Casting Out Nines, Structure and Function of Real Numbers

[junglelord]

I thought I pulled a spelling dodo. But your both my Angels and my Angles.

[lizzie]

Dyslexic means that you can read/write using both left and right sides of the brain and can function in perfect harmony with the Infinite Ninth. Mother Nature honors only the Infinite Ninth. In the Universe the left hand always knows what the right is doing and vice versa; it's only arrogant humans who think they are so smart that they need to use one side of their brains.

Famous dyslexic people
http://www.dyslexia-test.com/famous.html

[altonhare]

altonhare said: we will need to nail down exactly what he/you mean by "universe".

Our Universe? Our Universe and its mirror opposite? Or Multiverses?

What is universe?

[junglelord]

I am dsylexic. I am also the rarest personality type INFJ (1%).
I am also always testing Whole Brained since I was 16 and first did a hemisphere lateralization quiz.
I am a drummer and Ambidextrist in all four limbs. Four limb independance is real important.

Thats a whole brain job. I am not talking basic 4/4. I am talking Thomas Lang, bend your mind Independance! Playing four different tempos for each limb, overlay any 4 independent patterns top to bottom, left to right...with stick twirling on top!


You have no idea how much open minded co-ordination that requires. I have been using Hemi-Sync CD's with my daily exercise on the kit. I have used Hemi-Sync as a way to increase whole brain functions since I was 28. I thought one day I need to use the Hemi-Sync to overcome the lessons that Thomas Lang had developed. It has been a huge boost to my ability to over come mental hiccups of single minded functions. While we are on this subject. There is a very effective exercise program developed from whole brain studies. It is called Brain Gym.

Brain Gym is very good at helping Dsylexic and ADD, ADHD, children over come their hemisphere hic-cups via cross body co-ordination patterns. The neurological expression of handiness and lateral thinking is 2-D. Half brained and one handed. On the other two hands how ever, ambidextrist and whole brain thinking go hand in hand.
LOL

[lizzie]

http://typelogic.com/infj.html

[junglelord]

I got two packages of Green so I can work on Maxwell's 20 EM Quaternions

Green Quaternions, Tenacious Symmetry, and Octahedral Zome

We describe a new Zome-like system that exhibits octahedral rather than icosahedral symmetry, and illustrate its application to 3-dimensional projections of 4-dimensional regular polychora. Furthermore, we explain the existence of that system, as well as an infinite family of related systems, in terms of Hamilton’s quaternions and the binary icosahedral group. Finally, we describe a remarkably tenacious aspect of H4 symmetry that “survives” projection
down to three dimensions, reappearing only in 2-dimensional projections.

1. Introduction
This is a report on a journey of discovery we have shared over the past year, as we endeavored to gain deeper
insights into the mathematics surrounding the Zome System of Zometool, Inc. This collaboration has borne
some intriguing fruit, specifically the results we describe in this paper concerning generalizations of Zome,
and a surprising aspect of symmetry and projection.

Our interest in Zome centers on the way that it hints at deep underlying mathematics: serendipity becomes commonplace, and startling coincindences come to be expected. The “octahedral Zome” and “green quaternions”
of our title were quite surprising initially, but turn out to have a very straightforward explanation,
detailed below. Nonetheless, the explanation has opened up new vistas, by giving us the ability to characterize
some generalizations of Zome. The mechanism of “tenacious symmetry” is not so easy to explain, so
we must content ourselves with merely describing its characteristics and some examples.

Our collaboration was also fruitful as a synergy between pure mathematics and the applied science of
visualization and modelling software. Scott’s Zome modelling software, “vZome”, gained a number of
rich capabilities as he learned more mathematics from David, and David gained a deeper insight, and even
learned some geometry, by working with and talking about vZome. A highly productive feedback loop thus
developed. Since this is as much a story of a collaboration as it is about beautiful mathematics, we have
decided to tell it in roughly chronological order.

Along the way, we have seen many novel views of some classical polytopes, and here we present a few
of these as well. It is important to stress that, with all of our static art being 3-dimensional, it is notoriously
difficult to visualize the complicated and beautiful objects which exist in higher dimensions. Zome and
vZome have allowed us to see some fantastic properties of these objects.

2. Octahedral Serendipity
The journey began with David’s mention of the fact that one may inscribe five copies of the 600-cell in the
vertices of the 120-cell, [1]. One may see this in the usual three-dimensional Zome projection of the 120-
cell: Starting with any one of the projected dodecahedra, one selects any one of the ten regular tetrahedra
inscribed in its vertices. The faces of this tetrahedron are shared by four more tetrahedra, and one can
proceed in this way to construct a projection of all the tetrahedra in the 600-cell. Since the original 120-cell
has a dodecahedral cell at the center, rather than a face, edge, or vertex, it is a “cell-first” projection, and
hence the new 600-cell projection is necessarily also a cell-first projection. This projection of the 600-cell
had not been seen by either of us, but is certainly not unknown, [1, 7]. The figure below shows a “4Dcutaway”
view; it is halved in four dimensions to omit the central involution, then almost-halved again in
three dimensions. The left-hand pair is a parallel binocular stereo view, and the right-hand pair is a crosseyed
binocular stereo view.

It turns out that most of the edges of these tetrahedra do not correspond to any existing Zome struts. The
vZome program, however, can construct a virtual strut between any two connector balls. When constructing
such an “unknown” strut, vZome assigns a color in the same pattern as real Zome: All directions (“zones”)
that are equivalent under icosahedral symmetry are assigned the same color. This has the effect of highlighting
the symmetry (or asymmetry) of models. After performing the construction in vZome, when we
finally cleared away all the 120-cell “scaffolding” to see the 600-cell, we realized that the model used some
of the blue, yellow, and green zones from the original Zome System, and three new zones. We have since
christened these new zones with the colors maroon, olive, and lavender.

Although our original construction appeared to have tetrahedral symmetry overall, the full projection actually
has “pyritohedral” symmetry, with two tetrahedra combined as in Kepler’s stella octangula at the
center. The pyritohedral symmetry group is the symmetry group of an idealized pyrite crystal. Geometrically, this is the direct product of the group of 12 orientation-preserving symmetries of the tetrahedron with
the 2-element group generated by the “central involution” or “antipode” map.

Armed with some of this knowledge, Scott was able to quickly implement quaternion multiplication in
vZome when importing a four-dimensional data set or when generating one of the H4 polychora. In vZome,
one specifies a quaternion by selecting an existing strut. Although the strut is specified by a vector (x; y; z)
with only 3 coordinates, the above analysis shows that the fourth coordinate w is determined up to a sign
by the zone in which it lies. Selecting any green strut results in a quaternion having the same shape as
1 + i = (1; 1; 0; 0), and all such quaternions have effect equivalent to mapping 2I ! 2(1 + i)I. In
short, achieving the octahedral projections of the 120-cell or 600-cell is now as easy as three clicks, a vast
improvement over our original manual derivation.

Availability of quaternion multiplication in vZome immediately begged the question: What is the effect
of using the various “colors” of quaternions? First, since blue struts are all in the orbit of the quaternion
(2; 0; 0; 0), which is an axis of symmetry in H4, using a blue quaternion has no effect modulo a dilation. For
other colors, the answer proved serendipitous in the way we have come to expect of Zome. Applying a “red”
quaternion to an object with H4 symmetry yields a 3-dimensional object with the symmetry of a pentagonal
antiprism; the projection is symmetric around the red strut used as the quaternion. This results in a face-first
projection of the 120-cell with two overlapping pentagons in the center, and an edge-first projection of the
600-cell. The figure above is a cutaway that shows one example of each of the 9 different dodecahedral cell
shapes in the former model, with some faces present for clarity.

Naturally, applying a “yellow” quaternion produces projections symmetric around that yellow strut. This
yields a face-first 600-cell, centered on overlapping triangles, and an edge-first 120-cell. Both red and
yellow quaternion multiplications yield new zoning systems analogous to the octahedral system we have
described, but with different symmetries. In both cases, the vectors of I are mapped to a small number of 3-
dimensional shapes, although more shapes (thus colors) are required than for the octahedral system. Indeed,
any quaternion multiplication of I yields a zoning system capable of rendering orthogonal projections of H4
polychora.

4. Tenacious Symmetry
The group H4, with 14,400 elements, is moderately large and exotic, compared to the sizes and variety
of the finite groups which act in 4-dimensional space. Having so much symmetry, some unusual traces of
this symmetry remain when these objects are projected down to three and two dimensions. We refer to
this as “tenacious symmetry”: Much symmetry is necessarily lost in a projection to lower dimension, but it
somehow refuses to be totally eradicated. Moreover, due to the observation in [8], we see that the original
Zome System is directly related to the famous E8 “Gosset” lattice, whose point symmetries comprise a
group with nearly 700 million elements. Certainly we will see a wide variety of highly-symmetrical objects
by considering different views of this amazing object.

Tenacious symmetry is in fact displayed in all Zome-axis projections of any H4 polychoron, and similarly
if a yellow quaternion is applied rather than a red one. In other words, although most of the rich symmetry of
H4 is inevitably lost in these 3-dimensional projections, that symmetry is too “tenacious” to be completely
eradicated – traces of it remain when one projects again down to two dimensions along particular axes.

5. Conclusion
To reiterate, there are in fact an infinity of Zome-like systems based on the binary icosahedral group, one
for each unit quaternion. However, they get progressively less interesting as the elements of I are mapped
to more generic elements with respect to the group H4, and less and less symmetry is preserved in the threedimensional
projection. With icosahedral symmetry, the original blue-yellow-red Zome System is clearly
the most symmetric of this infinite set. As in the case of the octahedral system based on green-quaternion
multiplication, the red and yellow quaternions similarly generate Zome-like systems with a small set of
vector shapes. All of these systems share the useful property of arbitrary scalability by powers of , without
requiring additional, longer strut lengths. These scalability and “small inventory” properties make all such
systems potentially interesting to artists and engineers alike.

We are proposing to generalize and study a wide class of such “zoning systems”, such as those that have
been discussed here. Here is a review some of the critical properties shared by all of the zoning systems we
have seen. First, all of these systems are based on connector balls and struts. Second, there is a group G
which acts on the ambient space and for which the symmetry group of every model is necessarily a subgroup
of G; the symmetry of the connector ball is G. Third, the original 4-dimensional orbit of 120 elements in I
maps to a small set of orbits under G, with the size of that set dependent on the quaternion q used to map I
to ((2q)I).

As has been observed in [8], another characteristic of the Zome System is that it is closely related to a genuine
lattice in 8 dimensions. One may describe this lattice quickly as a subset of R8, but is is also embedded
naturally in R4 in such a way that the lattice points may be positioned arbitrarily close to each other. More
precisely, the lattice points comprise a dense subset of R4 under the usual norm. This property leads to a
fourth characteristic of all these zoning systems: The idealized locations of the connector balls comprise a
dense subset of the ambient space. From the perspective of one who wishes to create an interesting model,
we regard this property as critical; in a theoretical sense, it provides the user with the liberty to place objects
in virtually any location s/he desires.

http://www.zometool.com/pdfs/tenaciousymmetry2006.pdf

[altonhare]

We describe a new Zome-like system that exhibits octahedral rather than icosahedral symmetry, and illustrate its application to 3-dimensional projections of 4-dimensional regular polychora

-JL

What is dimension?

How can something be 4 dimensional? Can you show it to me?

Furthermore, we explain the existence of that system, as well as an infinite family of related systems, in terms of Hamilton’s quaternions and the binary icosahedral group.

-JL

What is existence?

It is important to stress that, with all of our static art being 3-dimensional, it is notoriously
difficult to visualize the complicated and beautiful objects which exist in higher dimensions.

-JL

Difficult? Or impossible? I've never seen a 4-D object. You will have to define "dimension" at least, first.

The figure below shows a “4Dcutaway”
view; it is halved in four dimensions to omit the central involution, then almost-halved again in
three dimensions. The left-hand pair is a parallel binocular stereo view, and the right-hand pair is a crosseyed
binocular stereo view.

-JL

Halving a 4-D object results in a 3-D object? That's weird. No matter how many times I chop a 3-D object in half it remains 3-D. You must be using a different "dimension" than me.

The pyritohedral symmetry group is the symmetry group of an idealized pyrite crystal. Geometrically, this is the direct product of the group of 12 orientation-preserving symmetries of the tetrahedron with
the 2-element group generated by the “central involution” or “antipode” map

-JL

I think this is based on group theory, a mathematical formalism developed to understand the symmetry of idealized models of molecules. Idealized being the keyword.

The rest is technical and detailed relative to the underlying mathematical and software aspects of the program. It's entirely incomprehensible until one defines the word "dimension".

[junglelord]

Because Zome replicates so many natural structures and can build so many different geometric designs, it is of great value for many professionals. Mathematicians use Zome to model everything from networks in discrete mathematics, to group theory, and projection models (shadows) of theoretical 4-dimensional objects. Crystallographers, chemists and material scientists build lattices of natural crystals and quasi-crystalline materials, Buckyballs and other Fullerenes, and models of chromosome bonds and protein molecules. Engineers and computer scientists design space frames, make visual models of data bases, and numerous other uses.

Zome is also used in corporate team building workshops by corporations such as Kimberly-Clark and Merrill Lynch.

Because Zome is a PHI ratio tool, it has not only been able to model all life forms and inorganic forms, but also seems to be a model for everything which is exceedingly simple. The razors edge.

Exceptionally Simple Theory of Everything.


Garrett Lisi's "Exceptionally Simple Theory of Everything" lives in E8, an 8-dimensional space that's Zometool accessible. David Richter and Scott Vorthmann show you how.

A. Garrett Lisi's Exceptionally Simple Theory of Everything
According to Wikipedia, "An Exceptionally Simple Theory of Everything is a physics paper submitted to the arXiv library on Nov. 6, 2007 by Antony Garrett Lisi. His theory claims to unify all fields of the Standard Model with gravity using a 248-point lattice of E8 geometry. It has not been peer-reviewed nor published in a scientific journal, but it has drawn a wide range of professional reaction and stirred public interest in the topic and its author."

Accoridng to Dr. Lisi himself, "Yes, the title is a little much. Technically, a Grand Unified Theory in physics is a theory unifying the electromagnetic, weak, and strong forces as parts of a single Lie group. And if gravity is described in a unified framework like this, it's called a Theory of Everything, because that's all the forces we know of. The paper describes a new theory of how to do this, with all these forces (and all matter) as parts of the largest simple exceptional Lie group, E8 (which is very beautiful). So the title is technically accurate, but I probably should have made it less sensational. Especially since the paper does not include the details of a complete quantum description, which is really necessary for it to qualify as a successful ToE. (I'm counting on combining my work with that of the Loop Quantum Gravity community to build a full quantum E8 theory of everything.)"

Fortunately for us, E8 seems to be a subset of Zome geometry (or vice versa.) In Two Results Concerning the Zome Model of the 600-Cell, Dr. David Richter says that the Zome System is a great tool for studying the associated geometries of the Coxeter group E8. He echos Dr. Lisi's wonder at the beauty of 8-dimensional space, and offers tips for building a 3-dimensional shadow of Gosset's Polytope, which lives in E8. David also coauthored a related paper with Dr. Scott Vorthmann, Green Quaternions, Tenacious Symmetry, and Octahedral Zome. Scott muses on Coxeter groups, including E8, and the Gosset Polytope at his web site, vorthmann.org. Of course, you can also find his wonderful vZome software there!

Garrett may even develop an "Exceptionally Simple Theory of Everything Zometool Kit" with us, and who knows? Maybe this stuff really will be exceptionally simple one of these days... we certainly hope so!


–Cool Links –
http://www.zometool.com/about-everything.html

[junglelord]

Wednesday, November 14, 2007
An Exceptionally Simple Theory of Everything


I'm not sure yet whether all the attention is good, or if all the hype will have a negative impact, but this has certainly been a strange week. The interest in my work among physicists has been building steadily over the past few months. I've been presenting at conferences, getting invited to cool places, and exchanging emails with some of the best people in physics. But things started getting a little out of control last week when I posted my paper to the physics archive:

An Exceptionally Simple Theory of Everything

Yes, the title is a little much. Technically, a Grand Unified Theory in physics is a theory unifying the electromagnetic, weak, and strong forces as parts of a single Lie group. And if gravity is described in a unified framework like this, it's called a Theory of Everything, because that's all the forces we know of. The paper describes a new theory of how to do this, with all these forces (and all matter) as parts of the largest simple exceptional Lie group, E8 (which is very beautiful). So the title is technically accurate, but I probably should have made it less sensational. Especially since the paper does not include the details of a complete quantum description, which is really necessary for it to qualify as a successful ToE. (I'm counting on combining my work with that of the Loop Quantum Gravity community to build a full quantum E8 theory of everything.)

The physics arxiv has gotten more restrictive on how they accept and classify papers. I originally submitted this article under the general relativity classification, but they immediately moved it to high energy particle theory. Then, a day after it came out, it got unceremoniously booted to the general physics classification -- the cesspool the arxiv uses to collect non-string and/or whacky, overreaching papers. Then, the next day, it got reclassified back to high energy theory! (This never happens, and I was quite amused.)

The paper immediately precipitated a physics blogalanche:
Backreaction This was the first, and probably the best summary of the paper.
Physics Forums
The Reference Frame Can you tell he's a string theorist? I love this guy, almost everything he says is dead wrong, and he just makes me look better.
Hidden Variables
Not Even Wrong
Arcadian Functor
Freedom of Science This one cracks me up. Apparently I'm a media whore, and only doing physics for the money; but at least I'm in good company.
Theoreman Egregium
Science Forums
And at this point I've stopped being able to keep track, which I suppose means this is my fifteen minutes of fame.

Yesterday morning, I presented a talk to the
International Loop Quantum Gravity Seminar
http://relativity.phys.lsu.edu/ilqgs/lisi111307.pdf
which is a teleconferece among physicists at a consortium of fourteen universities around the world. That went very well. Some of the key players agree that this theory and LQG make a good match. (The (very technical) talk and slides are available from that page, but the first two minutes are cut off.)

Then, a few hours ago, the story hit the popular press:
The Telegraph (Apparently, I'm to be immortalized for the words "Holy crap!")
New Scientist Top story. I haven't been able to read this article yet, because I don't have a subscription.

All the attention has been fun, but a bit overwhelming, and I think I just want to go back to playing with equations for a few months. I hope people can keep in mind that this is just a theory, it has no experimental support, and it might be wrong. I think it's got a shot, which is why I work on it, but it's still just a developing theory. So don't go crazy, people; but yes, it is pretty damn cool.
http://sifter.org/~aglisi/JournalG/20071114.html

[junglelord]

Today we are again facing a confusing multitude of particles, though on a more elementary level. The number of what we now believe are elementary particles hasn't grown for a while, but who knows what the LHC will discover? Given the previous successes with symmetry principles, it is only natural to try to explain the presently known particles in the standard model - their families, generations, and quantum numbers - as arising from some larger symmetry group in a Grand Unified Theory (GUT). One can do so in many ways; typically these models predict new particles, and so far unobserved features like proton decay and lepton number violation. This larger symmetry has to be broken at some high mass scale, leaving us with our present day observations.

Today's Standard Model of particle physics (SM) is based on a local SU(3)xSU(2)xU(1) gauge symmetry (with some additional complications like chirality and symmetry breaking). Unifying the electroweak and strong interaction would be great to begin with, but even then there is still gravity, the mysterious outsider. A theory which would also achieve the incorporation of gravity is often modestly called a 'Theory of Everything' (TOE). Such a theory would hopefully answer what presently is the top question in theoretical physics: how do we quantize gravity? It is also believed that a TOE would help us address other problems, like the observed value of the cosmological constant, why the gravitational interaction is so weak, or how to deal with singularities that classical general relativity (GR) predicts.

Commonly, gravity is thought of as an effect of geometry - the curvature of the space-time we live in. The problem with gravity is then that its symmetry transformations are tied to this space-time. A gauge transformations is 'local' with respect to the space-time coordinates (they are a function of x), but the transformations in space-time are not 'local' with respect to the position in the fibre, i.e. the Lie-Group. That is to say, usually a gauge transformation can be performed without inducing a Lorentz transformation. But besides this, the behavior of particles under rotations and boosts - depending on whether dealing with a vector, spinor or tensor - looks pretty much like a gauge transformation.

Therefore, people have tried to base gravity on an equal footing with the other interactions by either describing both as geometry, both as a gauge theory, or both as something completely different. Kaluza-Klein theory e.g. is an approach to unify GR with gauge theories. This works very nicely for the vector fields, but the difficulty is to get the fermions in. So far I thought there are two ways out of this situation. Either add dimensions where the coordinates have weird properties and make your theory supersymmetric to get a fermion for every boson. Or start by building up everything of fermionic fields.

Exceptional Simplicity

On the algebraic level the problem is that fermions are defined through the fundamental representation of the gauge group, whereas the gauge fields transform under the adjoint representation. Now I learned from Garrett that the five exceptional Lie-groups have the remarkable property that the adjoint action of a subgroup is the fundamental subgroup action on other parts of the group. This then offers the possibility to arrange both, the fermions as well as the gauge fields, in the Lie algebra and root diagram of a single group. Thus, Garret has a third way to address the fermionic problem, using the exceptionality of E8.

His paper consists of two parts. The first is an examination of the root diagram of E8. He shows in detail how this diagram can be decomposed such that it reproduces the quantum numbers of the SM, plus quantum numbers that can be used to label the behaviour under Lorentz transformations. He finds a few additional particles that are new, which are colored scalar fields. This is cute, and I really like this part. He unifies the SM with gravity while causing only a minimum amount of extra clutter. Plus, his plots are pretty. Note how much effort he put in the color coding!

Garrett calls his particle classification the "periodic table of the standard model". The video below shows projections of various rotations of the E8 root system in eight dimensions (see here for a Quicktime movie with better resolution ~10.5 MB)


However, just from the root diagram alone it is not clear whether the additional quantum numbers actually have something to do with gravity, or whether they are just some other additional properties. To answer this question, one needs to tie the symmetry to the base manifold and identify part of the structure with the behaviour under Lorentz transformations. A manifold can have a lot of bundles over it, but the tangential bundle is a special one that comes with the manifold, and one needs to identify the appropriate part of the E8 symmetry with the local Lorentz symmetry in the tangential space. The additional complication is that Garrett has identified an SO(3,1) subgroup, but without breaking the symmetry one doesn't have a direct product of this subgroup with additional symmetries - meaning that gauge transformations mix with Lorentz-transformations.

Garrett provides the missing ingredient in the second part of the paper where he writes down an action that does exactly this. After he addressed the algebraical problem of the fermions being different in the first part, he now attacks the dynamical problem with the fermions: they are different because their action is - unlike that of the gauge fields - not quadratic in the derivatives. As much as I like the first part, I find this construction neither simple nor particularly beautiful. That is to say, I admittedly don't understand why it works. Nevertheless, with the chosen action he is able to reproduce the adequate equations of motion.

This is without doubt cool: He has a theory that contains gravity as well as the other interactions of the SM. Given that he has to choose the action by hand to reproduce the SM (see also update below), one can debate how natural this actually is. However, for me the question remains which problem he can address at this stage. He neither can say anything about the quantization of gravity, renormalizability, nor about the hierarchy problem. When it comes to the cosmological constant, it seems for his theory to work he needs it to be the size of about the Higgs vev, i.e. roughly 12 orders of magnitude too large. (And this is not the common problem with the too large quantum corrections, but actually the constant appearing in the Lagrangian.)

To make predictions with this model, one first needs to find a mechanism for symmetry breaking which is likely to become very involved. I think these two points, the cosmological constant and the symmetry breaking, are the biggest obstacles on the way to making actual predictions [4].

Bottomline

Now I find it hard to make up my mind on Garrett's model because the attractive and the unattractive features seem to balance each other. To me, the most attractive feature is the way he uses the exceptional Lie-groups to get the fermions together with the bosons. The most unattractive feature are the extra assumptions he needs to write down an action that gives the correct equations of motion. So, my opinion on Garrett's work has been flip-flopping since I learned of it.

For more info: Check Garrett's Wiki or his homepage.

Update Nov. 10th: See also Peter Woit's post
Update Nov. 27th: See also the post by Jacques Distler, who objects on the reproduction of the SM.

http://backreaction.blogspot.com/2007/1 ... on-of.html

[altonhare]

Garrett Lisi's "Exceptionally Simple Theory of Everything" lives in E8, an 8-dimensional space that's Zometool accessible.

-JL

What's a dimension?

Accoridng to Dr. Lisi himself, "Yes, the title is a little much. Technically, a Grand Unified Theory in physics is a theory unifying the electromagnetic, weak, and strong forces as parts of a single Lie group.

-JL

What is electromagnetic?
What is force?

[junglelord]

Zome Makes Real Learning Exciting!

Zome is a new way to explore the numbers and structures connecting math, biology, chemistry, fine art, architecture and technology. Your students will become involved, motivated and ready to learn more!

Hands-on Approach
Makes Learning Easy and Fun

In the Third International Mathematics and Science Study (TIMSS)* conducted by the National Center for Education Statistics, researchers found a large disparity between U.S. and Japanese students. In 44 percent of Japanese lessons, students were assigned to invent new solutions, proofs, or procedures on their own which required them to think and reason.

According to the report, less than one percent of U.S. lessons used these methods. Zome is the ultimate math and science manipulative. Learning theorists argue that high-quality modeling tools make it easier and more enjoyable for students to learn, as their capacity for abstract reasoning is complemented by their tactile and visual skills. With Zome, students understand new concepts better, and find them more interesting
http://www.zometool.com/edu-schools-students.html

[Plasmatic]

JL this is not an advertising bulletin board!

[Divinity]

http://backreaction.blogspot.com/2007/1 ... on-of.html

Commonly, gravity is thought of as an effect of geometry - the curvature of the space-time we live in. The problem with gravity is then that its symmetry transformations are tied to this space-time. A gauge transformations is 'local' with respect to the space-time coordinates (they are a function of x), but the transformations in space-time are not 'local' with respect to the position in the fibre, i.e. the Lie-Group. That is to say, usually a gauge transformation can be performed without inducing a Lorentz transformation. But besides this, the behavior of particles under rotations and boosts - depending on whether dealing with a vector, spinor or tensor - looks pretty much like a gauge transformation.

Therefore, people have tried to base gravity on an equal footing with the other interactions by either describing both as geometry, both as a gauge theory, or both as something completely different. Kaluza-Klein theory e.g. is an approach to unify GR with gauge theories. This works very nicely for the vector fields, but the difficulty is to get the fermions in. So far I thought there are two ways out of this situation. Either add dimensions where the coordinates have weird properties and make your theory supersymmetric to get a fermion for every boson. Or start by building up everything of fermionic fields.

Hi Junglelord, Just curious as to whether this is your definition of gravity, too, please. Seems there's a lot of confusion out there about the reason for gravity and it would be most helpful if you could clarify (in layman's terms) for us, how you define the cause.

Thank you!

AA Div
xxxxxxxxxxxxxxx

[junglelord]

The way the symmetry develops from the E8 and the Standard Model while elegant, and worth while to pursue for many different Knowledge paradigms, may still be a inadequate TOE. I have to research the way gravity is presented in this model. What I am cautious of is any TOE from the Standard Model.

I think Dave Thompson and Blazelabs, etc, make important contributions beyond the Standard Model, Particle Zoo, mess of things. I find the Blazelabs view of gravity to resonate the most with me on a intuitive level. I believe Gravity is a result of radiation pressure as described by Blazelabs. It was Blazelabs that turned me on to Platonic Solids as Valence Shell Configurations for Distributed Electron Charges. They also explained Spin Domains to me which correlated with the Vortex Math. This seemed to lead directly to the Fuller Synergetics. Fuller also accounted Gravity as a resultant vector from two radiation vectors. TT Brown would seem also to point in this direction.