similar to those that exploded nine billion years ago and are just now seen by Hubble.

These latest results are based on an analysis of the 24 most distant known supernovae, most of them discovered within the last three years by the Higher-z SN Search Team. The images were taken between 2003 and 2005 with Hubble's Advanced Camera for Surveys.


Illustration of Cosmic Forces-Credit: NASA, ESA, and A. Feild (STScI)

Scientists using NASA's Hubble Space Telescope have discovered that dark energy is not a new constituent of space, but rather has been present for most of the universe's history. Dark energy is a mysterious repulsive force that causes the universe to expand at an increasing rate.

Investigators used Hubble to find that dark energy was already boosting the expansion rate of the universe as long as nine billion years ago. This picture of dark energy is consistent with Albert Einstein's prediction of nearly a century ago that a repulsive form of gravity emanates from empty space.

Data from Hubble provides supporting evidence that help astrophysicists to understand the nature of dark energy. This will allow scientists to begin ruling out some competing explanations that predict that the strength of dark energy changes over time.

Researchers also have found that the class of ancient exploding stars, or supernovae, used to measure the expansion of space today look remarkably similar to those that exploded nine billion years ago and are just now being seen by Hubble. This important finding gives additional credibility to the use of these supernovae for tracking the cosmic expansion over most of the universe's lifetime.

"Although dark energy accounts for more than 70 percent of the energy of the universe, we know very little about it, so each clue is precious," said Adam Riess, of the Space Telescope Science Institute and Johns Hopkins University in Baltimore. Riess led one of the first studies to reveal the presence of dark energy in 1998 and is the leader of the current Hubble study. "Our latest clue is that the stuff we call dark energy was relatively weak, but starting to make its presence felt nine billion years ago."

To study the behavior of dark energy of long ago, Hubble had to peer far across the universe and back into time to detect supernovae. Supernovae can be used to trace the universe's expansion. This is analogous to seeing fireflies on a summer night. Fireflies glow with about the same brightness, so you can judge how they are distributed in the backyard by their comparative faintness or brightness, depending on their distance from you. Only Hubble can measure these ancient supernovae because they are too distant, and therefore too faint, to be studied by the largest ground-based telescopes.

Einstein first conceived of the notion of a repulsive force in space in his attempt to balance the universe against the inward pull of its own gravity, which he thought would ultimately cause the universe to implode.

His "cosmological constant" remained a curious hypothesis until 1998, when Riess and the members of the High-z Supernova Team and the Supernova Cosmology Project used ground-based telescopes and Hubble to detect the acceleration of the expansion of space from observations of distant supernovae. Astrophysicists came to the realization that Einstein may have been right after all: there really was a repulsive form of gravity in space that was soon after dubbed "dark energy."

Over the past eight years astrophysicists have been trying to uncover two of dark energy's most fundamental properties: its strength and its permanence. These new observations reveal that dark energy was present and obstructing the gravitational pull of the matter in the universe even before it began to win this cosmic "tug of war."

Previous Hubble observations of the most distant supernovae known revealed that the early universe was dominated by matter whose gravity was slowing down the universe's expansion rate, like a ball rolling up a slight incline. The observations also confirmed that the expansion rate of the cosmos began speeding up about five to six billion years ago. That is when astronomers believe that dark energy's repulsive force overtook gravity's attractive grip.

The latest results are based on an analysis of the 24 most distant supernovae known, most found within the last two years.

By measuring the universe's relative size over time, astrophysicists have tracked the universe's growth spurts, much as a parent may witness the growth spurts of a child by tracking changes in height on a doorframe. Distant supernovae provide the doorframe markings read by Hubble. "After we subtract the gravity from the known matter in the universe, we can see the dark energy pushing to get out," said Lou Strolger, astronomer and Hubble science team member at Western Kentucky University in Bowling Green, Ky. Further observations are presently underway with Hubble by Riess and his team which should continue to offer new clues to the nature of dark energy.

Credit: NASA, ESA, and A. Feild (STScI)