Topology and Early History

Part of the effort here is to outlay the idealization of what Genus figures means and the relationship to string amplitutdes.


A diagram of the Königsberg bridges

Topological ideas are present in almost all areas of today's mathematics. The subject of topology itself consists of several different branches, such as point set topology, algebraic topology and differential topology, which have relatively little in common. We shall trace the rise of topological concepts in a number of different situations.

Part of the difficulties here for me, is understanding exactly what is going on in these higher dimensional places, that string theorists and mathematicians like to venture.


Throughout, I have shown the processes with which a smooth topological feature would have endowed movements like the donut into the coffee cup and wondered, about this idea of Genus figures and how they to become part of the fixtures of the terrain with which mathematicians like to enjoy themselves over coffee?:)

The idealization of string amplitutdes raised cosmological correlations in my mind as well as understanding these harmonics, so the String Amplitutde search was initiated within my blog, to lead one through other idealizationas that become evident for me.

Shadows in Plato's Cave

Earlier I referred to the work of Thomas Banchoff for consideration in how he interprets the computer screen and the graphics that he works with. I also brought forward the question of illusions and Miracles in the following article .

Through mathematical analogy, Abbott sought to show that establishing scientific truth requires a leap of faith and that, conversely, miracles can be explained in terms that don't violate physical laws. Like early scientific theories, miracles could be merely shadows of phenomena beyond everyday experience or intrusions from higher dimensions. Flatland raises the fundamental question of how to deal with something transcendental, especially when recognizing that one will never be able to grasp its full nature and meaning. It's the kind of challenge that pure mathematicians face when they venture into higher dimensions. How do mathematicians organize their insights? How do they see and understand multidimensional worlds? How do they communicate their insights? Flatland is a novel approach toward answering those questions.---Shadows from Higher Dimensions by Ivars Peterson

Initial Condition Determinations allow Predictability?

The Lorenz Attractor


One of the basis of using string theory to me, was to identify, the initial conditions? It would be like talking about the weather to me that we could engage such a topic as strings and then ask, how could a quantum mechanical system ever have any certainty?

HUP makes this clear I think and needs no introduction.

If you do not have some conception of the idealization that this principle is built upon, then how would you arrive at such bubble terminologies that would have raised the circumstances of those bubbles, from a home seething?

In the diagram above we can see both stable and unstable orbits as exhibited in a discrete dynamical system; the so-called standard map also known as the Cirikov-Taylor map. The closed loops correspond to stable regions with fixed points or fixed periodic points at their centers. The hazy regions are unstable and chaotic.

Sample Orbits of the Standard Map
(x, y) --> (x + y, y - 0.971635 sin (2px)/2p)
Different orbits are assigned different colors.

Such oceans, would have been a warm place for the new born to arise, and from such conditions, the idealization of new ideas becoming ever more amazing, that they could indeed have arisen from one's own subconcious?

This would mean that a theory of everything, would have to have a common language at it's basis of existance. Such predictabiltiy if ever used, would have found such small discrepancies in the initail conditions, might become very large in the macroworld?

From the first four lessons, you have learned that in a chaotic system, using the laws of physics to make precise long-term predictions is impossible, even in theory. Making long-term predictions to any degree of precision at all would require giving the initial conditions to infinite precision.

It was Socrates' turn to look puzzled.
"Oh, wake up. You know what chaos is. Simple deterministic dynamics leading to irregular, random-looking behavior. Butterfly effect. That stuff."
Of course, I know that," Socrates said in irritation. "No, it was the idea of dynamic logic that was puzzling me. How can logic be dynamic

Numbers at the Heart of Creation?

Peter Woit pasted a small thread on the question of the new show that is to begin on television soon.

Peter said:There's a new TV show called "NUMB3RS" starting tonight, whose main character is a mathematican named "Charlie", who solves crimes using mathematics. His motto is "Everything is Numbers".

This has intrigued me greatly this question of mathematics, that I wanted to understand how such a thing could originate in any mind and supposed to describe processes in nature. How would it ever explain something that was chaotic, and still come out with some thing, that we could figure would explain the very nature of reality?

Earlier in Peter's Blog Chris W. gave the interestng link that follows here for cosideration.

Number theory is the type of math that describes the swirl in the head of a sunflower and the curve of a chambered nautilus. Bhargava says it's also hidden in the rhythms of classical Indian music, which is both mathematical and improvisational. He sees close links between his two loves -- both create beauty and elegance by weaving together seemingly unconnected ideas.

As part of a Morning Edition series exploring the intersection of art and science, NPR's Richard Harris reports on the beauty of mathematics, its ties to art -- and the man who straddles both worlds.

One of the things I found interesting about string theory was this quest to me, that some method would speak to this rythymn in numbers, that would have spoken to the chaotic world and found some relevance to how we may interpret the nature of this reality through this math.

I ponder this idea here in relation to the very idea that math could have originated from someplace, and arrived in the thinking mind for consideration?

Looking at Pascal's triangle it made sense to me that such derivation of the math in which we choose to describe, would have arisen from some probabilistic determination, so if such views were orientated in regards to number theory, then how would the basis of reality really descirbe what we are seeing?

Steve Hsu mentions here the idea of AI and the SmartChild program. He refers too, as a possible advancement based on the Turing test, as to the question of what could be voiced from an probabilistic question of QM? The suttle dialogue of weather?

From such a chaotic event we would have to derive information processing:) from many sources to give a qualified answer? Yet smartchild gave many tidbits for a location?:) Here lies a greater question of what could have been derived from a lot(no diffeent then gravitatinal waves and LIGO, stei users modified by users to help deciminate that information?

What if we percieved the nature of this reality in a different way, where number theory would have based itself on the rhythmns as denoted within this article?

I think we are looking for some system that woud help orientate the new possibilties in ways that might have sparked the ideals of Smolins work, in computer construction, that had made its divergence away from the mainstream based on this new ideology?

I am just pondering here.

Where Memories are Stored In Time

Fortunately the person behind this lense caught a important part of my bloodline's history. Using the camera, they caught a "frame" of this history and quickly, it was dismissed to the realization, that the imagination no longer requires us to see what we could create in mind. We have come to rely on what can be created for us?


Life memory does not include the images that are beammed through time for us and encapsulated? Do we remember?  

Have we forgotten, the clean air that once pervaded this planet? They took the population of this countries people and urbanized them to city dwellings?


Everyone has a family history. This is part of mine. The world was very much different then. 

Have we forgotten the room that existed for people, to make there livelihoods? Today, to become more concerned with a window view of some office. Is it the status that would allow our mind to roam in a freer space, then the four walls confined?


City Dwellers have forgotten their roots. Water that might have been scarce in the summer sun, would be collected as ground water. This was used to feed the livestock, and support the families drinking concerns.

Today we turn on taps and and we don't give this another thought. 

As we look to our grandchildren skating on the pond, and look "beyond" to the landscape, what mind is it that the frame of all these images are recorded, and forgotten for ever?

Every child now does not see, what ever child before them saw. Every child does not know what the parent knows? Have we become good modulators of form?

The Abstract World

Sometimes you have to wonder about the "ole' art," that could have captured the mind and allowed it to see beyond to the world of abtractions we can live in. What purposes do they serve?


Melencolia II
[frontispiece of thesis, after Dürer 1514]

If you learn to percieve the world in different ways, you learn to understand the landscape, and by model of comprehension, the level of abstraction takes you to consider other possible views?

If you did not engage them, how could you have really gone beyond anything that you know for a fact?:)



The depth's of perception are greatly enhanced when you link to the sources of comment. What one offers for a view of the landscape I can quickly show I ha dbeen thinking of these things as well at a earlier time. Follow the yellow(picture links) brick road:)

Where Hockey Started, and Horses Live

Platos Human face?

There is a human side to the faces of Bloggers? We just tend to forget, that human attributes could have been wiped out in a very technical world.

This is of my grand children feeling the ice in November.


Why Canadians become Great at Hockey? 

It's always nice to feel the earth under your feet, or the smell of wood smoke from a fire burning. To hear the wind, and feel it effects on your face. The smell of horseshit is not always that endearing, but being touch with one's human side you learn to empathize with those around you.


At twenty five below celcius you have to wonder about cozy temperatures of the far south 

The fellow on the left facing you is my boy.:) In the middle is his son Jake, and the mother to the right, with head not seen, Tisha.

Is Special Relativity Wrong?

New Physics?

Possible violations of Lorentz invariance are an ideal signal of new physics because nothing in the Standard Model of particle physics permits the violation of special relativity. Therefore, no conventional process could ever mimic or cover up a genuine signal of Lorentz violation.

Now before I move to the jest of the post, a little clarification and wonder before moving on to the opening statement.

This is taken from the article in the Guardian, and then is requoted below, where I will requote ,the quote of the quote.

Peter Woit quotes:)

Witten's attitude towards string theory seems to remain unchanged, he's quoted as saying:

"Critics of string theory say that it might be too big a step. Most physicists in other fields are simply agnostic and properly so," says Witten. "It isn't an established theory. My personal opinion is that there are circumstantial reasons to suspect that it's on the right track."

Now I mentioned the difficulties that I was having in regards to Smolin and the string perspective and coming to look at the way in which experimentation might be the end all answer to model assumptions? Alas in recognition of the validity, a quick departure everyone is having with what model they are firmly entrenched in? As far as I know, Peter Woit doesn't have a model?:) A healthy skeptic maybe like the amazing Randi, as in science's mode of operandi requim? The clarifications seem to becoming loud and clear.

Anyway on to an important question and where I thought Smolin was working. Sorry I could be wrong, but I am trying awfully hard to gain perspective.


Our basic premise is that minuscule apparent violations of Lorentz and CPT invariance might be observable in nature. The idea is that the violations would arise as suppressed effects from a more fundamental theory.

We have shown in our publications that arbitrary Lorentz and CPT violations are quantitatively described by a theory called the Standard-Model Extension, which is a modification of the usual Standard Model of particle physics and Einstein's theory of gravity, General Relativity.

So here is the thing that has sort of stump me. I know Smolin is a quantum gravity man, or this is what I had surmise and appreciated greatly from his book, "Three Roads to Quantum Gravity." Well the thing is, if Smolin had stopped at SR then it is quite plain that he is attempting to define quantum grvaity scenario from this perspective?



Now comes the understanding of the image that I put on Lubos's site that he might have wondered, without anything to associate it with? Well wonder of all wonders.:) This is of course one of a few experiments the Alan has detailled for us.

• 
  observations of neutral-meson oscillations
  
• 
  observations of neutrino oscillations
  
• 
  clock-comparison tests on Earth and in space
  
• 
  studies of the motion of a spin-polarized torsion pendulum
  
• 
  spectroscopy of hydrogen and antihydrogen
  
• 
  comparative tests of QED in Penning traps
  
• 
  determination of muon properties
  
• 
  measurements of cosmological birefringence
  
• 
  tests with microwave cavities and lasers
  
• 
  observation of the baryon asymmetry
  

New Clock Comparison Searches for Lorentz and CPT Violation

Ronald Walsworth and his Harvard-Smithsonian colleagues, in conjunction with theorist Alan Kostelecky at Indiana University, look at how atoms prepared in special magnetic states (the precision of their light emissions allow them to serve as “clocks”) vary in their timekeeping when moving at certain velocities (or "boosts") relative to the hypothetical Lorentz-symmetry-violating fields that may permeate the universe.

Is Everyone Declaring their Position Clearly?

"Most string theorists are very arrogant," says Seiberg with a smile. "If there is something [beyond string theory], we will call it string theory."

I am going to comment on Peter Woit's reference to the article called String Fellows he has highlight from the Guardian.

Here's what Nathan Seiberg mentions and points to the difficulty of finding the means to describe the microstates of quantum geometry. I wanted to place his statement, in context of a poem earlier written. So I'll post his comment, and then link to the appropriate source for consideration. It's getting a little worn out already, without us constantly being reminded:)

Nathan Seiberg, a colleague of Witten's at the IAS, uses the analogy of blind men examining an elephant to explain the course of string theory until 1995. "One describes touching a leg, one describes touching a trunk, another describes the ears," he says. "They come up with different descriptions but they don't see the big picture. There is only one elephant and they describe different parts of it."The Guardian

Now I most definitely see there is a great wish to eliminate any familiarity with dimensional anaylsis in regards to Peter Woit, that I find many others now, all of a sudden clarfying for us the model distinctions that are being used, and I think Peter Woit understands this?

Model Building

I am not like the kind of people who would like to eliminate (and often they DO eliminate) every piece of data that is inconvenient to them. And moreover I think that John Ellis is an interesting person with inspiring ideas, and I have absolutely no reason to try to verbally eliminate him from some group---Posted by Luboš Motl at January 20, 2005 08:32 AM

.

In delving into the issue of dimenisons it has become pretty clear there are intelligent people who have paved the roads for us to count to the fourth dimension for sure and we have also heard, there is no such things as dimensions? So what the heck does this mean.

Maybe a expanded version of dimension is needed? But if you do this, you might go beyond string theory?:) Which of course brings me to the issue, that if dimension is to be used to the fourth, then anything that goes beyond the fourth if not a dimension has to be something else? Of course giving room to grow being expounded here, tells us what is beyond string theory, to have said, we are going beyond the standard model?


THOMAS BANCHOFF has been a professor of mathematics at Brown University in Providence, Rhode Island, since 1967. He has written two books and fifty articles on geometric topics, frequently incorporating interactive computer graphics techniques in the study of phenomena in the fourth and higher dimensions

With John Ellis' reference to what took place at Cern in 2003 brings to a head the idea of dimension, as it has been expounded by Thomas in regards to computer screens?

Today, however, we do have the opportunity not only to observe phenomena in four and higher dimensions, but we can also interact with them. The medium for such interaction is computer graphics. Computer graphic devices produce images on two-dimensional screens. Each point on the screen has two real numbers as coordinates, and the computer stores the locations of points and lists of pairs of points which are to be connected by line segments or more complicated curves. In this way a diagram of great complexity can be developed on the screen and saved for later viewing or further manipulation

As a reality greatly expanded from what the internet used to be, refering to the Cern Article. If you accept the conceptualization of higher dimension then indeed the work that Thomas moved into, was mind expanding and thought provoking in regards to the animations and reality in front of you with this two dimensional screen?

So has this computer screen okayed the analogy to the fifth dimension?

So What is this Dimenisonal Archetecture Built On?

3-d: no hidden dimensions 1/R2 in F = G(m1 x m2)(1/R2)
4-d: one “ “ 1/R3 replaces 1/R2
5-d: two “ “ 1/R4 “
6-d: three “ “ 1/R5 “

and so on.

The rule is that for n hidden dimensions the gravitational force falls off with the inverse (n + 2 ) power of the distance R. This implies that as we look at smaller and smaller distances (by banging protons together in particle accelerators) the force of gravity should look stronger and stronger. How much stronger depends on the number of hidden dimensions (and how big they are). There may be enough hidden dimensions to unify the all the forces (including gravity) at an energy level of around 1 TeV (1012 eV), corresponding to around 10-19 meters. This would be a solution to the hierarchy problem of the vast difference in energy scale between the three standard gauge forces and gravity. This is already partly solved by supersymmetry (as mentioned previously); but this new idea would be a more definitive solution--if it were the right solution!

The Microstates of Quantum Gravity

Science is the attempt to make the chaotic diversity of our sense-experience correspond to a logically uniform system of thought

-Albert Einstein

Fig.1: Generally Grouping Order increases the density of objects within a frame of reference, resulting in a more pronounced single object.

To see beyond what we have taken for granted it is important that you understand how we got to the way we are?:) Above, the diagram helps you too orientate these views in accordance with established sciences.

A lot of times if you do not understand the direction the Microstates are taking us, then it would not make much sense in understanding the manifestation of one end of the spectrum, to solids things, to have explored the other end of the spectrum to the greater potential of dimensional perspectives?

John Baez:

Indeed, now that the Standard Model seems to be giving a spectacularly accurate description of all the forces *except* gravity, quantum gravity is one of the few really big mysteries left when it comes to working out the basic laws of physics --- or at least, one of the few *obvious* big mysteries. (As soon as one mystery starts becoming less mysterious, new mysteries tend to become more visible.) But back when particle physics was big business, only a few rather special sorts of people were seriously devoted to quantum gravity. These people seem to be often more than averagely interested in philosophy, often more interested in mathematics (which is one of the few solid handholds in this slippery subject), and always more resigned to the fact that Nature does not reveal all her secrets very readily

It is with great desire that anyone of us would like to find a discription and mode of thinking that would help establish a geometry that would arise from such states, that it becomes very diffiuclt to know if such standings in regards to Loop will directly explain how GR would have ever came to be, while strings has denoted our comprehension of the world the way it is, as being derived from some other state of existance. A Microstate one?

Quantum gravity is the field devoted to finding the microstructure of spacetime. Is space continuous? Does spacetime geometry make sense near the initial singularity? Deep inside a black hole? These are the sort of questions a theory of quantum gravity is expected to answer. The root of our search for the theory is a exploration of the quantum foundations of spacetime. At the very least, quantum gravity ought to describe physics on the smallest possible scales - expected to be 10-35 meters. (Easy to find with dimensional analysis: Build a quantity with the dimensions of length using the speed of light, Planck's constant, and Newton's constant.) Whether quantum gravity will yield a revolutionary shift in quantum theory, general relativity, or both remains to be seen

But let's remember something very important about such microstates and the geometry that Brian Greene is referring too. If you do not have this idea set in mind about how we are directed to those same microstates, what is at odds here between loop and strings for consideration?

This has to be identidified for lay people where such generalizations and comments from those who are trying to build our views, understand well, that they arrive from an idealization that might have had it's spokesperson stand for a extreme, or the other, all the while leaving lay people in the dust, while the sanctity of each area continuously is debated?

Such polarizations of views far two distint from each other is a statement that Smolin reminds us that his area is most defintiely trying as well to speak about qunatum gravity. But of course I must continue on froma statement from Greene here so that sch microstates and its geometry is understood. What is quantum geometry?

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."

I am setting up for the next entry. In it I am trying to pierce the veil that is driving such polarizations into there respective veiws, in regard to LQG or Strings respectively. It is troubling indeed that I as a outsider have to look hard and long for why this has materialized? That of course I would like to instigate others to move forward in a most appropriate "dialogos to remember," what each is working on.

Can the mirror world explain the ortho-positronium lifetime puzzle? by R. Foota∗ and S. N. Gninenkob†

We suggest that the discrepant lifetime measurements of ortho-positronium can be explained by ortho-positronium oscillations into mirror ortho-positronium. This explanation can be tested in future vacuum experiments.