Pages

Showing posts with label Genus Figures. Show all posts
Showing posts with label Genus Figures. Show all posts

Tuesday, July 08, 2014

Algebraic Topology



A first course in Algebraic Topology, with emphasis on visualization, geometric intuition and simplified computations. Given by Assoc Prof N J Wildberger at UNSW. The really important aspect of a course in Algebraic Topology is that it introduces us to a wide range of novel objects: the sphere, torus, projective plane, knots, Klein bottle, the circle, polytopes, curves in a way that disregards many of the unessential features, and only retains the essence of the shapes of spaces. What does this exactly mean? That is a key question... The course has some novel features, including Conway's ZIP proof of the classification of surfaces, a rational form of turn angles and curvature, an emphasis on the importance of the rational line as the model of the continuum, and a healthy desire to keep things simple and physical. We try to use pictures and models to guide our understanding.

See Also:

Tuesday, August 16, 2011

Another Kind of Sideways

 I wanted to expand on where the title,"Another Kind of Sideways." This blog posting  came from an interview with Clifford of Asymptotia by PBS. He had a posting of his own entitled Multiverse Musings about a Nova series on PBS in the Fall related to Brian Greene's book, The Fabric of the Cosmos.

Where would these other universes be in relation to ours? Is there a way to envision it?

Well, we live in three spatial dimensions: We move back and forth, up and down, left to right. And then there's time, so that's our four-dimensional universe. Another universe might be essentially right next to ours by going in another direction that's not one of those four. We might call it "another kind of sideways." See: Riddles of the Multiverse

The whole context of the idea of the Multiverse could have in my layman view be classified as speaking about and argued as the basis of "existing outside of time." I just wanted to say that mathematically this definition of the Multiverse can actually exist in that framework, yet had to be extrapolated to the real universe we live in and how other universes may apply.


SOCRATES: But if he always possessed this knowledge he would always have known; or if he has acquired the knowledge he could not have acquired it in this life, unless he has been taught geometry; for he may be made to do the same with all geometry and every other branch of knowledge. Now, has any one ever taught him all this? You must know about him, if, as you say, he was born and bred in your house.SEE:Meno by Plato


I am always interested in the way a correlation is struck, from a scientist's mind when looking at the world and the comparisons they may find in the real world. I mean, to stand on top of a mountain as I did, you get this sense of the terrain, and how the landscape appears. How from an idealist position, a mathematical position is described and how the universe can be described?

LEE SMOLIN- Physicist, Perimeter Institute; Author, The Trouble With Physics

Thinking In Time Versus Thinking Outside Of Time

One very old and pervasive habit of thought is to imagine that the true answer to whatever question we are wondering about lies out there in some eternal domain of "timeless truths." The aim of re-search is then to "discover" the answer or solution in that already existing timeless domain. For example, physicists often speak as if the final theory of everything already exists in a vast timeless Platonic space of mathematical objects. This is thinking outside of time. See:A "scientific concept" may come from philosophy, logic, economics, jurisprudence, or other analytic enterprises, as long as it is a rigorous conceptual tool that may be summed up succinctly (or "in a phrase") but has broad application to understanding the world.

I find it hard sometimes to try and explain something that is "not outside of time."  That such description of reality while confounding to those like me less able to understand the mathematical world of such truths that contrary to Lee Smolin's opinion such schematics can be found to exist "within each of us." How we build our world from the inside, and how we contain it.

Is the mathematical description of  polytopes any less real as a mathematical basis?

If one is to believe that a mountain top represents some "perfect symmetry" then what said all those places in the valleys can exist and would not represent some genus figure? What are we saying about the possible universes, locations within the universe,  and the creation of?

That a pencil standing on point, could fall one way or another, or a description of a false vacuum to a true could represent something leading away from such symmetry? Why the problem with such mathematical and schematize attributes? Would you as a scientist turn your back on such mathematical interpretations of the world?

Monday, April 04, 2011

It's Lowest Energy State....Matter Formed?

Shape as Memory : A Geometric Theory of Architecture

also

The structure of paintings

 

 
I just wanted to lay out a perspective in relation to how one might describe the engine in relation to the design of the exhaust system as supportive of the whole frame of reference as the engine.

The pipe is a resonant chamber which shapes the exhaust pulse train in a way which uses shock waves to constrain the release of the combustion.Russell Grunloh (boatguy)
I mean it is not wholly certain for me that without perception, once realizing that potential recognizes that like some "source code" we are closer to recognizing the seed of our action, is an expression of the momentum of our being. It is a stepping off of all that we have known, is an innate expression of our being in action.

So as souls, we are immortalized as expressions of,  like a memory that tells a story about our life, our choices and the life we choose to live.

Dr. Mark Haskins
On a wider class of complex manifolds - the so-called Calabi-Yau manifolds - there is also a natural notion of special Lagrangian geometry. Since the late 1980s these Calabi-Yau manifolds have played a prominent role in developments in High Energy Physics and String Theory. In the late 1990s it was realized that calibrated geometries play a fundamental role in the physical theory, and calibrated geometries have become synonymous with "Branes" and "Supersymmetry".

Special Lagrangian geometry in particular was seen to be related to another String Theory inspired phemonenon, "Mirror Symmetry". Strominger, Yau and Zaslow conjectured that mirror symmetry could be explained by studying moduli spaces arising from special Lagrangian geometry.

This conjecture stimulated much work by mathematicians, but a lot still remains to be done. A central problem is to understand what kinds of singularities can form in families of smooth special Lagrangian submanifolds. A starting point for this is to study the simplest models for singular special Lagrangian varieties, namely cones with an isolated singularity. My research in this area ([2], [4], [6]) has focused on understanding such cones especially in dimension three, which also corresponds to the most physically relevant case.

So it is also about string theory in a way for me as well, and my attempts to understand those expressions in the valley.  Poincare's description of a pebble, rolling down from the hilltop.


It follows then that not all comments will not all be accepted, yet,  I felt it important for one to recognize what Poincare was saying and what I am saying.


HENRI POINCARE Mathematics and Science:Last Essays


Since we are assuming at this juncture the point of view of the mathematician, we must give to this concept all the precision that it requires, even if it becomes necessary to use mathematical language. We should then say that the body of laws is equivalent to a system of differential equations which link the speed of variations of the different elements of the universe to the present values of these elements.

Such a system involves, as we know, an infinite number of solutions, But if we take the initial values of all the elements, that is,their values at the instant t =(which would correspond in ordinary language to the "present"), the solution is completely determined, so that we can calculate the values of all the elements at any period
whatever, whether we suppose />0, which corresponds to the "future," or whether we suppose t<0, which corresponds to the "past." What is important to remember is that the manner of inferring the past from the present does not differ from that of inferring the future from the present.

Contrast the pebble as an issuance of,  from symmetry, and the top of mountain(a sharpened pencil standing straight up) and the decay(asymmetry), as an expression of the solidification of who we are in that valley. as a pebble?? After the example, we are but human form with a soul encased. The present, is our future? Our past, our presence?

Mathematics and Science: Last Essays, by Henri Poincare

8 Last Essays

    "But it is exactly because all things tend toward death that life is
    an exception which it is necessary to explain.

    Let rolling pebbles be left subject to chance on the side of a
    mountain, and they will all end by falling into the valley. If we
    find one of them at the foot, it will be a commonplace effect which
    will teach us nothing about the previous history of the pebble;
    we will not be able to know its original position on the mountain.
    But if, by accident, we find a stone near the summit, we can assert
    that it has always been there, since, if it had been on the slope, it
    would have rolled to the very bottom. And we will make this
    assertion with the greater certainty, the more exceptional the event
    is and the greater the chances were that the situation would not
    have occurred."

Of course I do not believe our lives are just an expression of chance,  but choice as "a memory" we choose. Of course too, how do you set up a life as an expression if you do not continue to learn?



In the pool of symmetry, how did we ever begin? I looked for such expressions as if mathematically deduced from a time where we might be closer to the idea of such a pool. Ramanujan comes to mind.

Then too, if we are to become spiritually immersed back again from where we came from,  then how can we individually be explained "as a spark of measure,"  for each soul as a memory to be chosen from all that has existed before, for such an expression in this life as the task of it's future??

Thursday, February 24, 2011

Shape as Memory : A Geometric Theory of Architecture

I have yet to read the book.

What came to mind as I was looking at this has to do with the landscape of ideas.

It has to do with what is lying in those valleys. This may supply some understanding of how something can evolve from symmetry, as an expression of asymmetry geometrical objects. Pebbles on the side of mountains. So the idea then is that the memory is a form of geometrical expression of the energy. The object itself contains the information.

How do buildings store information and experience in their shape and form? Michael Leyton has attracted considerable attention with his interpretation of geometrical form as a medium for the storage of information and memory. In this publication he draws specific conclusions for the field of architecture and construction, attaching fundamental importance to the complex relationship between symmetry and asymmetry.


LIST OF CONTENT


1. Geometry and Memory 8
1.1 Introduction 8
1.2 Conventional Geometry: Euclid to Einstein 8
1.3 Special and General Relativity 10
1.4 New Foundations to Geometry 12
1.5 The Memory Roles of Symmetry and Asymmetry 15
1.6 Basic Procedure for Recovering the Past 18
1.7 Architecture 21

2. A Process-Grammar for Shape 24
2.1 Curvature as Memory Storage 24
2.2 General Symmetry Axes 25
2.3 Symmetry-Curvature Duality 26
2.4 The Interaction Principle 27
2.5 Undoing Curvature Variation 28
2.6 Extensive Application 29
2.7 A Grammatical Decomposition of the Asymmetry Principle 31
2.8 Process-Grammar and Asymmetry Principle 35
2.9 Scientific Applications of the Process-Grammar 36
2.10 Artistic Applications of the Process-Grammar 40
2.11 Architectural Applications of the Process-Grammar 41

3. Architecture as Maximal Memory Storage 54
3.1 Introduction 54
3.2 The Two Fundamental Principles 54
3.3 Groups 55
3.4 Generating a Shape by Transfer 56
3.5 Fiber and Control 58
3.6 Projection as Memory 59
3.7 Regularity in Classical Architecture 62
3.8 Breaking the Iso-Regularity 69
3.9 Reference Frames 70
3.10 New Theory of Symmetry-Breaking 70
3.11 Maximizing Memory Storage 72
3.12 Theory of Unfolding 75

4. Architecture and Computation 86
4.1 Introduction 86
4.2 New Foundations for Science 86
4.3 New Foundations for Art 89
4.4 New Foundations for Computation 90
4.5 What is a Building? 91

Thursday, November 19, 2009

Coffee and Donut?




A continuous deformation (homeomorphism) of a coffee cup into a doughnut (torus) and back.
Similarly, the hairy ball theorem of algebraic topology says that "one cannot comb the hair flat on a hairy ball without creating a cowlick."
***
This fact is immediately convincing to most people, even though they might not recognize the more formal statement of the theorem, that there is no nonvanishing continuous tangent vectorfield on the sphere. As with the Bridges of Königsberg, the result does not depend on the exact shape of the sphere; it applies to pear shapes and in fact any kind of smooth blob, as long as it has no holes.

In order to deal with these problems that do not rely on the exact shape of the objects, one must be clear about just what properties these problems do rely on. From this need arises the notion of homeomorphism. The impossibility of crossing each bridge just once applies to any arrangement of bridges homeomorphic to those in Königsberg, and the hairy ball theorem applies to any space homeomorphic to a sphere.

Intuitively two spaces are homeomorphic if one can be deformed into the other without cutting or gluing. A traditional joke is that a topologist can't distinguish a coffee mug from a doughnut, since a sufficiently pliable doughnut could be reshaped to the form of a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle. A precise definition of homeomorphic, involving a continuous function with a continuous inverse, is necessarily more technical.

Homeomorphism can be considered the most basic topological equivalence. Another is homotopy equivalence. This is harder to describe without getting technical, but the essential notion is that two objects are homotopy equivalent if they both result from "squishing" some larger object.
Equivalence classes of the English alphabet in uppercase sans-serif font (Myriad); left - homeomorphism, right - homotopy equivalence



 


An introductory exercise is to classify the uppercase letters of the English alphabet according to homeomorphism and homotopy equivalence. The result depends partially on the font used. The figures use a sans-serif font named Myriad.

Notice that homotopy equivalence is a rougher relationship than homeomorphism; a homotopy equivalence class can contain several of the homeomorphism classes. The simple case of homotopy equivalence described above can be used here to show two letters are homotopy equivalent, e.g. O fits inside P and the tail of the P can be squished to the "hole" part.

Thus, the homeomorphism classes are: one hole two tails, two holes no tail, no holes, one hole no tail, no holes three tails, a bar with four tails (the "bar" on the K
is almost too short to see), one hole one tail, and no holes four tails.
The homotopy classes are larger, because the tails can be squished down to a point. The homotopy classes are: one hole, two holes, and no holes.

To be sure we have classified the letters correctly, we not only need to show that two letters in the same class are equivalent, but that two letters in different classes are not equivalent. In the case of homeomorphism, this can be done by suitably selecting points and showing their removal disconnects the letters differently. For example, X and Y are not homeomorphic because removing the center point of the X leaves four pieces; whatever point in Y corresponds to this point, its removal can leave at most three pieces. The case of homotopy equivalence is harder and requires a more elaborate argument showing an algebraic invariant, such as the fundamental group, is different on the supposedly differing classes.

Letter topology has some practical relevance in stencil typography. The font Braggadocio, for instance, has stencils that are made of one connected piece of material.

Thursday, October 22, 2009

Artifacts in the Exploration of Geometry



Ashmolean Museum, Oxford, UK

It should not be lost on individuals who have followed this blog, that there is a range of connection to Platonic Forms idealization, that such an artifact in Ashmolean Museum although modeled to represent a reality and constituent forming basis, it is by this choice,  that I exercised a" foundational attitude"  about what I can use to push my own perspective forward in science. What others were using.


"The Artist and his Museum"

The first public showing of the mastodon (also known as the "Mammoth", the American incognitum and the "animal de l'Ohio") took place next door to Independence Hall, the building in which both the Declaration of Independence and Constitution were finalized. The venue, known variously as Peale's Museum, the American Museum or simply as The Museum, was the remarkable product of a resourceful, versatile and passionate artist and showman, Charles Wilson Peale.

Peale (1741-1827) was born and raised in Maryland. A vocal opponent of the Stamp Act, he was effectively driven from his first trade, saddle making, when loyalist merchants cut off his credit. He turned to a traveling life of a self-taught, itinerant portrait painter. After a short apprenticeship with Benjamin West in London, Peale returned to Maryland in 1769 to paint wealthy patrons throughout the Chesapeake region.
In 1776 he moved to the largest city of the colonies, Philadelphia, in the hopes of further developing his career. Through his contacts made while serving as a captain of the Continental Army, Peale painted a remarkable assemblage of Revolutionary War figures, including the most comprehensive portrait series ever painted of George Washington
. See:Charles Willson Peale's Museum

After doing quite a bit of reading over the years it is surprising what one can come across as they look at the historical perspective with artifacts which sat on shelves to curious onlookers as they examine these items.

Shown here are the models in the mathematical wunderkammer located in the Department of Mathematics at the University of Arizona. Like those in most modern mathematics departments, the collection is a combination of locally-made student and faculty projects together with a variety of commercially produced models. Sadly, a century since their Golden Age, many of the models are in disrepair and much of their documentation has been lost. However, some recent detective work, with the help of the Smithsonian Institution in Washington, has helped the department identify models by the American educators W. W. Ross and R. P. Baker in the collection.

Also see here for further thoughts on this




So you have in fact "forerunners of museums today" revealed in pursuits by individuals to catalog items according to the range of professions and undertakings. In this case, I was interested on geometrical forms as it was some interest to me that we could move our minds around in abstract spaces . I followed the surfaces of "dynamic movement"  issued forth by theoretical application. These would be,  modular forms or Genus figures of string theory, that raised my interest about the space we are working in.


Sylvester's models lay hidden away for a long time, but recently the Mathematical Institute received a donation to rescue some of them. Four of these were carefully restored by Catherine Kimber of the Ashmolean Museum and now sit in an illuminated glass cabinet in the Institute Common Room.

Now you must know that I do not have the education of the universities but this did not stop me from trying to understand what these artifacts in geometry actually represented. Where they were placed by theoreticians to represent the figurative evolution of what actual begins in this universe, from beyond time and space and arrived to a direction of expressions unfolding in the arrow of time. This was a recognition of the times in microseconds that had been "used in minutes" of Steven Weinberg.


A giddy craze was sweeping across Europe at the turn of the 17th century. The wealthy and the well-connected were hoarding things—strange things—into obsessive personal collections. Starfish, forked carrots, monkey teeth, alligator skins, phosphorescent minerals, Indian canoes, and unicorn tails were acquired eagerly and indiscriminately. Associations among these objects, if they were made at all, often reflected a collector's personal vision of an underlying natural "order". Critical taxonomy was rarely in evidence.

So this historical perspective of the artifacts moved my perspective to today and what is going on in mathematical abstraction. What are these shapes actually representing in reality? Is there such a thing once perception has been granted of the close correlative function of the description of that microscopic reality?

It would be that the mind has become capable of moving into the realm of the microscopic, that by measure of energy used, details the plethora of particle and constituents of that energy, that each artifact is leading toward ever finer issues of what began in the formation of the matter, to allow us to see it's constitutions as they are revealed today macroscopically.

Tuesday, March 11, 2008

Tipping LightCones and the Escape Velocity of a Photon

"Black Hole" by Tamsin van Essen Also see: Tamsin van Essen-Ceramic Design

Wonderful and creative thinking to what remains a mystery to a lot of people who do not ever get to see what cancer looks like or what it can do to one's family. This physical process, and the creative representation is a very interesting one to me.


Figure 2. Clebsch's Diagonal Surface: Wonderful.
We are told that "mathematics is that study which knows nothing of observation..." I think no statement could have been more opposite to the undoubted facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activity of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world, ...that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of imagination and invention. ...Were it not unbecoming to dilate on one's personal experience, I could tell a story of almost romantic interest about my own latest researches in a field where Geometry, Algebra, and the Theory of Numbers melt in a surprising manner into one another.


It also reminded me of the Wunderkammern and the move to "geometrical design," which was housed in Glass cases and for a time lost to the public eye. Sylvester surfaces is a case in point when looking at the nature of these geometrical models

I am interested in determining how one can detect a blackhole.

So the following post is in latex language that can be copied and those who have latex can place for examination. Clifford's spam checker(just recently checked and see that it was posted.) will not allow me to complete the rest of the comment entry so I will just put it here and go to bed. I tried putting in his latex sandbox(this now worked as well), but to no avail either.

Text book or not, it gives a clearer picture of what a "strong gravitational space" does to the photon.

Gravity and the Photon

The relativistic energy expression attributes a mass to any energetic particle, and for the photon

[tex]E=mc^2=hv[/tex]

The gravitational potential energy is then

[tex]\LARGE U=\frac{-GMm}r=\frac{-GMh}{rc^2}{vo}[/tex]

When the photon escapes the gravity field, it will have a different frequency

[tex]\large hv=hv_o[{1-}\frac{GM}{rc^2}] \hspace9 v=v_o[{1-}\frac{GM}{rc^2}] \hspace9 \frac{\bigtriangledown v} {v_o}={-}\frac{GM}{rc^2}[/tex]

Since it is reduced in frequency, this is called the gravitational red shift or the Einstein red shift.

--------------------------------------------------
Escape Energy for Photon

If the gravitational potential energy of the photon is exactly equal to the photon energy then

[tex]\normal hv_o=\frac{GM}{rc^2}{v_o} \hspace9 \text or r=\frac {GM}{c^2}\\ \text so if Mass M collapses to radius r a photon will be redshifted to zero frequency[/tex]

Note that this condition is independent of the frequency, and for a given mass M establishes a critical radius. Actually, Schwarzchilds's calculated gravitational radius differs from this result by a factor of 2 and is coincidently equal to the non-relativistic escape velocity expression

[tex]v_e_s_c_a_p_e_ = \sqrt {\frac{2GM}{r}} \hspace9 \\ \text which if V is set equal\\to c gives a radius r=\frac {2GM}{c^2}\hspace9 \text Schwarzchild Radius[\tex]

This equivalence is used as a mnenomic, but does not imply this is a valid way to derive the Schwarzchild Radius

You can delete from your tipping light thread. Have a nice day. I acknowledge fully I am the student. While we see tipping light cones there is an actual qualitative understanding for the determination of the blackhole in this context? By your definition you were right to let me know, how you are presenting this for better consumption and how I might be interfering with that process. So my apology (my bad).

Previously, I left a comment in relation to Susskind's thought experiment about the elephant and Bob on the back of the elephant B moving toward the horizon of the blackhole. My thoughts were about the "entanglement process" and how Alice on the back of elephant A would reveal aspects of the nature of the blackhole as elephant B move closer to that horizon.

This point, while understanding the representation of CFT in this regard, I thought it quite humorous that Susskind did in fact use the elephant as a representative thinking in relation to Quantum gravity? I do not know if people picked up on this?

Tuesday, October 09, 2007

The Landscape Again and again....




Of course I am not qualified to have an opinion about whether the landscape is of value or not. That there are people on two sides that have differing opinions, and based on what they have as proof to the contrary, of one or another, is whether the issue is ready for a forgone conclusion? Whether the person in association is a forgone conclusion.

Topography of Energy?

7. dorigo - October 8, 2007
Hi anomalous,

I will take your word for it - I must admit I was not aware of the breadth of his works. However, Nima’s position on the anthropic landscape of ST is enough for me to warn any student about his views.
Cheers,
T.


Stanley Mandelstam Professor Emeritus Research: Particle Physics
My research concerns string theory. At present I am interested in finding an explicit expression for the n-loop superstring amplitude and proving that it is finite. My field of research is particle theory, more specifically string theory. I am also interested in the recent results of Seiberg and Witten in supersymmetric field theories.



So by looking at a statement of a person, I wondered, has such a conclusion been reached and support by documentation that will help me decide?

Outrageous Fortune

There’s an article in this week’s Nature by Geoff Brumfiel entitled Outrageous Fortune about the anthropic Landscape debate. The particle physicists quoted are ones whose views are well-known: Susskind, Weinberg, Polchinski, Arkani-Hamed and Maldacena all line up in favor of the anthropic Landscape (with a caveat from Maldacena: “I really hope we have a better idea in the future”). Lisa Randall thinks accepting it is premature, that a better understanding of string theory will get rid of the Landscape, saying “You really need to explore alternatives before taking such radical leaps of faith.” All in all, Brumfiel finds “… in the overlapping circles of cosmology and string theory, the concept of a landscape of universes is becoming the dominant view.”

The only physicist quoted who recognizes that the Landscape is pseudo-science is David Gross. “It’s impossible to disprove” he says, and notes that because we can’t falsify the idea it’s not science. He sees the origin of this nonsense in string theorist’s inability to predict anything despite huge efforts over more than 20 years: “‘People in string theory are very frustrated, as am I, by our inability to be more predictive after all these years,’ he says. But that’s no excuse for using such ‘bizarre science’, he warns. ‘It is a dangerous business.’”

I continue to find it shocking that the many journalists who have been writing stories like this don’t seem to be able to locate any leading particle theorist other than Gross willing to publicly say that this is just not science.

For more about this controversy, take a look at the talks by Nima Arkani-Hamed given today at the Jerusalem Winter School on the topic of “The Landscape and the LHC”. The first of these was nearly an hour and a half of general anthropic landscape philosophy without any real content. It was repeatedly interrupted by challenges from a couple people in the audience, I think David Gross and Nati Seiberg. Unfortunately one couldn’t really hear the questions they were asking, just Arkani-Hamed’s responses. I only had time today to look at the beginning part of the second talk, which was about the idea of split supersymmetry.

Update: One of the more unusual aspects of this story is that, while much of the particle theory establishment is giving in to irrationality, Lubos Motl is here the voice of reason. I completely agree with his recent comments on this article. For some discussion of the relation of this to the Intelligent Design debate, see remarks by David Heddle and by Jonathan Witt of the Discovery Institute.


A sphere with three handles (and three holes), i.e., a genus-3 torus.

Jacques Distler :

This is false. The proof of finiteness, to all orders, is in quite solid shape. Explicit formulæ are currently known only up to 3-loop order, and the methods used to write down those formulæ clearly don’t generalize beyond 3 loops.

What’s certainly not clear (since you asked a very technical question, you will forgive me if my response is rather technical) is that, beyond 3 loops, the superstring measure over supermoduli space can be “pushed forward” to a measure over the moduli space of ordinary Riemann surfaces. It was a nontrivial (and, to many of us, somewhat surprising) result of d’Hoker and Phong that this does hold true at genus-2 and -3.


So by following the conversation I meet up with was offered as evidence, this then, leads me to follow up in even greater depth. How can one give a person such a title of "in question," based on what another posts, as to their characrter of study?

The equations of string theory specify the arrangement of the manifold configuration, along with their associated branes (green) and lines of force known as flux lines (orange). The physics that is observed in the three large dimensions depends on the size and the structure of the manifold: how many doughnut-like "handles" it has, the length and circumference of each handle, the number and locations of its branes, and the number of flux lines wrapped around each doughnut.

11. Plato - October 9, 2007
Tammaso:However, Nima’s position on the anthropic landscape of ST is enough for me to warn any student about his views.
So is this support for what you think is relevant. I have followed the discussions between Lee Smolin, Jacques Distler, Clifford of Asymptotia and Peter Woit of “Not Event Wrong.”

I wonder if you had “more information,” if this might change your statement above, and conclusion, you may have drawn from seeing another view? One you might not of seen before?

Is mathematical consistency of value to you when it is developing?


So with a certain knowledge already gain from following other discussions I am quick to ask if such a link to another is good enough for assigning credibility to another person. Especially one who holds a "view point" other then one held by Peter Woit. After all is Peter Woit not a mathematics man? I am really asking.



So based on this assumption(what I ask others not to do) about Peter Woit or string theorist while having a basis in mathematics. I am asking, that if such a development that is, "current and consistent in mathematics" why would this contradict and qualify any individual "to other then" what mathematics requires to move forward. To try and attempt too, "connect to reality" in a phenomenological way?

The basis of my insight is in fact current collider technologies, and the relationship I see to bulk production gravitons. If Gr is an outcome of String theory then, any pocket universe that demonstrates some mathematical consistency should, be of relevances in one's decision?

It is always a work in progress that such questions continue to push me forward. In that process I "vaguely recall" that Jacques did not think the association to modular form in terms of the genus figure could ever be related to that pocket universe?

I must say to you that in my case I am asking of Calabi Yau's, can have some predictability to how universe selection is accomplished and thus any steady development in mathematics pushing that landscape to credibility?

Monday, September 24, 2007

Are there Patterns to Life?

Its grandness, goodness, beauty and perfection are unexcelled. Our one universe, indeed, the only one of its kind, has come to be.Timaeus concludes


I was just thinking about the idea of being a mathematical structure, and having been made aware of Max Tegmark, it drew me back to the idea of the "soccer ball universe."

"If this holds up to the test of time, it's a real landmark," said Max Tegmark, a cosmologist and cosmic microwave expert at M.I.T. "I really feel like the universe has given up one more clue," he said.
See: Scientists Get Glimpse of First Moments After Beginning of Time by DENNIS OVERBYE


Now yes I'd admit the universe is a far cry from the person we are, but we are much more complex, and I'd liken it to the universe. Why not?

Namagiri, the consort of the lion god Narasimha. Ramanujan believed that he existed to serve as Namagiri´s champion - Hindu Goddess of creativity. In real life Ramanujan told people that Namagiri visited him in his dreams and wrote equations on his tongue.
See:Srinivas Ramanujan(1887-1920):

Anyway twice I have been reminded of the mathematics "are not" the reality of the situation, and that governing such thought is devoid of the reality we are dealing with. I have an issue with this because, we have discovered number patterns that underly nature just as Coxeter believes that "the process" is just awaiting to be discovered. Then, we have found the thread through things.

So, people do not like to believe that we are a mathematical structure, yet, we have seen where hidden numbered processes have been detailed for us in the expressions of nature.

The Valley and our Place in the universe


Jacques Distiler:
Rather, it is assumption 2) that is suspect. I argued that it is suspect in much greater generality in the comment thread I linked to above. But, in the specific case of the proton lifetime, we already have seen two mechanisms, discussed in this thread, either of which could constrain the proton lifetime to be far longer than the anthropic bound.


Jacque Distler:
Obviously, no one has yet found a convincing candidate for the Standard Model, among the string vacua explored to date (in that sense, no one has made any predictions yet). But that’s not what you’re saying(Peter Woit). You are claiming that the framework itself is inherently unpredictive.


Italicized is my addition.

A mathematics man who does not like math?

So you see we are looking for the constants(a product of the standard model), yet, we do not know what that constant will look like in the valley. While it is based on a "gravitational inclination," the formation has a probability "greatly enhanced" when thinking about the entropy of the blackhole. The "energy valuation" from mass while in gravitational collapse, creates the multitude of possibilities(heat)?

Wednesday, June 06, 2007

The Cosmic Landscape

I noticed a few blogs mentioning the landscape.

Asymptotia(Clifford Johnson), The Reference Frame(Lubos Motl), and Not Even Wrong (Peter Woit's) blog.

The Cosmic Landscape:String Theory and the Illusion of Intelligent Design by Leonard Susskind

After reading Susskind's book in regards to the landscape issue, I was intrigued by the First Three Microseconds previous as it helped iilucidate some of this information for me. As well as giving me some indications from the blogs mentioned and the topic therein.

What struck me a quite profound in reading Susskind's book, was that what was to all appearances a troubling issue with "eyesight," in regards to Peter Woits idea of intelligent design attributed to the landscape of string theory, that Susskind, was actually answering him by pronoucing the title of this book of his. It's obvious, he has been watching the discussions.

Now what was profound, was that the idea of the landscape was a mathematical construct. If you were so concerned about the idea of the landscape, then why would anyone with "math skills" reject the landscape? If the day is announcing itself in blog voices and now say hmmm.... with interest, I see that it is becoming more acceptable?

If you did not see the "hills and valleys" for what they were, then why would you reject what was leading in terms of the finiteness of Mandelstam, and then say, there was no more future in regards to where math had left off?

This is Lee Smolin's downfall I think when discussing the issue of Polchinski's concepts, reitereated with regards to Lee's book, and the "ventures of mathematics" as it has been spelted out and had pointed towards the landscape issues.

This is where Peter Woit made his mistake as well.

I accept that a lot of people don't like it. But that's not the point in terms of mathematical development, as it had been argued by Polchinski, against his reading and comments in regards to Lee Smolin's book.

See:The First Three Microseconds

This infomration has lead me to insights about the landscape that had missed most people, even those who are well educated. My point above is in regards to Mandelstam, and the arguments against Lee by Jacques distiller, was important from this aspect.

Reject the notion of the topological figures in relation to the landscape issue, and what is left? Yes, Lee's and Peter Woits ideas about the landscape, which is not finished. Which is leading with concepts, by mathematical deduction.

Can't always answer in post responses, but please let me know that you are visiting? :)

My son and I are starting our foundation. I write when I can, but read in the hours without our electricity and by battery alone.

Thursday, April 12, 2007

The CrossOver Point within the Perfect Fluid?

I had been following this research because of what I had been trying to understand when we take our understanding down to a certain level. That level is within the context of us probing the collision process for evidence of "some new physics" that we had not seen before.

Evidence for Neutrino Oscillations from the LSND Experiment
One of the only ways to probe small neutrino masses is to search for neutrino oscillations, where a neutrino of one type (e.g. numubar ) spontaneously transforms into a neutrino of another type (e.g. nuebar ) For this phenomenon to occur, neutrinos must be massive and the apparent conservation law of lepton families must be violated. The probability for 2-flavor neutrino oscillations can then be expressed as P=sin2(2theta) sin2(1.27 m2L/E) , where theta is the mixing angle, m2 is the difference in neutrino masses squared in eV2, L is the neutrino distance in meters, and E is the neutrino energy in MeV. In 1995 the LSND experiment [1] published data showing candidate events that are consistent with numubar->nuebar oscillations. [2] Additional data are reported here that provide stronger evidence for numubar->nuebar oscillations [3] as well as evidence for numu->nue oscillations. [4] The two oscillation searches have completely different backgrounds and systematics from each other.


What valuation of this process allows us to think that while speaking to "probing this perfect fluid" that we had not discovered some mechanism within it, that allows us to see Coleman Mandula effects being behind, as a geometrical unfoldment from one state into another?

If we had looked at the Genus 1 figure then what avenue would help us discern what could come from the string theory landscape and the "potential hill" discerned from the blackhole horizon? What tunnelling effect could go past the hill climbers and valley crossers to know that you could cut "right through the hill?"

MiniBooNE opens the box

BATAVIA, IllinoisScientists of the MiniBooNE1 experiment at the Department of Energy's Fermilab2 today (April 11) announced their first findings. The MiniBooNE results resolve questions raised by observations of the LSND3 experiment in the 1990s that appeared to contradict findings of other neutrino experiments worldwide. MiniBooNE researchers showed conclusively that the LSND results could not be due to simple neutrino oscillation, a phenomenon in which one type of neutrino transforms into another type and back again.

The announcement significantly clarifies the overall picture of how neutrinos behave.


So while I am looking for some indications as I did in the strangelet case, as, evidence of this crossover, this had to have some relation to how we seen the neutrinos in development. This was part of the development as we learnt of the history of John Bahcall.

John Bahcall 1934 to 2005 See also "John Bahcall and the Neutrinos"


Plato Apr 11th, 2007 at 8:47 pm

the quark-gluon plasma behaves according to hydrodynamic calculations in which the matter is like a liquid that flows with no viscosity whatsoever.” See here

No cross over point? What role would Navier Stokes play in this?
See here

This does not minimize the work we see of Gran Sasso in relation to the LHC project.

Honestly, I do not know how someone who could work on the project, could not know what they were working on? It as if the "little parts" of the LHC project only cater to the worker Bees working just aspects of the project and their specializations.

Whilst now, you go way up and overlook this project. To see the whole context measured within that "one tiny big bang moment." Trust me when I say, we shall not minimize the effect of calling the collision process as "one tiny moment," for you may never see the whole context of this project being developed for this "one thing."

I did not realize the shortcomings that scientists place on themselves when they do specialize. I just assumed they would know as much as I did and see the whole project? I do not say this unkindly, just that it is a shock to me that one could work the string theory models and not realize what they are working on. I have heard even Jacques say there is no connection and listening to Peter Woit, I was equally dismayed that he did not realize what the string theory model was actually doing as it found it's correlation in the developing views of how we look at the moments of creation.

Bigger is better if you’re searching for smaller

Neutrinos may be in CERN's Future

The next step will again be taken in Japan, with the new J-PARC accelerator starting in 2009 to send neutrinos almost 300 km, again to the Super-Kamiokande experiment, to probe the third neutrino mixing angle that has not yet been detected in either atmospheric or solar neutrino experiments. This may also be probed in a new experiment being proposed for the Fermilab NuMI beam. One of the ideas proposed at CERN is to probe this angle with an underwater experiment moored in the Gulf of Taranto off the coast of Italy, viewing neutrinos in a modified version of CERN's current Gran Sasso beam.
See "CERN and Future Experiments"

Plato Apr 12th, 2007 at 7:31 am

I think my comment on previous post of looking for the perfect fluid should have been here.

Also I do not think this changes how we look at string theory as a model probing the perfect fluid, and "the understanding" of developing a mechanism for this "cross over point?"

Topologically, how would this have been revealed in the string theory landscape??
See here and know that Clifford again deleted the short little post above. The point is I think for some reason once I mention string theory or evn M theory in relation to what is transpiring in the views of model development he doe not like this and would be support by Jacques as well.

That would be my job to convince them and anyone else that hold their views that taking our view to the microseconds, there is a definite relation to the timeline whether you agree with this or not. By introducing "the point of the cross over" you in effect have taken the model and presented it as part of the mechanism for this universe and effectively given new meaning to the "string theory landscape."

You may want it to be "background independent" like Lee wants it to be, but if you view the background as a oscillatory one, then any idea as configured to the mass of any particle, then you have define this particle as a energy relation? So Lee does not like the oscillatory universe?

See "Finiteness of String Theory and Mandelstam"

It is contained "within the moment" of the creation of this universe, yet, we do not know what design this particle is to be in context of the microscopic view of geometrical topologically finishes? As the Genus 1 figure and as an expression of this universe? You had to know what was lying in those valleys, and the potentials of expression, and I relay that in the blackhole horizon as a potential hill.

The time has come for some changes in this blog and I have been thinking about moving on. While a layman, I do not like to be treated like a fool. Maybe not educated fully and with some work to do, but never as a fool.

Thursday, April 05, 2007

Nurturing Creativity

See here and here


It looks as if moderation, or maybe technical problems, has set in for me at Cosmic Variance. So I have to go from the last statement made there by Lee that I was allowed to contribute. To continue with the points I am making.

I was glad to see Jacques was continuing where David B seems to have decided the futility of dealing with these issues of the String theory backlash.

Lee Smolin:When there was little selection we naturally got a wide diversity of types of scientists, which was good for science. My view is that we need that diversity, we need both the hill climbers and the valley crossers, the technical masters and the seers full of questions and ideas.

Raphael Bousso and Joseph Polchinski in "The String Theory Landscape" September 2004 Scientific issue speak exactly to what Lee is saying and descriptively allow us to see the pattern underlying Lee's comment. Maybe George Musser will release it for the group to inspect here

Take full note of the diagrams.

See OFF THE HOOK. Line-by-line crocheting instructions that tell where to increase or decrease numbers of stitches create the global shape of the Lorenz manifold.Univ. of Bristol

Clifford:Hooking Up Manifolds
The artlcle goes a great deal into the story of how mathematician Hinke Osinga and her partner mathematician Bernd Krauskopf got into this, and why they find it useful. You’ll also hear from mathematicians Carolyn Yackel, Daina Taimina, and Sarah-Marie Belcastro. This has been going on for a while, and there are even published scientific papers with crocheting instructions for various manifolds! How did I miss out on this?! This is great!


If you did not continue with understanding the "topography of the energy involved" in terms of what the string theory landscape was doing, then you would have never understood the "hills and valleys" in the context of string theory landscape being described?

HYPERBOLIC FABRIC. Many of the lines that could be inscribed on this crocheted hyperbolic plane curve away from each other, defying Euclid's parallel postulate.
Taimina


IN retrospect decisions we make will always resound with what we should have done, but that misses the boat when coming to the "creative abilities?" What we see may "institute a productive research group?" You exchange one for another?

Lee Smolin:Is string theory in fact perturbatively finite? Many experts think so. I worry that if there were a clear way to a proof it would have been found and published, so I find it difficult to have a strong expectation, either way, on this issue.

The fact that a way had been describe in terms of developing the "Triple Torus" speaks to the continued development of the string theory landscape? How could you conclusively finish off this statement and then from it describe the state of the union, when this had already been explained technically?

We say that E8 has rank 8 (the maximum number of mutually commutative degrees of freedom), and dimension 248 (as a manifold). This means that a maximal torus of the compact Lie group E8 has dimension 8. The vectors of the root system are in eight dimensions, and are specified later in this article. The Weyl group of E8, which acts as a symmetry group of the maximal torus by means of the conjugation operation from the whole group, is of order 696729600.


You had to see the context of the triple torus in relation too where the string landscape places were placing these modular forms. If I had said E8 and the continued development of modular form, what would this represent?

The complexity of the forms themself are limited and finite so how could one claim that such work on the landscape is futile in regards to infinities?

Thursday, December 14, 2006

Against Symmetry

The term “symmetry” derives from the Greek words sun (meaning ‘with’ or ‘together’) and metron (‘measure’), yielding summetria, and originally indicated a relation of commensurability (such is the meaning codified in Euclid's Elements for example). It quickly acquired a further, more general, meaning: that of a proportion relation, grounded on (integer) numbers, and with the function of harmonizing the different elements into a unitary whole. From the outset, then, symmetry was closely related to harmony, beauty, and unity, and this was to prove decisive for its role in theories of nature. In Plato's Timaeus, for example, the regular polyhedra are afforded a central place in the doctrine of natural elements for the proportions they contain and the beauty of their forms: fire has the form of the regular tetrahedron, earth the form of the cube, air the form of the regular octahedron, water the form of the regular icosahedron, while the regular dodecahedron is used for the form of the entire universe. The history of science provides another paradigmatic example of the use of these figures as basic ingredients in physical description: Kepler's 1596 Mysterium Cosmographicum presents a planetary architecture grounded on the five regular solids.





The basic difference that I see is the way in which Lee Smolin adopts his views of what science is in relation too, "Two traditions in the search for fundamental Physics."

It is strange indeed to see perfection of Lee Smolin's comparison and having a look further down we understand the opening basis of his philosophical thoughts in regards to the title "against symmetry?"

Some reviews on the "Trouble With Physics," by Lee Smolin

  • Seed Magazine, August 2006
  • Time magazine August 21, 2006
  • Discover Magazine, September 2006 &
  • Scientific American, September 2006
  • Wired September 2006:15 :
  • The Economist, Sept 14, 2006
  • The New York Times Book review, Sep 17, 2006 by Tom Siegfried
  • The Boston Globe, Sept 17, 2006
  • USA Today, Sept 19, 2006
  • The New York Sun, by Michael Shermer, Sept 27, 2006
  • The New Yorker,  by Jim Holt Sept 25,2006
  • The LA Times, by K C Cole, Oct 8, 2006
  • Nature,
  • by George Ellis (Nature 44, 482, 5 Oct. 2006)
  • San Fransisco Chronicle , by Keay Davidson, Oct 13, 2006
  • Dallas Morning News, by FRED BORTZ, Oct 15, 2006
  • Toronto Star, by PETER CALAMAI, Oct 15, 2006


  • But before I begin in that direction I wanted people to understand something that is held in the mind of the "condense matter theorist." In terms of the building blocks of nature. This is important basis of understanding, that any building block could emergent from anything, we had to identify where this symmetry existed, before it manifested in the "matter states of reality."

    Everyone knows that human societies organize themselves. But it is also true that nature organizes itself, and that the principles by which it does this is what modern science, and especially modern physics, is all about. The purpose of my talk today is to explain this idea.


    So it is important to understand what is emergent and what exists in the "theory of everything" if it did not consider the context of symmetry? AS a layman trying to get underneath the thinking process of any book development, it is important to me.

    Symmetry considerations dominate modern fundamental physics, both in quantum theory and in relativity. Philosophers are now beginning to devote increasing attention to such issues as the significance of gauge symmetry, quantum particle identity in the light of permutation symmetry, how to make sense of parity violation, the role of symmetry breaking, the empirical status of symmetry principles, and so forth. These issues relate directly to traditional problems in the philosophy of science, including the status of the laws of nature, the relationships between mathematics, physical theory, and the world, and the extent to which mathematics dictates physics.


    The idea here then is to find super strings place within context of the evolving universe, in terms of, "the microseconds" and not the "first three minutes" of Steven Weinberg.

    So it is important to see the context with which this discussion is taking place, in terms of the high energy and from that state of existence to what entropically manifests into the universe now.

    Confronting A Position Adopted By Lee Smolin


    A sphere with three handles (and three holes), i.e., a genus-3 torus.

    This is only "one point of contention" that was being addressed at Clifford Johnson's Asymptotia.

    Jacques Distler :

    This is false. The proof of finiteness, to all orders, is in quite solid shape. Explicit formulæ are currently known only up to 3-loop order, and the methods used to write down those formulæ clearly don’t generalize beyond 3 loops.

    What’s certainly not clear (since you asked a very technical question, you will forgive me if my response is rather technical) is that, beyond 3 loops, the superstring measure over supermoduli space can be “pushed forward” to a measure over the moduli space of ordinary Riemann surfaces. It was a nontrivial (and, to many of us, somewhat surprising) result of d’Hoker and Phong that this does hold true at genus-2 and -3.


    There is no doubt that the "timeliness of statements" can further define, support or not, problems that are being discussed. I don't mind being deleted on the point of the post above, because our good scientist's are getting into the heat of things. I am glad Arun stepped up to the plate.

    Part of finally coming to some head on debate, was seeing how Peter Woit along with Lee Smolin were being challlenged for their views, while there had been this ground swell created against a model that was developed, like Loop quantum gravity was developed. One of the two traditions in search for the fundamental physics. Loop qunatum Gravity and String theory(must make sure there is the modification to M theory?) Shall this be included?


    Click on link Against symmetry (Paris, June 06)

    But as they are having this conversation, it is this openness that they have given of themselves that we learn of the intricacies of the basis of arguments, so the public is better informed as to what follows and what has to take place.


    Against symmetry (Paris, June 06)

    So while this issue is much more complex then just the exchange there, I have not forgotten what it is all about. Or why one may move from a certain position after they have summarize the views they had accumulated with regards to the subject of String/M theory as a model that has out lived it's usefulness, in terms of not providing a experimental frame work around it.

    Saturday, December 02, 2006

    Finiteness of String Theory and Mandelstam



    It might be that the laws change absolutely with time; that gravity for instance varies with time and that this inverse square law has a strength which depends on how long it is since the beginning of time. In other words, it's possible that in the future we'll have more understanding of everything and physics may be completed by some kind of statement of how things started which are external to the laws of physics. Richard Feynman



    I was lead into this subject of Quantum Gravity, by Lee Smolin's book called, "Three Roads to Quantum Gravity." As a lay person reading what our scientist's have to say, I have a vested interest in what can start one off and find, that changes are being made to the synopsis first written. Did I understand his position correctly from the very beginning? I'll have to go back over my notes.

    But with this format now I have the opportunity to...ahem... get it..directly from the horses mouth(no disrespect intended and written based on knowing how to read horses). As I said, I tried early on to see how the situation of string theory could be refuted. I "instigated" as a comparative front for Lubos Motl and Peter Woit to speak from each of their positions. I had to disregard "the tones" set by either, as to the nature of whose what and how ignorant one might be, and comparatively, one might be to intelligent design? To get "some evidence" of why string theory might not be such a good idea?

    Now I believe this is a more "civil situation" that such a format has been proposed and that Lee Smolin can speak directly. As well as, "further information" supplied to counter arguments to Lee's position.


    A sphere with three handles (and three holes), i.e., a genus-3 torus.


    Jacques Distler :
    This is false. The proof of finiteness, to all orders, is in quite solid shape. Explicit formulæ are currently known only up to 3-loop order, and the methods used to write down those formulæ clearly don’t generalize beyond 3 loops.

    What’s certainly not clear (since you asked a very technical question, you will forgive me if my response is rather technical) is that, beyond 3 loops, the superstring measure over supermoduli space can be “pushed forward” to a measure over the moduli space of ordinary Riemann surfaces. It was a nontrivial (and, to many of us, somewhat surprising) result of d’Hoker and Phong that this does hold true at genus-2 and -3.


    Just a reminder about my skills. While I do things like carpetry, plumbing, electrical, I do not call myself a Carpenter, a Plumber or a Electrician. Nor shall I ah-spire to be more then I'm not, as I am to old this time around.

    Greg Kuperberg:
    The string theorists are physicists and this is their intuition. Do you want physical intuition or not?

    Okay, Smolin is also a physicist and his intuition is radically different from that of the strings theorists. So who is right?


    Yet, least I not read these things, can I not decipher "the jest" while it not being to technical? Shall I call it a Physicists intuition or I will only call my intuition what it is?

    Jacques Distler:
    When most people (at least, most quantum field theorists) use the term “finiteness,” they are referring to UV finiteness.


    While the things above talked about from Jacques are served by hindsight, "the jest" follows what comes after this point.

    The Jest of the Problem?

    My present research concerns the problem of topology changing in string theory. It is currently believed that one has to sum over all string backgrounds and all topologies in doing the functional integral. I suspect that certain singular string backgrounds may be equivalent to topology changes, and that it is consequently only necessary to sum over string backgrounds. As a start I am investigating topology changes in two-dimensional target spaces. I am also interested in Seiberg-Witten invariants. Although much has been learned, some basic questions remain, and I hope to be able at least to understand the simpler of these questionsStanley Mandelstam-Professor Emeritus Particle Theory


    Gina has asked questions in context of "academic excellence" in relation to what is being seen in relation to string theory. Of course we thank Clifford for providing the format for that discussion.

    The Trouble With Physics,” by Lee Smolin, Index page 382, Mandelstam, Stanley, and string theory finiteness, pages 117,187, 278-79, 280, 281, 367n14,15

    For reference above.

    Gina:
    I raised 16 points that I felt Lee’s arguments were not correct or problematic. This is an academic discussion and not a public criticism, and I truly think that such critique can be useful, even if I am wrong on all the 16 points.

    Three of my 16 points were on more technical issues, but I feel that I can understand Lee’s logical argument even without understanding the precise technical nature of “finiteness of string theory” (I do have a vague impression of what it is.) I think that my interpretation of this issue is reasonable and my critique stands.


    I find this interesting based on what information has been selected to counter the arguments that Lee Smolin used to support his contentions about what is being defined in string theory.


    Stanley Mandelstam Professor Emeritus Research: Particle Physics
    My research concerns string theory. At present I am interested in finding an explicit expression for the n-loop superstring amplitude and proving that it is finite. My field of research is particle theory, more specifically string theory. I am also interested in the recent results of Seiberg and Witten in supersymmetric field theories.


    So of course, here, I am drawn to the content of his book and what is the basis of his argument from those four pages. I hope my explanation so far summarizes adequately. For the lay person, this information is leading perspective as to the basis of the argument.

    Lee Smolin:
    Perturbative finiteness is a major element of the claim of string theory as a potential theory of nature. If it is not true then the case for string theory being a theory of nature would not be very strong.

    -Perturbative finiteness has not been proven. There is evidence for it, but that evidence is partial. There is a complete proof only to genus two, which is the second non-trivial term in an infinite power series, each term of which has to be finite. The obstacles to a complete proof are technical and formidable; otherwise we would certainly have either a proof or a counterexample by now. There is some progress in an alternative formulation, which has not yet been shown to be equivalent to the standard definition of string theory.

    -This is not an issue of theoretical physicists rigor vrs mathematical rigor. There is no proof at either level. There is an intuitive argument, but that is far from persuasive as the issue is what happens at the boundaries of super-moduli space where the assumption of that argument breaks down. In the formulation in which there is a genus two result it is not clear if there is an unambiguous definition of the higher order terms.

    Is string theory in fact perturbatively finite? Many experts think so. I worry that if there were a clear way to a proof it would have been found and published, so I find it difficult to have a strong expectation, either way, on this issue.


    It should be known here and here that all along I have been reacting to Lee Smolin's new book. The title itself should have given this away?

    The explanation of scientific development in terms of paradigms was not only novel but radical too, insofar as it gives a naturalistic explanation of belief-change. Thomas Kuhn


    So of course knowing the basis of my thought development is a "good idea" as the links show what spending our dollars can do, having bought what our good scientist Lee Smolin has written.

    There is a little "tit for tat" going on right now, but I think the point has been made sufficiently clear as to where Gina's thoughts in regards to the points on Finiteness is being made beyond 2?

    In these lectures, recent progress on multiloop superstring perturbation theory is reviewed. A construction from first principles is given for an unambiguous and slice-independent two-loop superstring measure on moduli space for even spin structure. A consistent choice of moduli, invariant under local worldsheet supersymmetry is made in terms of the super-period matrix. A variety of subtle new contributions arising from a careful gauge fixing procedure are taken into account.


    Yes I think I have to wait now to see if the discussion can now move beyond the first three points raised? Hopefully Lee will respond soon?

    How do you fight sociology

    Because this by any of the leaders of string theory. it was left to someone like me, as a quasi "insider" who had the technical knowledge but not the sociological commitment, to take on that responsibility. And I had done so because of my own interest in string theory, which I was working on almost exclusively at the time. Nevertheless, some string theorists regarded the review as a hostile act.

    The trouble with Physics, by Lee Smolin, Page 281


    I have discovered one of Lee Smolin's objection to a string theorist. They are only craftsman, and not seers.