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

13th Sphere of the GreenGrocer

I suppose you are two fathoms deep in mathematics,
and if you are, then God help you, for so am I,
only with this difference,
I stick fast in the mud at the bottom and there I shall remain.
-Charles Darwin

How nice that one would think that, "like Aristotle" Darwin held to what "nature holds around us," that we say that Darwin is indeed grounded. But, that is a whole lot of water to contend with, while the ascent to land becomes the species that can contend with it's emotive stability, and moves the intellect to the open air. One's evolution is hard to understand in this context, and maybe hard for those to understand the math constructs in dialect that arises from such mud.

For me this journey has a blazon image on my mind. I would not say I am a extremely religious type, yet to see the image of a man who steps outside the boat of the troubled apostles, I think this lesson all to well for me in my continued journey on this earth to become better at what is ancient in it's descriptions, while looking at the schematics of our arrangements.


How far back we trace the idea behind such a problem and Kepler Conjecture is speaking about cannon balls. Tom Hales writes,"Nearly four hundred years ago, Kepler asserted that no packing of congruent spheres can have a density greater than the density of the face-centered cubic packing."

Kissing number problem

In three dimensions the answer is not so clear. It is easy to arrange 12 spheres so that each touches a central sphere, but there is a lot of space left over, and it is not obvious that there is no way to pack in a 13th sphere. (In fact, there is so much extra space that any two of the 12 outer spheres can exchange places through a continuous movement without any of the outer spheres losing contact with the center one.) This was the subject of a famous disagreement between mathematicians Isaac Newton and David Gregory. Newton thought that the limit was 12, and Gregory that a 13th could fit. The question was not resolved until 1874; Newton was correct.[1] In four dimensions, it was known for some time that the answer is either 24 or 25. It is easy to produce a packing of 24 spheres around a central sphere (one can place the spheres at the vertices of a suitably scaled 24-cell centered at the origin). As in the three-dimensional case, there is a lot of space left over—even more, in fact, than for n = 3—so the situation was even less clear. Finally, in 2003, Oleg Musin proved the kissing number for n = 4 to be 24, using a subtle trick.[2]

The kissing number in n dimensions is unknown for n > 4, except for n = 8 (240), and n = 24 (196,560).[3][4] The results in these dimensions stem from the existence of highly symmetrical lattices: the E8 lattice and the Leech lattice. In fact, the only way to arrange spheres in these dimensions with the above kissing numbers is to center them at the minimal vectors in these lattices. There is no space whatsoever for any additional balls.

So what is the glue that binds all these spheres in in the complexities that they are arrange in the dimensions and all that we shall have describe gravity along with the very nature of the particle that describe the reality and makeup that we have been dissecting with the collision process?

As with good teachers, and "exceptional ideas" they are those who gather, as if an Einstein crosses the room, and for those well equipped, we like to know what this energy is. What is it that describes the nature of such arrangements, that we look to what energy and mass has to say about it's very makeup and relations. A crystal in it's molecular arrangement?

Look's like grapefruit to me, and not oranges?:)

Symmetry's physical dimension by Stephen Maxfield

Each orange (sphere) in the first layer of such a stack is surrounded by six others to form a hexagonal, honeycomb lattice, while the second layer is built by placing the spheres above the “hollows” in the first layer. The third layer can be placed either directly above the first (producing a hexagonal close-packed lattice structure) or offset by one hollow (producing a face-centred cubic lattice). In both cases, 74% of the total volume of the stack is filled — and Hales showed that this density cannot be bettered.....

In the optimal packing arrangement, each sphere is touched by 12 others positioned around it. Newton suspected that this “kissing number” of 12 is the maximum possible in 3D, yet it was not until 1874 that mathematicians proved him right. This is because such a proof must take into account all possible arrangements of spheres, not just regular ones, and for centuries people thought that the extra space or “slop” in the 3D arrangement might allow a 13th sphere to be squeezed in. For similar reasons, Hales’ proof of greengrocers’ everyday experience is so complex that even now the referees are only 99% sure that it is correct....

Each sphere in the E8 lattice is surrounded by 240 others in a tight, slop-free arrangement — solving both the optimal-packing and kissing-number problems in 8D. Moreover, the centres of the spheres mark the vertices of an 8D solid called the E8 or “Gosset” polytope, which is named after the British mathematician Thorold Gosset who discovered it in 1900.

Coxeter–Dynkin diagram

The following article is indeed abstract to me in it's visualizations, just as the kaleidescope is. The expression of anyone of those spheres(an idea is related) in how information is distributed and aligned. At some point in the generation of this new idea we have succeeded in in a desired result, and some would have "this element of nature" explained as some result in the LHC?



A while ago I related Mendeleev's table of elements, as an association, and thought what better way to describe this new theory by implementing "new elements" never seen before, to an acceptance of the new 22 new particles to be described in a new process? There is an "inherent curve" that arises out of Riemann's primes, that might look like a "fingerprint" to some. Shall we relate "the sieves" to such spaces?

At some point, "this information" becomes an example of a "higher form "realized by it's very constituents and acceptance, "as a result."

Math Will Rock Your World by Neal Goldman

By the time you're reading these words, this very article will exist as a line in Goldman's polytope. And that raises a fundamental question: If long articles full of twists and turns can be reduced to a mathematical essence, what's next? Our businesses -- and, yes, ourselves.

Numerical Relativity and the Human Experience?

"I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Donald (H. S. M.) Coxeter

I contrast the nature of Numerical Relativity to the computer and the way we would think human consciousness could have been linked in it's various ways. Who hasn't thought that the ingenuity of the thinking mind could not have been considered the Synapse and the Portal to the thinking Mind?:)

Also think about what can be thought here as Gerardus t" Hooft asked as to think about in the limitations of what can be thought in relation to computerizations.

There is something to be said here about what conscious is not limited too. It is by it's very nature "leading perspective" that we would like to have all these variables included in or assertions of what we can see while providing experimental data to the mind set of those same computerization techniques?

Numerical Relativity Mind Map

So we of course like to see the mind's ingenuity( computerized or otherwise) when it comes to how it shall interpret what is the road to understanding that gravity is seen in Relativities explanation.

Source:Numerical Relativity Code and Machine Timeline


It is a process by which the world of blackholes come into viewing in it's most "technical means providing the amount of speed and memory" that would allow us to interpret events in the way we have.

The information has to be mapped to computational methodology in order for us to know what scientific value scan be enshrined in the descriptions of the Blackhole. Imagine that with current technologies we can never go any further then what we can currently for see given the circumstances of this technology?


Source:Expo/Information Center/Directory-Spacetime Wrinkles Map

So on the one hand there is an "realistic version" being mapped according to how we develop the means to visualize of what nature has bestowed upon us in the according to understanding Blackhole's and their Singularities.

Numerical Relativity and Math Transferance

Part of the advantage of looking at computer animations is knowing that the basis of this vision that is being created, is based on computerized methods and codes, devised, to help us see what Einstein's equations imply.

Now that's part of the effort isn't it, when we see the structure of math, may have also embued a Dirac, to see in ways that ony a good imagination may have that is tied to the abstractions of the math, and allows us to enter into "their portal" of the mind.

NASA scientists have reached a breakthrough in computer modeling that allows them to simulate what gravitational waves from merging black holes look like. The three-dimensional simulations, the largest astrophysical calculations ever performed on a NASA supercomputer, provide the foundation to explore the universe in an entirely new way.

Scientists are watching two supermassive black holes spiral towards each other near the center of a galaxy cluster named Abell 400. Shown in this X-ray/radio composite image are the multi-million degree radio jets emanating from the black holes. Click on image to view large resolution. Credit: X-ray: NASA/CXC/AIfA/D.Hudson & T.Reiprich et al.; Radio: NRAO/VLA/NRL

According to Einstein's math, when two massive black holes merge, all of space jiggles like a bowl of Jell-O as gravitational waves race out from the collision at light speed.

Previous simulations had been plagued by computer crashes. The necessary equations, based on Einstein's theory of general relativity, were far too complex. But scientists at NASA's Goddard Space Flight Center in Greenbelt, Md., have found a method to translate Einstein's math in a way that computers can understand.

Quantum Gravity

Now their is a strange set of circumstance here that would leave me to believe, that the area of quantum gravity has lead Numerical Relativity to it's conclusion? Has the technology made itself feasible enough to explore new experimental data that would allow us to further interpret nature in the way it shows itself? What about at the source of the singularity?

See: Dealing with a 5D World

I would not be fully honest if I did not give you part of the nature of abstract knowledge being imparted to us, if I did not include the "areas of abstractness" to include people who help us draw the dimensional significance to experience in these mathematical ways. It is always good to listen to what they have to say so that we can further developed the understanding of what becomes a deeper recognition of the way nature unfolds of itself.

There are two reasons that having mapped E8 is so important. The practical one is that E8 has major applications: mathematical analysis of the most recent versions of string theory and supergravity theories all keep revealing structure based on E8. E8 seems to be part of the structure of our universe.

The other reason is just that the complete mapping of E8 is the largest mathematical structure ever mapped out in full detail by human beings. It takes 60 gigabytes to store the map of E8. If you were to write it out on paper in 6-point print (that's really small print), you'd need a piece of paper bigger than the island of Manhattan. This thing is huge. Emphasis and underlined, my addition.

Computer Language and Math Joined from Artistic Impressionism?

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."- Lisa Randall

THOMAS BANCHOFF has been a professor of mathematics at Brown University in Providence, Rhode Island, since 1967. He has written two books and fifty articles on geometric topics, frequently incorporating interactive computer graphics techniques in the study of phenomena in the fourth and higher dimensions

The marriage between computer and math language(Banchoff) I would say would be important from the prospective of displaying imaging, seen in the development of abstract language as used in numerical relativity? Accummalated data gained from LIGO operations. Time variable measures?

See:Computer Graphics In Mathematical Research

Where Spacetime is flat?

......A Condensative Result exists. Where "energy concentrates" and expresses outward.

I mean if I were to put on my eyeglasses, and these glasses were given to a way of seeing this universe, why not look at the whole universe bathed in such spacetime fabric?

This a opportunity to get "two birds" with one stone?

I was thinking of Garrett's E8 Theory article and Stefan's here.

On March 31, 2006 the high-resolution gravity field model EIGEN-GL04C has been released. This model is a combination of GRACE and LAGEOS mission plus 0.5 x 0.5 degrees gravimetry and altimetry surface data and is complete to degree and order 360 in terms of spherical harmonic coefficients.

High-resolution combination gravity models are essential for all applications where a precise knowledge of the static gravity potential and its gradients is needed in the medium and short wavelength spectrum. Typical examples are precise orbit determination of geodetic and altimeter satellites or the study of the Earth's crust and mantle mass distribution.

But, various geodetic and altimeter applications request also a pure satellite-only gravity model. As an example, the ocean dynamic topography and the derived geostrophic surface currents, both derived from altimeter measurements and an oceanic geoid, would be strongly correlated with the mean sea surface height model used to derive terrestrial gravity data for the combination model.

Therefore, the satellite-only part of EIGEN-GL04C is provided here as EIGEN-GL04S1. The contributing GRACE and Lageos data are already described in the EIGEN-GL04C description. The satellite-only model has been derived from EIGEN-GL04C by reduction of the terrestrial normal equation system and is complete up to degree and order 150.

How many really understand/see the production of gravitational waves in regards to Taylor and Hulse?

To see Stefan's correlation in terms of "wave production" is a dynamical quality to what is still be experimentally looked for by LIGO?

As scientists, do you know this?

6:41 AM, November 11, 2007

See here

Thus the binary pulsar PSR1913+16 provides a powerful test of the predictions of the behavior of time perceived by a distant observer according to Einstein's Theory of Relativity.

Since we know the theory of Relativity is about Gravity, then how is it the applications can be extended to the way we see "anew" in our world?

A sphere, our earth, not so round anymore.

Uncle has tried to correct me on "isostatic adjustment."

Derek Sears, professor of cosmochemistry at the University of Arkansas, explains. See here

Planets are round because their gravitational field acts as though it originates from the center of the body and pulls everything toward it. With its large body and internal heating from radioactive elements, a planet behaves like a fluid, and over long periods of time succumbs to the gravitational pull from its center of gravity. The only way to get all the mass as close to planet's center of gravity as possible is to form a sphere. The technical name for this process is "isostatic adjustment."

With much smaller bodies, such as the 20-kilometer asteroids we have seen in recent spacecraft images, the gravitational pull is too weak to overcome the asteroid's mechanical strength. As a result, these bodies do not form spheres. Rather they maintain irregular, fragmentary shapes. K. Shumacker. Scientific America

Do not have time to follow up at this moment.

7:02 AM, November 11, 2007

.....and here.


In context of the post and differences, I may not have pointed to the substance of the post, yet I would have dealt with my problem in seeing.

In general terms, gravitational waves are radiated by objects whose motion involves acceleration, provided that the motion is not perfectly spherically symmetric (like a spinning, expanding or contracting sphere) or cylindrically symmetric (like a spinning disk).

A simple example is the spinning dumbbell. Set upon one end, so that one side of the dumbell is on the ground and the other end is pointing up, the dumbbell will not radiate when it spins around its vertical axis but will radiate if it tumbles end-over-end. The heavier the dumbbell, and the faster it tumbles, the greater is the gravitational radiation it will give off. If we imagine an extreme case in which the two weights of the dumbbell are massive stars like neutron stars or black holes, orbiting each other quickly, then significant amounts of gravitational radiation would be given off.

Given the context of the "whole universe" what is actually pervading, if one did not include gravity?



So singularities are pointing to the beginning(i), yet, we do not know if we should just say, the Big Bang, because, one would had to have calculated the energy used and where did it come from "previous" to manifest?

So some will have this philosophical position about "nothing(?)," and "everything as already existing."

Wherever there are no gravitational waves the space time is flat. One would have to define these two variances. One from understanding the relation to "radiation" and the other "perfectly spherically symmetric."

E8 and the Blackhole

"I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Donald (H. S. M.) Coxeter

There are two reasons that having mapped E8 is so important. The practical one is that E8 has major applications: mathematical analysis of the most recent versions of string theory and supergravity theories all keep revealing structure based on E8. E8 seems to be part of the structure of our universe.

The other reason is just that the complete mapping of E8 is the largest mathematical structure ever mapped out in full detail by human beings. It takes 60 gigabytes to store the map of E8. If you were to write it out on paper in 6-point print (that's really small print), you'd need a piece of paper bigger than the island of Manhattan. This thing is huge.

See:Pasquale Del Pezzo and E8 Origination?-Monday, March 19, 2007

If I had thought there was a way to describe the "interior" of the blackhole, it would be by recognizing the dimensionality the blackhole had to offer. One had to know where to locate "this place in the natural world." If we had understood the energy values of the particle world colliding(that space and frame of reference, then what were we finding that such a place in dimensionality could exist in the natural world? Yoyu had to accept that there was dynamical moves that werre being defined as a possiility.

Thus RHIC is in a certain sense a string theory testing machine, analyzing the formation and decay of dual black holes, and giving information about the black hole interior.The RHIC fireball as a dual black hole-Horatiu Nastase

So what ways would allow us to do this, and this is part of the idea that came to me as I was thinking about the place where all possibilities could exist. Yet, what existed as "moduli form in the valleys" was being extended. So I am connecting other things here too.

Cascading Showers from the Cosmos

3) It is claimed that cosmic rays can energy exceeding that of colliders, and they have not caused trouble, suggesting that colliders will not cause trouble either. However, the analogy is not precise. It assumes two things that may not be true. First, cosmic ray center of mass energy exceeding that of colliders has never been measured directly. Measurements that seem to show this are based on showers of secondary particles. Second, the product of a collision between a cosmic ray and an earth particle will always be moving at an appreciable fraction of the speed of light. If it has a small capture radius, it will always pass right through earth like a neutrino. The product of a collider collision can (sometimes) be moving at less than escape velocity from earth. If so, it will fall into earth where it will have forever to accrete other matter. Some calculations show rapid accretion.

See: Risk Evaluation Forum

Using this above as one basis of the argument, it was by these assumptions that I too was convinced things would be okay. There are a lot of things that go with this statement that currently is not expressed given current information in regards to Pierre Auger experiments. That when clearly seen in the light of current research into LHC, does not allow one to take in all that they should be.

Contact

Go back to John Ellis and current research if you must, and thinking in terms of the cosmos. It's infancy, and one does not disregard the "origins and beginnings" of this universe. Are there reasons that are less then desired that would govern any legal defence team based on some "religious affiliation" and driven from this religious context? I hope not.



We would not want some Woitian backlash, as done with string theory, from a intelligent design standpoint, as a recognized motived factor in that legal defense. It is far beyond me that I ask these associative questions, yet, these images come to mind when ever the establishment hosting the world's collective scientists, is confronted by the very issues that seem evasive in regards to safety?

Energies Used in Particle Creation



It would behove any person to take the time to travel to the links I am supplying, to help you absorb as much information as possible.With the full intention that what I am describing does have a distillation process that will become very simple in qualitative design.



Finding the energy range with which we are dealing within our colliders, has awakened the realization of the complexity dimensional attributes would have considering E8.

"I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Donald (H. S. M.) Coxeter

The complexity of the blackhole would have allowed the possibilities of describing the source of "all dimensional attributes" knowing that the collapse of the blackhole would bring temperatures to the point of the quark Gluon plasma. What would be happening to allow such complexity?

This basis of thought on my part is, "the equivalence determined" and thought about in terms of Lagrangian considerations. This another topic. But does deal with the understanding of the potential microscopic blackholes that could be produced, determined by the energy levels

Thus RHIC is in a certain sense a string theory testing machine, analyzing the formation and decay of dual black holes, and giving information about the black hole interior.

See:Are Strangelets Natural?

LHC Safety?

I am writing this blog entry because of Walter's comments on the side.

It is very hard for me knowing that there is a train of thought developed through my research. This question of cascading showers, were with the understanding of "energy events" that allowed us to see a "greater plethora of mapping" that would direct us to the very essence of symmetry breaking, based on experimental processes herein this blog described.

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

See: How Particles Came to Be

In doing my own research, I tried to follow the thinking of the literature presented on the topic of microscopic blackholes. Now there was to my understanding a theoretical position assumed, from what we understood when dealing with the topic, and the understanding of what Cern was to produce.

Fig. 2. Image showing how an 8 TeV black hole might look in the ATLAS detector (with the caveat that there are still uncertainties in the theoretical calculations).

Now to me the basis of settling the questions of safety, were answered by association of "what was natural" within the domains of these cascading particle showers in terms of these cosmic rays.

If we were after the origins and beginnings to our universe, we were in essence, describing and mapping the beginning times of these particle showers. Also, the dimensional attributes of the interior of the blackhole.

Nurturing Creativity

See here and here


It looks as if moderation, or maybe technical problems, has set in for me at Cosmic Variance. So I have to go from the last statement made there by Lee that I was allowed to contribute. To continue with the points I am making.

I was glad to see Jacques was continuing where David B seems to have decided the futility of dealing with these issues of the String theory backlash.

Lee Smolin:When there was little selection we naturally got a wide diversity of types of scientists, which was good for science. My view is that we need that diversity, we need both the hill climbers and the valley crossers, the technical masters and the seers full of questions and ideas.

Raphael Bousso and Joseph Polchinski in "The String Theory Landscape" September 2004 Scientific issue speak exactly to what Lee is saying and descriptively allow us to see the pattern underlying Lee's comment. Maybe George Musser will release it for the group to inspect here

Take full note of the diagrams.

See OFF THE HOOK. Line-by-line crocheting instructions that tell where to increase or decrease numbers of stitches create the global shape of the Lorenz manifold.Univ. of Bristol

Clifford:Hooking Up Manifolds

The artlcle goes a great deal into the story of how mathematician Hinke Osinga and her partner mathematician Bernd Krauskopf got into this, and why they find it useful. You’ll also hear from mathematicians Carolyn Yackel, Daina Taimina, and Sarah-Marie Belcastro. This has been going on for a while, and there are even published scientific papers with crocheting instructions for various manifolds! How did I miss out on this?! This is great!

If you did not continue with understanding the "topography of the energy involved" in terms of what the string theory landscape was doing, then you would have never understood the "hills and valleys" in the context of string theory landscape being described?

HYPERBOLIC FABRIC. Many of the lines that could be inscribed on this crocheted hyperbolic plane curve away from each other, defying Euclid's parallel postulate.
Taimina

IN retrospect decisions we make will always resound with what we should have done, but that misses the boat when coming to the "creative abilities?" What we see may "institute a productive research group?" You exchange one for another?

Lee Smolin:Is string theory in fact perturbatively finite? Many experts think so. I worry that if there were a clear way to a proof it would have been found and published, so I find it difficult to have a strong expectation, either way, on this issue.

The fact that a way had been describe in terms of developing the "Triple Torus" speaks to the continued development of the string theory landscape? How could you conclusively finish off this statement and then from it describe the state of the union, when this had already been explained technically?

We say that E8 has rank 8 (the maximum number of mutually commutative degrees of freedom), and dimension 248 (as a manifold). This means that a maximal torus of the compact Lie group E8 has dimension 8. The vectors of the root system are in eight dimensions, and are specified later in this article. The Weyl group of E8, which acts as a symmetry group of the maximal torus by means of the conjugation operation from the whole group, is of order 696729600.

You had to see the context of the triple torus in relation too where the string landscape places were placing these modular forms. If I had said E8 and the continued development of modular form, what would this represent?

The complexity of the forms themself are limited and finite so how could one claim that such work on the landscape is futile in regards to infinities?

The Elixir of the Bee Community

You should know that that the names of the Bee people have their names protected, to protect the community at large. Some larger human species, like to use the benefits of this society, without recognizing the constructive efforts that goes into this elixir Production.

Marc D. Hauser:

We know that that kind of information is encoded in the signal because people in Denmark have created a robotic honey bee that you can plop in the middle of a colony, programmed to dance in a certain way, and the hive members will actually follow the information precisely to that location. Researchers have been able to understand the information processing system to this level, and consequently, can actually transmit it through the robot to other members of the hive.

See Bumblebee Wing Rotations and Dancing

Many times people have used Ant world to illustrate their ideas, but the time has come, that the relationship to perspective dynamics at that level should think about the vast literature of Bee people.

The second of five Lagrangian equilbrium points, approximately 1.5 million kilometers beyond Earth, where the gravitational forces of Earth and Sun balance to keep a satellite at a nearly fixed position relative to Earth.

See Second of Five Lagrangian Equilibrium Points

One should not think these people have been disassociated from reality, and that it has only been our ignorance of the economics and flight patterns, that we failed to see the dynamical community that bee propagation goes through, in order to continue it's rich development. The elixir production is coming out of that community.

There are two reasons that having mapped E8 is so important. The practical one is that E8 has major applications: mathematical analysis of the most recent versions of string theory and supergravity theories all keep revealing structure based on E8. E8 seems to be part of the structure of our universe.

The other reason is just that the complete mapping of E8 is the largest mathematical structure ever mapped out in full detail by human beings. It takes 60 gigabytes to store the map of E8. If you were to write it out on paper in 6-point print (that's really small print), you'd need a piece of paper bigger than the island of Manhattan. This thing is huge.

See Solidification of Geometrical Presence

Flower pollination is a interesting thing having considered the world that the Bee people live in. After all, the dynamics and travel used, one could not help being enamoured with the naturalness with which one may try to reproduce in human mechanistic movement, that the Bee people live and breathe.

Humanistic intelligences is a larger format, to what they do in that Bee community?

Cell construction provides for the further propagation of the community, but no where do the Bee people give the particulates of the cell construction? Humanistic intelligences only see the community with regards to the Bee movements :)The Bee people have a greater depth to what is seen.

Observing the community at large, the Bee people have much more to present then thinking just in the way they work. Who is Navier Stokes of the humanistic intelligences to think only he could reveal anomalistic perception in the nature of viscosity, not to think there is relativistic conditions that the Bee people bring to reductionism views in physics?

Worker bees perform a host of tasks from cleaning the hive cells to looking after the larvae

The workers have a variety of tasks to perform – some collect nectar from flowers, others pollen, some are engaged in constructing new combs, or looking after the developing larvae, some perform the duty of cleaning the cells or feeding the larvae on special secretion that they regurgitate from their mouth parts. In these insects the exact task of any individual depends largely on its age, although there is a certain flexibility, depending on the requirements of the hive.

So I've taken a different tack here. If it is so hard for the community at large to comprehend that extra dimensional thinking then there has to be some way in which we as lay people can envision the acrobatics of a busy bee and their flight plans? What the community is all about. Who is doing what?

How many dimensions are there?

Consider ants crawling on a tabletop. In their daily experience, they can explore only 2 dimensions, those of the table surface. They may see a bee up flying, or occasionally landing on the table top, but that 3rd dimension is something they can only see or imagine, not experience. Perhaps we are in an analogous situation. Instead of a tabletop, we live in a 3-dimensional space called 3-brane (a name generalizing 2-brane, i.e., membrane). For some reason, we (i.e., atoms, molecules, photons etc.) are stuck in this 3-brane, even though there are 6 additional dimensions out there. Gravity, like the bee, can go everywhere. We call this the brane world, a rather natural phenomenon in superstring theory. At the moment, physicists are working hard to understand this scenario better and to find ways to experimentally test this idea.

The Bee people had graduated from the world of the ant people, jsut by their evolutionary timeline. They were "much more visionary" then the ant people. Because they could leave their three dimensional world of the table top, and pop into ant world's frame of reference. Ant people were never the wiser. Just that, Bee people existed.

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

See Wolf-Rayet star

Brane theory development needed a boost from the Bee people. Not only now do we understand the "dynamical thinking that goes with the Bee's flight patterns," we are now thinking, hey, "can these things apply" to the current solutions the humanistic intelligences persevere to unfold in their space travels?

Not just "our waist lines" as some might think in regards to "lensing" and the circles we apply in "computerize efforts." The range of territory of the Bee's community is well considered?

Solidification of Geometrical Presence

While I might infer the "attributes of Coxeter here," it is with the understanding such a dimensional perspective which has it's counterpart in the result of what manifests as matter creations. Yet we have taken our views down to the "powers of ten" to think of what could manifest even before we see the result in nature.

When you go to the site by PBS of where, Nano: Art Meets Science, make sure you click on the lesson plan to the right.



Buckyballs

Visitors' shadows manipulate and reshape projected images of "Buckyballs." "Buckyball," or a buckminsterfullerene molecule, is a closed cage-structure molecule with a carbon network. "Buckyball" was named for R. Buckminster "Bucky" Fuller (1895-1983), a scientist, philosopher and inventor, best known for creating the geodesic dome.
Photo Credit: © 2003 Museum Associates/Los Angeles County Museum

Fundamentally the properties of materials can be changed by nanotechnology. We can arrange molecules in a way that they do not normally occur in nature. The material strength, electronic and optical properties of materials can all be altered using nanotechnology.

See Related information on bucky balls here in this site. This should give some understanding of how I see the greater depth of what manifest in nature, as solids in our world, has some "other" possibilities in dimensional attribute, while it is given association to the mathematical prowess of E8.

I do not know of many who will take in all that I have accumulated in regards to how one may look at their planet, can have the depth of perception that is held in to E8.?

One may say what becomes of the world as it manifest into it's constituent parts, has this energy relation, that it would become all that is in the design of the world around us.



While some scientists puzzle as to the nature of the process of E8, little did they realize that if you move your perception to the way E8 is mapped to 248 dimensions, the image while indeed quite pleasing, you see as a result.

It can include so much information, how would you know that this object of mathematics, is a polytrope of a kind that is given to the picture of science in the geometrical structure of the bucky ball or fullerene.

Allotropes



Diamond and graphite are two allotropes of carbon: pure forms of the same element that differ in structure.

Allotropy (Gr. allos, other, and tropos, manner) is a behaviour exhibited by certain chemical elements: these elements can exist in two or more different forms, known as allotropes of that element. In each different allotrope, the element's atoms are bonded together in a different manner.

For example, the element carbon has two common allotropes: diamond, where the carbon atoms are bonded together in a tetrahedral lattice arrangement, and graphite, where the carbon atoms are bonded together in sheets of a hexagonal lattice.

Note that allotropy refers only to different forms of an element within the same phase or state of matter (i.e. different solid, liquid or gas forms) - the changes of state between solid, liquid and gas in themselves are not considered allotropy. For some elements, allotropes can persist in different phases - for example, the two allotropes of oxygen (dioxygen and ozone), can both exist in the solid, liquid and gaseous states. Conversely, some elements do not maintain distinct allotropes in different phases: for example phosphorus has numerous solid allotropes, which all revert to the same P4 form when melted to the liquid state.

The term "allotrope" was coined by the famous chemist Jöns Jakob Berzelius.

Pasquale Del Pezzo and E8 Origination?

"I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Donald (H. S. M.) Coxeter

There are two reasons that having mapped E8 is so important. The practical one is that E8 has major applications: mathematical analysis of the most recent versions of string theory and supergravity theories all keep revealing structure based on E8. E8 seems to be part of the structure of our universe.

The other reason is just that the complete mapping of E8 is the largest mathematical structure ever mapped out in full detail by human beings. It takes 60 gigabytes to store the map of E8. If you were to write it out on paper in 6-point print (that's really small print), you'd need a piece of paper bigger than the island of Manhattan. This thing is huge.

Clifford of Asymptotia drew our attention to this for examination and gives further information and links with which to follow.

He goes on to write,"Let’s not get carried away though. Having more data does not mean that you worked harder to get it. Mapping the human genome project involves a much harder task, but the analogy is still a good one, if not taken too far."

Of course since the particular comment of mine was deleted there, and of course I am okay with that. It did not mean I could not carry on here. It did not mean that I was not speaking directly to the way these values in dimensional perspective were not being considered.

Projective Geometries?

A theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry.

There had to be a route to follow that would lead one to think in such abstract spaces. Of course, one does not want to be divorced from reality. So one should not think that because the geometry of GR is understood, that you think nothing can come from the microseconds after the universe came into expression.

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

The Holy Grail sure comes up lots doesn't it:) Without invoking the pseudoscience that Peter Woit spoke of. I thought, if they could use Babar, and Alice then I could use the Holy Grail?

See more info on Coxeter here.

Like Peter I will have to address the "gut feelings" and the way Clifford expressed it. I do not want to practise pseudoscience as Peter is about the landscape.:)



When ones sees the constituent properties of that Gossett polytope 4₂₁ in all it's colours, the complexity of that situation is quite revealing. Might we not think in the time of supergravity, gravity will become weak, in the matter constitutions that form.

As in Neutrino mixing I am asking you to think of the particles as sound as well as think them in relation to the Colour of Gravity. If you were just to see grvaity in it's colourful design and what value that gravity in face of the photon moving within this gravitational field?

We detect the resulting "wah-wah-wah" in properties of the neutrino that appear and disappear. For example, when neutrinos interact with matter they produce specific kinds of other particles.

For example, when neutrinos interact with matter they produce specific kinds of other particles. Catch the neutrino at one moment, and it will interact to produce an electron. A moment later, it might interact to produce a different particle. "Neutrino mixing" describes the original mixture of waves that produces this oscillation effect.

The "geometry of curvature" had to be implied in the outcome, from that quantum world? Yet at it's centre, what is realized? You had to be lead there in terms of particle research to know that you are arriving at the "crossover point." The superfluid does this for examination.

5. Regular polytope: If you keep pulling the hypercube into higher and higher dimensions you get a polytope. Coxeter is famous for his work on regular polytopes. When they involve coordinates made of complex numbers they are called complex polytopes.

Pasquale Del Pezzo, Duke of Cajanello, (1859–1936), was "the most Neapolitan of Neapolitan Mathematicians".

He was born in Berlin (where his father was a representative of the Neapolitan king) on 2 May 1859. He died in Naples on 20 June 1936. His first wife was the Swedish writer Anne Charlotte Leffler, sister of the great mathematician Gösta Mittag-Leffler (1846-1927).

At the University of Naples, he received first a law degree in 1880 and then in 1882 a math degree. He became a pre-eminent professor at that university, teaching Projective Geometry, and remained at that University, as rector, faculty president, etc.

He was mayor of Naples starting in 1919, and he became a senator in the Kingdom of Naples.

His scientific achievements were few, but they reveal a keen ingenuity. He is remembered particularly for first describing what became known as a Del Pezzo surface. He might have become one of the strongest mathematicians of that time, but he was distracted by politics and other interests.

So what chance do we have, if we did not think this geometry was attached to processes that would unfold into the bucky ball or the fullerene of science. To say that the outcome had a point of view that is not popular. I do not count myself as attached to any intelligent design agenda, so I hope people will think I do not care about that.

NATHAN MYHRVOLD

I found the email debate between Smolin and Susskind to be quite interesting. Unfortunately, it mixes several issues. The Anthropic Principle (AP) gets mixed up with their other agendas. Smolin advocates his CNS, and less explicitly loop quantum gravity. Susskind is an advocate of eternal inflation and string theory. These biases are completely natural, but in the process the purported question of the value of the AP gets somewhat lost in the shuffle. I would have liked more discussion of the AP directly

See here for more information

So all the while you see the complexity of that circle and how long it took a computer to map it, it has gravity in it's design, whether we like to think about it or not?

But of course we are talking about the symmetry and any thing less then this would have been assign a matter state, as if symmetrical breaking would have said, this is the direction you are going is what we have of earth?

Isostatic Adjustment is Why Planets are Round?

While one thinks of "rotational values" then indeed one would have to say not any planets is formed in the way the sun does. Yet, in the "time variable understanding" of the earth, we understand why it's shape is not exactly round.



Do you think the earth and moon look round if your were considering Grace?

On the moon what gives us perspective when a crater is formed to see it's geological structure? It's just not a concern of the mining industry, as to what is mined on other orbs, but what the time variable reveals of the orbs structure as well.



Clementine color ratio composite image of Aristarchus Crater on the Moon. This 42 km diameter crater is located on the corner of the Aristarchus plateau, at 24 N, 47 W. Ejecta from the plateau is visible as the blue material at the upper left (northwest), while material excavated from the Oceanus Procellarum area is the reddish color to the lower right (southeast). The colors in this image can be used to ascertain compositional properties of the materials making up the deep strata of these two regions. (Clementine, USGS slide 11)

See more here

Struggle within Self Becomes Strugge of Nation

The link post titled nameabove in title above will have to be corrected, and can be done in other places, but for now it has to remain as it is here.

Those CV people are Radicals for change, eh?:) See here, here, here?

"If you are not with us you are against us". Imagine such sentiments even within your own country? Could such a country become divisive within itself, that there is the emergence of a "left" and "right." and that you have just now assume the dubious "left." :)

I'm thinking of Sean's entry on perspective. The sound of "one hand clapping." Sort of the recognition, that if you change the "idealization to nonviolence," it acted as a force with which anger and aggressive attitudes of the "right" to control behavior of the left, had nothing against with which it could push?

Reserve one's judgement on the speech? :( What am I asking? Would automatically send up the hackles Qui! NOn!

Seeing the same cartoonist construct three different pieces on the same topic, from three standpoints, is really an edifying experience. Not only for my meager acuity in the visual arts, but to understand message and framing. I’ll share these three cartoons with you, as well as the rough draft.

There would be no sound. There would be no clapping. Just the recognition that "non violent" action would call sane citizens of the state, to recognzie diversity in opinion, and not polarize around such distinctions.

I know it's hard walking the (A)middleway. Sometimes this "heartway for expression" has to have applications moved to the head for correct thinking, least we are circumvented to the childish antics of emotive reactions in the probable future.

The "child" is the future, and to continunally challenge our emotive constructs( these things well imprinted in our own realities) that we say we cannot change of what has already happened? We can certainly change, how we will react in the future by challening these perspectives. A Clear mind and consise thinking, to combat what is embedded, will have fortunate consequences, although, the struggle to implement such a strategy, must unfold in order to change how we see into that future.

I am "constantly fighting"( my own battle with self) to bring sane recognition out of the historical background and "relative phrases" to situations that might become the struggle of nations, if one had thought to extend it's appliciability to such lengths? It's not that you fight your parents, and all that has been encoded in you, or that you change the reactionary way( this is part of our psychological makeup) in which you will emotively react(a "positive anger" for change is possible), but that there is a third choice, and one in which a better logic would materialize? Held to political distinctions that we had all might revert too.

That the emotive forced garnered a better visulaization then, not to be lead, by illusions of the religious right or to default on the irreligiousness of the left(?).

Would I have just been as guilty here in that last statement?

Now we've arrived at the end of the century, where crime, moral chaos, and politics driven by the often hollow sophistications of sociology and psychology all alert us to the breakdown of too many previous assumptions, particularly the coming apart of what might be called our ethical agreements with one another. Late capitalism, in apparent triumph, seems to encourage self-interest over any lingering sense of a commonwealth.

Who then are the better nation builders? That to continue to perfect this war that rages within ourselves would take this to the political stage and make the war happen on a much wider and divisive scale?

So who then who would the better nation builders be? Those that seek the third choice and the choice that recognizes change is very fast and becoming. That there is no time standing, always new.

As the Discussion continues

The point is that if any of you, "censored" like Peter likes too, then I would have thought the way they censored your comments Mark and Joanne, would have been felt an affrontation about getting to the heart of issues, "equally frustating" in other venues.

I recognize your efforts as well of doing "something" amidst such censorhips. Getting to the heart of issues against "flagrant attitudes" politicized, requires that we think twice about what some who contribute, and what cannot work to the advanges of clear thinking?

A double edged sword? :)

Would one defend another of equal stature in regards to science who ID intelligent conversation as to express one's own agenda not deterrred as "negative way" to the right way? :)

I would rather focus on "nation building" as you have.

How has profound thinking been changed? I think the teachers are suppose to let us decide instead of them deciding for us. We are suppose to find our way as you lay correct infomration before us instead of packaging it, and saying ,this is wrong becuase I say so?

Maybe these are the failing attributes as parents, we assign to our children in those hidden meme's?:)