Binomial theorem

Pascal's triangle for binomial expansion:

A Point in Space

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

Can we be through physicality such a place,  through which  "a point" can be expressed, as the space in which we live?

Three-dimensional space is a geometric model of the physical universe in which we live. The three dimensions are commonly called length, width, and depth (or height), although any three directions can be chosen, provided that they do not lie in the same plane.

In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called 3-dimensional Euclidean space.

I mean the borders with which perspective is guaranteed is to fill, is to which all life evolves around,  is the perception that is limited to a defined space given through which that point becomes nothing more then the regurgitation of all their own parameters with which the individual builds their own confines? This is what is funneled into their way of thinking, yet out of complexity, such individuality is using the same system with which one can explain universality? How large is your universe?

I presented the idea of Entheorizing as an example of what can be placed over top of Pascal's triangle of possible numbered systems so as to be defined "as a funnel of a parameter spaces" complex and chaotic indeed that can be moved down through a point to a defined position?

Hi Steven,

Yes Pascal has been of quite interest to me as well.

The Galton Box is a interesting correlation in thinking as to outcome? Some might use mountains and pebbles...others still out comes as numbered systems as to the way in which the world expresses itself.

I tried abstractly to show that from symmetry(where is this?) has an asymmetrical relation as to the bean, as if, the energy enters into expression at the peak and arrives somewhere at it's based? Yes pyramidal:)

Sacks Spiral

Dyson, one of the most highly-regarded scientists of his time, poignantly informed the young man that his findings into the distribution of prime numbers corresponded with the spacing and distribution of energy levels of a higher-ordered quantum state. Mathematics Problem That Remains Elusive —And Beautiful By Raymond Petersen

Sacks Spiral of prime numbers

Robert Sacks devised the Sacks spiral, a variant of the Ulam spiral, in 1994. It differs from Ulam's in three ways: it places points on an Archimedean spiral rather than the square spiral used by Ulam, it places zero in the center of the spiral, and it makes a full rotation for each perfect square while the Ulam spiral places two squares per rotation. Certain curves originating from the origin appear to be unusually dense in prime numbers; one such curve, for instance, contains the numbers of the form n2 + n + 41, a famous prime-rich polynomial discovered by Leonhard Euler in 1774. The extent to which the number spiral's curves are predictive of large primes and composites remains unknown.

A closely related spiral, described by Hahn (2008), places each integer at a distance from the origin equal to its square root, at a unit distance from the previous integer. It also approximates an Archimedean spiral, but it makes less than one rotation for every three squares.

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.). See more info on Mersenne Prime.

***

See:

Quantum Mechanics: Determinism at Planck Scale

The Whole World is a Stage

Nature's Experiment on the Meaning of Weight

Foundational Issues

Mathematics Problem That Remains Elusive — And Beautiful By Raymond Petersen

Dyson, one of the most highly-regarded scientists of his time, poignantly informed the young man that his findings into the distribution of prime numbers corresponded with the spacing and distribution of energy levels of a higher-ordered quantum state

See:Riemann Hypothesis: A Pure Love of Math

One will argue of course how such a natural thing can arise out of numbers and we see the Pascalian triangle as providing an encounter with probabilistic interpretations as our fortunes in the selection of scenarios. How natural then is siuch a progression to say the Fibonacci numbers are chosen this time in the connstruct of matter defined world?

But I should warn you, I think beyond the capabilities of experiment here to include a look into dynamics that are "not scientifically recorded in the human being," but hold to the understanding that "such resonances exist" just as well as numbers and spaces are allocated in relation to these jumps.

See: Foundational Perspectives Also see:PLATO:Mathematician or Mystic ?

If one were to look a little deeper into the essence of any home, one might find elements of Plato's own Academy hidden here to suggest, that the self accounting that goes on, might have been preceded by the pursuance of bringing a healthy response to the future in regard to that "universal language." This resides very deeply in the unconscious plethora of images that are revealed to the awareness of the observant mind and it's dealings with society.

Starring: Kevin Kline, Kristen Scott Thomas, Hayden Christensen, Jena Malone, Mary Steenburgen, Mike Weinberg, Scotty Leavenworth, Ian Somerhalder, Jamey Sheridan, Scott Bakula, Sandra Nelson, Sam Robards, John Pankow, Kim Delgado, Barry Primus Director: Irwin Winkler See: When Is a House A Home?

It has always been of some difficulty that I could get to one the "whole image in mind" to say it is complete, that to follow ALONG with what I am saying, had to preclude with some ground work first, before I could draw along those who better understand now, the full scope of what I am saying. It would indeed have been better that such a flash could indeed "take the time of all the work" then to have to endure pieces being selected and focused on, without the understanding of the language that is presented here. It requires enormous patience, and the endurance of ridicule to move beyond these limitations.

Plato here in this Bloggery siad,"

Most know of my time helping my son last year constructing his home. The journey of pictures that I have here within this bloggery. It has also some "dimensional aspect" in it's development, so I thought this might help those who are working Euclidean coordinates, may help to seal this process in some way, by being introduced to house construction.

" See:House Building

The Geologist and the Mathematician

In an ordinary 2-sphere, any loop can be continuously tightened to a point on the surface. Does this condition characterize the 2-sphere? The answer is yes, and it has been known for a long time. The Poincaré conjecture asks the same question for the 3-sphere, which is more difficult to visualize.

On December 22, 2006, the journal Science honored Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year," the first time this had been bestowed in the area of mathematics

I have been following the Poincaré work under the heading of the Poincaré Conjecture. It would serve to point out any relation that would be mathematically inclined to deserve a philosophically jaunt into the "derivation of a mind in comparative views" that one might come to some conclusion about the nature of the world, that we would see it differences, and know that is arose from such philosophical debate.

Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

Previous links in label index on right and relative associative posts point out the basis of the Poincaré Conjecture and it's consequent in developmental attempts to deduction about the nature of the world in an mathematical abstract sense?

Jules Henri Poincare (1854-1912)

The scientist does not study nature because it is useful. He studies it because he delights in it, and he delights in it because it is beautiful.

HENRI POINCARE

Mathematics and Science:Last Essays

8 Last Essays

But it is exactly because all things tend toward death that life is
an exception which it is necessary to explain.

Let rolling pebbles be left subject to chance on the side of a
mountain, and they will all end by falling into the valley. If we
find one of them at the foot, it will be a commonplace effect which
will teach us nothing about the previous history of the pebble;
we will not be able to know its original position on the mountain.
But if, by accident, we find a stone near the summit, we can assert
that it has always been there, since, if it had been on the slope, it
would have rolled to the very bottom. And we will make this
assertion with the greater certainty, the more exceptional the event
is and the greater the chances were that the situation would not
have occurred.

How simple such a view that one would speak about the complexity of the world in it's relations. To know that any resting place on the mountain could have it's descendants resting in some place called such a valley?

Stratification and Mind Maps

Pascal's Triangle

By which path, and left to some "Pascalian idea" about comparing some such mountains in abstraction to such a view, we are left to "numbered pathways" by such a design that we can call it "a resting" by nature selection of all probable pathways?


Diagram 6. Khu Shijiei triangle, depth 8, 1303.

The so called 'Pascal' triangle was known in China as early as 1261. In '1261 the triangle appears to a depth of six in Yang Hui and to a depth of eight in Zhu Shijiei (as in diagram 6) in 1303. Yang Hui attributes the triangle to Jia Xian, who lived in the eleventh century' (Stillwell, 1989, p136). They used it as we do, as a means of generating the binomial coefficients.

It wasn't until the eleventh century that a method for solving quadratic and cubic equations was recorded, although they seemed to have existed since the first millennium. At this time Jia Xian 'generalised the square and cube root procedures to higher roots by using the array of numbers known today as the Pascal triangle and also extended and improved the method into one useable for solving polynomial equations of any degree' (Katz, 1993, p191.)

Even the wisest of us does not realize what Boltzmann in his expressions would leave for us that such expression would leave to chance such pebbles in that valley for such considerations, that we might call this pebble, "some topological form," left to the preponderance for us in our descriptions to what nature shall reveal in those same valleys?

The Topography of Energy Resting in the Valleys

The theory of strings predicts that the universe might occupy one random "valley" out of a virtually infinite selection of valleys in a vast landscape of possibilities

Most certainly it should be understood that the "valley and the pebble" are two separate things, and yet, can we not say that the pebble is an artifact of the energy in expression that eventually lies resting in one of the possible pathways to that energy at rest.

The mountain, "as a stratification" exists.



Here in mind then, such rooms are created.

The ancients would have us believe in mind, that such "high mountain views do exist." Your "Olympus," or the "Fields of Elysium." Today, are these not to be considered in such a way? Such a view is part and parcel of our aspirate. The decomposable limits will be self evident in what shall rest in the valleys of our views?

Such elevations are a closer to a decomposable limit of the energy in my views. The sun shall shine, and the matter will be describe in such a view. Here we have reverted to such a view that is closer to the understanding, that such particle disseminations are the pebbles, and that such expressions, have been pushed back our views on the nature of the cosmos. Regardless of what the LHC does not represent, or does, in minds with regards to the BIG Bang? The push back to micros perspective views, allow us to introduce examples of this analogy, as artifacts of our considerations, and these hold in my view, a description closer to the source of that energy in expression.

To be bold here means to push on, in face of what the limitations imposed by such statements of Lee Smolin as a statement a book represents, and subsequent desires now taken by Hooft, in PI's Status of research and development.

It means to continue in face of the Witten's tiring of abstraction of the landscape. It means to go past the "intellectual defeatism" expressed by a Woitian design held of that mathematical world.

Mind Maps: Mathematical Structures?

Plato's doctrine of recollection, however, addresses such criticism by saying that souls are born with the concepts of the forms, and just have to be reminded of those concepts from back before birth, when the souls were in close contact with the forms in the Platonic heaven. Plato is thus known as one of the very first rationalists, believing as he did that humans are born with a fund of a priori knowledge, to which they have access through a process of reason or intellection — a process that critics find to be rather mysterious

What are Mind Maps?

A mind map is a diagram used to represent words, ideas, tasks or other items linked to and arranged radially around a central key word or idea. It is used to generate, visualize, structure and classify ideas, and as an aid in study, organization, problem solving, decision making, and writing.

It is an image-centered diagram that represents semantic or other connections between portions of information. By presenting these connections in a radial, non-linear graphical manner, it encourages a brainstorming approach to any given organizational task, eliminating the hurdle of initially establishing an intrinsically appropriate or relevant conceptual framework to work within.

A mind map is similar to a semantic network or cognitive map but there are no formal restrictions on the kinds of links used.

The elements are arranged intuitively according to the importance of the concepts and they are organized into groupings, branches, or areas. The uniform graphic formulation of the semantic structure of information on the method of gathering knowledge, may aid recall of existing memories.

Well straight to the point then I guess.

Bee:

The important thing about the basis of our societies is not actually its fixed structure but the way to readjust it. A bit of scientific method would be good there.

As I mentioned previously on Backreaction site and in giving subsequent information about this process. It has been a journey of my own discovery, that I would say that at the basis of reality is such a mathematical structure.

I know when this process started for me and it would not serve any purpose at this point to speak to it directly. People have their reasons for and against such a proposal as their being such a mathematical structure, so what currently leads me to say that their are these two opposing views?


Wigner’s Gift Horse By JULIE REHMEYER • Feb 1, 2008 See here for article.

Stephen Wolfram argues that the way to unlock the rest of science is to give up on mathematics and look for explanations analogous to computer code. Very simple computer programs can produce remarkably complex behavior that mimics phenomena science has had difficulty modeling, like the motion of fluids, for example. So studying the behavior of these programs may provide scientists with new insights about these phenomena. Indeed, Wolfram thinks the universe itself may be generated by a computer program simple enough to be expressed in a few lines of code. “If the laws are simple enough, if we look in the right way we’ll find them,” he says. “If they’re not, it will be tougher. The history of physics makes one pessimistic that we could ever end physics. I don’t share that pessimism.”

Tegmark believes in an extreme form of Platonism, the idea that mathematical objects exist in a sort of universe of their own. Imagine that, Tegmark says, “there’s this museum in this Platonic math space that has these mathematical objects that exists outside of space and time,” Tegmark says. “What I’m saying is that their existence is exactly the same as a physical existence, and our universe is one of these guys in the museum.”

Also worth reading is the sum of any position that would infer the stance of Plato versus anti-Plato, to help distinguish whether or not one might have something of value in terms of the question of whether Mathematics is invented or discovered.

Mathematical Platonism and its Opposites by Barry Mazur January 11, 2008. See here.

For the Platonists. One crucial consequence of the Platonic position is that it views mathematics as a project akin to physics, Platonic mathematicians being—as physicists certainly are—describers or possibly predictors—not, of course, of the physical world, but of some other more noetic entity. Mathematics—from the Platonic perspective—aims, among other things, to come up with the most faithful description of that entity.

For the Anti-Platonists. Here there are many pitfalls. A common claim, which is meant to undermine Platonic leanings, is to introduce into the discussion the theme of mathematics as a human, and culturally dependent pursuit and to think that one is actually conversing about the topic at hand.

Mapping the interaction from a scientific point of view?

As I read through the article I had previous insights while reading through Sir Roger Penrose's lecture on the Extended Physical WorldView. While I myself had picked the title, it would have been nicer to show the very image on the start of that lecture.



This is a important statement I am making below because it distinguishes between where we think we might be going in terms of computer technologies versus what will always remain within the human domain.

So on the one hand one might think about technologies in the 21st Century and wonder if computer technology can ever reach the status of Consciousness with which the "synaptic event" could include images, all the while it would include all the history to that point?

While it is never clear to me about the origins of the universe, it had some relation in my mind to what first allowed any soul's expression. While I had shown the relation to the synaptic event, there had to be a place created for such an expression, to be fortunate and validated.

Do I know what plan for every individual is, of course not, but that you choose such an expression is self evident. There is much to the word, "self evident" that remains to be explored within context of this site, and of value, in the iconic image of Raphael's expression with Plato and Aristotle at it's centre.

Now, neuronic networking is supposedly the platform computer technologies can take in their designs, but what true aspect of the emergent process could ever define the human being and one's potential? The information that could enter such an synaptic event within your own thinking mind?

So the process is one of self discovery. About processes within your own self that allow one to possibly develop the new mathematics that speak directly to the very unfolding of the universe?

The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner

The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess. However, this is not our present subject. The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.

[3 M. Polanyi, in his Personal Knowledge (Chicago: University of Chicago Press, 1958), says: "All these difficulties are but consequences of our refusal to see that mathematics cannot be defined without acknowledging its most obvious feature: namely, that it is interesting" (p 188).]

What can arise from any person, to have defined that it reaches back into the forms. That it chooses to manifest "as the person" you have become? What lies dormant, that you awake to it in such a way that it will manifest in all that you do, and become part of the "history of recollection" that you unfold in this life, and have learnt these things before? You dream?

I, Robot:

....signs of new life emerge as images photonically flicker in the new logic forming apparatus....

I had a dream....

We might like to think that computers are capable, while the very idea of the "image" holds such vasts amount of information. This is not a new idea from an historical perspective if one ever thought to consider the alchemists of our early science.

How would you contain all the probability and outcomes, with ever looking beyond space and time, to realize that the "heavens" in some way, meet the earth. Manifest within you? Can find re-birthing through you? Inner/outer become one.

The Founder of Probabilty Theory?

I want to understand what makes the world tick. Einstein said he wanted to know what was on God's mind when he made the world. I don't think he was a religious man, but I know what he means.Lenny Susskind

Pierre de Fermat IPA: [pjɛːʁ dəfɛʁ'ma] (August 17, 1601 – January 12, 1665)

With Blaise Pascal, Pierre de Fermat became the founders of the theory of probability.

A Short History of Probability

"A gambler's dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Antoine Gombaud, Chevalier de Méré, a French nobleman with an interest in gaming and gambling questions, called Pascal's attention to an apparent contradiction concerning a popular dice game. The game consisted in throwing a pair of dice 24 times; the problem was to decide whether or not to bet even money on the occurrence of at least one "double six" during the 24 throws. A seemingly well-established gambling rule led de Méré to believe that betting on a double six in 24 throws would be profitable, but his own calculations indicated just the opposite.

Euler's Konigsberg's Bridges Problem

"Liesez Euler, Liesez Euler, c'est notre maître à tous"
("Read Euler, read Euler, he is our master in everything") - Laplace

I should say here that the post by Guest post: Marni D. Sheppeard, “Is Category Theory Useful ?” over at A Quantum Diaries Survivor, continues to invoke my minds journey into the abstract spaces of mathematics.

The river Pregel divides the town of Konigsberg into four separate land masses, A, B, C, and D. Seven bridges connect the various parts of town, and some of the town's curious citizens wondered if it were possible to take a journey across all seven bridges without having to cross any bridge more than once. All who tried ended up in failure, including the Swiss mathematician, Leonhard Euler (1707-1783)(pronounced "oiler"), a notable genius of the eighteenth-century.

As a lay person being introduced to the strange world of mathematics it is always interesting to me in the way one can see in abstract processes.

The Beginnings of Topology...The Generalization to Graph Theory
Euler generalized this mode of thinking by making the following definitions and proving a theorem:

Definition: A network is a figure made up of points (vertices) connected by non-intersecting curves (arcs).

Definition: A vertex is called odd if it has an odd number of arcs leading to it, other wise it is called even.

Definition: An Euler path is a continuous path that passes through every arc once and only once.

Theorem: If a network has more than two odd vertices, it does not have an Euler path.

Euler also proved the converse:

Theorem: If a network has two or less odd vertices, it has at least one Euler path.

Leonhard Paul Euler (pronounced Oiler; IPA [ˈɔʏlɐ]) (April 15, 1707 – September 18 [O.S. September 7] 1783) was a pioneering Swiss mathematician and physicist, who spent most of his life in Russia and Germany. He published more papers than any other mathematician of his time.[2]

Euler made important discoveries in fields as diverse as calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[3] He is also renowned for his work in mechanics, optics, and astronomy.

Portrait by Johann Georg Brucker- Born April 15, 1707(1707-04-15)Basel, Switzerland and Died September 18 [O.S. September 7] 1783
St Petersburg, Russia

You have to understand that as a lay person, my education is obtained through the internet. This is not without years of study(many books) in a lot of areas, that I could be said I am in a profession of anything, other then the student, who likes to learn a lot.

To find connections between the "real world" and what a lot think of as "to abstract to be real."

Any such expansionary mode of thinking, if not understood, as in the Case of Riemann's hypothesis seen in relation to Ulam's Spiral, one might have never understood the use of "Pascal's triangle" as well.

These are "base systems of mathematics" that are describing processes in nature?

See:Euler - 300th anniversay lecture

Are there Patterns to Life?

Its grandness, goodness, beauty and perfection are unexcelled. Our one universe, indeed, the only one of its kind, has come to be.Timaeus concludes

I was just thinking about the idea of being a mathematical structure, and having been made aware of Max Tegmark, it drew me back to the idea of the "soccer ball universe."

"If this holds up to the test of time, it's a real landmark," said Max Tegmark, a cosmologist and cosmic microwave expert at M.I.T. "I really feel like the universe has given up one more clue," he said.

See: Scientists Get Glimpse of First Moments After Beginning of Time by DENNIS OVERBYE


Now yes I'd admit the universe is a far cry from the person we are, but we are much more complex, and I'd liken it to the universe. Why not?

Namagiri, the consort of the lion god Narasimha. Ramanujan believed that he existed to serve as Namagiri´s champion - Hindu Goddess of creativity. In real life Ramanujan told people that Namagiri visited him in his dreams and wrote equations on his tongue.

See:Srinivas Ramanujan(1887-1920):

Anyway twice I have been reminded of the mathematics "are not" the reality of the situation, and that governing such thought is devoid of the reality we are dealing with. I have an issue with this because, we have discovered number patterns that underly nature just as Coxeter believes that "the process" is just awaiting to be discovered. Then, we have found the thread through things.

So, people do not like to believe that we are a mathematical structure, yet, we have seen where hidden numbered processes have been detailed for us in the expressions of nature.

The Valley and our Place in the universe


Jacques Distiler:

Rather, it is assumption 2) that is suspect. I argued that it is suspect in much greater generality in the comment thread I linked to above. But, in the specific case of the proton lifetime, we already have seen two mechanisms, discussed in this thread, either of which could constrain the proton lifetime to be far longer than the anthropic bound.

Jacque Distler:

Obviously, no one has yet found a convincing candidate for the Standard Model, among the string vacua explored to date (in that sense, no one has made any predictions yet). But that’s not what you’re saying(Peter Woit). You are claiming that the framework itself is inherently unpredictive.

Italicized is my addition.

A mathematics man who does not like math?

So you see we are looking for the constants(a product of the standard model), yet, we do not know what that constant will look like in the valley. While it is based on a "gravitational inclination," the formation has a probability "greatly enhanced" when thinking about the entropy of the blackhole. The "energy valuation" from mass while in gravitational collapse, creates the multitude of possibilities(heat)?

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.

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.

Gold and Fool's Gold

Gold

Perhaps the highest density known is reached in neutron star matter (see neutronium). The singularity at the centre of a black hole, according to general relativity, does not have any volume, so its density is undefined.

The most dense naturally occurring substance on Earth is iridium, at about 22650 kg·m-3.

A table of densities of various substances:

So of course seeing this new posting and the ideas of what the gold nugget "is," is supposed to be here in our thinking is of course. Being clarified in terms of how we look at the LHC, most defintiely. Having expert opinion on this is always important. for sure.

Fool's Gold ?

Who is not without some blemish on the "heart values" when it had been held to a goal like truth, and had gone astray? It just matters that you try, and that you hold this value in front of your eyes, as you progress through life.

I was at a loss for what would describe "this beginning" and having looked at what is attained in the "Pascalian triangle", how could I not learn of the spiral induced numbers that lie at the very heart of such creations.

You have to understand what the basis of what this triangle is based upon. I gave clues here.

Some fractorial mathematical based idea, exposed to the matters, as crystaline objects of perception unfolding? Wolfram?

NPR's Richard Harris reports on the beauty of mathematics

How are some things built, that you would ignore "the mathematics at the basis of experience." Having such a geometrical basis is very important. I may call it "Algebraic equations" of Dirac(Lubos take note:), but it is more then that, and it is in the emergence of strings, that we recognize where the conditions are, as the strings basis? You had to understand "the entropic" as well as the CFT issues from the blackhole state? What are the initial conditions?

If I say microseconds, you should immediately assume it is after the big bang.:)Topological "geometrics" eh? :) is much different, then what we see classically of the 3+1? You remember "Klein's ordering of the geometries," of course? Right?

Gold in the Landscape?

I was looking for a specific posting on "Fool's gold" so I thought of Clifford's at Cosmic Variance and the post he created. A specific comment that I made. No, this does not imply anything against Clifford. :)

Here you might refer to the points between Lubos and Bee, about the "initial conditions?" It's "beyond" the placement of what is held in microseconds, and the arrow of time. What! Before time began?

So where is that? What already existed?

However, don't be fooled! The charm of the golden number tends to attract kooks and the gullible - hence the term "fool's gold". You have to be careful about anything you read about this number. In particular, if you think ancient Greeks ran around in togas philosophizing about the "golden ratio" and calling it "Phi", you're wrong. This number was named Phi after Phidias only in 1914, in a book called _The Curves of Life_ by the artist Theodore Cook. And, it was Cook who first started calling 1.618...the golden ratio. Before him, 0.618... was called the golden ratio! Cook dubbed this number "phi", the lower-case baby brother of Phi.

What a Cosmologist Wants From String theory by David Wand


I mean have tried to instill a good foundational perspective of what happens, and what is percieved, in terms of the joining of microsperspective views in regards to the nature of the cosmo?

So what is not revealled here in "my thinking" although we have been directed to the process of the "collidial views" imparted by expert opinion and further glossed by Q's blog building to face this thinking process? :)




A debate/dialogue is always a good thing to initiate, and I have not be too lucky to have somebody to run against my thinking. It's a relief Q. As you say, "I am looking for truth."

So where I am going to go from here? :) Should I go?

Well science has this thingy about experiment and beyond that, beyond the standard model, what thinking shall I introduce? Something "beyond the 3+1" perhaps? :)

Supersymmetry<->Simplistically<-> Entropically Designed?

So of course I am troubled by my inexperience, as well as, the interests of what could have been produced in the "new computers" of the future? So in some weird sense how would you wrap the dynamics of what lead to "Moore's law" and find that this consideration is now in trouble? While having wrapped the "potential chaoticness" in a systemic feature here as deterministic? Is this apporpriate?

In the presence of gravitational field (or, in general, of any potential field) the molecules of gas are acted upon by the gravitational forces. As a result the concentration of gas molecules is not the same at various points of the space and described by Boltzman distribution law:

What happens exponetially in recognizing the avenues first debated between what was a consequence of "two paths," One that would be more then likely "a bizzare" while some would have consider the other, the cathedral? Leftists should not be punished Lubos:)

So what is Chaos then?

The roots of chaos theory date back to about 1900, in the studies of Henri Poincaré on the problem of the motion of three objects in mutual gravitational attraction, the so-called three-body problem. Poincaré found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point. Later studies, also on the topic of nonlinear differential equations, were carried out by G.D. Birkhoff, A.N. Kolmogorov, M.L. Cartwright, J.E. Littlewood, and Stephen Smale. Except for Smale, who was perhaps the first pure mathematician to study nonlinear dynamics, these studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and Littlewood. Although chaotic planetary motion had not been observed, experimentalists had encountered turbulence in fluid motion and nonperiodic oscillation in radio circuits without the benefit of a theory to explain what they were seeing.

13:30 Lecture
Edward Norton Lorenz
Laureate in Basic Sciences
“How Good Can Weather Forecasting Become ? – The Star of a Theory”

So this talk then is taken to "another level" and the distinctions of WeB 2.0 raised it's head, and of course, if you read the exponential growth highlghted in communities desemmination of all information, how could it be only Web 1.0 if held to Netscape design?



I mean definitely, if we were to consider "the Pascalian triangle" and the emergence of the numbered systems, what said the Riemann Hypothesis would not have emerged also? The "marble drop" as some inclusive designation of the development of curves in society, that were once raised from "an idea" drawn, from some place?

Pattern Recognition

Strominger:

That was the problem we had to solve. In order to count microstates, you need a microscopic theory. Boltzmann had one–the theory of molecules. We needed a microscopic theory for black holes that had to have three characteristics: One, it had to include quantum mechanics. Two, it obviously had to include gravity, because black holes are the quintessential gravitational objects. And three, it had to be a theory in which we would be able to do the hard computations of strong interactions. I say strong interactions because the forces inside a black hole are large, and whenever you have a system in which forces are large it becomes hard to do a calculation.

The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did.

I mean sure we can say to ourselves, "that one day I was very ignorant" and I had all these speculative ideas about the "Golden Ratio," but then, I learnt the math and the truth of it all?

But while we were being crazy......?:) Ahem!

Namagiri, the consort of the lion god Narasimha. Ramanujan believed that he existed to serve as Namagiri´s champion - Hindu Goddess of creativity. In real life Ramanujan told people that Namagiri visited him in his dreams and wrote equations on his tongue.

In "past life bleed throughs," it was very important to realize that while speaking in context of "overlapping," the underlying archetecture allowed for expression of those different interpretive assignments I had given. These were significant for me, because it help me to realize the "mapping" that we can unconsciously have revealled in such "experience dream/real patterns," that had one not be aware it, would have escape one's notice as a mundane realization.

You had to understand how "geometrical seeing" is held in context of Dirac's wording, to know that this tendency to draw lines at the basis of consciousness, was also evident in Feynman's toy model construction. It is something that we do, do.

So what did I learn?

1. That it revealled a model for consciousness, from the reality of the day, to the transcendant.

2. That it housed an experience in the way it can overlapped using "1" as a central pattern of emergence.

3. That present day models now use this schematic are psychologically endowed in speculation(liminocentrically structured), but has a basis in fact, as I am showing it here.

"Betrayal of Images" by Rene Magritte. 1929 painting on which is written "This is not a Pipe"

What sense would any of this "cognitive idealization" make, if one did not have some model in which to present, and know, that it was the underlay of all experience, and that the time of our day, might see us use it in topologically in different ways?

I used Sklar for this example.

But more then this what use is "Pascal Triangle" if we did not understand the emergence of "patterned numbers" from some initial beginning and cognitive realization, had we not recognized Pascal's model intepretation?



With no know emergent principals, or geometry arising from inside the blackhole, it was important that the basis of expression be realized as a pattern forming recognitive valuation? Is it right? I am not sure, but part of the developing model application had me wonder about how we could have encapsulated the cyclical nature of, what was collapsing into the singularity, was now actually, the motivational force for the developing new universe?

When it was discovered that black holes can decay by quantum processes, it was also discovered that black holes seem to have the thermodynamic properties of temperature and entropy. The temperature of the black hole is inversely proportional to its mass, so the black hole gets hotter and hotter as it decays.

So it was important to know the basis of D brane recognitive values, in how the blackhole is interpreted?

Earth Bound Solutions to All Possible Pathways

Will I might have been guilty of taking Physics down a road so similar in conceptualization bastardizing, that I would have driven a nail in the very deaths of what could have emerged from the outcome of all possibilties? That we were indeed attached to the consequences of our ever actional decisive forays into human contact. Decision making, action orientated, outcomes, of the original simplectic intiated ideas?

It had to arise from something?

Would it be so easy to lay out the pathway required, that each of us woud have recognized our time in existance, would have indeed been the measure of all things that we choose to endorse in our ever perfecting evolution as cyclcical choices of perfecting our thinking.

This is a interesting thought held in my mind when you think of about what is held in context thinking, if we hold the photons in context of earthbound recognitions of those time orientated distances.

Many will know instantly what this means while others, scoff at the notion that we could have seen such influences telling us anything useful about the space of these interactions.

All the while the initial plectic recognition of Gellman's arose to complexities. We lost sight of the simple ideas about what might happen to the spin rotations over those vast distances? That the connectiveness, would have ever acknowledged equative relations that these two photons under the squared earthbound views, would include all probabilites being still held to view. While we still look at all possible actions? So what about time indeed.

Einstein's prettty girl scenario and hot stove, served to help me see conceptual framesworks about speed attributions of the nature of fast and slow moving world in terms of our earthbound considerations. This action was decisive, and held in context of that experience. He helped me to see that experience is indeed fleeting, depending on our circumstances, where such nature would have embedded the very nature of the spacetime fabric itself to include, how we will measure that distance of mind.

Is there another story here that we might be convinced of a rational behind?

Here is something that Brian Greene mentions to reinforce where I had come to in looking at the completion of that chapter.

the quantum entanglement would become so spread out through these interactions with the environment that it would become virutually impossible to detect. For all intents and purposes, the original entanglement between photons would have been erased.

Never the less it is truly amazing that these connections do exist, and that craefully arranged labratory conditions they can be observed over significant distances. They show us, fundamantally, that space is not what we once thought it was. What about time?

Page 123, The Fabric of the Cosmo, by Brian Greene

Does gravity vary over time?

If you did not have this in mind, what value would you attribute gravity in any scenario, as you mull over all the geometrical implications if a positive geometric solutions to Riemann's spherical solutions. The persective that GR holds for us, in our considerations?

Theory, experiment and fine structure

Were it not for relativity, the three states with different J would all have the same energy, and the light emitted in the transition would have a single frequency of about 277 000 GHz. However, relativistic effects mean that the states have slightly different energies, and when this light is analysed carefully, splittings of the order of 10 GHz are seen.

If ever driven to micro-perspectives how would time been of value if held to the quantum perspective as a strong enviriomental influence. One which spreads out all interactive phases that we could no longer discern, a viable solution to what is presented to us, unless in "symmetry breaking" realizations. So what was that beginning. Again Kravstov computer simulations help to drive that concept home.

Another laser beam is used to make the atoms fluoresce, and the amount of fluorescence is measured as a function of the microwave frequency to plot a "resonance curve". An ultra-precise measurement of time can be made by measuring the frequency of the peak in this resonance curve (see "Atomic clocks" by Pierre Lemonde in Physics World January 2001 pp39-44).

So simplicity for me asks what image in mind would hep one to discern entropic valuation to what this universe had become from temperature orientated view of that early universe, to have said, "that the probabilites that are evident now, have become like this?"

Two things formed in my mind as to the consequence of numbered systems, and pascal triangle, as to the source of all probabilitistic valuations and the marble drop held in context of BINOMIAL DISTRIBUTION.

So having defined the early universe and quantum valution arising from temerature, it helps to think about the outcome emerging from what had never been understood or have in "measured stick," to what would become our universe today? It still is the earthboud experience that we have, has emerge from astate that was equal in it's determinations. Ideas are like that.

So you had to see simplicity settling into our minds in such a way that If Plato indeed points up, then you would understand immediately, what he is pointing too. If you hold that image in mind of the triangle, then how would you ever assess Riemann's hyptohesis, as to the spirlaic outcome of Ulam's spiral indications? While the spiral opens up to the vast potential of outcome originating from ideas, it still settles into minds in it's concrete form.

So you have to define this relationship very carefully, and if I had said Liminocentrically topologically organized, what the heck would I have been saying?


Heaven's ephemeral Qualities?

It seems it would have far reaching enlightening features of what the buddhist mind might have to offer? What subtle arrangement the conceptual framework might have said about our everyday interactions with each other? Then you might have said what color indeed are the emphemeral qualities to our [mathematical]decisive minds that we would choose such abstract colors as yellow in our mental appreciations of what nature hides in the color of flowers around us? :)

Wolfram's Ring Tone

What makes this a little bit, well more then a bit interesting is the evaluation you might try to assign reality of the unseen. IN Mendeelev's table, I like to think in a different way, and if one held the Riemann hypothesis up for grabs, what said that any elemental consideration would have been derived from some Probabilistic evaluated state, not to have formed into views with which all nature might have embued itself?

Lubos Motl:

If you're interested in the more precise isomorphisms between the cellular automata and the anthropic principle, there is a cute analogy invented by Nima that looks as follows: the negative cosmological constant is mapped to the automata that die out (big crunch) while the large positive cosmological constant is mapped to the trivial (solvable) automata - and the nontrivial automata that don't die out represent the anthropically allowed window for the cosmological constant. :-)

You need a background for this, about how such perceptions could have arisen from the very nature that all things, will continue to vibrate even in a empty space.The quantum harmonic oscillator would have something to say to this, and if held to the very nature of flat spacetime, where would this be stopped?

Wolfram's Theory of Everything


So such expansions to the entropically large valuation of all that is in materiality, had to come from some kind of "soup of thnking" that rests itself from all the myriad forms that could have been emitted? So our thnking is "colored" then from musical interludes analogistically based. But indeed, how did you get there and you have this strict regimentation to follow in the probabilitic valution that the Pascal triangle would have surmounted, when thinking of Wolfram's work.

Plato:

How do such things make there way into reality and these prime numbers as signatures of the atoms and ways in which they would relate themself to this elemental table for viewing, and something then shifts in my perception. I don't know why? :)

How can you not help but think in new ways, once your given perspective about the ways we have always done things. A Serpinski fractoriallization about the nature of the world in a myriad of ways, and the probabilistic valuation about events in the unseen. How could they ever be captured?

Blaise Pascal

Blaise Pascal (June 19, 1623 – August 19, 1662)

Born in Clermont-Ferrand (France), the young Pascal was introduced to mathematics and physics by his father. So precocious was his talent in these disciplines that he published his innovative Essai pour les coniques [Essay on conics] in 1632, at only sixteen. In 1631, he moved to Paris, where he frequented the intellectual circle of Marin Mersenne (1588-1648)—a forum for the discussion of the most topical scientific and philosophical questions. In 1644, he became interested in the technological aspects of scientific research, devising a calculating machine that could perform additions and subtractions. In 1646, he conducted path-breaking research on the vacuum and fluid dynamics. He devoted two major works to fluids—Équilibre des liqueurs [Equilibrium of liquids] and De la pesanteur de la masse d'air [On the weight of the mass of air]—written in 1651-1654, but not published until 1663. In 1653-1654, he composed some brief but seminal papers on combinatory calculus, infinitesimal calculus, and probability. Pascal repeated Evangelista Torricelli's experiment, using various liquids and containers of different shapes and sizes. This research, in addition to the publication of Expériences nouvelles touchant le vide [New experiments on the vacuum], culminated in the famous experiment performed in 1648 on the Puy-de-Dôme, in which he demonstrated that atmospheric pressure lessens with an increase in altitude.

In parallel with his scientific pursuits, Pascal displayed a deep and abiding concern with religious and moral issues. In his youth, he espoused Jansenism and began to frequent the Port-Royal group. These contacts form the background to the Lettres provinciales (1656-1657) and the Pensées (published posthumously in 1670).

I had to lay this out before I continued to speak to the world Lubos motl directs us too. In a way, these mathematical pursuance and comprehensions, are revealing, when they speak to the greater probability of discovering the root systems mathematically as well as philosophically. Cases in point, about compaction scenarios are self explanatory when it comes to energy determination and particle reductionism . This relationship to idealization of supergravity, points thinking to a vast overall comprehension suited to the culminations of a model employed such as string theory?

But back to the point of focus here.

Earlier derivation of Pascal's thinking, "are roads that even he was lead too," that we have this fine way in which to speak about the root of mathematical initiative, and these roots leading to mathematical forays into the natural world.


Diagram 6. Khu Shijiei triangle, depth 8, 1303.

The so called 'Pascal' triangle was known in China as early as 1261. In '1261 the triangle appears to a depth of six in Yang Hui and to a depth of eight in Zhu Shijiei (as in diagram 6) in 1303. Yang Hui attributes the triangle to Jia Xian, who lived in the eleventh century' (Stillwell, 1989, p136). They used it as we do, as a means of generating the binomial coefficients.

It wasn't until the eleventh century that a method for solving quadratic and cubic equations was recorded, although they seemed to have existed since the first millennium. At this time Jia Xian 'generalised the square and cube root procedures to higher roots by using the array of numbers known today as the Pascal triangle and also extended and improved the method into one useable for solving polynomial equations of any degree' (Katz, 1993, p191.)

See I am somewhat starting with a disadvantage because buried in my head is the reasons for describing math more then it's intuitionist valuation in computer generated idealizations. It all of a sudden brings into perspective a deeper sense of the possibilities and probabilities?

Here I am quickly reminded of Gerard t'hooft, and the thinking, about reductionistic views of information in computerized versions. Philosophically how can we have reduced information to such sizes and find the world a much more complex place. Would we not realize that such intuitionist attempts too have to undergo revisions as well?

A Short History of Probability

"A gambler's dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Antoine Gombaud, Chevalier de Méré, a French nobleman with an interest in gaming and gambling questions, called Pascal's attention to an apparent contradiction concerning a popular dice game. The game consisted in throwing a pair of dice 24 times; the problem was to decide whether or not to bet even money on the occurrence of at least one "double six" during the 24 throws. A seemingly well-established gambling rule led de Méré to believe that betting on a double six in 24 throws would be profitable, but his own calculations indicated just the opposite.

Shall we quickly advantage to a age of reason where understand well the beginnings of mathematical systems and lead into Boltzman? But before I do that, I wanted to drawn attention to the deeper significance of this model appreciation.

Discovering Patterns



While we get some understanding here of what Pascal's triangle really is you learn to sense the idea of what culd have ever amounted to expressionand this beginning? Did nature tell us it will be this way, or some other form of expression?

So overall the probability of expressionism has devloped the cncptual basis as arriving from soem place and not nothing. True enough, what is this basis of existance that we would have a philosphical war between the background versus non background to end up in stauch positional attitudes about how one should approach science here?

So to me, I looked for analogies again to help me understand this idea of what could have ever arisen out of string theory that conceptually mad esense . Had a way in which to move forward, with predictable features? Is their sucha things dealing with the amount of information that we have in reductionsitic views. These views had to come to a end, and I will deal with this later.

Of course now such idealization dealng with probabilties off course, forces me to contend with what has always existed and helps deal with this cyclcial nature. You have to assume soemthing first. That will be the start of the next post.

But back to finishing this notion of probability and how the natural order of the universe would have said folow this way young flower, that we coud seen expansionism will not only be detailled in the small things, but will be the universe, in it's expression as well?


The Pinball Game

The result is that the pinball follows a random path, deflecting off one pin in each of the four rows of pins, and ending up in one of the cups at the bottom. The various possible paths are shown by the gray lines and one particular path is shown by the red line. We will describe this path using the notation "LRLL" meaning "deflection to the left around the first pin, then deflection right around the pin in the second row, then deflection left around the third and fourth pins".

So what has happened here to force us to contend with certain issues that the root numbers of all things could have manifested, and said, "nature shall be this way?"


Ludwig Boltzmann (1844-1906)

In 1877 Boltzmann used statistical ideas to gain valuable insight into the meaning of entropy. He realized that entropy could be thought of as a measure of disorder, and that the second law of thermodynamics expressed the fact that disorder tends to increase. You have probably noticed this tendency in everyday life! However, you might also think that you have the power to step in, rearrange things a bit, and restore order. For example, you might decide to tidy up your wardrobe. Would this lead to a decrease in disorder, and hence a decrease in entropy? Actually, it would not. This is because there are inevitable side-effects: whilst sorting out your clothes, you will be breathing, metabolizing and warming your surroundings. When everything has been taken into account, the total disorder (as measured by the entropy) will have increased, in spite of the admirable state of order in your wardrobe. The second law of thermodynamics is relentless. The total entropy and the total disorder are overwhelmingly unlikely to decrease

So what has happened that we see the furthest reaches of our universe? Such motivation having been initiated, had been by some motivator. Shall you call it intelligent design(God) when it is very natural process that had escaped our reasoning minds?

So having reached it's limitation(boundry) this curvature of the universe, has now said, "such disorder having reached it's reductionistic views has now found it's way back to the beginning of this universe's expression? It's cyclical nature?

This runs "contray to the arrow of time," in that these holes, have somehow fabricated form in another mode of thought that represents dimensional values? This basis from which to draw from, had to have energy valuations missing fromthe original expression? It had to have gone some place. Where is that?

But I have digressed greatly, to have missed the point of Robert Lauglin's principals, "of building blocks or drunk sergeant majors", and what had been derived from the energy in it's beginning? To say the complexity of those things around us had to returned our thinking back to some concept that was palitable.

Why the graduation to ISCAP, and Lenny's new book, is the right thing to do

(LEONARD SUSSKIND:) What I mostly think about is how the world got to be the way it is. There are a lot of puzzles in physics. Some of them are very, very deep, some of them are very, very strange, and I want to understand them. I want to understand what makes the world tick. Einstein said he wanted to know what was on God's mind when he made the world. I don't think he was a religious man, but I know what he means.

The thing right now that I want to understand is why the universe was made in such a way as to be just right for people to live in it. This is a very strange story. The question is why certain quantities that go into our physical laws of nature are exactly what they are, and if this is just an accident. Is it an accident that they are finely tuned, precisely, sometimes on a knife's edge, just so that the world could accommodate us?