The Math of Supersymmetry

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[MathematicalPhysicist]

how do you use category theory to see that physics is philosophicaly rendered?

[sol]

Originally posted by loop quantum gravity
how do you use category theory to see that physics is philosophicaly rendered?

Your question forced me to do research.(I guess you forgot to read this loop)


Sol

[MathematicalPhysicist]

Originally posted by sol
Your question forced me to do research

I ask Jeff to explain the mathematical language in one of his posts and to generalize what he was saying. See I understand that in order for Jeff to write the mathematics, he had to have generalized it first? Then symbolically, with the right math, he was able to construct. Those better equiped could understand, while being junior here, I had to understand the developement of the concepts. Without the proper concepts, that math could turn out to be wrong?;) Does this sound logical?


Sol
so you dont know?

[Ramanujan12]

"Category theory, a comparatively new field of mathematics, provides a universal framework for discussing fields of algebra and geometry. While the general theory and certain types of categories have attracted considerable interest, the area of homological algebra has proved most fruitful in areas of ring theory, group theory, and algebraic topology." - Math Atlas

The interesting thing about category theory is that it catagorizes the sort of first principles of mathematics and topology into a holoarchical structure. Central to this holoarchy is the topos category used to undermine the Set and Calculi categories. Topology being differentated from mathematics, where mathematics is a methodology and topology is a science proper, the categorical logic sets the topos as the main power set category for all descending maths interacting on it. The problem with applied topology, as a general science, is that it's founded on mathematics which is a methodic deliberation of first principles. Thus category modeling refounds mathematics like calculus and algebra from a scientific topological ground. Category theory is the 22nd-Century mathematical logic for calculus, differential geometry, and algebra and will probably be found to work very well with current trends in bioinformatics.

Category theory can be drawn allong the lines of mathematical physics, see John Baez. It can also be used in advanced forms of geometry called SDG (synthetic differential geometry) and SIA (smooth infinitesimal analysis), John Bell writes on these subjects.

Riemannian geometry can also be done through category theory using the notion of formal manifolds. Classical C∞-manifolds are topologically generalized to formal structures (as apose to being mathematically generalized through calculus). Simillar to how homotopy theory, using maps. is able to generalize it's n-dimensional stuctures to higher-dimensions. M is a formal n-dimensional manifold and (Uiφi M) is a monomorphic manifold covering. φ is a monomorphism transformable on it's image φU. Formal manifolds can also capacitate tangent vectors, which are useful for scaling compactness in algebraic topology. Maps can be classified as metric tensors in such a way g : TMXM TM≡(MAP)R where the tangent vector of the formal manifold is a product of the Riemannian structure mapped on all points in Rn, being a manifold, and g a metric tensor for a Riemannain space if g(v,v)>0 for all g#0 has also a vector norm, luckily, being ||v|| = √g(v,v) .

Developing first principles from categorical techniques with these notions can be used to model GR in toposes, particularly in relation to geometry and algebra. Physics at this level becomes rendered philosophicaly and we have a complete map of all pieces of the π.

[sol1]

The Math of Supersymmetry (http://www.superstringtheory.com/forum/metaboard/messages18/366.html)

[sol1]

Gravity and the Envelope (http://www.superstringtheory.com/forum/futureboard/messages9/123.html)

I have given some perspective in the direct relation between dimension and symmetry? The difference in the grvaity field speak to the ideas of the differences in the field. One no longers looks at the idea of the matter and their points, but moves to consideration of how the grvaity field is determined? That is the direct relation?

Symmetry and the continuity speaks to gravitation distinction as much more dynamical in expression. This is the importance of vision and seeing(having incorporated all the functions of the standard model)

Is my reasoning wrong in relation to dimension and symmetry of string theory? I have incorporated, the weak with the strong? Tat is what dimension does. The crystalization is the defined state of the element? In a eculidean sense this is a flat plane, a zero point oscillation consideration that is unique to the element?

Sol

[sol1]

Why Iron? (http://superstringtheory.com/forum/dualboard/messages14/57.html)

[sol1]

Boson Production off the Brane (http://superstringtheory.com/forum/dualboard/messages14/185.html)

[sol1]

Dimensional Analysis (http://www.superstringtheory.com/forum/superboard/messages4/199.html)

The same question that is being asked in link I am opening here as well.

Sol

[pelastration]

Sol, and others,

SST has closed again a number of forums for posting (MM, BlackHole, etc.).
Remarkable is the non-communicatation of Patricia.

d

[sol1]

Originally posted by pelastration
Sol, and others,

SST has closed again a number of forums for posting (MM, BlackHole, etc.).
Remarkable is the non-communicatation of Patricia.

d

Dirk,

It is important I think at this point to make sure that what ever your posting has been saved somewhere. My fear, is the archives will have been lost, and it is a host of much information. Does anyone know how to save the entire archive of Superstringtheory.com?

Sol

[sol1]

Spectral and Gravitational Calibrator (http://www.superstringtheory.com/forum/futureboard/messages9/127.html)

Based on the understanding of Symmetry(is dimensionally related), as a overall idea here behind dimension, we are able to measure the differenes between the early universe, and condensive features on planet formations.

It is extremely important that we recognize the information that exists in the spacetime fabric, that is sent out as ripples, will give us the information we need about structural failures, as well as answers to those condensive feature of planetary formation.

The idea here is to formulate a langauge that will be capable of translation to the antennas that we are currently using in LIGO and LISA.

This is my attempt at helping to increase our vocabulary in regards to geophysical understandings, as well as changes in the planetary formations. Changes in the envelope will have been designed on the sensitivities we can gain from reading the envelope.

Any thoughts or corrections.

Sol

[sol1]

I thought it better I remove my post from Probability statistics The basis of this post is th equestion of application, and reocgnition of the Uncertainty Principal. But I am asking if I have found a way around it like the probability diagrams.

Thanks for any response?



Probability Diagrams......... (http://www.superstringtheory.com/forum/philboard/messages23/4.html)

From a energy perspective, my perceptions have been formed around the understanding of curvature. To me, energy congregations, depending on the strength and value of that energy, would indicate the understanding of gravity(dimension), and the amount of curvature inherent in that congregation.

Because I have indicated the value range, in regards to energy between 300000 years after the big bang, to now, the value of this curvature, is relevant to the curvature present at energy scaled events. Continuity at the supersymmetric level would have defined gravity, and so would gravity at the furtherest extend of the horizon, where cooling functions, would have demonstrated condensive features of planetary formations?

Besides removing Heisenberg's uncertainty I see the relevant nature of curvature, as satisfing Hup as well. Is there any arguements that would dispute what I am saying?
-------------------------------------------

Taken from another post of mine:

How would we give a picture to someone, who is very visual under the heading of certainty, knowing full well there are areas of uncertainty?

It requires that we understand something about strings that is inherent in its very inception, and only could this have been realized, had we understood such groupings of energy, as constitutions defined in a way.

Now under the heading of certainty, where probabilistic determinations might have been interpreted on a gathering of chance, we find that the heavier concentration of probbailistic determinations, will have been defined in this peak. BEC condensate, soliton, or even flipping a coin.

Second to this, is the understanding that such groupings , and again I refer to the energy here, that a shape might have been gathered from the very idea of such determinations, that when energy is in such concentration, it will define the innate curvature implied from such gatherings.

Now in the following link (http://www.superstringtheory.com/forum/stringboard/messages25/52.html), I am showing what I have expounded in words, yet visually, I have described this concentration of energy, as a feature of curvature, so it tells us something about the movement of that energy. Why, we would move to consider topological movements, as greater or lessor, concentrations of that energy.

From this point, such movement will have considered isomorphsms and self similarities inthe cosmos (http://www.amherst.edu/~rlolders/stars2/isomorphism.html ), as relevant issues in the world of the very small.

Orbital consideration are being defined now in shape, and as this energy concentration is considered, we now find it being described in a whole library of movements (http://www.orbitals.com/orb/index.html)

Visually, we have now given the mind a determination on such concentrations of energy, and have topologically given perception a view of movement in the world of energies. The distance from the peak, in the Bell curve or the heavier concentration defined at the center of any atom, would have pointed us into the explanation of inherent curvatures implied by such energies.

So under this heading I hope I have been true to your definition, and expounded on the relevance of how one might have discribed frequency and rare events, under the heading of energy congregations.

I will give one more example of the logic I have implored here. In terms of particle/wave, a line is realized, that gives definition to a understanding of such energies. Geometrically considered, it represents the real geometry that is espoused and nature has supplied us with it. It is Fuzzy.

In the example to follow, numbers here , as in O to 1, is defined in that line. The logic of my arguement rests in the fact that when you consider this line, it's defintion can only exist, had two considerations(dualism) be given.

Line of shadow, line of light. Without either, the shadow and the light, the line cannot be defined? As a proposition then, any deviation from the inherent distinction of that line, will rest in the defintion and grayness of the shadow.

Even though that line is straight, its curvature will have been understood in the greyness of the areas? Consolidation of any energy gathering( energy never rests in terms of zero point and the understanding of harmonic oscilations)will have been defined in the line.

Hopefully I have given food for thought here.

If not, please correct in these examples.

Sol

[lethe]

i wish you would stop posting links to superstringtheory.com. if you want to have a discussion with us here, you should have it here.

[sol1]

Originally posted by lethe
i wish you would stop posting links to superstringtheory.com. if you want to have a discussion with us here, you should have it here.


See my post above yours? I linked to physics forum so I could get a response from physics forum(Probability statistics). I was told I was hijacking there so I will remove my post there if no one responds.

Do you understand why?

Maybe superstringtheory.com should join with Greg's as well:)

Can you exist in this forum without reference to any other information? The work in superstringtheory.com was apart of the initiation of two years of work, paltry compared to the endeavors of students who engaged with heartfelt sincerity the interest of physics, sciences and such. Personally(research) I have covered a wide range for many years so I am no stranger to the attitudes that can develope in communities(classroms). I did not develope in the school system, which I am sorry to say will be the work in my next life:)Now I use the wide open spaces of the internet. Not much you can hide from me:)

I was told to start my own thread which I am doing in the math of supersymmetry, so I am basically folowing the order of someone who told me I am hijacking. I am deeply interested in superstringtheory and LQG, and I am been working at it for two years, and all its associative requirements.

I think there is a consensus forming, with which there is nothing I can do( until others open up), and that's part of joining new communities(classrooms). A new guy and all?:) I am really trying to opened my self to corrections, as this is the hallmark of my learning process. Etiqiette and conduct becoming, in forum exchange.

That if what I post is wrong, that I be told so , so as not to give out wrong information. I do my homework when I am told otherwise. I am learning and "hope" to be guided properly? As you must know better perspectives, can pick and choose, who they will respond too. Feynmen had good insight, and like to joke a lot. I wonder why?:)

Once one realizes the humour of it, it is indeed a surpize at such simplicity. Toys model reduced, amazingly, bring clarity to complex issues. Simplifing is very important. How does one gain that vision?

Sol

[sol1]

The Philosophy of the Mathematic of String and Loops (http://en.wikipedia.org/wiki/Philosophy_of_mathematics)

I am trying to gain perspective from the understanding of Supersymmetry, yet the conflict with temperature is well evident here with the continuity of energy congregation and distance.

In a weak field measure how would scale have been understood but by understanding that dimension had varying intensities of gravitational considerations? From the very weak, to the very strong?

Sol

[sol1]

The Search for Truth (http://cerval.murdoch.edu.au/kissane/e162lect06/sld001.htm)

We can start off with Euclid's first four postulates, but when we get to the fifth, the "world" seems to take on new dimensions?:)

Sol

[sol1]

I am trying to pin down the ideas of hyperbolic and sphere considerations.

If we talk about space(euclidean) and we move to Minkowski metric, we have spacetime.

How we got to spacetime? (http://www.theory.caltech.edu/people/patricia/grelb.html)

I am working from a paper here, and want to provide a good comprehension of this movement. It goes like this, that the Minkoswski metric, had a distance function dS² that can be negative, positive or zero, whereas the distance functions in space dL² can only be positive.

Geodesics for the Euclidean metric are straight lines, so space geodesics in the distance function is the pythagorean Rule. dL²=dX²+dY²

From space to spacetime, recognizes the ability of spacelike geodisics, null geodisics and time like geodisics.

Simplifiing this movement then, in higher geometries, seem easy, from the understanding of movement that is dynamical, but it definitely needs a deeper explanation and undertanding. I hope to seal that in mind.

[sol1]

At a heighten state of perception (http://www.physicsforums.com/showthread.php?s=&goto=lastpost&forumid=47)

We have exceled quite dramatically to what can be done with understanding dimenisonal interpetations base on the values of graviational considerations(mass and density in relation to planet formation).

How does one get a sense of this movement?

The Friedmann Equation helps greatly here from the cosmological standpoint, and, undertanding the curvature parameters.

The K values.

I believe these views are consistent, in terms of what might have been understood in terms of the gravity.

Topological movement well considered in this movement as well. The values in strings speak to this nature of gravitational consideration, that we might have raised the issue here of orbital, and the isometric relations such topological movements could have revealed? Inside the blackhole, yet this is like asking what nothing is:)But the string as a graviton, and in such concentration, what would its effect be. Curvature in my understanding from Friedmans universe and the K values,speak to the involution and evolution, geometrically considered, as a effect of gravitational considerations?

Geometrical consideration, in terms of Eisnteins use of spacetime, and Rienmanns sphere, spoke to me of what happens in those K values of Friedman, as a dynamical expression of movement in topological consideration. The + and - as effects of what could happen to a sphere. On the positive side, hyperdimensional considerations, and on the negative, what we have understood in the blackhole creation?

Key indicator on the moment such a blackhole will have collapse, was raised, around what Mooreglade offered, in the sonolumince experiment we had banter around here.

That the very effects of creating the vibration in that bubble, could have increased its size and just before its collapse, what happened? Temperature values were very important here, in the determination of such a collapse.

I realize, that Dickt has mentioned there was no connection, but from a string point of view, gravity implied in the interior of this bubble, initiated the collapse?

Mooreglade figures there is a reaction started here, that lies at the heart of, the creation of a sun. I have not seen this idea yet, alhtough it would be refering to blackholes not as the orignators of universe, but of new suns born. Singularities are not in the view here although such a collapse reveals interesting ideas in terms of compaction and ignited reactions, as a basis of such heat generation?

[sol1]

How long have we come to understand that the Euclidean geometries having been in a state for the last 2000 years and within the short time in a historical sense Ivanovitch Lobachevski, Janos Bolyai and Karl Guass made good use of the fifth postulate, from Euclid's Elements? They moved our understanding to Hyperbolic geometry. Einstein also used this in taking us to the understnding of Spacetime(curvature?)

The sphere becomes a interesting object in which to speak about triangles. This movement is demonstrated, by our recognition of the Friedmann equation, and our understnding of the universe or in the every shapes we might have understood in the orbitals. It become a interesting perspective in terms of topological movement as well.

What is the Time Issue,as a four dimensional understanding? (http://www.cs.unm.edu/~joel/NonEuclid/space.html)


It is one of curvature.

If gravity is so weak, in the three dimensions we know, at what point do we now look at the distortion of space, as a relevant issue, with which we must understand, is not the same rigid structures, we had taken for granted?

Moving into a fifth dimensional perspective, we have move our view into the understanding of energy and what it does?

The gravitational presence here, in terms of the distance, becomes a interesting issue, when in that distance, we also speak to the understanding of what energy is contained in that space(dimension).

If a string is one dimensional and a plane(brane) two, when does a brane reveal of three?

What is Omega? (http://superstringtheory.com/forum/dualboard/messages5/114.html)


Sol

[sol1]

I have seen it compared too, and in this house of cards let's say there are 8, and in this we will assume:

Dickt said:<i>In 10 dimensional superstring theory, I assume the number of transverse dimensions is 8 (=24/3. coincidence?)</i>

Now of course even in this heighten speculation and numbered correlation, we know the content of a brane in the 2 plus 1 time dimension, and all of a sudden how complex is the dynamics of brane "intersection"[a resulting figure of the boson in production], when we have intergrations[nodal point, morie effect, holographical] based on this method?

Boson production in such a mode has released it's funcitonability to the closed string boson, and of it, goes creating branches and the sort, and in that topological world, where did all these possibilties begin from?

The views had to be changed sometime back, when we had moved our vision to the KK stance and out of that ability, the world was lead too, and from, the undertanding from GR.

QM in statistical relation, and complexity of information, allow greater abiltiy in discription in the topolgoical features and movements. To have redcued that complexity to 10, also reduced the function of this interpreation from a comlex set of points too, and here, how would you undertand complexity unless you graduated from a set of points in GR and to have expanded this undertanding in QM?

I hope one can see the confusion here. Any corrections?

Sol

[sol1]

......how would we measure the differences?

One way that it is being pursued, is Grace. A way that is now mapping the globe. I would put a link, but if I do that, then I am confronted with people who think I should be dealing with the here and now, what ever that might mean?:)

So far no response and what has being put forward in the PBS series is a journey I had to go through without the benefit of clear and consise explanatins of people froma global perspective) from all facets who have gathered to help us undertand this issue. But once that is done, were is it one might think minds can go? I am giving one direction and dealing with the specifics.

Eveyone is still locked in the mathematics, and philosophically the math is derived from exploration, and such generalizations now transmitted to us in this show, has been a trail of years. But the next step. What is it? Experimentation? That is being done in what is being revealed to us in LIGO WEBER bars and the road to gravity exploration. Why has strings not coupled to the current research and experimental developement?


Fundamentals of Spin and the index (http://www.superstringtheory.com/forum/stringboard/messages21/56.html)

[sol1]

Hmmm....collected facts.

I mentioned induction and deduction. There is a process here that required the understanding of first principles( I'll explain my thnking here).

Einstein had a special ability, as did Feynman.

You see, in probabilitiy statistics, if we are so concerned with the matters, how is it some men can see into the very basis of such statistics, and through insight, develope the roads to understanding, and they had not even ventured through the math yet?

What capabilties allowed a Feynman to understand such complexities and come up with simple solutions(Toy models?)? If the quantum mechanics were understood, and we had identified the matters to which such attentions are drawn, the pathways(S matrixes) and highways these men understood were simple examples to a complex issue. Such simplicity, the real beauty of the math, that comes in insight? The math comes later.:)Yet it was embedded in the insight:)

Einstein became quite unhappy in his later years as he tried to come to grips with his unified theory, as a road that became , a mathematical venture, became a loss to what was always easy for him.

Thought experiments that challenged the every basis of Bohr? Well success was humour to what men already understood that they could play the games, and with Feynman, always the trickster?

What allows men to see into such complexities? To see a string that ties together a pattern that not one of us might have seen, yet through all that information, it became quite plain to them. They could make predictions on it, because they had a model in their head already?

So lets look at what string can do as they come together in their intersections. Two loops that become one. Lets look at the geometrical quest for pattern formation, and what came of it?

We understand now, that such schematics were the basis of complex issues for Feynman, and what do we have today, simple drawings, that explain processes that we speak about in a way that is very different.( New language perhaps, and a logic, that philosphically became the math for understand interactions of photons?)

If you find correspondance now is this example, to what I have been telling you, it has only come lately to my own understanding, so there was no way for me to know this.

Correlation of Cognition(A example of a cognitive style of math that comes from relating how such maths might have originated), helps here sometimes, where we had lack the teachers to show us the truth( not saying it is always the truth, why one continues to ask), and what had we found from such links and correlations( I have always spoken of the gravity of things:)?

Something that is quite moveable in the way such dynamics might have revealed of the zeropoint vibration, and in this, a signature of the very matters to which that small world is spoken too, in much the same way, such dynamics are exposed in the cosmos?:)

Do you think strings has found some basis in this pattern forming to have geometrically defined, itself much the same way, that Feynman and Einstein made use of such insight?

So there is to be a joining of a kind, of relativity (the very large) and Quantum mechanics(the very small). In relativity, there is a beginnning and a end, yet in such fuzzy quarters, we find the discription of the small world very hard to pinpoint, so we talk about strings.:)

If there is no beginning, and no such zero point is ever reached, where have such oscillations come to a stop? How is it, we could have ever had found value in relativity, being joined in superstrings? There had to a be a way in which such a process is understood in terms of the energy, to have seen where such densities of energy gatherings would have found examples in the blackholes and the congregations there? There is information loss that a photon release might have explained something to us about the time dilation, here and what has happened to the photon?

It is only by our own consensus that such measures wil have allowed us to agree on the substance of reality, yet we are observers in this world. Remove the measure then you have removed our consciousness of things?

The Taoist symbol is something I found that moves very much like the movements I had been telling you about, A Mobius or a Klien bottle, and what could be learnt here about things turning inside/out. If it were so irrational( these insights, how is it such a sphere can ever have a hole in it and how is this movement accomplished? How could a triangle ever become more then 180 degrees, and how could we have ever understood something less then?

Is there no movement implied here? Does it not require the math, and where did it come from? You understand the essence of such maths must describe the the very genralizations that such insights can reveal, or why would we be so amazed?:)

Sol

[sol1]

Cognitive Science of Mathematics (http://www.wikipedia.org/wiki/Cognitive_science_of_mathematics)

How does "first principles" apply to what can emminate from any mind, and where would such a beginning start from? We are always searching for a beginning are we not? Some are searching for God? Some for meaning as to who they are?


How does a idea come into being? (http://www.superstringtheory.com/forum/metaboard/messages18/128.html)

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Some modern theories in the philosophy of mathematics deny the existence of foundations in the original sense. Some theories tend to focus on mathematical practice, and aim to describe and analyze the actual working of mathematicians as a social group. Others try to create a cognitive science of mathematics, focusing on human cognition as the origin of the reliability of mathematics when applied to the 'real world'. These theories would propose to find foundations only in human thought, not in any 'objective' outside construct. The matter remains controversial. (http://www.wikipedia.org/wiki/Foundations_of_mathematics)


If U(1)=5D, THEN FROM WHAT REALM WOULD ALL INFORMATION BE CONTAINED?

A point described, and from this, the extension of what could have arisen from expansitory modes, to have realized the continuation moves beyond spherical considerations to the hyperdimensional geometrical formations. If U(1) can arise from the mind in its cognitive phase then what has happen within the realm of mind? It has taken shape and form, and it arose from a idea?

If dimension is to be realized in the gravitational field differences(metric point considerations), then what is space in measure, that every discrete structure, could have such energies flow through it, and describe the nature and distinction as a elemental consideration?

Holography and Dimensional Relevance (http://www.superstringtheory.com/forum/metaboard/messages18/119.html)


Sol