Missing - My Hyphen-Underline Key

The Above is my rendered 3D model of my missing Hyphen-Underline key from my current keyboard that I use to do my work.  The image above shows the key sitting upon a solid oak plywood desk, just like the desktop that the key had bounced twice upon, and then went quiet.   In the image you can see me looking back, waiting for the return of the lost key.  Seeing how as it seems yet once again that my insanity has return, I intend to take a wait and see approach.  After all, the longer the time it takes to come back, the closer it will be in distance when it returns.

It officially left @ 11:30 PM PDT Thursday on  September 26, 2013, and it is currently 7:41 PM PDT October 4, 2013, so a week has gone by, and no key yet.  Presumably, based upon previous observations, it will have the numbers '365', in the measurement.  The 3rd wormhole that took a small plastic nasal spray bottle, just guessing here, took 36.5 months in time to move through a distance of  3.65 in through space.  So we will see what transpires this decade.

Oh if anyone finds my black plastic one one their desk, please make a note of the date, time, and place of it discovery location, and then post it here someplace.  Thanks for you time and effort in this insanity of mine.

The Insanity has Returned ...

It's official, I have gone stark raving insane!  The cosmological implications are ,,,,  !??
[1:37:51 AM] donald.p.hutchins: @11:30pm PDT, California: (please note that any '-' used in this post comes from using the minus key on the numeric key pad)

I had been at my computer typing up physics piece on 'A 3D Field Model, Continuous or Discrete?' that was inspired by another paper, 'The Discrete Field Model ...' by Peter A. Jackson of the UK, et all.  I had just finished my work for the store at 10:PM PDT, I had eaten earlier at 7:PM and had returned to the premises, wherein I got myself squared away, and set to my daily routine tasks of answering E-mail.  I had gotten hungry again and ordered pizza at about 10:30 PM.  It arrived just after 11:PM.  I had sat down to eat at the desk, the one wherein my computer sits.  I had moved things mostly out of the way, and been sitting and eating, when a fly comes and finds me and starts bugging me.  So I close my food container, move the things out of the way that I don't want to hit with the fly swatter.  It's 11:25 PM and I have cleared the desk, turned off the lights so the fly would be attracted to the lit monitor.  Works like a charm.  I swat the fly as it sits on the monitor.  The swatter came down so hard onto my keyboard it popped off a key, the underscore hyphen key.  Well I heard the black square of plastic bounce a couple of times off the desk top and some other cardboard item and then go silent, as I thought it had to have landed on the desk top somewhere.  OK, so no real problem.  Just clean the wooden desk top off, inspect, clean and recheck each and every item, very carefully with my reading glasses, so as to not miss finding the Key, I said to myself out loud, thinking the worst.  Boy, I had not seen so much dust collected in one location since the last fall cleaning.   Such is the desk, that my computer is sitting upon, that is to say, upon the solid oak plywood desk top that is flush installed to the wall so that nothing can fall behind it ... obsessive person that I have become, I know I must have cleaned and gone through everything, recleaning with paper towels and spray cleaner, on this near 30 square foot desk, twice, but to no avail, for I did NOT find the innocent little square bit of plastic with a couple of little lines on it.  And here I am typing on the very same keyboard, without the key, 2+ hours later, and still no black plastic key to be found.  I am now sure I have truly lost it ... again ...again ...again ...again ...only this time, I believe that I, yours truly, some how may have caused it to happen ... again ...again ...again ... yes it seems that I can be a Wormhole Activator via Cranial Kinetic Output, that's right, you heard it here first, from the horse's mouth, I can be, or rather I am, a WACKO! 

Further Explorations

In the dictionary there is an entry about Vector Space, 3D.  Most mathematicians understand the concept of a vector.  In my case I am talking about a Hypervector Space 4D.  So, if then, I'm really talking about a hyper-vector space, depending on parameters, the parameters being in a manifold, as described by my One Equation, and the Kinetic Information Structure Simulation design system that provides the dynamic drive force behind the One Equation which describes and forms such manifolds, which is then expressed as the expansion rate of  "all that we can see" = the universe, which appears to be accelerating, because we exist within a 'surface', formed over a 'volume' object, the radius of said object, that for all intents and purposes, hypothetically, is expanding at a constant velocity, while said surface increases exponentially, i.e. radius vs. area-dependent-upon-radius, is one way to correctly state cause and affect / effect, for said "Problem of Accelerating Expansion Rate of the Universe"?

I was told on one occasion, "My fellow physicists throw mass around in such a way as to imply it is already well understood and even suppose it a property of vacuum without any explanation of what it is or its cause or how it can warp space and time and explain inertia only during acceleration and ....."

So my answer could only be, In my geometry model using 4DFR, Space-Time (Hyperspace) is shaped as the outside of a hyper-Torus, and is a curved Hypersurface, so space and time ARE warped but only in terms of 4DFR.  OK you say, so how does that work for vacuum and gravity?  Well, even though local space is a 'flat Euclidean space', as A.E. implied, it is curved, warped, in 4D, and any Hypersurface element(3D) on the hyper-Torus shaped Hyperspace object(4D), will appear, as observed, 'flat'.  The curve, and its direction, in 4D, is what is important here, in speaking about expansion, vacuum and gravity.

Since, then if we exist within the Dynamic Hypersurface, the convex and concave shapes of either side of the Dynamic Hypersurface, provide an action (acts as a 'mass' vector) that is 'normal to' the Hypersurface in the direction of the dimension that is perpendicular to the three dimensions in which we live, that appear as 'Gravity' and as 'Vacuum', and the same action parallel to the Hypersurface, as expansion or extension of the Hypersurface. Here, again we have a 3-is-1 situation of the action of Change.  The 3 actions: the Extension/Expansion of Spacetime, the action of Gravity is against any 2D surface on a 3D object, as in if it has surface it has 'mass', this action is OUT from all '3D+1T' Points, 'pushes' on all 2D surface, on a 3D object, acting to push it together, so surface wants to contract, (all 2D surface is 'outside'), and the third action that that of vacuum, which works in the opposite direction to that of gravity, this action is IN from all '3D+1T' Points, 'pulls' on all 2D surface, on a 3D object, acting to pull it apart, so surface wants to expand.

A Hypervector has, in this universe, 3 parts to one Hypervector of 'Existing-Reality'.  Yes, another 3-is-1 concept.  We use the concept of 'Distance' to define the concept of dimension, so we have '3D' or 'DxDxD' for Space.  So then Hyperspace is DxDxDxD, or 4D.  Yet we also experience Time, and it works equally, like distance, in all the same directions that 'distance' goes, in 3D, so maybe we really have 3T, and it just feels 'linear' and acts 'linear', just the same way Space acts 'linear' or feels 'flat'.  Then again, Time is really just a part of the concept we call Change, as is Distance.  We can measure both distance and time, in all directions.  So, if we use the concept of 'Extension' which includes the concepts of 'Distance' and 'Time', then we really have 'DT' in all directions, which then is 3E, where extension = distance * time, as the 'new' 6D.

We have Distance and Time, that is the first 2 parts.  Next is the "what causes action" part of the Hypervector.  We know that neither distance, area, nor volume can cause action.  Usually, an action such as motion, happens over a distance, across an area, or through a volume.  We know that time can not be at cause of action either.  We tend to experience time indirectly as we do things on a 'per second' basis.  We age, thus we accumulate experiences, our birthdays and the number of days we have been alive grow in number when counted.  This a direct use of time that is linear.  If one can run, someone may reach a speed of one pace per second, that's two steps (a left and a right) per pace which is 120 steps per minute is linear but an indirect use of time.

What is left, is the "what causes action", the third part of, what is now, the 'Dynamic Hypervector'?  I will call it 'dynamic mass'.  It is the 'unit' vector that arrears to be specifically in the axis of the 'linear' 4th dimension, the dimension perpendicular to all of the ones in which we live. So, if what we call vacuum and what we call gravity and what we call mass are all related this 4th dimension, and each of these three 'action type concepts', exist, yet we don't really know the 'source' of these dynamic expressions of our universe. Most

Then how might 'distance' and 'time' express themselves in the three dimensions?

"How is it that an electron has mass and neutrinos appear not to have mass and travel at the speed of light? Both are classed and half-spin leptons. To argue a lower speed for neutrinos in vacuum means some humanly-accessible inertial reference frame where they are at rest for us to examine their properties to the fullest extent possible." I say, "How does vacuum have mass? "


The perception of the realities we learned as children, is very different from the perception of the realities that we faced as teenagers, then again as adults, and then again as aging adults. One's views of reality are shaped by religion, mom, dad, teachers, peers, co-workers, neighbors, TV, news, government, media and friends. What is tangible, is the most definitively real experience we get from this world and universe. If it hurts, it is real, that is why corporal punishment brings a sense of reality to those who seem to need to reminded of what reality can be, and to choose their future actions more wisely and with care, unless they wish for more pain, which then is easily applied.

Fiction and fact in today's world, and the lines in between, are getting blurrier and blurrier. That which is real, can grab you by the top of your head, lift you up, give you a shake, put you back down on the ground. If malevolent, a bloody mess. If benevolent, then be healed, and walk with spine aligned. The lines between, the illusion of reality, and the virtual reality of illusion are defined by one's perceptions of one's experience.

When what was theory, illusion, unreal, a non-fact, someone else's hypothetical science, small in possibility and non-existent probability, become just the opposite, how does one respond, how would you respond?

What Is "Space", And What I Mean When I Use the Term 'Space'

"Space", What is it?


We are born, we live, we die.  That is our human condition.  As a human, we are typically a, self-mobilized, self-organized pile, of a mixture of various kinds of matter.  Growing in the womb, we were in a liquid 'space', where we floated, effortlessly, and without a care, in a state of perfect peace.  The neutral buoyancy that we experienced for that period of gestation, gave us our first experience of life.  It creates within each of us, the gestation period of neutral buoyancy, an innate genetically integrated feeling of sensual containment, with freedom, that of total love and total peace combined.  It also gives us our first physical concept of boundaries, for as we grew, we found that the 'space' we had come into was getting cramped, and we were literally bouncing off the walls.  Towards the end of the gestation, were are more aware of being confined, and less aware of any feeling of floating, with a building need for that feeling of comfort of floating free, in neutral buoyancy, that we had initially found coming into this 'space'.  Then we are born.  This can happen one of two ways.  The natural method, we come out the way we came in, or the oven is ripped open, and we are pulled out, the oven is fixed afterwards, and the procedure is named after some guy who survived the same procedure first (Cesarean). 


So the concept of 'space' is out first realization, we just didn't know it as an intellectual concept that can be measured, and be used in many ways, including that as topic of understanding, knowledge, conversation, and what we Blog into.


There are many concepts out there, and that their immediateness is based upon the basic concept of 'space', is more a subjective, than objective, trait that we are more prone to employ as a deterministic format of how we want to perceive our environment, from our organic  perspective, that of a 'natural' viewpoint. 


The Physical Nature of things, objects that are real and are repeatably measurable, i.e., objects of mobile solid 'space', that have a measurable distance, and a measurable existence of time, or the Physics of the Natural, is the study of Nature, the natural viewpoint, through the discipline of the Philosophy of Physical Science, aka, Physics.   

From Wikipedia, the free encyclopedia:   "Space":

This article is about the general framework of distance and direction. 

For the space beyond Earth's atmosphere, see Outer space. For all other uses, see Space (disambiguation). 

Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction.^[1] Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. In mathematics one examines "spaces" with different numbers of dimensions and with different underlying structures. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

 From the above definition in Wikipedia, 'Space', is a rather complex subject to tackle in just one or two Kilobytes of text.

Once, we as humans, grow and live long enough to learn, then survive to tell about it, and then grow again, a cyclical process, we often get a better, more refined, and a more well defined, concept of 'Space', that of  'my space!' and then have to learn about the 'other's space!' as in other humans, and shared common space, and so on.  We are all made very aware of how much useless space we take up, including that space between the ears.  These all use the basic concept of  'Space' where "Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction."  It is our common inborn 'natural' viewpoint of the cold environment in which we live.  All of these kinds of 'space' concepts can be contained in a category called "Subjective Space".

So, What is it I mean when I use the 'Space'?
If you got this far e-mail me and I'll do the next segment sooner than later.
 

The Theories and Math's that have led to BIGTOE

An overt statement was made to say: "The boson is a natural outcrop of the Higgs mechanism . Why is it so difficult to corner the cagey Higgs Boson?"  To which I replied:

How is the Boson, a natural outcrop of the Higgs mechanism? You may ask better,

"It appears that, the Boson, is a natural outcrop of the Higgs mechanism, how is it that it is so difficult to corner the cagey Higgs boson?"

Otherwise I am going to have to ask you for your math proof for your statement, or reference to whom has proved the boson to be, ..."a natural outcrop of the Higgs mechanism".

It is simple, Bosons, by definition, are slippery. They carry no effective electrically charged surface differential providers, which makes them slippery. Having an effective electrically charged surface differential provider, that's created dynamically, what we view as a spiny constant mono static field of charged electric potential, that is perpendicular to the surface, with the magnetic field counterpart, that is in concentric spheroidal shells, parallel to the electrically charged surface differential provider, is a fermion, like an electron, or Proton.

Neutral particles are Bosons, and are not easily affected by magnets, except for very, very strong magnets that will align the axis of the magnetic moment, that is bipolar in nature and results from the singular average spin axis, and the triangular spinning and rotating structure of the 3, point shaped quarks, that form the triangle, the spinning and rotation of said triangle structure, forms the larger neutral particle.

Photons are a strange case, because they lack a structure, such as that of a sphere that seems to hold for point particles, and larger, one that gives them a more 'solid feel', instead it is more of a 'solid rod'. Photons are more like a rod of a finite length, that spins and rotates through 4D hyperspace, that gives us up to 3 different ways, so far, to view the Photon, each dependant upon the measuring device used, and the relative position / direction of the rod, (photon), at impact / absorption, that gives us the concept of a particle, wave, or field.

Neutrinos are the strangest, in that they have next to zero interaction with anything the size of an atom and larger. They seem to be subnucleonic, and all matter is transparent to them, except to very slow moving ones, that will hit an electron, kicking out a photon out of the electron cloud, to be detected by very sensitive instruments. More at, IMHO, these neutrinos, with a dense flux streaming in from the Sun and elsewhere, actively work with the neutrons, to produce the electron and proton "pairs" that form the nuclei of atoms with the electron clouds around them, leaving an average of one neutron to one proton in all stable atoms, and a few extra neutrons in the not so stable isotopes.          

From wikipedia:
In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking.

The above leads to qualifying questions, "How is a gauge boson different from any other boson?"; "What, exactly, is a gauge boson?"; If mass can vanish, and then reappear, that would explain another 3 experiences I have had, if the mechanism is KNOWN in how the mass vanishes, then comes back, let alone be non-vanishing. Who are Nambu and Goldstone, how did they get their bosons, what makes them different from the standard boson, or the gauge boson, or the one I have discovered, an ⓒ"Intermediate Hypervector Boson"™ = IHB, and don't have it named after me as yet, that might be the affect that created an effect that I witnessed.

Hmm let's see ... Gauge Theory - In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a **continuous group of local transformations**.

The term gauge refers to redundant degrees of freedom in the Lagrangian. The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as Lagrangian mechanics. In classical mechanics, the Lagrangian is defined as the kinetic energy, T, of the system minus its potential energy, V:: L = T - V; 

Under conditions that are given in Lagrangian mechanics, if the Lagrangian of a system is known, then the equations of motion of the system may be obtained by a direct substitution of the expression for the Lagrangian into the Euler–Lagrange equation, a particular family of partial differential equations.

The transformations between possible gauges, called gauge transformations, form a Lie group which is referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding vector field called the gauge field.

In mathematics, a Lie algebra ( /ˈliː/, not /ˈlaɪ/) is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used.

A Lie algebra is a vector space over some field F together with a binary operation [·, ·]
[*,*] : g x g -> g, called the Lie bracket, which satisfies the following axioms:

Bi-linearity:
[ax + by , z] = a[x , z] + b[y , z] , [z , ax + by] = a[z , x] + b[z , y]
for all scalars a, b in F and all elements x, y, z in g.

Alternating on g :
[x , x] = 0 for all x in g.

The Jacobi identity:
[x , [y , z]] + [y , [z , x]] + [z , [x , y]] = 0
for all x, y, z in g.

Note that the bi-linearity and alternating properties imply anticommutativity, i.e., [x , y] = -[y , x] for all elements x, y in g, while anticommutativity only implies the alternating property if the field's characteristic is not 2.[1]

For any associative algebra A with multiplication * , one can construct a Lie algebra L(A). As a vector space, L(A) is the same as A. The Lie bracket of two elements of L(A) is defined to be their commutator in A: [a , b] = a * b - b * a;  

Please see : xxx http://en.wikipedia.org/wiki/File:E8PetrieFull.svg xxx is a nice 2D spherical representation. Simple Lie groups include many classical Lie groups, which provide a group-theoretic underpinning for spherical geometry, projective geometry and related geometries in the sense of Felix Klein's Erlangen programme. It emerged in the course of classification of simple Lie groups that there exist also several exceptional possibilities not corresponding to any familiar geometry. These exceptional groups account for many special examples and configurations in other branches of mathematics, as well as contemporary theoretical physics. Secondly the Lie algebra only determines uniquely the simply connected (universal) cover G* of the component containing the identity of a Lie group G. It may well happen that G* isn't actually a simple group, for example having a non-trivial center. We have therefore to worry about the global topology, by computing the fundamental group of G (an abelian group: a Lie group is an H-space). This was done by Élie Cartan.            

In mathematics, an H-space is a topological space X (generally assumed to be connected) together with a continuous map μ : X × X → X with an identity element e so that μ(e, x) = μ(x, e) = x for all x in X. Alternatively, the maps μ(e, x) and μ(x, e) are sometimes only required to be homo-topic to the identity (in this case e is called homotopy identity), sometimes through base point preserving maps. These three definitions are in fact equivalent for H-spaces that are CW complexes. Every topological group is an H-space; however, in the general case, as compared to a topological group, and from what I have seen, H-spaces do not lack associativity and inverses.

In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial complexes, but still retains a combinatorial nature that allows for computation. 

Roughly speaking, a CW-complex is made of basic building blocks called cells. The precise definition prescribes how the cells may be topologically glued together. The C stands for "closure-finite", and the W for "weak topology".

An n-dimensional closed cell is a topological space that is homeomorphic to an n-dimensional closed ball. For example, a simplex is a closed cell, and more generally, a convex polytope is a closed cell. An n-dimensional open cell is a topological space that is homeomorphic to the open ball. A 0-dimensional open (and closed) cell is a singleton space.
A CW complex is a Hausdorff space (H-space) X together with a partition of X into open cells (of perhaps varying dimension) that satisfies two additional properties:

• For each n-dimensional open cell C in the partition of X, there exists a continuous map f from the n-dimensional closed ball to X such that
  • the restriction of f to the interior of the closed ball is a homeomorphism onto the cell C, and
  • the image of the boundary of the closed ball is contained in the union of a finite number of elements of the partition, each having cell dimension less than n.
• A subset of X is closed if and only if it meets the closure of each cell in a closed set.

If the largest dimension of any of the cells is n, then the CW complex is said to have dimension n. If there is no bound to the cell dimensions then it is said to be infinite-dimensional. The n-skeleton of a CW complex is the union of the cells whose dimension is at most n. If the union of a set of cells is closed, then this union is itself a CW complex, called a sub-complex. Thus the n-skeleton is the largest sub-complex of dimension n or less.

A CW complex is often constructed by defining its skeleton inductively. Begin by taking the 0-skeleton to be a discrete space. Next, attach 1-cells to the 0-skeleton. Here, the 1-cells are attached to points of the 0-skeleton via some continuous map from unit 0-sphere, that is, S₀. Define the 1-skeleton to be the identification space obtained from the union of the 0-skeleton, 1-cells, and the identification of points of boundary of 1-cells by assigning an identification mapping from the boundary of the 1-cells into the 1-cells. In general, given the n-1-skeleton and a collection of (abstract) closed n-cells, as above, the n-cells are attached to the n-1-skeleton by some continuous mapping from S_{n − 1}, and making an identification (equivalence relation) by specifying maps from the boundary of each n-cell into the n-1-skeleton. The n-skeleton is the identification space obtained from the union of the n-1-skeleton and the closed n-cells by identifying each point in the boundary of an n-cell with its image.
Up to isomorphism every n-dimensional complex can be obtained from its n-1 skeleton in this sense, and thus every finite-dimensional CW complex can be built up by the process above. This is true even for infinite-dimensional complexes, with the understanding that the result of the infinite process is the direct limit of the skeleta: a set is closed in X if and only if it meets each skeleton in a closed set.

Singular homology and cohomology of CW-complexes is readily computable via cellular homology. Moreover, in the category of CW-complexes and cellular maps, cellular homology can be interpreted as a homology theory. To compute an extraordinary (co)homology theory for a CW-complex, the Atiyah-Hirzebruch spectral sequence is the analogue of cellular homology.  There is a technique, developed by Whitehead, for replacing a CW-complex with a homotopy-equivalent CW-complex which has a simpler CW-decomposition.  Consider, for example, an arbitrary CW-complex. Its 1-skeleton can be fairly complicated, being an arbitrary graph. Now consider a maximal forest F in this graph. Since it is a collection of trees, and trees are contractible, consider the space X / ∼ where the equivalence relation is generated by x∼y if they are contained in a common tree in the maximal forest F.
The quotient map is a homotopy equivalence. Moreover, X / ∼ naturally inherits a CW-structure, with cells corresponding to the cells of X which are not contained in F. In particular, the 1-skeleton of X / ∼ is a disjoint union of wedges of circles.  Another way of stating the above is that a connected CW-complex can be replaced by a homotopy-equivalent CW-complex whose 0-skeleton consists of a single Point. 

In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of algebraic invariants of a topological space X, the so-called homology groups H_n(X). Intuitively spoken, singular homology counts, for each dimension n, the n-dimensional holes of a space. Singular homology is a particular example of a homology theory, which has now grown to be a rather broad collection of theories. Of the various theories, it is perhaps one of the simpler ones to understand, being built on fairly concrete constructions.

In brief, singular homology is constructed by taking maps of the standard n-simplex to a topological space, and composing them into formal sums, called singular chains. The boundary operation on a simplex induces a singular chain complex. The singular homology is then the homology of the chain complex. The resulting homology groups are the same for all homo-topically equivalent spaces, which is the reason for their study. These constructions can be applied to all topological spaces, and so singular homology can be expressed in terms of category theory, where the homology group becomes a functor from the category of topological spaces to the category of graded abelian groups.  By dualizing the homology chain complex (i.e. applying the functor Hom(-, R), R being any ring) we obtain a cochain complex with co-boundary map δ. The cohomology groups of X are defined as the cohomology groups of this complex; in a quip, "cohomology is the homology of the co- (dual complex)".  The cohomology groups have a richer, or at least more familiar, algebraic structure than the homology groups. Firstly, they form a differential graded algebra as follows:

• the graded set of groups form a graded R-module;
• this can be given the structure of a graded R-algebra using the cup product;
• the Bockstein homomorphism β gives a differential.

There are additional cohomology operations, and the cohomology algebra has addition structure mod p (as before, the mod p cohomology is the cohomology of the mod p cochain complex, not the mod p reduction of the cohomology), notably the Steenrod algebra structure. 

The multiplicative structure of an H-space adds structure to its homology and cohomology groups. For example, the cohomology ring of a path-connected H-space with finitely generated and free cohomology groups is a Hopf algebra. Also, one can define the Pontryagin product on the homology groups of an H-space.

The fundamental group of an H-space is abelian. To see this, let X be an H-space with identity e and let f and g be loops at e. Define a map F: [0,1]×[0,1] → X by F(a,b) = f(a)g(b). Then F(a,0) = F(a,1) = f(a)e is homotopic to f, and F(0,b) = F(1,b) = eg(b) is homotopic to g. It is clear how to define a homotopy from [f][g] to [g][f]. 

Adams theorem: S0, S1, S3, S7 are the only spheres that are H-spaces (e.g., using multiplication restricted from the reals, complexes, quaternions, and octonions, respectively). In fact, S0, S1, and S3 are groups (Lie groups) with these multiplications. But S7 is not a group in this way because octonion multiplication is not associative, nor can it be given any other continuous multiplication for which it is a group. However S7 is associative and has other continuous multiplication for which it is a group, when an actual spherical coordinate system, in conjunction with my One equation, is used in place of the octonions with their linearity of cubism restrictions.

Then with the continuous group of local transformations in mind, I came up with: xxx http://youtu.be/59157zE-u6s  xxx

So, I would say that: 'The Higgs mechanism is the natural outcrop of the Gauge Field Boson Theory, so why is the Higgs Boson so cagey?' if I thought the Higgs field Boson was even real or remotely possible, let alone findable, because it is like trying to create a particle of space. Space is an empty concept, while particle is a fully solid concept. In my theory, and the One Equation, they are related, but different structures. The primary vectors form dynamic relationship hypervectors that spin on 4 axis', which form into a surface element triangle that rotates with 4 degrees of freedom, that depending on the scalar values of the dynamic relationship hypervectors, with each hypervector perpendicular to the others, and the ratios of any 2 hypervectors that form dynamically a third hypervector, form S7, as there are 7 geometric functions in the group, a group that exhibits continuous local transformations between the 7 geometries within the group. 

Please note that in the above concepts: gauge theory, Lagrangian, Lie group and Lie algebra, H-space, CW complexes, were composited from information found on wikipedia, (don't forget to donate, no ads) to which I added what I know, and hopefully made a coherent contribution.  And on YouTube : http://youtu.be/1_HrQVhgbeo Higgs                              

References That Created an Understanding

[1] M. Morris and K. S. Thorne, American J. Phys. 56, 39 (1988)

[2] M. Visser, S. Kar and N. Dadhich Phys.Rev.Lett.90, 201102 (2003)

[arXiv: gr-qc /0301003]

[3] P. Kuhfittig Phys.Rev. D68: 067502,2003 [arXiv: gr-qc / 0401048]

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Sorting Concepts

The concepts under consideration: Space, Time, Mass, Energy, Gravity, Polarity, Charge, Matter, Photons, Infinite Hyperplanes, Higher Linear Dimensions, Blackholes, and Wormholes.

Space is a 3DFR dynamic vector of Extension, established in a relationship by the One Equation.  There is a 4th DFR of Space that gives us a fourth linear dimension that is perpendicular to all of the other three spacial dimensions with which we are most familiar, i.e. distance or length (1D), surface or area (2D), and volume or space (3D).  This 4DFR dynamic vector of Extension is termed Hyperspace (4D) which is an example of Higher Linear Dimensions. 

Time is a 3DFR dynamic vector of Change.  It is not as easy to distinguish our immediate three dimensions of Time, as it is to distinguish our immediate three dimensions of Space.  The Flow of Time is perceived as Linear to normal human beings.  When one is under stress, or pressure, Time seems to crawl.  This is the same effect that occurs in larger and larger mass objects.  Time flows the fastest in free Space, as it does when one is having fun.  Frequency, Velocity, Acceleration, and other related concepts are dynamic vectors of Change.  A young brilliant patent agent, long ago, A.E., had a result in his equation for a Cosmological Constant, a term that looked like: 8╥ x c⁴ the term 'c' is special as it is the term of 'the speed of light' where speed is the term for a measured Velocity.  Velocity is distance / time.  So the term c⁴ is the same as saying "distance*distance*distance*distance" / "time*time*time*time" thus one can see the four linear dimensions of both Hyperspace and Hypertime, eight linear dimensions to examine together.  Hypertime is a 4DFR dynamic vector of Change. 

Mass is a 3DFR dynamic vector of Dynamic Force that is most often associated with Matter and Energy, all forms of it.  It is difficult to separate out aspects of mass that don't require the previous two concepts of Space and Time. Mass, in and of itself, is a form of measure, that has a standard, of a specific kind of matter in the shape of a cylinder, of a specific volume and is called the 'kilogram'.  A.E. has defined Energy = mass * c² , where 'c' is the same as 'velocity', or "mass" * "distance*distance / time*time" and when one has contemplated on the concepts of mass, time and distance, one starts to see the validity of Mass = Energy / (Velocity²).  Matter, is similarly defined here as being equal to "mass" * "distance*distance*distance" * "time", i.e. Mass x Space x Time = Matter, that is a mass that has a finite volume or space that it takes up, and that it 'Exists', as such, for some finite amount of Time.  Matter has four states or forms, i.e. Solid, Liquid, Gas, Plasma.  Each form is simply a level of Density, with a solid as having the highest density, and a hot ionized gas, plasma, having the lowest density.  Density is a measure of matter that is equal to "mass" / "volume".  There many kinds of matter.  Each solid form of matter has a density that is different from the next, as are the liquids and gases.  Different liquids have different densities, all are dependent on temperature as well as volume for the same 'weight' of material.  Mass can measure the same in a gravity-free space as it can here on planet earth.  All forms of Matter can be defined by the concept of 'density'.  The denominator for 'density' is volume or Space.  One can have 'grams per inch', 'grams per square inch', or 'grams per cubic inch' and have it refer to a kind of density. 

Energy, Heat, Force, Momentum, and Power all use "mass" as the 'unit' that defines them.   Momentum is linear 1D, and is directed, in any direction in 3D space.  Force is non-linear, directed perpendicular to the surface of application, area function.  Energy is linear, and is directed, in any direction in 3D space perpendicular to the surface of application.  Heat, in physical units of mass*distance, is being transferred from one place or another in each case. Momentum = Mass x Velocity, and could also be termed as "Heat per Second or Heat Frequency".  Force = Mass X Acceleration, and could also be termed "Frequency of Momentum".  Energy = Mass x Velocity² = Heat x Acceleration, which can be viewed as "Heat Acceleration".  Apply, apply frequently, applying very frequently are terms of Change, as one can apply over a distance (per inch) or a length of time (per sec), or using some matter (per gram) .  Power = Energy Frequency, and so "time³" is in the denominator, so at a minimum, Time has at least 3DFR, and when used in the denominator, refers to 'future-present, available to be applied', as opposed the present-past.

Gravity, Thrust, and Push = "mass" / "time", all cause the acceleration of matter.  Momentum can be also looked at as 'Push' * 'distance', and is similar to the 'Newton-meter' which is a quantity of Heat (per second).  Force can be looked at as 'Push' * 'velocity', and Energy as 'Push' * 'velocity' * 'distance', and Power as 'Push' * 'velocity' * 'velocity', which quantitatively, has a nicer progressive look to it in terms of velocity.  Gravity is always given as standard of acceleration.  Gravity, here on earth, accelerates matter at 9.8 meters/sec².  If one releases matter at a rate of 10 kg/sec and at a velocity of 10 meters/sec one needs to generate a force of 100 Newtons in order to do it.  It takes mass to move mass, and it takes a surface for application to happen.  Impacts of different kinds are surface area dependant.  If Gravity is a function of the 4DFR of Dynamic Force and is the same strength at every Point in free empty space with nothing but a vacuum, then matter attenuates it.  The larger and denser the cross-section of the mass-plane, or what is termed here as an Infinite Mass Plane, because the closer one gets to it the more infinite it looks, and the greater is its attenuation of gravity, and thus its greater Push application, and thus its greater acceleration.  Smaller objects of mass are accelerated toward larger objects of mass. 

The seven Geometries of the One Equation, generated by scalar values between -1 and 1, including 0, for R1 and R2, gives rise to a Point at 0,0; gives rise to lines, edges, and planes of rotation which yield surface elements at R2 = 0, and R1 equal to the range of -1 to +1 not including 0, also appears to be a sizing or scale factor, as the shape of the geometry does not change; gives rise to a sphere at R1 = 0, and R2 equal to the range of -1 to +1 not including 0, as the shape of the geometry does not change while the value of R2 does change, also appears as a scaling function that seems to define Matter; gives rise to the hourglass shape that has been defined as Blackhole / Whitehole that has a Point at its middle at R1 = -1, R2 = 1, or R1 = 1, R2 = -1; gives rise to the outside half of a standard, plain cake, round with hole, 'doughnut' shaped surface that seems to define Space, its vacuum on the inside - Dynamic Force, its gravity on the outside at R1 = 1, R2 = 1, or R1 = -1, R2 = -1; gives rise to the inside half of a standard, plain cake, round with hole, 'doughnut' shaped surface that defines the Wormhole function at R1 = 1, R2 = -1 < x < 0 OR R1 = -1, R2 = 0 < x < 1; gives rise to the 'Candy Wrapper' function, at R2 = 1, R1 = -1 < x < 0 OR R2 = -1, R1 = 0 < x < 1, which may be the cause of 'charged'  particles, bi-polar magnetism, and photons.

Photons, charge and polarity.