What First principle was-- was it the geometry

I thought I would contrast this quote of Dirac's with the one of Feynman's.

You see the very idea of a constancy that spread through all Maxwell's equations was a necessary one which allowed Einstein to move into positive and negative valuations within the geometries? So did Dirac know how this was to be approached?

Dirac:

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

Feynman:

‘Maxwell discussed … in terms of a model in which the vacuum was like an elastic … what counts are the equations themselves and not the model used to get them. We may only question whether the equations are true or false … If we take away the model he used to build it, Maxwell’s beautiful edifice stands…’ – Richard P. Feynman, Feynman Lectures on Physics, v3, c18, p2.

Paul Dirac Talk: Projective Geometry, Origin of Quantum Equations Audio recording made by John B. Hart, Boston University, October 30, 1972

The quote below is in response to Dirac's comments

[ROGER PENROSE]

"One particular thing that struck me... [LAUGHTER]...is the fact that he found it necessary to translate all the results that he had achieved with such methods into algebraic notation. It struck me particularly, because remember I am told of Newton, when he wrote up his work, it was always exactly the opposite, in that he obtained so much of his results, so many of his results using analytical techniques and because of the general way in which things at that time had to be explained to people, he found it necessary to translate his results into the language of geometry, so his contemporaries could understand him. Well, I guess geometry… [INAUDIBLE] not quite the same topic as to whether one thinks theoretically or analytically, algebraically perhaps. This rule is perhaps touched upon at the beginning of Professor Dirac's talk, and I think it is a very interesting topic."

So the question might have been, how this was viewed and what the result was through such a axiomization? What was the first principe here? Was there one that became the guiding principal?

I mentioned the compass for Einstein, as a modelled perception that grew into the later years, but here, we might have seen the beginnings Feynmans toys model for such geometries?

Foundations of Mathematic

Mathematics, rightly viewed, possesses not only truth, but supreme beautya beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.

--BERTRAND RUSSELL, Study of Mathematics

In a Question below, is it worth it, to look at the context of what groups who gather might spark to the rest of society(click on it)? Look at what it has done for myself, and the reasons why such inductive/deductive features seem to be a part of the origins of cognitive functions that mathematically display itself?

Is there a theme in this regard through my blog that I had questioned earlier and links brought forth to raise awareness of what might have been implied in that true "consciousness sense" about the very nature of our involvement in the nature of reality?

But then too, awareness, about the death of such sensations. This is most troubling to me, if such model consumptions had made this impression then what had happened to the views as they exploded into the other realms? Other Realms? Why would I introduce Thales as a culminative vision about what could emerge and the father of geometry? Models make our view culmnative and increase the vision capabilites. Is there no one here that see differently after they had crossed a page to find that in our new tomorrows we see reality a little different now?

You have been touched at a most deep level, that goes beyond the death of such sensations as Toposense, or momentums of curvatures. A microscopic eye now, to the quantum nature, right next to your reading from this screen. It's in the air all around you, this potential? :)

Plato:

Mathematics(logic?) and experiment?

I respond in that thread, and although it would seems disjointed from the rest of the commentaries, I thought I was talking directly to Sean's opening post. So I have linked the post on the very title as I have done with previous entires, as they have been setting the pace for my thinking about what views they share and what safety net is placed out there for us lay readers.

Would this impede my question as to the relation of philosphy in Sean's opening statement, to find that it had found a trail that leads to reasons why funding and perspective on it, should be thought about most carefully. Held in the esteem, with which one's adventures in physics and mathematics might have benefited society?

I understand this need for determination, and as well, the need to reaffirm what philosophy might hold in regards to truly active memebers of the science community and the projects they are engaged in. Would they have a distain for the philosophy of mathematics?

I left a question mark out there, and this question although never answered did see some slight comment in relation to the philosophy that where such logic might have gained in relation, being mentioned. I'll have to explain this some more so you understand that I am working hard to make sense of what is out there and viewed, whether in the tabloids, or what ever generalizations made by mathematicians, or the physicist who looks that little bit further.

Shall I quickly respond to the thread commetary or should I continue? I thnk it important that I respond to the comments rasied but I'll do this after by highlighting the area that spoke to me in relation to this train of thought.

I linked a quote from Plato on the idea of philosophy in my comment. I wil be moving from that position.

Philosophy of Mathematics

Foundations Study Guide: Philosophy of Mathematics by David S. Ross, Ph.D.
The philosophy of mathematics is the philosophical study of the concepts and methods of mathematics. It is concerned with the nature of numbers, geometric objects, and other mathematical concepts; it is concerned with their cognitive origins and with their application to reality. It addresses the validation of methods of mathematical inference. In particular, it deals with the logical problems associated with mathematical infinitude.

Among the sciences, mathematics has a unique relation to philosophy. Since antiquity, philosophers have envied it as the model of logical perfection, because of the clarity of its concepts and the certainty of its conclusions, and have therefore devoted much effort to explaining the nature of mathematics.

You have to understand that although I am deficient in the math skills many have, it is not without effort that I am enaging myself in what appears to be beautiful and simplistic design when completed as a model. When we look at what the Wunderkammern had to offer in a revitalizing and dusting off of, models that were concretized for us. Did they lanquish until they were refurbished to the museums of time, so that we may again look at what mathematics has accomplished for us. In ways, that are very abstract and beautiful? What then exist as you gazed into the magnetic field, the dynamcis of brane held issues and the exemplification of design in those branes? It had to follow consistent and progressive developement in the physics of.



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

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

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

Social constructivism or social realism

Now here is the part, that while I saw the devloping nature of the tread of thinking and comments how would I answer and stay in tune? I previously spoke of John Nash and the inherent nature of mathematics as it could pierce the bargaining process, that to have this moved t a dynamcial social and constructive pallette developed in the ongoing relations of nations, why would such a scoial construct not be recognized as to the direction and strength of what mathematics might mean from a cognitive and developing brain that we have.

This theory sees mathematics primarily as a social construct, as a product of culture, subject to correction and change. Like the other sciences, mathematics is viewed as an empirical endeavor whose results are constantly compared to 'reality' and may be discarded if they don't agree with observation or prove pointless. The direction of mathematical research is dictated by the fashions of the social group performing it or by the needs of the society financing it. However, although such external forces may change the direction of some mathematical research, there are strong internal constraints (the mathematical traditions, methods, problems, meanings and values into which mathematicians are enculturated) that work to conserve the historically defined discipline.

This runs counter to the traditional beliefs of working mathematicians, that mathematics is somehow pure or objective. But social constructivists argue that mathematics is in fact grounded by much uncertainty: as mathematical practice evolves, the status of previous mathematics is cast into doubt, and is corrected to the degree it is required or desired by the current Mathematical Community. This can be seen in the development of analysis from reexamination of the calculus of Leibniz and Newton. They argue further that finished mathematics is often accorded too much status, and folk mathematics not enough, due to an over-belief in axiomatic proof and peer review as practices.

This gets very comlicated for me. Yet I recognize the inhernet pattern at the basis of these negotiatons and the games involved. More to follow, and short on time.

Aristotle and the Logic of the Natural World

Aristotle's logic, especially his theory of the syllogism, has had an unparalleled influence on the history of Western thought. It did not always hold this position: in the Hellenistic period, Stoic logic, and in particular the work of Chrysippus, was much more celebrated. However, in later antiquity, following the work of Aristotelian Commentators, Aristotle's logic became dominant, and Aristotelian logic was what was transmitted to the Arabic and the Latin medieval traditions, while the works of Chrysippus have not survived.

First and formost one should be drawn to the very highlighted statement emblazoned at the top of this blog.

PLato saids,"Look to the perfection of the heavens for truth," while Aristotle saids "look around you at what is, if you would know the truth"

I have to move quick forward here and reveal why the thinking is quite intense in terms of what such logic would have been revealling by "looking around you at what is." While I recognize this basis implanted in the natural world, such divisions arises from what had already existed. What we could accesss, as tangible realities of the ideas around us. "From whence they come?"

So maybe a list of the maths involved so far? If we can wrap these maths then what had we done from the perspective of the natural world? Would such creation of a new math help here?:) I have an idea, but all that thngs that currently exist and that will exist are already here. We just have to access them right? So what would support such adventures froma philosophy that had endured to realites of the natural process from the logic of a math? What math would this be?:)

Algebra

Geometry

Trigonometry

Calculus (single variable)

Analytic Geometry

Linear Algebra

Ordinary Differential Equations

Partial Differential Equations

Methods of approximation

Probability and statistics

Real analysis

Complex analysis

Group theory

Differential geometry

Lie groups

Differential forms

Homology

Cohomology

Homotopy

Fiber bundles

Characteristic classes

Index theorems

Supersymmetry and supergravity

K-theory

Noncommutative geometry (NCG for short)

So the idea is that Plato and Aristotle stand together, as a basis of what is happening in our world now. Between those of science and the resulting needs for experimentation. The roads to lead from the underlying avenues of philosophical thought, that would include math develoepment.

Now how is this possible you ask? How is it possible such logic coud have been so revealling of nature that we would strive to find it's meaning in patterns underlying the nature of this reality, are actually abstract rules of engagement, that had been developed through philosophical thought? How so?

If we look at the number of mayh creations what uses are these when moved into the basis is of the natural world? Would you not think these modes of thinking would be tempered by such logic, that math would find it's birthing as to the need for such expressions from this natural world?

So part of the realization is that the creation of the math had to have already existed in the forms of natures response, and that such access gained to these ideas, are worth noting as a means to what already existed in nature. That is my logic:)

Experimentation

So is there a method to the madness of all these tidbits of information that would wrap all of this in a easy way to divine the logic of the natural world? Is it beyond comprehension? I don't believe so, or why would I waste my time as a lay person, to move into this world of a higher standard of abstract thought and developing sciences, to wonder about the origins of the nature of this reality and the cosmolgical equivalent of asking what happened in that beginning of creation?

Would it be so subtle that such logic woud have been driven to ask where this beginning was, and what roads had currently lead all these minds to this very question.

Some act very safe, and walk safe ground, by what methods are currently tangible in our assessments, while other are quite adventurous. Some ask, that you stay in line, with current experimentation or suffer the wrath of deriving illusionary tales of ideas, that had not matured yet, as to the feasibility to what will express this logic of the natural world.


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

So mine is a simple philosophy, that holds complex variables. A simple painting, that holds a thuosand words?:) To me Math is like that, yet I am deficient in all the logic it had to bear down on the natural processes in this world. While my collegues are simple folk, I recognized the diversity of that group that Lubos and Clifford belong too. This is the origins of my statement. I understand as well, about the crackpostism that follows aether rejuvenation, yet I see the graviton as a member of that spacetime fabric.

Is this enough to speak on the creation and fabrications we like to embue to that natural world? Is it enough to understand these concepts, and find such roads leading too, are the very fringes of what is known and came from a brighter light that shines from behind us, to those shadows on the wall?

Charlatan's Who Use Graviton?

Are Gravity people Charlatan's?:)I certainly don't think so.:)



well this is a good perspective with which one could move forward and explain it for us lay people here? :)

Lubos Motl:

The graviton is, on the contrary, an example of a correct derivation from semiclassical gravity - a legitimate approximate unification of GR and QM. Its existence follows from the theories we have, even given some degree of ignorance of quantum gravity at higher energies, and at the semiclassical level, it is absolutely analogous to the photon.

The only difference is the value of the spin, the geometric interpretation of the graviton, and ultraviolet divergences from loops.

I might have had wrong ideas here about what the graviton as a force carrier "proposed?" To exemplified what gravity is...as a further extension of the theory of general relativity? Lubos sets it straight then on such joinings.

This is the crucial difference between the dark energy and modified gravity hypothesis, since, by the former, no observable deviation is predicted at short distances," Dvali says. "Virtual gravitons exploit every possible route between the objects, and the leakage opens up a huge number of multidimensional detours, which bring about a change in the law of gravity."

Dvali adds that the impact of modified gravity is able to be tested by experiments other than the large distance cosmological observations. One example is the Lunar Laser Ranging experiment that monitors the lunar orbit with an extraordinary precision by shooting the lasers to the moon and detecting the reflected beam. The beam is reflected by retro-reflecting mirrors originally placed on the lunar surface by the astronauts of the Apollo 11 mission.

I myself might find it nice to have the origins of how this graviton came about. How one might be mistaken to have seen the bulk as a teaming with them(blackholes?), and such congregations telling, about places stronger then, while others are weaker.

How telling is the photon as it travels through these spaces? What was the initial trigger that set things free as Hawking radiation? Some analogies there to consider as well:)

So it would be nice then if one could find analogies that would sit well and sink deep. You know that the general public likes to think easy, and not finding relevant all the dressings of mathematical explanations. Or do they?

Is it wrong to move so far ahead theoretically to be called a charlatan, by those who recognized the limitiations of experimentally proving it?

The 5th Dimension and the Networld

Hi Darwin,

You thought my statement foolish, about Immanuel Kant?

Instead of Darwin I thought maybe you might envision yourself as Aristotle, as you stand beside me, under the "arche.":)

That what religion does is build concrete things, and so to models, for apprehension. If you stand and look at the room, why would I ever direct you to the picture on the wall? You have to draw back and take in a wider picure of what you see of Plato?:)

To them, I said,
the truth would be literally nothing
but the shadows of the images.

-Plato, The Republic (Book VII)

Gerard t'Hooft, as well as Heisenberg, used comparative views establish from the Dialogues. These things were taken into the schools of learning.

So by your reasoning, condensed matter physicists would be really happy to just deal with matter principles(whatever the building blocks of matter are?)The bottom up approach, while holography by philosophical attachment, should become irrelevant while we discuss the dimensional significance of where we are now in the networld?:)

I am a student and learning, please be kind.:)

Unity of disparate Pieces

damptdweller:

Even if you take the string theorists viewpoint that the energy may “leak” away into a brane instead of actually disappearing I think I’m correct in saying that you still need to ensure that energy is conserved regardless.

Plato:While some might of thought it "dreamy," there is a direct physics correlation to that leaking in the collider. Although it is encompassed, like you said.

So where did it go, and how is "it" encompassed?

Sean:

understanding the unity of disparate natural phenomena.

So some people tried to form "new models" to help extend the way perceptions in science have always existed?

In a similar manner, in string theory, the elementary particles we observe in particle accelerators could be thought of as the "musical notes" or excitation modes of elementary strings.

While there was "particle states" to consider in terms of fermionic realizations, there was bosonic(force) interpretations that arose as well?

If such states were considered in the colliders, then, what valuation would have seen the extension of what is leaking to have been encompassed? Here the onion signatures are relevant.

Bulk Perceptions?

While the "brane features" seem to answer this, what moved the ideas of bosonic interpetations as features beyond the colliders? This all had to make sense to me. So the history of the expansion of processes, have been altered much as you would look at sound? Gia's example of hitting metal plates, to sound created when billiard balls collide, to exemeplfy a greater understanding of what theoretics is doing here?

Sound in relation to collision had a effect? It was this effect beyond the brane that was considered.

How could such thinking have lead to such abstractions and analogies if the theoretics had not be connected in the consistancies that are required of science?

As Maxwell equations were encompassing. As Einsteins theory of gravity was encompassing. By this methodology what came next? You has to understand this "tree of expression," in the modes of this thinking society "branched" to followed a format?


Time-Variable Gravity Measurements

As well as, the expansion capabilities of our brains?:) Osmosis, would have greater impact then:) From the ground up, as this tree grew? :)

Developement of Disbelief

As you read, hold on to the thought about stringy/M theory developement.

Richard Denton:

I discovered that it was simply philosophy on its own that had played the very much larger role in the gradual erosion of belief.

This is a interesting statement to me since some scientists might think that to have even included this in our "developing perspective" might have showed immediate signs of weakness? Evil?

As if, math came out of all natural things, on it's own?

So how did such views change us if we did not think about them more critically?

See, I am not sure I like to think that there is "no God" that can be substitued by taking this power of belief outside of ourselves to religions and institutions. Crippling us, as to the empowerment we have for such changes in our own life?

While we had seen the topic of "stringevangelism" introduced, there wasn't this concerted effort to make string as a all empowering "theory of everything( what underlying reality was referred too?)", even though, some would try to "invoke" these Godly powers of discrimmination. As a facist group, that would censor any views contrary to their own, as to what seemed, "stringevangelistic?" :)

It then became the same institution, that it despises? Some might know who I mean here. If I stood up to it, could I change reality as well, as to that this group invokes into society?

Anyway while I used Jo-Annes thread, "A little Bit of Heaven," to highlight this quality of earthly senses?

Topo-sense

Plato:

This intuitive feeling that is generated once math processes are understood are realized in dynamical movement revealled in the brains thinking? Had to arrive from lessons it learnt previously? Pendulums, time clocks, great arcs, and gravity?

I sought to internalize Gr's momentums, with Mecuries orbital patterns, or Hulse and Taylors expanding awareness of other things(gravity). I started to ask myself if this internalization was wrong? Is Topo-sense wrong? As too, intuitive unfoldments of the subject, in regards to Genus figures(holes)? Would it perish too? Revelations, leading to maths used?

Internal developement would have revealled a greater core depth of the realities around us. Which are highly abstract, yet, could have lead to insight and convictions held in astronomy happenings in the cosmo(isomorphic relations?)? So this internalization developed conviction, with the basis of Gr's valuation of quantum mechanical things, to cosmological proportions?

Strings as a model then, that could lead to perspectives with "langangian valuations" not only in terms of supersymmetry(concentration of a all pervading "beginning" that we could resort too,) as I espoused in Andrey Kravtsov computer's model.

That such relations in our philosophical orientation of physics would endure in measure, culminate with "fineness" and valuations of gravity perspectives. Could you do this, without some model?

So, would the "counter of belief in God," be the lesson the valuation of what one holds by introducing atheistic valautions, AS TO ROADS LEADING TO "COMMON SENSE?"

While I used stringy comparison for examination, this leads back again to what models can be used to keep the human beings empowered, without stealing this away from them by such institutionalizations? Continued reflection, thwarted, as to no experimental valuations yet philosphically introduced. You remember the opening statement I used?

I thought about the choices we make then, and the convictions we have. Would this have been irrelevant in our assessments of our own characters? After all, it would be you who walked back into society to think about the Smolins and Susskinds who would debate the essence of the backgrond?? What is understood, and what stringy needs to do?

Music of the Spheres

Strange Geometriesby Helen Joyce

Both spherical and hyperbolic geometries are examples of curved geometries, unlike Euclidean geometry, which is flat. In spherical geometry, the curvature is positive, in hyperbolic geometry, it is negative.

I thought I should add the "ascoustic variation" of the struggle for music in the world of "good and evil" as well.

That such "chaos created" in the minds of our youth, would have been frowned upon in Plato's academy.

By such reasonings and understandings of how such sound valuation may have been taken to spherical proportions? Should be no less then the consolidation points, as poincares distribution of eschers angel and demons pictures describe?

What avenues had been less then discribed on those chaldni plates that they had been reduced to dimensional avenues discriptive of the chaldni plates, as a fifth dimensional understanding? Langrangian discription of points L1 or L2, and a visionary context of Sylvestor surfaces as proponents of B field manifestations as part of genus figures with holes?

See:

Angels and Demons

Heaven's ephemeral Qualities?

"Materialism:

Basically, the view that everything is made of matter. But what is matter? Probably the most innocent and cheerful acceptance of it comes right at the start of materialism with Democratius of Abdera (in Northern Greece) in the fifth century B.C., for whom the world consisted entirely of 'atoms', tiny, absolutely hard, impenetrable, incompressible, indivisible and unalterable bits of 'stuff', which had shape and size, but no other properties, and scurried about in the void, forming the world as we know it by jostling each other and either rebounding (despite being incompressible) or getting entangled with each other because of their shapes. They and the void alone are real, the colours, flavours and temperatures that surround us being merely subjective. This model has lasted, with various modifications and sophistications right down to modern times, though the notion of solidity was causing qualms at least as early as Locke. But, in the last century, all has been thrown into confusion by Einstein's famous, E=mc2 and also by general relativity. Mass, the sophisticated notion that has replaced crude matter, is interchangeable in certain circumstances with energy, and in any case is only a sort of distortion of the space in which it was supposed to be floating. Photons and neutrons have little or no mass, while particles pop out of the void, destroy each other and pop back in again.

'The Oxford Companion To Philosophy', edited by Ted Honderich. Oxford University Press, 1995




Heaven in one sense, as a ephemeral quality(violet or blue), but in the gratification of savoring smell and tastes, these are not true bearers of the "quality of thought" are they? These sense are more.....earthly then?

I struggle. :)


If such senses are to perish, then what shall be everlasting? If intuition, is to only serve it's purpose until the math is adorned, then what shall this math be, in the state of the abstract mind(yellow)?

An equation means nothing to me unless it expresses a thought of God.

Srinivasa Ramanujan

Ramanujan's thought about equation is emotively charged (red), that this too issues from such a mental abstract, as to be from heaven and descending?

Wait! It's about heaven on earth? Really? :) Heaven is only a state of mind? (r/light)?

Am I Okay on analogies then, to confuse the mind about these states of heaven, that I could have mixed heaven up, as to the varities of "time and segments," as our own colorful experiences?

What song sung then, that each musical octave gain, and of loss is its own vibratory tone? Yet, it existed in the very fields of the sun, as a chemist combines?

A Clear Presence

Can one miscontstrue your words even more? :)

Lee Smolin said:

Of course if the theory is right-and we never assume so-we must show more. We must show that the ground state is semiclassical, by solving the dynamics. This is a hard problem, analogous to showing that the ground state of water is a solid. But as this is the focus of attention there are beginning to be significant, non-trivial results on how classical spacetime can emerge from a background independent quantum theory.

Jacques Distler:

But the mere possibility of such surprises should not reduce us to labelling every as-yet-not-experimentally-verified statement to the status of mere “opinion” or rank “speculation.”

While I am extreme with my "Angels and Demon" such comparative functions had not been limited too, the basics of such assumptions, but had indeed been dressed up by good science woman/man.

We all like a good story. Those, in regards to time travel or Contact like movie(science that is consulted as to the edge of what theoretcial positions had beem pushed).

Yet indeed even within the boundaries of work sciencetists bring here a division of what is hoped for, as a "reduced basis of assumption," could have been misleading as to the real science or not?

Is it illusion that we play with, that we would want the purity of thought manifested on the public scene, as warped mentalities of what many scientists would disgust them? This "clear presence?" An "open heart clear mind."

The story of Angel and demons has been misconstrued in science by very bright scientists, using the nature of right and wrong, as inherent features of negative and positive curvatures?

Taken to mean this theoretics and that, are indcative anomalies of the good and evil in society. Is it political? Or shall we play with the very concepts and misconstrue them for what they really are?

Raphael Rooms

The fog is immmense and greatly hides the idea of this clear presence. Opening good hearts and minds as to the attempts to get rid of the illusions that would take hold of society? Allow the greater vision of perspective, a picture, that had been piecemealed, to raise a reality of what the picutre is painted on, the room it sits in, and what each parts of it, are telling the story about the geometers of the world?