Induction and Deduction

Our attempt to justify our beliefs logically by giving reasons results in the "regress of reasons." Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are "first principles." The "Problem of First Principles" arises when we ask Why such reasons would not need to be proven. Aristotle's answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.

The interesting thing about developing vision is of course recognizing the framework with which you will make deductions about the world, and the structures with which you will deal. If held to pre-establish routes, and leading indicators of geometrical design, leading to higher dimensional attributes revealled in topological discourses, then such vision would have required the mind accept higher dimensional attributes first?



Often the very idea, of distilling information, inductively looking at the object of consideration, would have been like sitting in front of a picture and realizing that the very ideas about inductive and deductive reasoning would have made them self know in some way or form. So for me, recognizing the piecing that has gone on with the royal road to geometry, Plato's discourse with Aristotle at the top of this web page, part of deciphering this global village of ideas, is to soak up the picture of Rapheal.

So what I have done here is brought together another idea(the arch), in the comprehension of this picture for consideration. That in model comprehension( and just for the sake of it accept string theory for a moment) it is always much easier to accept the picture as it is, without really understanding the deeper implications of it.

Now in my research, and looking at what happened with Lenny Susskind and the work he was doing, such a inspirative insight of the string vibration in his head would have been a recognition and culmination of other things, before, this image materialized in his brain.

If we understand the topic of this thread, inductive and deductive modelling would have helped one recognize that the model acceptance would have immediately forced the mind to consider inductive and deductive features, as topological expressions of the roads leading from this geometry of expression to higher dimensinal attributes no less then what John Baez describes for us in using Platonic Solids for comparison.



In order to get to what is self-evident, such realizations of higher dimensions would have asked the mind to exercise it's ability to move in these higher abstract worlds, by looking at differents model comprehensions and acceptances, to prepare it for extensions and realizations of those same realities we live in?

"We hold these truths to be self evident"

Should have been emblazoned on the American mind, and the realization of the way in which such truths once accepted, help us to move on and further develope the models we would want of the society as recognition of this whole picture. Simplified, such realizations signify the grokking and acceptance of the model and the ability, to play with other avenues of consideration, and in this case, strings as an example.

It could be Loop or Penrose as well and recognition, that the standard model is part and parcel of the whole view. One would have recognized this if they had understood that to go beyond the standard model and include gravity they had already bypassed this idea and formulation in a conprehensive whole.

From the planck epoch in cosmological understanding, grand unification, made this implicite in the design as part of a comprehensive whole of the dimensional significance of the developing cosmos.

The Sound of the Landscape

Ashmolean Museum, Oxford, UK

As you know my name is Plato (The School of Athens by Raphael:)I have lived on for many years now, in the ideas that are presented in the ideas of R Buckminister Fuller, and with the helping hands of dyes, have demonstrated, the basis of these sounds in balloon configuration worth wondering, as simplice's of these higher dimensional realizations.

A Chladni plate consist of a flat sheet of metal, usually circular or square, mounted on a central stalk to a sturdy base. When the plate is oscillating in a particular mode of vibration, the nodes and antinodes set up form a complex but symmetrical pattern over its surface. The positions of these nodes and antinodes can be seen by sprinkling sand upon the plates;

Now you know from the previous post, that I have taken the technical aspects of string theory, and the mathematical formulations, and moved them into a encapsulated state of existance, much as brane theory has done.

I look at this point(3 sphere derivation from euclid point line plane), on the brane and I wonder indeed, how 1R radius of this point becomes a circle. Indeed, we find this "idea" leaving the brane into a bulk manifestation of information, that we little specks on earth look for in signs of, through our large interferometers called LIGO's



John Baez:

Ever make a cube out of paper? You draw six square on the paper in a cross-shaped pattern, cut the whole thing out, and then fold it up.... To do this, we take advantage of the fact that the interior angles of 3 squares don't quite add up to 360 degrees: they only add up to 270 degrees. So if we try to tile the plane with squares in such a way that only 3 meet at each vertex, the pattern naturally "curls up" into the 3rd dimension - and becomes a cube!

The same idea applies to all the other Platonic solids. And we can understand the 4d regular polytopes in the same way!

The Hills of M Theory

The hills are alive with the sound of music
With songs they have sung for a thousand years.
The hills fill my heart with the sound of music
My heart wants to sing every song it hears....

It's a wonder indeed that we could talk about the spacetime fabric and the higher dimensions that settle themselves into cohesive structures(my solids) for our satisfaction? What nodal points, do we have to wonder about when a string vibrates, and one does not have to wonder to much about the measure of the Q<->Q distance, as something more then the metric field resonates for us?

This higher dimensional value seen in this distance would speak loudly to its possiblites of shape, but it is not easily accepted that we find lattice structures could have ever settled themselves into mass configurations of my solids.



Lenny Susskind must be very pround of this landscape interpretation, as it is shown in the picture above. But the question is, if the spacetime fabric is the place where all these higher dimensions will reveal themselves, then what structure would have been defined in this expression from it's orignation, to what we see today?

Alas, I am taken to the principles of," Spacetime in String Theory," by Gary T. Horowitz

If one quantizes a free relativistic (super) string in flat spacetimeone finds a infinite tower of modes of increasing mass. Let us assume the string is closed,i.e., topologically a circle

THE ANTHROPIC PRINCIPLE

The String Theory Landscape, by Raphael Bousso and Joseph Polchinski

Given the success of replacing the gravitational force with the dynamics of space and time, why not seek a geometric explanation for the other forces of nature and even for the spectrum of elementary particles? Indeed, this quest occupied Einstein for much of his life. He was particularly attracted to work by German Theodor Kaluza and Swede Oskar Klein, which proposed that whereas gravity reflects the shape of the four familiar spacetime dimensions, electromagnetism arises from the geometry of an additional fifth dimension that is too small to see directly (at least so far). Einstein's search for a unified theory is often remembered as a failure. In fact, it was premature: physicists first had to understand the nuclear forces and the crucial role of quantum field theory in describing physics--an understanding that was only achieved in the 1970s.

.



Previous, a discussion took place there in Peter's Blog on Susskind and Smolin. I would like to know if Peter supports Smolin's position?

I had mention to Lubos about the fact that strings/M theory had changed the concept of the quantum mechanical discription of the spacetime fabric. Part of this question, was based on how Smolin and LQGists would be limited in there perceptions, if acceptance of GR, does not go through any revision? Compton scattering amplitudes would have pointed to Glast determinations and support of Smolin in his valuation. But what was deeper in my mind, was the question of what graviton intersection might have implied, if such a unity would have been established, based on KK theory and unification of electromagnetism and gravity?

In Kaku's preface of Hyperspace, page ix, we find a innocent enough statement that helps us orientate a view that previous to all understanding, is counched in the work of Kaluza.

In para 3, he writes,

Similarily, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then equations governing light and grvaity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained inthe fifth dimension. In this way, we see the laws of light and gravity become simpler in five dimensions.

NATHAN MYHRVOLD

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

The thing I like about the oppositon of minds who embrace the Solvay attitude, is that it forces another to bring forward a history that few of us would have seen. So outside of the comments of opposing views what kind of harmony could have been produced?


SMOLIN VS. SUSSKIND: THE ANTHROPIC PRINCIPLE



Leonnard Susskind and Lee Smolin

While this is a conversation written by physicists for physicists, it should nonetheless be of interest for Edge readers as it's in the context of previous Edge features with the authors, it's instructive as to how science is done, and it's a debate that clarifies, not detracts.

Quantum Geometry

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.

- Hermann Weyl

I know I said I would post the discussion between Susskind and Smolin again for refreshing but I wanted to post the issue of Quantum Geometry first and then move there.

My area of research is superstring theory, a theory that purports to give us a quantum theory of gravity as well as a unified theory of all forces and all matter. As such, superstring theory has the potential to realize Einstein's long sought dream of a single, all encompassing, theory of the universe. One of the strangest features of superstring theory is that it requires the universe to have more than three spatial dimensions. Much of my research has focused on the physical implications and mathematical properties of these extra dimensions --- studies that collectively go under the heading "quantum geometry".

Quantum geometry differs in substantial ways from the classical geometry underlying general relativity. For instance, topology change (the ``tearing" of space) is a sensible feature of quantum geometry even though, from a classical perspective, it involves singularities. As another example, two different classical spacetime geometries can give rise to identical physical implications, again at odds with conclusions based on classical general relativity.

If one did not understand where this geometry will begin, then it does not make much sense for a person to consider the mathematics that will arise from this situation?

The Elegant Universe, by Brian Greene, pg 231 and Pg 232

"But now, almost a century after Einstein's tour-de-force, string theory gives us a quantum-mechanical discription of gravity that, by necessity, modifies general relativity when distances involved become as short as the Planck length. Since Reinmannian geometry is the mathetical core of genral relativity, this means that it too must be modified in order to reflect faithfully the new short distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Reinmannian geometry, string theory asserts this is true only if we examine the fabric of the universe on large enough scales. On scales as small as planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometry is called, quantum geometry."

So I have shown I thnk the importance of the math involved and how it might address the quantum nature of the world in small things. We find, we can be quite comfortable in looking at the achievemets of Einstein, in leading us to a good perception about things on a cosmological scale. But moving back to the "quantum geometry," what are we describing here?

Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

The same vigor with which string theory/M theory is attack for is fundamental points about the nature of the geometric world is no less important then what achivements and attempts are made by Rovelli. Each aspect of the societal influence theoretists and physics people engage in, is part and parcel of the individuals who are, hands on with the Elephant.


Edward Witten

Reflections on the Fate of Spacetime

The Holographical Principle

I must add a very important note. It is still hard for me to believe that Lee Smolin wrote something that could imply that *he* was the author of the conjecture. Lee Smolin has nothing to do with the discovery of the holographic principle and I hope that he always refers to the real authors properly-and it was just you who did not read carefully enough. The holographic conjecture, based on the Bekenstein's bounds and the Bekenstein-Hawking entropy of the black hole,has been first proposed by Gerard 't Hooft and discussed in more detail by Lenny Susskind: