What Does It Mean For An Equation To Be Beautiful Or Elegant?

Nima Arkani-Hamed Lectures

Nima Arkani-Hamed on developments in Physics and future vision

The Salam Lecture Series 2012, with a week-long series of lectures by renowned theoretical physicist Nima Arkani-Hamed. Giving his audience a panoramic view of 400 years of physics in his first lecture, Arkani-Hamed provided insights into the various concepts that have dominated the world of fundamental physics at different points in history. "Everything that we have learned [over the past 400 years] can be subsumed with a basic slogan, and the slogan is that of unification," he said. "More and more disparate phenomena turn out to be different aspects of the same thing." "Physics," he stressed "forces you to remove artificial distinction between disciplines.

See Also:

• Nima Arkani-Hamed Lecture: Day 1
• Nima Arkani-Hamed Lecture: Day 2 
• Nima Arkani-Hamed Lecture: Day 5
• The Amplituhedron
• Guest Post: Lance Dixon on Calculating Amplitudes

Questions on the History of Mathematics

Arthur Miller
Einstein and Schrödinger never fully accepted the highly abstract nature of Heisenberg's quantum mechanics, says Miller. They agreed with Galileo's assertion that "the book of nature is written in mathematics", but they also realized the power of using visual imagery to represent mathematical symbols.

For most people I am sure it is of little interest that such an abstract language could have ever amounted to anything,since we might have been circumscribed to the natural living that is required that we could do without it. But really,  can we?

 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 of course one appreciates those who start the conversation to help raise the questions in ones own mind. Might it be a shared response to something existing deeper in our society that it would warrant descriptions that we might be lacking in. Ways in which to describe something about nature. There is something definitely to be said about the geometer that can visualize the spaces within which they are working. It has to make sense. It has to describe something? Why then not just plain English(whatever language you choose)

String theory's mathematical tools were designed to unlock the most profound secrets of the cosmos, but they could have a far less esoteric purpose: to tease out the properties of some of the most complex yet useful types of material here on Earth.What Good are Mathematics in the Real World?

Do you know how many mathematical expressions are needed in order to describe the theory?

 The language of physics is mathematics. In order to study physics seriously, one needs to learn mathematics that took generations of brilliant people centuries to work out. Algebra, for example, was cutting-edge mathematics when it was being developed in Baghdad in the 9th century. But today it's just the first step along the journey.Guide to math needed to study physics

Conversations on Mind, Matter, and Mathematics

How mathematics arose from cognitive realizations. Ex. Newton and Calculus. The branches of mathematics. Who are it's developers and what did they develop and why?

 It may be as important as the history in relation to how one may perceive the history and development of mathematics. These were important insights into the way one might of asked how did emergence exist if such things could have been imagined in the mind of the beholder. To attempt to describe nature in the way that one might do by invention? So are these mathematical things discovered or are they invented? Why the history is important?

 This is the basis of the question of what already exists in terms of information has always existed and we are only getting a preview of a much more complicated system. It does not have to be a question of what a MBT exemplifies in itself, but raises the questions about what already exists, exists as part of what always existed. Where do ideas and mathematics come from?

This is a foundation stance that is taken right throughout science? If it exists in the universe, it exists in you? How does one connect?

See Also:

WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION? 

See Also: Some Educational links to look at then.

•  Wolfram\alpha
-What is Wolfram\Alpha
• Khan Academy

Presenting a New Theoretical Position

All our dreams can come true, if we have the courage to pursue them.
Walt Disney

Here's the thing that I would caution such a quote, that any work can produce results, but, if we leave life unattended, the future is already written. The artist in you is very capable, and if you thought this aspect of yourself could msilead you, think twice, for the story telling can produce wonderful results and in such abstraction, it draws a conclusion for you.

What enters this room of the mind came from outside the box, and what constitutes this frame of reference is a room you will create. This creation is a subtle part of identification when you assess yourself and are given the warnings as to what shall become in the possibilities if not adjusted or taken care of. This pre-ordination does not imply you are without freewill, but on the contrary, are part and parcel of the greater wholeness defined in the universe. Defined within context of the understanding of ones own capability.

This has to be introduced in our assessment as to the nature of this universe.

JONATHAN SAUNDERS FOR TIMEEdward Witten:The World In A String-Time Magazine

Witten once called string theory "a bit of 21st century physics that somehow dropped into the 20th century." If so, Witten clearly has the 21st century mind to handle it.

There is no doubt, an historical significance to the topic under the heading of theoretics, and what calculable information retention would then lead you beyond the borders of reason, to know it is an attempt to go farther then we had ever gone before. How many combinations of the maths and you soon learn of the complexity of the situation.

But remember now, how "a thinking process" had been moved from the 21st Century.:)

The Decomposable limits of the Definition Conceptually Introduced.

While such reference to the subjective analysis of the current ministrations given by Sean Carroll on the article in the current Scientific Magazine, on the current state of the universe, it is with such presentation that I also included "the subjective side of my own nature," regardless of the warning about doing the physics first, and have one lead to such conclusions. It seems a difficult way in which to send the mind into the future, and while there, bring back the current state of the universe for a proper view of it's own continued existence.

Do you remember the theoretics of the 21 Century? So we now see that I include a facet of our mind that takes a leap, and while in it's most reflective state, while it rests, all that information manifests in a new possibility? From whence this come, and from which "directional face of the box" in it six dimensional rotational possibility, and we are indeed now looking from inside the box possibility? But how is it any new information can enter, if we had but closed all doors, to think like a "Close minded Wotian experience" will reveal of itself?:)Order of chapters, that exist as a fundamental indexed site for those who think in the box, and those who think outside of it?

Well you can now see where such introductions hold such a position for a mind like mine to consistently ever better the views for such abstraction that they be given to a new valley for consideration, that while there are such views of topos theory introduced, they now have become an aspect of the universe, not just the many possibilities, but one aspect for the consideration abstractly given such a state of existence. Who knew right?

Lee Smolin had all but said it was dead, and so too, even Witten himself convinced that such a landscape not worthy of such consideration? The work continues at least from my perspective, and now, some of the junior minds in this respect, and to those who had respect none given, know there is a little more to the story then what is the subjective journeys of a dreamer.

The false vacuum. The Hill. The Valley. Our Universe. Totally dissociatively words for the lay person to be introduced too, and together, sparked the neuron firing to include a "new thought process" about what exists beyond the 3+1 we'd given to our locations in time.

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.

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.

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.

Against Symmetry

The term “symmetry” derives from the Greek words sun (meaning ‘with’ or ‘together’) and metron (‘measure’), yielding summetria, and originally indicated a relation of commensurability (such is the meaning codified in Euclid's Elements for example). It quickly acquired a further, more general, meaning: that of a proportion relation, grounded on (integer) numbers, and with the function of harmonizing the different elements into a unitary whole. From the outset, then, symmetry was closely related to harmony, beauty, and unity, and this was to prove decisive for its role in theories of nature. In Plato's Timaeus, for example, the regular polyhedra are afforded a central place in the doctrine of natural elements for the proportions they contain and the beauty of their forms: fire has the form of the regular tetrahedron, earth the form of the cube, air the form of the regular octahedron, water the form of the regular icosahedron, while the regular dodecahedron is used for the form of the entire universe. The history of science provides another paradigmatic example of the use of these figures as basic ingredients in physical description: Kepler's 1596 Mysterium Cosmographicum presents a planetary architecture grounded on the five regular solids.

The basic difference that I see is the way in which Lee Smolin adopts his views of what science is in relation too, "Two traditions in the search for fundamental Physics."

It is strange indeed to see perfection of Lee Smolin's comparison and having a look further down we understand the opening basis of his philosophical thoughts in regards to the title "against symmetry?"

Some reviews on the "Trouble With Physics," by Lee Smolin

Seed Magazine, August 2006

Time magazine August 21, 2006

Discover Magazine, September 2006 &

Scientific American, September 2006

Wired September 2006:15 :

The Economist, Sept 14, 2006

The New York Times Book review, Sep 17, 2006 by Tom Siegfried

The Boston Globe, Sept 17, 2006

USA Today, Sept 19, 2006

The New York Sun, by Michael Shermer, Sept 27, 2006

The New Yorker,  by Jim Holt Sept 25,2006

The LA Times, by K C Cole, Oct 8, 2006

Nature,

by George Ellis (Nature 44, 482, 5 Oct. 2006)

San Fransisco Chronicle , by Keay Davidson, Oct 13, 2006

Dallas Morning News, by FRED BORTZ, Oct 15, 2006

Toronto Star, by PETER CALAMAI, Oct 15, 2006

But before I begin in that direction I wanted people to understand something that is held in the mind of the "condense matter theorist." In terms of the building blocks of nature. This is important basis of understanding, that any building block could emergent from anything, we had to identify where this symmetry existed, before it manifested in the "matter states of reality."

Everyone knows that human societies organize themselves. But it is also true that nature organizes itself, and that the principles by which it does this is what modern science, and especially modern physics, is all about. The purpose of my talk today is to explain this idea.

So it is important to understand what is emergent and what exists in the "theory of everything" if it did not consider the context of symmetry? AS a layman trying to get underneath the thinking process of any book development, it is important to me.

Symmetry considerations dominate modern fundamental physics, both in quantum theory and in relativity. Philosophers are now beginning to devote increasing attention to such issues as the significance of gauge symmetry, quantum particle identity in the light of permutation symmetry, how to make sense of parity violation, the role of symmetry breaking, the empirical status of symmetry principles, and so forth. These issues relate directly to traditional problems in the philosophy of science, including the status of the laws of nature, the relationships between mathematics, physical theory, and the world, and the extent to which mathematics dictates physics.

The idea here then is to find super strings place within context of the evolving universe, in terms of, "the microseconds" and not the "first three minutes" of Steven Weinberg.

So it is important to see the context with which this discussion is taking place, in terms of the high energy and from that state of existence to what entropically manifests into the universe now.

Confronting A Position Adopted By Lee Smolin


A sphere with three handles (and three holes), i.e., a genus-3 torus.

This is only "one point of contention" that was being addressed at Clifford Johnson's Asymptotia.

Jacques Distler :

This is false. The proof of finiteness, to all orders, is in quite solid shape. Explicit formulæ are currently known only up to 3-loop order, and the methods used to write down those formulæ clearly don’t generalize beyond 3 loops.

What’s certainly not clear (since you asked a very technical question, you will forgive me if my response is rather technical) is that, beyond 3 loops, the superstring measure over supermoduli space can be “pushed forward” to a measure over the moduli space of ordinary Riemann surfaces. It was a nontrivial (and, to many of us, somewhat surprising) result of d’Hoker and Phong that this does hold true at genus-2 and -3.

There is no doubt that the "timeliness of statements" can further define, support or not, problems that are being discussed. I don't mind being deleted on the point of the post above, because our good scientist's are getting into the heat of things. I am glad Arun stepped up to the plate.

Part of finally coming to some head on debate, was seeing how Peter Woit along with Lee Smolin were being challlenged for their views, while there had been this ground swell created against a model that was developed, like Loop quantum gravity was developed. One of the two traditions in search for the fundamental physics. Loop qunatum Gravity and String theory(must make sure there is the modification to M theory?) Shall this be included?


Click on link Against symmetry (Paris, June 06)

But as they are having this conversation, it is this openness that they have given of themselves that we learn of the intricacies of the basis of arguments, so the public is better informed as to what follows and what has to take place.


Against symmetry (Paris, June 06)

So while this issue is much more complex then just the exchange there, I have not forgotten what it is all about. Or why one may move from a certain position after they have summarize the views they had accumulated with regards to the subject of String/M theory as a model that has out lived it's usefulness, in terms of not providing a experimental frame work around it.

Visual Abstraction to Equations

Sylvester's models lay hidden away for a long time, but recently the Mathematical Institute received a donation to rescue some of them. Four of these were carefully restored by Catherine Kimber of the Ashmolean Museum and now sit in an illuminated glass cabinet in the Institute Common Room.

Some of you might have noticed the reference to the Ashmolean Museum?


Photo by Graham Challifour. Reproduced from Critchlow, 1979, p. 132.

It seems only the good scientist John Baez had epitomes the construction of the Platonic solids? A revision then, of the "time line of history" and the correction he himself had to make? Let's not be to arrogant to know that once we understand more and look at "the anomalies" it forces us to revise our assessments.

The Art form

I relayed this image and quote below on Clifford's site to encourage the thinking of young people into an art form that is truly amazing to me. Yes I get excited about it after having learnt of Gauss and Reimann's exceptional abilities to move into the non euclidean world.

Some think me a crackpot here? If you did not follow the history then how would you know to also include the "physics of approach," as well? Also, some might ask what use "this ability to see the visual abstraction" and I think this art form is in a way destined, to what was kept in glass cabinets and such, even while the glass cabinet in analogy is held in the brain/space of them) who have developed such artistic abilities.

It's as if you move past the layers of the evolution of the human being(brain casings) and it evolution and the field that surrounds them. Having accomplished the intellect( your equations and such), has now moved into the world of imagery. Closet to this is the emotive field which circumvents our perspective on the greater potential of the world in the amazing thought forms of imagery. This move outward, varies for each of us from time to time. Some who are focused in which ever area can move beyond them. This paragraph just written is what would be considered crackpot(I dislike that word)because of the long years of research I had gone through to arrive at this point.

Of course, those views above are different.

Mapping



Is it illusionary or delusional, and having looked at the Clebsch's Diagonal Surface below, how is it that "abstraction" written?

The enthusiasm that characterized such collections was captured by Francis Bacon [1, p. 247], who ironically advised "learned gentlemen" of the era to assemble within "a small compass a model of the universal made private", building

... a goodly, huge cabinet, wherein whatsoever the hand of man by exquisite art or engine has made rare in stuff, form or motion; whatsoever singularity, chance, and the shuffle of things hath produced; whatsoever Nature has wrought in things that want life and may be kept; shall be sorted and included.

There is no doubt that the long road to understanding science is the prerequisite to mapping the images from an equation's signs and symbols. While not sitting in the classroom of the teachers it was necessary to try and move into the fifth dimensional referencing of our computer screen to see what is being extolled here not just in image development, but of what the physics is doing in relation.

In 1849 already, the British mathematicians Salmon ([Sal49]) and Cayley ([Cay49]) published the results of their correspondence on the number of straight lines on a smooth cubic surface. In a letter, Cayley had told Salmon, that their could only exist a finite number - and Salmon answered, that the number should be exactly 27

So of course to be the historical journey was established like most things, Mandelstam current and what is happening there as an interlude, as well as helping to establish some understanding of the abstractions that had been developed.



But yes, before moving to current day imagery and abstraction, I had to understand how these developments were being tackled in today's theoretical sciences.

Graviton in a Can?

After you consume "graviton in a can," you might never be the same? Brane thinking may then dominate your every view of the world. Then, it will all make sense?

Imagine while we peer deeper into the subject of the "perfect fluid/soup" we find that certain aspects of the reductionist work done, has indeed lead us to speculate on how the "new physics" formed through the research and understanding currently being worked in the LHC?

Is there some architectural design to the "Degree's of Freedom?" Why anything more then the spacetime we have come to recognize, which placed new parameters on our thinking? Moved it from the recogition of Maxwellian and Gaussian coordinates to Riemann geometries in the theory of General Relativity, to become known, as the Theory of gravity. Why "anything" more then that?


A picture of flux lines in QED (left) and QCD (right).

Although it didn't properly describe strong interactions, in studying string theory physicists stumbled upon an amazing mathematical structure. String theory has turned out to be far richer than people originally anticipated. For example, people found that a certain vibrational state of the string has zero mass and spin 2. According to Einstein's theory of gravity, the gravitational force is mediated by a particle with zero mass and spin 2. So string theory is, among many other things, a theory of gravity!

I mean how are such abstract notions in the mathematics supposed to make sense, if we can not see the logic of these formulations working in some kind of reality frame of reference?


by Jacob D. Bekenstein

TWO UNIVERSES of different dimension and obeying disparate physical laws are rendered completely equivalent by the holographic principle. Theorists have demonstrated this principle mathematically for a specific type of five-dimensional spacetime ("anti–de Sitter") and its four-dimensional boundary. In effect, the 5-D universe is recorded like a hologram on the 4-D surface at its periphery. Superstring theory rules in the 5-D spacetime, but a so-called conformal field theory of point particles operates on the 4-D hologram. A black hole in the 5-D spacetime is equivalent to hot radiation on the hologram--for example, the hole and the radiation have the same entropy even though the physical origin of the entropy is completely different for each case. Although these two descriptions of the universe seem utterly unalike, no experiment could distinguish between them, even in principle.

So we have these diagrams and thought processes developed from individuals like Jacob D. Bekenstein to help us visualize what is taking place. Gives us key indicators of the valuation needed, in order to determine what maths are going to be used? In this case the subject of Conformal Filed Theory makes itself known, for the thought process to hone in on what is going to be spoken too?

Holography encodes the information in a region of space onto a surface one dimension lower. It sees to be the property of gravity, as is shown by the fact that the area of th event horizon measures the number of internal states of a blackhole, holography would be a one-to-one correspondence between states in our four dimensional world and states in higher dimensions. From a positivist viewpoint, one cannot distinguish which description is more fundamental.Pg 198, The Universe in Nutshell, by Stephen Hawking

So we are given the label in which to speak about the holographical ntions of what is being talked about in the case of the blackhole's horizon.


Campbell's Soup Can by Andy Warhol Exhibited in New York (USA), Leo Castelli Gallery

While it is difficult of such images to be found displayed in the bloggery here to show what Dr. Gary Horowitz is saying you get the jest when you go right to the image of the tomato soup can.

Spacetime in String Theory-Dr. Gary Horowitz, UCSB-Apr 20, 2005

This year marks the hundredth anniversary of Einstein's "miraculous year", 1905, when he formulated special relativity, and explained the origin of the black body spectrum and Brownian motion. In honor of this occasion, I will describe the modern view of spacetime. After reviewing the properties of spacetime in general relativity, I will provide an overview of the nature of spacetime emerging from string theory. This is radically different from relativity. At a perturbative level, the spacetime metric appears as ``coupling constants" in a two-dimensional quantum field theory. Nonperturbatively (with certain boundary conditions), spacetime is not fundamental but must be reconstructed from a holographic, dual theory. I will conclude with some recent ideas about the big bang arising from string theory.

Imagine containing everything we know in this can. Yet,we find that the "soup image" has somehow been translated to other factors and values that seem beyond what we know is real. Is real within the confines and boundaries, and is not evidence of the "infinities" that arise from such non containment?

So, what of the "dilation field" that accumulates, as we speak to what the photon is in the measure of Glast. High energy photon determinations that may also be the valuation of the graviton in expression, as the photon travels through these fields?

Such unification is important once we move into the bulk perspective and what we see of the 2d image of the brane, as a value, and discernation of the label of the soup can?


The ALICE TPC in its clean room, where it is undergoing commissioning of all its sectors.

One of the first cosmic-ray events recorded and reconstructed in two sectors of the TPC.

The tests use the ALICE cosmic muon trigger detector ACORDE, as well as a specially designed UV laser system, to produce tracks in the detector. Preliminary analysis of the cosmic-ray events and the laser-induced tracks indicate that the drift velocity and diffusion of electrons liberated by traversing charged particles, as well as the spatial resolution, are very close to the design values.

So here we are then, having graduated in perspective about what is real, as one may ask the sociological aspect of this whole adventure?



If such missing energy is, "not accounted for" then what happens to the graviton as it is produced and causes energy to travel with them?

For example, people found that a certain vibrational state of the string has zero mass and spin 2. According to Einstein's theory of gravity, the gravitational force is mediated by a particle with zero mass and spin 2. So string theory is, among many other things, a theory of gravity!

The Radius of the Little Circle

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

With such a statement, the "purity of thought," is speaking to a much more schematic understanding as we discuss the sociological thinking of mathematicians and the worlds they fantasize about? While deeper in reality the thought process(meditative) was engaged at a very subtle level, associated with the energy all pervasive.




Lee Smolin :

Another wonderful spin-off is that it turns out that the charge of the electron is related to the radius of the little circle. This should not be surprizing: If the electric field is just a manifestation of geometry, the electric charge should be, too.

THE TROUBLE WITH PHYSICS-Published by Houghton-Mifflin, Sep. 2006/Penguin (UK), Feb. 2007, Page 46

In "Star Shine," we start from a very large circle, but there is much to see from this circle, when we consider it's radius. We think "continuity" is somehow not involved, if we freeze this circle, and call it a discrete measure of the universe's age? Yet we know to well that the motivation of this universe from a "distant point" measure today entropically lives in the multitude of complexities?

Plato:

Model apprehension is part of the convergence that Lee Smolin and Brian Greene talk about, and without it, how could we look at nature and never consider that Einstein's world is a much more dynamical one then we had first learned from the lessons GR supplied, about gravity in our world?

On page 47 of the Trouble with Physics Lee goes on to say further down the page:

Lee Smolin:

Unfortunately, Einstein and the other enthusiasts were wrong. As with Nordstrom's theory, the idea of unification by adding a hidden dimension failed. It is important to understand why.

If all one had was the "cosmological view" one could be very happy about the way in which his observations have been deduced from the measures of our mechanical means, that we say that GR is very well suited.

Yet it has been through th efforts of reductionism that we have said, "hey there is indeed more depth to the views we have, that the mechanical measures are being tuned accordingly?"



Juan Maldacena:

The strings move in a five-dimensional curved space-time with a boundary. The boundary corresponds to the usual four dimensions, and the fifth dimension describes the motion away from this boundary into the interior of the curved space-time. In this five-dimensional space-time, there is a strong gravitational field pulling objects away from the boundary, and as a result time flows more slowly far away from the boundary than close to it. This also implies that an object that has a fixed proper size in the interior can appear to have a different size when viewed from the boundary (Fig. 1). Strings existing in the five-dimensional space-time can even look point-like when they are close to the boundary. Polchinski and Strassler1 show that when an energetic four-dimensional particle (such as an electron) is scattered from these strings (describing protons), the main contribution comes from a string that is close to the boundary and it is therefore seen as a point-like object. So a string-like interpretation of a proton is not at odds with the observation that there are point-like objects inside it.

While energy is being exemplified according to the nature of the particles we see in calorimetric design, what said that the energy here is not topologically smooth in it's orientations? Even we we move our views to the quantum regime.

Maybe having solved the "Continuum Hypothesis," we learned much about Einstein's inclinations?

The surface of a marble table is spread out in front of me. I can get from any one point on this table to any other point by passing continuously from one point to a "neighboring" one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing "jumps." I am sure the reader will appreciate with sufficient clearness what I mean here by "neighbouring" and by "jumps" (if he is not too pedantic). We express this property of the surface by describing the latter as a continuum.Albert Einstein p. 83 of his Relativity: The Special and the General Theory

Even Einstein had to add the "extra dimension" so we understood what non-euclidean views meant in a geometrical sense. I again refer here to Klein's Ordering of Geometries so one understands the schematics and evolution of that geometry.

The History of "Star Shine to Now"

In "The String Saga of Star Shine" I gave a distant measure of how we might seen any event from that time to now.

But before I begin I wanted to link Lubos's mention of article from David G to him, to point out the method and determinacy with which I gave the "String Saga Star Shine" it's inital point of measure "from" to our currrent infomration present in this universe now.

The Universe on a String By BRIAN GREENE

This striking pattern of convergence, linking concepts once thought unrelated, inspired Einstein to dream of the next and possibly final move: merging gravity and electromagnetism into a single, overarching theory of nature's forces.

In hindsight, there was almost no way he could have succeeded. He was barely aware that there were two other forces he was neglecting — the strong and weak forces acting within atomic nuclei. Furthermore, he willfully ignored quantum mechanics, the new theory of the microworld that was receiving voluminous experimental support, but whose probabilistic framework struck him as deeply misguided. Einstein stayed the course, but by his final years he had drifted to the fringe of a subject he had once dominated.

Low and behold we measure the "high energy in our sun" but least we remember the lower ends of the spectrum how shall we ascertain the images of the Sun if we did not include the lower measures in what we discern of the "sterile neutrino?"

Lest we forget about the "idea of convergence here" we might again refer to Lee Smolin's Book, The Trouble with Physics." Might Brian Greene be referring to the "latest debate?"

The relationship here being expounded upon, holds this principal that Lee Smolin talks about in what a new theory can do. Pastes it in our heads as I have shown the historical value of what began with "Pauli's Ghost particle" as the "now" of today, askes us to consider the value of the "sterile Neutrino" as a value in the discernation of that weak gravitational field?

Arrow of Time?

Let's look at Kip Thornes definition of the "timeline(star shine's) history" shall we?


Dr. Kip Thorne, Caltech 01-Relativity-The First 20th Century Revolution

So here we are, fully appreciating and understanding the "measure of distance" as we look at the "new image" of the sun?



Yes, we are to include now not only the valuation of high energy dissertations here but what value we have of the immediate presence of the neutrinos from the sun. We now have a much more comprehensive view of what the sun saids to us over "this distance of time?" How we may look at the image as we look at the way the sun looks in that picture shown by JoAnne of Cosmic Variance above.

A lot of people do not understand that if you look to the cosmo, you do not just look at what is evident from observation, but that your observation is increased, as you enhance your perceptions about the "real depth" of that universe.

So the lesson here, is that the mathematics "first born to mind" is a very suttle thing, as we peer deeper into the very beginning of this universe. While Einstein did not see in the way we do now, the relevance of that distance in time, is still held to every mind to consider in GR, that the depth of perception s still needed on a quantum level.

While the point made here is "gravitational in nature," the issuance is from the "other dimensions" to now. Quantum dynamcically this has been revealled while the discrete notion has been applied to our thinking as the "oscillation factor" has been understood in the muon to electron neutrino?

So should I point to the nature spread out before us, as you look at the effect of the neutrinos on the Kamiokande screen? Other ways, that I have shown, as we look at the aurora borealis, or the rainbow in our skies?



The effect of "our reason" for such processes in physics are extremely versatile on a sociological level, that one might question indeed where such "pure thoughts in mathematics" could arise to the "symbolistic nature predating( monte carlo methods of computerization)" of that physics?

Model apprehension is part of the convergence that Lee Smolin and Brian Greene talk about, and without it, how could we look at nature and never consider that Einstein's world is a much more dyamical one then we had first learnt from the lessons GR supplied about gravity in our world?

Yes GR is still a theory, but with experimental consequences, much as the model string theory offers you, as we look at the oscillatory nature of what asymmetry provides for us, from that pure "high energy state?" Gravity, very strong, to what is weak in the measures of the neutrino characters?

I gave some pictures to consider while I continue. Some may move ahead of me if they like:) Maybe Stefan and Bee of Backreaction?

Doppelgänger Favors Oscillate

"Observations always involve theory."Edwin Hubble

Of course I relate the "Ghost Particle to Pauli" here so that people would recognize the faint discerning image in "mirror world," as some calculation that paved the way for some future spoken from Feynman's point of view, to John Bahcall. Imagine what began as a theory/concept/idea, could have brought on this whole subject of neutrinos.

Of course here I could relate the story of "Alice in Wonderland" and Ivars Peterson may have some thoguhts on this as well. About fantasy, and what a good mathematcian should have in her/his arsenal for future prospects which will manifest as Nikolai Lobachevsky relates in quote below.

So the idea here is of course that we are looking at the neutrinos as a mechanism responsible for the matter/anti-matter asymmetry. But hold this thought while we continue through here at the unimaginable, to the manageable in testing theory.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.Nikolai Lobachevsky

I couldn't help but think of the new TV series "Heroes" that is now playing. Of course there are intriguing ideas here about time travel, regeneration, and what do you know, the "Doppelgänger," of mirror world.

Niki Sanders, a 33-year-old Las Vegas showgirl who can do incredible things with mirrors

Well under that pretense the idea is one of the dark side being show in mirror world, while the unconsicous stae of mind is somehow dropped in place of it's dark resurgence? How do you ever calculate something like that? Imagine, "Angels and Demons" as some sphere related by Escher as the revolving sphere of understanding?


All M.C. Escher works (c) 2001 Cordon Art BV - Baarn - the Netherlands. All rights reserved. www.mcescher.com

A doppelgänger (pronunciation (help·info)) is the ghostly double of a living person. The word doppelgänger is a loanword from German, written there (as any noun) with an initial capital letter Doppelgänger, composed from doppel, meaning "double", and gänger, as "walker". In English, the word is conventionally not capitalized, and it is also common to drop the German diacritic umlaut on the letter "a" and write "doppelganger", although the correct spelling without umlaut would be "doppelgaenger".

Right Handed Neutrino

Anyway there is this idea/concept/theory that refers to the combining gravity with the other forces. They call this supersymmetry. This requires that each particle to have a supermassive shadow particle?

Like many detectors, this experiment at the Fermi National Accelerator in Batavia, Illinois investigates the oscillation of neutrinos from one type to another. Since 2003, it has observed neutrinos created from protons in Fermilab's particle booster, part of the system that the lab normally employs to accelerate protons to higher energies for other experiments. MiniBooNE is a 40-foot-in-diameter spherical steel tank filled with 800 tons of mineral oil and lined with 1,280 phototubes (some of which are being adjusted in this image) that produce a flash of light when charged particles travel through them. Analyses of these light flashes are already providing tantalizing information

So if the assumption is that the "sterile neutrino" could roam in higher dimensions being undetected by us, and make it's presence felt through the influence of gravity, what does this say about grvaity currently measure at this time in the universe?

Might it mean that when only measuring high energy collidial events, that we have within the presence of the cosmo, also the the effect of weak grvaitation measures allotted to the sterile neutino, then what does this say to us about the extension of the standard model as new physics?

Current evidence shows that neutrinos do oscillate, which indicates that neutrinos do have mass. The Los Alamos data revealed a muon anti-neutrino cross over to an electron neutrino. This type of oscillation is difficult to explain using only the three known types of neutrinos. Therefore, there might be a fourth neutrino, which is currently being called a "sterile" neutrino, which interacts more weakly than the other three neutrinos.

BooNE will determine the oscillation parameters and possibly yield further information about the mass of a neutrino

See:

The Right Spin for a Neutrino Superfluid

George Gabriel Stokes

Sir George Gabriel Stokes, 1st Baronet (13 August 1819–1 February 1903) was an Irish mathematician and physicist, who at Cambridge made important contributions to fluid dynamics (including the Navier-Stokes equations), optics, and mathematical physics (including Stokes' theorem). He was secretary, then president of the Royal Society.

I mean this discourse on the nature of viscosity is leading in the sense that what has been currently going in terms of RHIC "is the physics" and understanding that came about by the pursuate of elementary considerations.

Physicists Andrew Strominger and Cumrin Vafa, showed that this exact entropy formula can be derived microscopically (including the factor of 1/4) by counting the degeneracy of quantum states of configurations of strings and D-branes which correspond to black holes in string theory. This is compelling evidence that D-branes can provide a short distance weak coupling description of certain black holes! For example, the class of black holes studied by Strominger and Vafa are described by 5-branes, 1-branes and open strings traveling down the 1-brane all wrapped on a 5-dimensional torus, which gives an effective one dimensional object -- a black hole.

This is part of the understanding that with those who try to diminish the substance of this avenue of research have missed in their wide sweeping generalizations, less then adequate of string theory. You do not dismiss Strominger lightly as part of that generalization.



So in regard to multiplicities, should we dismiss the substance of the viscosity nature here while those who are less then kind about the avenue of research regarding the model string theory, find that people like Lee Smolin have decided to work with people like Clifford to deal with these physic's issues. Although he is not changing his tune in regards to the substance of this theoretical/concept/idea model, he does appreciate the science behind it.

For those who up hold the laws, and I mean the badge of the peace officer here at Backreaction. It is nice that we understand this history as it is being explained. Shall we succumb to the mechanical modes of being and we disavow "creativity" according to the limits of the law, or must we push ahead in the "greater courts" of theoretics and challenges to these laws.

Again I am reminded of Einstein's quote here.

...the creative principle resides in mathematics. In a certain sense therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.Albert Einstein

Some would have you believe that you have acted irresponsibly in regards to model apprehsnsion about nature? Don't let them fool you or coierce you into thinking that you have disvorced yoruself from reality. If "pure thought" resides in the essence of these "mathematical forms," then where do these ensue from?


See:

Navier-Stokes equations

What is Cerenkov Radiation?

...the creative principle resides in mathematics. In a certain sense therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.Albert Einstein

Many do not recognize the process that unfolds in the developing perspectives about theoretics? Does one think it is divorced from reality that you could say, "hey this idea of course has no attachment to what exists and what we know exists and asks that you move forward with it."

Often you hear the "dreaded reference" to the AEther, and who can help but see where such revisions in thinking changed the society of scientists to put them on a new course?

Do you think the title was changed from the aether to the valuation of strings and the boson production evident in the bulk just to replay itself in the developing scenarios of our historical past? The past included a revision to the way we view that concept? That is it's effect in today's world. "The correction?"

As we know from Einstein’s theory of special relativity, nothing can travel faster than c, the velocity of light in a vacuum. The speed of the light that we see generally travels with a slower velocity c/n where n is the refractive index of the medium through which we view the light (in air at sea level, n is approximately 1.00029 whereas in water n is 1.33). Highly energetic, charged particles (which are only constrained to travel slower than c) tend to radiate photons when they pass through a medium and, consequently, can suddenly find themselves in the embarrassing position of actually travelling faster than the light they produce!

The result of this can be illustrated by considering a moving particle which emits pulses of light that expand like ripples on a pond, as shown in the Figure (right). By the time the particle is at the position indicated by the purple spot, the spherical shell of light emitted when the particle was in the blue position will have expanded to the radius indicated by the open blue circle. Likewise, the light emitted when the particle was in the green position will have expanded to the radius indicated by the open green circle, and so on. Notice that these ripples overlap with each other to form an enhanced cone of light indicated by the dotted lines. This is analogous to the idea that leads to a sonic boom when planes such as Concorde travel faster than the speed of sound in air

But we have to go back in history here to see where such influences have taken hold of the mind, from what was instituted in the neutrino search, to have the ideas swirl around and form new prospect researches, based on the ideas of women/men?



The story will follow here shortly. I would like to thank Paul on his early recognition of the bubble chamber events as they encourage research in 1998 to ponder the experiments in Cern to say?

Add your story so that this can be completed. I will add mine for a wonderful view of what research and developement does in regards to the way of "modelling to experiment."

Well since starting this blog entry there has only been two other examples that may be added to this entry as of today, yet, one by Commentor NC at Cosmic Variance while the other materialized over at Backreaction on the post done by Bee and Stefan.

A Look Back

Have a look at this image below first.



Variation of Cosmic ray flux and Global cloud coverage-a missing link in Solar-climate relationshipsby Henri Svensmark and Eigil Friis-Christensen, 26 NOvember 1996

So this is wonderful that in one way, where my mind rebukes the lashing out of Peter Woit by evidence of ICECUBe and my ir/relevant comments, could have found sustenance in how things are to be explained further? More physics ...wonderful.

But I want to go back historically to view, so that one sees what was a picture "written by Paul" and his trip to Canada, held an observation that sends us back in time experimentally to look at, to find out, what Cern was doing in 1998. Thanks Paul

You ready?

CERN plans global-warming experiment(1998)

A controversial theory proposing that cosmic rays are responsible for global warming is to be put to the test at CERN, the European laboratory for particle physics. Put forward two years ago by two Danish scientists, Henrik Svensmark and Eigil Friis-Christensen, the theory suggests that it is changes in the Sun's magnetic field, and not the emission of greenhouse gases, that has led to recent rises in global temperatures.

Experimentalists at CERN will use a cloud chamber to mimic the Earth's atmosphere in order to try and determine whether cloud formation is influenced by solar activity. According to the Danish theory, charged particles from the Sun deflect galactic cosmic rays (streams of high-energy particles from outer space) that would otherwise have ionized the Earth's lower atmosphere and formed clouds.

So what is this science based on?

The production of a high-intensity neutrino beam at CERN requires a complex facility. A proton beam produced and accelerated by the CERN accelerators is directed onto a graphite target to give birth to other particles called pions and kaons. These particles are then fed into a system comprising two magnetic horns which focus them into a parallel beam that is directed towards Gran Sasso. Next, in a 1000 metre-long tunnel, the pions and kaons decay into muons and muon neutrinos. At the end of this decay tunnel, an 18 metre thick block of graphite and metal absorbs the protons, pions and kaons that did not decay. The muons are stopped by the rock. Impervious to all such obstacles, the muon neutrinos will leave the CERN tunnels and streak through the rock on their 732 kilometre journey to Italy.

Now what does this have to do with Cerenkov radiation? Okay. I'm scratching my head now.

“CERN has a tradition of neutrino physics stretching back to the early 1960s,” said Dr Aymar, “this new project builds on that tradition, and is set to open a new and exciting phase in our understanding of these elusive particles.”

From the 1960's. Wow!

Imagine that someone might say to you that this is a "Rube Goldberg Machine" analogy as to what was the road leading to the understanding and the inclusiveness of microstate blackhole creation from particle collisions, as part of the continued story of the neutrino in action?

See:

So What Did I mean By Olympics?

Pulsars and Cerenkov Radiation

Evidence for Extra Dimensions and IceCube

Box Counting or "Points" on the Strings Length?

The jump from conventional field theories of point-like objects to a theory of one-dimensional objects has striking implications. The vibration spectrum of the string contains a massless spin-2 particle: the graviton. Its long wavelength interactions are described by Einstein's theory of General Relativity. Thus General Relativity may be viewed as a prediction of string theory! Author Unknown

We understand I think the relevance in regards ot the cosmological views that GR helps us understand in the curvatures inherent as an expression of the cosmos.

What we may have trouble with is the value we may assign such curvatures taken down to the quantum regime. This may seem incompatible, yet, the dynamical nature of the energy is never really that far from speaking from the particle/energy inhernet in nature, as a energy determinant value?

Why would you treat the quantum realm any different then you would the cosmological one, if the assumption is that GR is predicted?



Fractal Dimenison-Tree Silhoutte

I like to think of the "roots and the rings of history" here so that you may see the comparative value of thinking of the "building blocks" not so much as "boxes" but as energy values related to the circle.

There really was a reason to fear pathological entities like the Koch coastline and Peano's monster curve. Here were creations so twisted and distorted that they did not fit into the box of contemporary mathematics. Luckily, mathematics was fortified by the study of the monsters and not destroyed by them. Whatever doesn't kill you only makes you stronger.

Take the Koch coastline and examine it through a badly focused lens. It appears to have a certain length. Let's call it 1 unit. Sharpen the focus a bit so that you can resolve details that are ⅓ as big as those seen with the first approximation. The curve is now four times longer or 4 units. Double the resolution by the same factor. Using a focus that reveals details 1/9 the first focus gives us a coastline 16 times longer and so on. Such an activity hints at the existence of a quantifiable characteristic.

To be a bit more precise, every space that feels "real" has associated with it a sense of distance between any two points. On a line segment like the Koch coastline, we arbitrarily chose the length of one side of the first iterate as a unit length. On the Euclidean coordinate plane the distance between any two points is given by the Pythagorean theorem

Planck time and what new physics would we have shown once we got down to these lengths? The energy of discernation has deluded us into what was once uncertainty has now QGP idealizations and the inherency of the thinking along side of high energy considerations.

Discretium and continuity are not at odds here just that the "realm of thinking" is limited to the GR suppositons about what the world is in cosmological discretium views? Yet, we know at such levels, the "continuity" of the energy has taken over. The coast lines appear fuzzy, yet in "box counting" it doesn't seem that way. What are it's limitations then, when our views meet uncertainty about what discribes the coast line? Shall we now refer to the days, weeks, months, as an energy valuation of the circle, in the trees root and the history it contains?

Pick a "ring/circle" of the tree and tell me what happen during that time?