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Showing posts with label Thomas Banchoff. Show all posts
Showing posts with label Thomas Banchoff. Show all posts

Tuesday, October 05, 2010

Quantum suicide and immortality

But for the first time, quantum physicist Seth Lloyd of the Massachusetts Institute of Technology suggests that memories of entanglement can survive its destruction. He compares the effect to Emily Brontë’s novel Wuthering Heights: “the spectral Catherine communicates with her quantum Heathcliff as a flash of light from beyond the grave.Where Susskind leaves off, Seth Lloyd begins

In Max' Tegmark's assessment of Quantum Immortality, "Although quantum immortality is motivated by the quantum suicide thought experiment, Max Tegmark has stated that he does not believe that quantum immortality is a consequence of his work,"I thought to trace some perspective about what happened with the thought experiment of Susskind's versus the telling tale of what happens inside the blackhole based on the idea of something that is left outside the blackhole for consideration.

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The consequence of sound in analogy serves to help us not only orientate causal action from direct contact, but the realization that such contact has consequences. It is befitting such thought experiments or analogies can help push the mind toward accepting the world in a different light so it understands that there is more to the world in which we see as observers, but also of what we meet through such contact as a manifestation through experiences.

Savas Dimopoulos

Here’s an analogy to understand this: imagine that our universe is a two-dimensional pool table, which you look down on from the third spatial dimension. When the billiard balls collide on the table, they scatter into new trajectories across the surface. But we also hear the click of sound as they impact: that’s collision energy being radiated into a third dimension above and beyond the surface. In this picture, the billiard balls are like protons and neutrons, and the sound wave behaves like the graviton.See Also: The Sound Of Billiard Balls

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In quantum mechanics, quantum suicide is a thought experiment. It was originally published independently by Hans Moravec in 1987 and Bruno Marchal in 1988 and was further developed by Max Tegmark in 1998.[1] It attempts to distinguish between the Copenhagen interpretation of quantum mechanics and the Everett many-worlds interpretation by means of a variation of the Schrödinger's cat thought experiment. The experiment involves looking at the Schrödinger's cat experiment from the point of view of the cat.

Quantum immortality is a metaphysical speculation derived from the quantum suicide thought experiment. It states that the many-worlds interpretation of quantum mechanics implies that conscious beings are immortal.[2] Hugh Everett is reported to have believed in quantum immortality, although he never published on either quantum suicide or quantum immortality.[3]

Contents


The quantum suicide thought experiment

Unlike Schrödinger's cat-in-a-box thought experiment which used poison gas and a radioactive decay trigger, this human version involves some sort of lethal weapon and a machine which measures the spin value of a photon. Every 10 seconds, the spin value of a randomly passing photon is measured. Depending on the orientation of the spin, either the weapon is deployed and the man is killed, or it is not and he lives.

With each run of the experiment there is a 50-50 chance that the weapon will be triggered and the experimenter will die. According to the Copenhagen interpretation, the weapon will (in all likelihood) eventually be triggered and the experimenter will die. If the many-worlds interpretation is correct then at each run of the experiment, the experimenter will be split into several worlds in which he dies and a few worlds in which he survives. In the worlds where the experimenter dies, he will cease to be a conscious entity.

However, from the point of view of the non-dead copies of the experimenter, the experiment will continue running without his ceasing to exist, because at each branch, he will only be able to observe the result in the world in which he survives, and if many-worlds is correct, the surviving copies of the experimenter will notice that he never seems to die, therefore "proving" himself to be invulnerable to the killing mechanism in question, from his own point of view.

If the many-worlds interpretation is true, the measure (given in the many-worlds interpretation by the squared norm of the wavefunction) of the surviving copies of the experimenter will decrease by 50% with each run of the experiment, but will remain non-zero. So, if the surviving copies become experimenters, those copies will either die during their first attempt, or survive creating duplicates of themselves (copies of copies, that will survive finitely or die).

 Quantum immortality

The idea behind quantum immortality is that, in running the quantum thought experiment, the experimenter may remain alive and, thus, be able to experience at least one of the universes in this set (even though these universes form a tiny subset of all possible universes). Over time, the experimenter would therefore never perceive his or her own death.

Surviving the quantum thought experiment

The small-probability remaining branches are in effect, though unlikely to be experienced by most of the copies of the experimenter that started out. Most of the observer-moments in the universe will not be in such low-measure situations because measure is proportional to the number of copies and therefore the number of that type of observer-moment.

However, the rareness of an observer moment has no relation to presence or absence of experience; if the many-worlds interpretation is true, all non-zero observer moments are experienced, even rare ones. Believers in quantum suicide think it gives a recipe for entering into rare observer moments. The experimenter indeed knows that this type of observer moment is rare, which is why it would be unlikely to occur in interpretations of quantum physics that don't have many worlds.

In the branching worlds, the observer has one of two possibilities, live or die. If he is alive, then presumably he does not recall the death. In the other reality, he is dead (and ceases to exist in that reality). If the experiment is repeated over and over, there will always be a reality where the observer never dies. This reality will finally convince the observer that it is impossible to die.

Required assumptions

Proponents of the quantum immortality point out that, although it is highly speculative, the theory does not violate any known laws of physics—but only if certain controversial assumptions are made:
  1. That the many-worlds interpretation is the correct interpretation of quantum mechanics, as opposed to the Copenhagen interpretation, the latter of which does not involve the existence of parallel universes. Note, though, that parallel universes may be possible through other mechanisms in the Copenhagen interpretation.
  2. Not dying some finite number of times (perhaps in parallel universes) constitutes immortality.
  3. Permanent cessation of the consciousness, along with the ability to observe, occurs at physical destruction (death).

Arguments against quantum immortality

David Papineau argues against the quantum suicide argument thus: "If one outcome is valuable because it contains my future experiences, surely an alternative outcome which lacks those experiences is of lesser value, simply by comparison with the first outcome. Since expected utility calculations hinge on relative utility values rather than absolute ones, I should be concerned about death as long as the outcome where I die is given less utility than the one where I survive, whatever the absolute value."[4]

Jacques Mallah expands on this "utility" argument,[5] suggesting that quantum suicide cannot give a recipe for "entering into" rare or "low measure" observer moments. This is because the amount of consciousness or "measure" of these rare observer moments is exactly as much as it would have been without the quantum suicide; in that case quantum suicide merely removes the other observer-moments. This is equivalent, in Mallah's view, to a single-world situation in which one starts off with many copies of the experimenter, and the number of surviving copies is decreased by 50% with each run. Therefore, according to this argument, the quantum nature of the experiment provides no benefit to the experimenter; in terms of his/her subjective life expectancy or rational decision making, or even in terms of his/her trying to decide whether the many-worlds interpretation is correct, the many-worlds interpretation gives results that are the same as that of a single-world interpretation.[5]
Mallah also gives a "general argument against immortality" which argues that if people are immortal, then it is vanishingly unlikely to find oneself to be of a normal age rather than abnormally old.

It has been countered that in a many-worlds interpretation, the amplitude of being the living experimenter can be halved repeatedly without ever reaching zero. However, this point is not disputed by opponents of quantum suicide; rather, they claim that it is not the issue, while Mallah claims that the decrease in measure is the issue.

Max Tegmark's work

Using logic similar to that of Greg Egan's Dust Theory, Max Tegmark argues that under any sort of normal conditions, before someone dies they undergo a period of diminishment of consciousness, a non-quantum decline (which can be anywhere from seconds to minutes to years), and hence there is no way of establishing a continuous existence in this world to an alternate one in which the person ceases to exist.[6] Although quantum immortality is motivated by the quantum suicide thought experiment, Max Tegmark has stated that he does not believe that quantum immortality is a consequence of his work.

David Lewis's work

The philosopher David Lewis, in "How Many Lives Has Schrödinger's Cat?", remarked that in the vast majority of the worlds in which an immortal observer might find himself (i.e. the subset of quantum-possible worlds in which the observer does not die), he will survive, but will be terribly maimed. This is because in each of the scenarios typically given in thought experiments (nuclear bombing, Russian roulette, etc.), for every world in which the observer survives unscathed, there are likely to be far more worlds in which the observer survives terribly disfigured, badly disabled, and so on. It is for this reason, Lewis concludes, that we ought to hope that the many-worlds interpretation is false.[7]

Derek Parfit's work

In Reasons and Persons Derek Parfit used thought experiments ranging from teleportation to gradual changes to your psychology to argue that personal identity isn't a deep fact about the world. After quantum suicide there would be worlds with persons that shared your memories and there would be worlds without such persons. There is no Cartesian ego which does or doesn't survive.

Other criticism and controversy

Critics[who?] contend quantum suicide fails as a thought experiment to achieve its intended purpose. Nonetheless, there are arguments[specify] involving anthropic considerations among entire universes which do provide evidence[specify] for the many-worlds interpretation.[8]
Quantum suicide and quantum immortality remain controversial because a number of thinkers[who?] disagree on its success or failure and, particularly, its relevance to life expectancy and decision making.

In fiction

Authors[who?] of science fiction have used themes involving both quantum suicide and quantum immortality. The idea that authors exploit is that a person who dies in one world may survive in another world or parallel universe.

Quantum suicide

Quantum suicide themes have been explored in the following works:

Quantum immortality

Quantum immortality themes have been explored in several works:

Books

See also

References

  1. ^ Tegmark, Max The Interpretation of Quantum Mechanics: Many Worlds or Many Words?, 1998
  2. ^ Goertzel, Ben; Bugaj, Stephan Vladimir (2006). The path to posthumanity: 21st century technology and its radical implications for mind, society and reality. Academica Press, LLC. p. 343. 
  3. ^ See Keith Lynch's recollections in Eugene Shikhovtsev's Biography of Everett [1]
  4. ^ Papineau, David "Why you don’t want to get in the box with Schrödinger's cat" Analysis 63: 51–58. 2003
  5. ^ a b Mallah, Jacques Many-Worlds Interpretations Can Not Imply 'Quantum Immortality', 2009
  6. ^ Tegmark, Max Quantum immortality, November 1998
  7. ^ David Lewis. How Many Lives Has Schrödinger's Cat? The Jack Smart Lecture, Canberra, 27 June 2001. Australasian Journal of Philosophy. Vol. 82, No. 1, pp. 3–22; March 2004, pp. 21.
  8. ^ Observational Consequences of Many-Worlds Quantum Theory, 1999.

External links

Monday, March 31, 2008

Numerical Relativity and the Human Experience?

"I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Donald (H. S. M.) Coxeter


I contrast the nature of Numerical Relativity to the computer and the way we would think human consciousness could have been linked in it's various ways. Who hasn't thought that the ingenuity of the thinking mind could not have been considered the Synapse and the Portal to the thinking Mind?:)

Also think about what can be thought here as Gerardus t" Hooft asked as to think about in the limitations of what can be thought in relation to computerizations.

There is something to be said here about what conscious is not limited too. It is by it's very nature "leading perspective" that we would like to have all these variables included in or assertions of what we can see while providing experimental data to the mind set of those same computerization techniques?

Numerical Relativity Mind Map

So we of course like to see the mind's ingenuity( computerized or otherwise) when it comes to how it shall interpret what is the road to understanding that gravity is seen in Relativities explanation.

Source:Numerical Relativity Code and Machine Timeline


It is a process by which the world of blackholes come into viewing in it's most "technical means providing the amount of speed and memory" that would allow us to interpret events in the way we have.

The information has to be mapped to computational methodology in order for us to know what scientific value scan be enshrined in the descriptions of the Blackhole. Imagine that with current technologies we can never go any further then what we can currently for see given the circumstances of this technology?


Source:Expo/Information Center/Directory-Spacetime Wrinkles Map

So on the one hand there is an "realistic version" being mapped according to how we develop the means to visualize of what nature has bestowed upon us in the according to understanding Blackhole's and their Singularities.

Numerical Relativity and Math Transferance

Part of the advantage of looking at computer animations is knowing that the basis of this vision that is being created, is based on computerized methods and codes, devised, to help us see what Einstein's equations imply.

Now that's part of the effort isn't it, when we see the structure of math, may have also embued a Dirac, to see in ways that ony a good imagination may have that is tied to the abstractions of the math, and allows us to enter into "their portal" of the mind.

NASA scientists have reached a breakthrough in computer modeling that allows them to simulate what gravitational waves from merging black holes look like. The three-dimensional simulations, the largest astrophysical calculations ever performed on a NASA supercomputer, provide the foundation to explore the universe in an entirely new way.

Scientists are watching two supermassive black holes spiral towards each other near the center of a galaxy cluster named Abell 400. Shown in this X-ray/radio composite image are the multi-million degree radio jets emanating from the black holes. Click on image to view large resolution. Credit: X-ray: NASA/CXC/AIfA/D.Hudson & T.Reiprich et al.; Radio: NRAO/VLA/NRL

According to Einstein's math, when two massive black holes merge, all of space jiggles like a bowl of Jell-O as gravitational waves race out from the collision at light speed.

Previous simulations had been plagued by computer crashes. The necessary equations, based on Einstein's theory of general relativity, were far too complex. But scientists at NASA's Goddard Space Flight Center in Greenbelt, Md., have found a method to translate Einstein's math in a way that computers can understand.


Quantum Gravity

Now their is a strange set of circumstance here that would leave me to believe, that the area of quantum gravity has lead Numerical Relativity to it's conclusion? Has the technology made itself feasible enough to explore new experimental data that would allow us to further interpret nature in the way it shows itself? What about at the source of the singularity?

See: Dealing with a 5D World

I would not be fully honest if I did not give you part of the nature of abstract knowledge being imparted to us, if I did not include the "areas of abstractness" to include people who help us draw the dimensional significance to experience in these mathematical ways. It is always good to listen to what they have to say so that we can further developed the understanding of what becomes a deeper recognition of the way nature unfolds of itself.

There are two reasons that having mapped E8 is so important. The practical one is that E8 has major applications: mathematical analysis of the most recent versions of string theory and supergravity theories all keep revealing structure based on E8. E8 seems to be part of the structure of our universe.

The other reason is just that the complete mapping of E8 is the largest mathematical structure ever mapped out in full detail by human beings. It takes 60 gigabytes to store the map of E8. If you were to write it out on paper in 6-point print (that's really small print), you'd need a piece of paper bigger than the island of Manhattan. This thing is huge.
Emphasis and underlined, my addition.

Computer Language and Math Joined from Artistic Impressionism?

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."- Lisa Randall



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


The marriage between computer and math language(Banchoff) I would say would be important from the prospective of displaying imaging, seen in the development of abstract language as used in numerical relativity? Accummalated data gained from LIGO operations. Time variable measures?

See:Computer Graphics In Mathematical Research

Wednesday, April 11, 2007

Bee Movie and Science Today

Bee of Backreaction was highlighting the Dimensional perspective of the way we are going to see Dream Works animation developing new movies. See "DreamWorks goes Extra Dimensional."

I thought it important that I reveal the coincidence of the story I have here in this blog about the Bee people. I wonder how the script arose in the person who wrote this story for the animation market?

Synopsis
Bee Movie is a comedy that will change everything you think you know about bees. Having just graduated from college, a bee by the name of Barry B. Benson (Jerry Seinfeld) finds himself disillusioned with the prospect of having only one career choice – honey. As he ventures outside of the hive for the first time, he breaks one of the cardinal rules of the bee world and talks to a human, a New York City florist named Vanessa (Renée Zellweger). He is shocked to discover that the humans have been stealing and eating the bees’ honey for centuries, and ultimately realizes that his true calling in life is to set the world right by suing the human race for stealing their precious honey.



Also I must admit I was thinking about the extra dimensional work that is going on in science today and to find that the animations are being introduced in this way, I thought it somehow appropriate. If we wanted people to think differently about the dimensional perspectives, instead of using "Abbott" why not present the fictional world to our children as Bees introduce to "ant world."

Worker bees perform a host of tasks from cleaning the hive cells to looking after the larvae

PLato the seer is somehow transported to the world of "human beings" where in the space ship, he is filled with all this information about the creation of being. The new laws were somehow planted his memory and thus Plato was to serve to disseminate to all the Bee people, so they could adjust to the new paradigmatic shift his community was to undergo in the future.

It was as if "this information" dropped into his lap from the 21st century.


The Elixir of the Bee Community

Plato:
You should know that that the names of the Bee people have their names protected, to protect the community at large. Some larger human species, like to use the benefits of this society, without recognizing the constructive efforts that goes into this elixir Production.


Now I would be so happy that the Bee in this movie show up as a scientist who may be called "Plato" who plays the part of the "seer," who is keeper of this vast reserves, and is in charge of "the science" of this community.

All the worker bees are the vast amount of craftsman who construct the reality for the Bee people to house the developers and researchers who are being employed in theoretics of the future.

Now instead of the seven wonders of the world and the Pyramid being created, or "the LHC ringer, The Bee people had their own way of producing this perfect fluid. It required some other model monumental design to allow this production to continue, in face of loosing the "Secret of the Golden Flower."

Bumblebee Economics with a new preface Bernd Heinrich-
In his new preface Bernd Heinrich ranges from Maine to Alaska and north to the Arctic as he summarizes findings from continuing investigations over the past twenty-five years--by him and others--into the wondrous "energy economy" of bumblebees.
See Bumblebee Wing Rotations and Dancing

Now the dance steps that some of the signature bees go through to tell the others, undergoes some step procedure changes.

Fechner, Plato, and shadow figuresThe first person to develop the dimensional analogy in the 19th century was the psychologist and physiologist Gustave Fechner in Leipzig. He wrote a small story, Space has Four Dimensions, as part of his collection Vier Paradoxe published in 1846 under the pseudonym of Dr. Mises. Fechner's two-dimensional creature was a shadow man projected to a vertical screen by an opaque projector. He could interact with other shadows, but, based on his limited experience, he could not conceive of a direction perpendicular to his screen. Fechner suggests that for such a being, time would be a third dimension, expressing the movement of his whole screen in a direction which he cannot comprehend spatially. The idea of treating shadow figures goes back much further, to Plato's Allegory of the Cave in the seventh book of The Republic. There the shadows are merely representations of objects to be viewed by three-dimensional observers who are artificially limited to seeing only these lower-dimensional views. Plato does not suggest that the shadows have the capability of interacting with one another, and this is the heart of Fechner's insight.
For further information see, "Shadows in Plato's Cave," and also see, "Is Everyone Declaring their Position Clearly"?

Here is a copy of the biblical transmission below that is relayed to all child bee kids as they graduate from the school of, To Bee Thomas Banchoff. This Founder help give perspective to the "2d" community that evolved and helped the community move into the larger dynamics of space travel. Although only with the contents of the computer screen these little bee children sit at, they had to be prepared.

The Bee theoretical Fellows

Predictably, Witten is modest about his achievement. "It's an exaggeration to say that I came up with M-theory," he says. "We came up with bits and pieces but there's a long history behind it."


Another perspective of the Being Witten took the issues of string and gave them more depth.

The Macarena step by Geoff Larvey is introduced to the community, and all the worker Bees react to this sudden change.

You start with the brane
and the brane is BPS
Then you go near the brane
and the space is AdS
Who knows what it means
I don't I confess
Ehhhh! Maldacena!

Super Yang Mills
With very large N
Gravity on a sphere
flux without end
Who says they're the same
holographic he contends
Ehhhh! Maldacena!

Black holes used to be
a great mystery
Now we use D-brane
to compute D-entropy
And when D-brane is hot
D-free energy
Ehhhh! Maldacena!

M-theory is finished
Juan has great repute
The black hole we have mastered
QCD we can compute
Too bad the glueball spectrum
is still in some dispute
Ehhhh! Maldacena!




The ways of travel is supposed to proceed "to the source" have undergone a paradigmatic shift. Who helped construct the community of Bee theorists and honey comb developers, are now in disarray. They look toward the "Queen Bee." What are the directions this community is supposed to go?

Such a drastic change to the developing science community and the education of the Bee Kids, are now considering the dramatic changes in the way they see the computer screen work. While the dance was to include E8 considerations, G3 modular forms held complicated travel pathways this would astound even the brightest Bee students.

Imagine going beyond that. Plato being the seer, thought long and hard about what was to come next.

Thursday, July 06, 2006

Lisa Randall's Theoretical Insights



The picture above was shown because of another picture in which I thought deserved comparison. The reason for this, would help the mind understand how such an image could be explained in a "easy and suttle way?"

So look at this picture above and then at the one to follow.



The very ideas are of extra dimensions are very progressive, and are not without some history. Some people will label anything as crackpot, without undertanding the history of these discussions.



I was thinking here of Banchoff, and the imaging that he deals with. While he is speaking from a mathematical position that imaging of a 2d screen does wonders in how 5d perception are presently engaged in the veryday world of computer screens and the like.



But to think about the picture painted by Dali, it is not without it's mathematical inclinations, that a painter like him may wonder about the "elevation" to spiritual thinking, with such thought embued with our look at the mathematical world, with which we assign our "spiritual principles?"

Wednesday, April 12, 2006

Computer Language and Math Joined from Artistic Impressionism?

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."- Lisa Randall




Cubist Art: Picasso's painting 'Portrait of Dora Maar'
Cubist art revolted against the restrictions that perspective imposed. Picasso's art shows a clear rejection of the perspective, with women's faces viewed simultaneously from several angles. Picasso's paintings show multiple perspectives, as though they were painted by someone from the 4th dimension, able to see all perspectives simultaneously.


Sean from Cosmic Variance writes his opening post by including the title, "The language of Science".


I would have said maths as well, yet, as a Layman there is much for me to learn.


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


The marriage between computer and math language(Banchoff) I would say would be important from the prospective of displaying imaging, seen in the development of abstract language as used in numerical relativity? Accummalated data gained from LIGO operations. Time variable measures?



My first demonstration was with a Calabi Yau model of the torso. Visually seeing this way, helped to progress understanding. The transferance from the math structure to imaging in computer, to me, seemed very hard thing to do.


Alain Connes

Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition.



If the math is right, the "concepts spoken," will be right also?



How such reductionism is held to the values of science, is seen in the work of the calorimeters. Glast and LHC designs give introspective views of how fine our perspective is being shaped. Can we see the underlying imaging as a toll, respective of reductionism as seeing the dynamical and geoemtrical background to all events measured? LIGO in data accumulation, describing the infomration released into the bulk perspective.

Toroidal_LHC_ApparatuS

In the theory of relativity, momentum is not proportional to velocity at such speeds.) Thus high-momentum particles will curve very little, while low-momentum particles will curve significantly; the amount of curvature can be quantified and the particle momentum can be determined from this value.

Saturday, October 08, 2005

Mathematical Models

"Backwards" might mean, from a "5d understanding" to a three dimensional fabrication. You had to understand how the 5d world is explained here, before judgement is cast.

While I would like nothing more then to cater to the struggles of good professors, to the aims they had set for themselves, it has come to me, that mathematic modelling is culminative. Where does this point too?

If indeed a good understanding has been established, regardless of string theory or any association for that matter, this stand alone item on Langlands or what ever one might associated it too, would of itself, painted it's own picture and further associations, from a basis and exposition of that mathemtical derivative.

It does not have to be associated it either to historical figures (like Plato), other then the ones we trace to the orignation and factors that brought other areas of mathematics together. This should be readily available, by doing searches which I did. Although I sahl say there is much that needs to be resolved, in our determinations of truth. I am working on understanding this here.

But then to take it further, I wanted to illustrate this point just a little more on imaging.

Thomas Banchoff has set this straight in terms of modelling in computerization and what it can do for us in 5D expressions? While in the Wunderkammern of this site such model although concretize in form have relative associations in computerization value much like the model of the Klein bottle exemplified of itself in acme products.


x = cos(u)*(cos(u/2)*(sqrt_2+cos(v))+(sin(u/2)*sin(v)*cos(v)))

y = sin(u)*(cos(u/2)*(sqrt_2+cos(v))+(sin(u/2)*sin(v)*cos(v)))

z = -1*sin(u/2)*(sqrt_2+cos(v))+cos(u/2)*sin(v)*cos(v)

or in polynomial form:

Yep, no doubt about it: Your Acme's Klein Bottle is a real Riemannian manifold, just waiting for you to define a Euclidean metric at every point.



Felix Klein
When Klein became a Professor in Leipzig in 1880, he immediately started to acquire mathematical models and establish a model collection. Klein was a geometer and used these plaster models in his university lectures. Model collections became very popular in mathematics departments world-wide. When he then moved to Göttingen, Klein, together with his colleague Hermann Amandus Schwarz, expanded his new department's collection of mathematical models and instruments so much that at peak times up to 500 models were on permanent display. When you think that a model could cost about £150, this was a major investment in education.




This idea is and has been lost to the model archives of the Wunderkammern respectively and such a resurgence is making it's way back. Such O ->an outward expression is no less the road taken in artistic expression entitled, "When is a Pipe a pipe," exemplified in the manifestation of mathematical modelling.

Our computer screen although reduced to two dimensional factors, is a fifth dimensional expression, in terms of our visulization capability. The work then is translation of computerization, to imaging.

The "Torso" once mathematically derived, and help enlisted in the Cave, brought mathematical equation through a complete rotation in the Calabi Yau. Until then, the efforts relied on by men/woman whose visualization capabiltes, were equivalent to 5d imaging?

So if I ask, if there is a image of a culminative mathe, without out this the understanding is not complete.

Wednesday, September 21, 2005

Point--> Line-->Plane <---> Point<-- String<-- Brane

Under the heading of Klein`s Ordering of the Geometries :

A theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry.


Now the usual thinking here has been placed under intense thinking by the introduction of a new way in which to look at "geometry" that has gone through a "revision" in thinking.

New trigonometry is a sign of the times

Lubos Motl introduces this topic and link in his blog entry and from this this has caused great consternation in how I am seeing. I see Lisa Randall might counter this in terms of what the brain is capable of, in line with this revisionary seeing, and comparative examples of this geometry Lubos links.

Dangling Particles,By LISA RANDALL
Published: September 18, 2005 New York Yimes

Lisa Randall:
Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen." I do theoretical research on string theory and particle physics and try to focus on aspects of those theories we might experimentally test. My most recent research is about extra dimensions of space. Remarkably, we can potentially "see" or "observe" evidence of extra dimensions. But we won't reach out and touch those dimensions with our fingertips or see them with our eyes. The evidence will consist of heavy particles known as Kaluza-Klein modes that travel in extra-dimensional space. If our theories correctly describe the world, there will be a precise enough link between such particles (which will be experimentally observed) and extra dimensions to establish the existence of extra dimensions.



But first before I get to the essence of the title of my blog entry, I like to prep the mind for what is seemingly a consistent move towards geometry that has it's basis in applicabilty to physics, and move through GR to a vast new comprehsnsion in non-euclidean geometries. Must we now move backwards that we had gained in insight, or was it recognition of the "length scales" that we now say, how could such a dynamcial view ever be assigned to the eucildean discription under the guise of brane world recognitions?

Moving Backwards?

What exactly do I mean here?

Well the idea is that if you move to fifth dimensional views, and there are ways to wrap this within our "Brains":) We then see the dynamcial nature of our neurons have found acceptable ways in which to see this brane feature. As well as, approaches in use of new processes in geometerical considerations as those linked by Lubos.

Dealing with 5D world



Thomas Banchoff is instrumental here is showing us that fifth dimensional views can be utilized in our computer screens, and such comparisons, reduce to a two dimensional frame, makes it very easy to accept this new way in which to attack the dynamcial nature of reality.

How indeed now could our computer screen act a liason with the reality of our world, when see from screen imagery effects, that all the rules of order have been safely applied for inspection and consistancy in physics approaches.

Friday, September 02, 2005

UV Fixed Point

Clifford draws our attention to further talks here in his post and directs us to what Jacque Distler has to say.

I must say this is a refreshing look with Jacques contribution to further the layman point of view. Such links are worth while in the advancement of the "sentient being" that Clifford might have thought the computer world could have developed into once we assign our geometries to that world, as we would of numerical relativity and the designs we get from this look. Thomas Banchoff should be commended forthis contribution to fifth dimensional idealism in the computer world, with the notion of graphics design as a whole new approach to this understanding. Who said mathematics guys are a little to abstract for the laymen view?

Jacque Distler:
Yeah. I had hoped I was being clear.

I meant a nontrivial (non-Gaussian) UV fixed point. A Gaussian fixed point would be too much to hope for.


Now you must know that to see what he was saying, "Gaussian coordinates" determined below this post helped me to relate what was being said here. But more then this the statement of Jacques orientates what might be further implied and what had missed in my thinking.

So just to carry on a bit with this point "P" in gaussian coordinated of frame of UV, what realization exists that we could not find some relevance here in the geometry to have further exploited the mind's capabilties by venturing into the Wunderkammern of thinking. By association, of Nigel Hitchin's "B Field manifestations geometries" to realize that althought these might be limited to what Jacque is saying , then what value this geometry if we can not see the landscape as something real in time variable measures?

That we might attribute a globe, that while spherical in it's design, holds much more in it's determination. That while it might issue it's electronmagnetic field of lines, that it too could have found greater relevance in the issues of Quantum gravity, with those same inclinations of time variablenesss, that I allude too?



What am I missing that such events held to the brane in fermion distinction would not find boson production off the brane, as real as, the topic of time variableness that we might issue in geometrical feature of a globe. A globe, that is very bumpy indeed. Is this thinking limited in terms of landscape valuation? Not only in terms of brane and fermionic response, but of the real live correlation of the topic of branes in a more realistic sense, held to these geometries?

While indeed such B Field Manifestation becomes real in tangibles in our arguement of where our UV perspective might be held too, then "P" becomes of value in time variablemess, as a landscape ideology spread throughtout the brane world features? While it is also intriciately linked to our formation of landscape futher out in the recognition of the bumpy world?

So while we might see this landscape in terms of photon calorimetric association with Glast, what value besides gauusian coordinate might be freed, when we see dimensinal sigificance being represented with Glast as well. Is this thinking wrong?

Sunday, July 24, 2005

The Black Hole Final State

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

It was a nice vacation and now being back, I see Lubos is clarifying some issues here for us to consider.

"Lubos Motl:
However, Hawking's semiclassical calculation leads to an exactly (piecewise) thermal final state. Such a mixed state in the far future violates unitarity - pure states cannot evolve into mixed states unitarily - and it destroys the initial information about the collapsed objects which is why we call it "information loss puzzle". A tension with quantum mechanics emerges.


The Gepner point demonstrates greater potential recognition of the brane world understandings and two dimensional views from a five dimenisonal developmentment for those who do not like such abstract adventures P.P. Cook helps to enlighten us on this subject.

So have I done justice to the developing perspective, that we are now ready to take what what demonstrated, and move it to a greater format for those who will lead us laymen through the world of the abstract mathematics? To help us enjoy what was mathematically unenduring for those not gifted to see the B field manifestaion, is a continuance of what we like to engage at higher dimensional perspectives. And really, it is all about imagery is it not?




Lee Smolin:
It was worry about the possibility that string theory would lead to the present situation, which Susskind has so ably described in his recent papers, that led me to invent the Cosmological Natural Selection [CNS] idea and to write my first book. My motive, then as now, is to prevent a split in the community of theoretical physicists in which different groups of smart people believe different things, with no recourse to come to consensus by rational argument from the evidence.


You must understand the state of thinking and dualistic nature that continues to force minds to engage the process, and this quest for wholeness, between two thoughts that are part and parcel of the same thing? Relativity and Quantum Nature. The larger circle is RElativity, and the smaller, the quantum nature. LQG and STring work from their respective positions.

So do we select the basis for this model, and find that LQG and Strings are formulated on principals embedded in association with the blackhole topic? This throws light back again on a topic that has been shared more then once by such trends in thinking as Lubos exemplfies for us, and again directs our thoughts towards Lenny Susskind and Lee Smolin, in contrast to each other.

I see people are teaming up appropriately, such as Cosmic Variance, and this of course has already been lead by Lubos and Peter's contrast to each other. Whether some like to speculate on co-joining for such comparsions on the validity of strings, versus no strings approach, as resolutions, had already been developed while we see this new means to develope, much as Brain Greene and others in ISCAP foundations principals.

So of course onward and forward, we push the topic and the expertise for the layperson like me, that we see and continue to find, developmental processes appropriately gathering for future thoughts shared? Again too, we see Quantum Diaries has indeed served it's purpose more then once in what John Ellis and other's have shared, have open the doorway to how we see such developmental attitudes expanding in contrast to the larger circle of possibilties.

See John's latest entree and for me, hitting big objects and particle collisions still open the mind for the natural cosmic interactive processes ongoing in nature around us.

Anyway back to the title of this post. I have some thinking here to do.

Gary T. Horowitz1 and Juan Maldacena,2

The purpose of this note is to provide a possible answer to this question. Rather than the radical modification of quantum mechanics required for pure states to evolve into mixed states, we adopt a more mild modification. We propose that at the black hole singularity one needs to impose a unique final state boundary condition. More precisely, we have a unique final wavefunction for the interior of the black hole. Modifications of quantum mechanics where one imposes final state boundary conditions were considered in [6,7,8,9]. Here we are putting a final state boundary condition on part of the system, the interior of the black hole. This final boundary condition makes sure that no information is “absorbed” by the singularity.


If indeed we started to think about the point on the brane then what kind of simplification can be drawn so that those less enclined to such abstract thinking could find a greater potential to that dimensionnal thinking?

(a) Compactifying a 3-D universe with two space dimensions and one time dimension. This is a simplification of the 5-D space­time considered by Theodor Kaluza and Oskar Klein. (b) The Lorentz symmetry of the large dimension is broken by the compactification and all that remains is 2-D space plus the U(1) symmetry represented by the arrow. (c) On large scales we see only a 2-D universe (one space plus one time dimension) with the "internal" U(1) symmetry of electromagnetism.


Here such thoughts begin to form around the idealization of computer graphics imagery developed and leading in this idealization of this two dimensional screen. We see where the likes of Thomas Banchoff demonstrate where such new roads to the developing insight ot this imagery can be seen in Smolins views of the Bekenstein Bound, that we we now understand a greater potential exists in how we view the screen, and what is being described in the blackhole horizon?



Let me show this image again, for greater clarity of what I mean.

Wednesday, June 01, 2005

Wunderkammern

For me this is a wonderful view of abstraction, that had gone into model making, to help those less inclined to "the visonistic qualities of those same abstractions."


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.


So having been allowed through internet developement to understand the work of fifth dimensional qualites could exist (why Thomas Banchoff must be added below), has far exceeded the understanding of those currently engaged in the mathematics? I do not mean to undermine or cast uncertainty in the direction of those who are helpijng us, but make for recognition of what technology has done for us, in the use of these internet capabilities.


Long before the advent of the World-Wide Web, Tom Banchoff was experimenting with ways of using electronic media to enhance mathematical research and aid in mathematical education. Banchoff helped install one of the first mathematics computer labs in the country, and continues to lead the development of innovative geometric software and curricula for undergraduate mathematics courses. He uses computer graphics as an integral part of his own research, and has used mathematical videos for the last 30 years as a means of disseminating his results.


I have been exploring these issues in regards to the Sylvester Surfaces, and the relationship seen in matrix development. It wasn't without some understanding that "isomorphic images" might have been revealled in orbital images categories, that dealing with this abstract world, didn't require some explanation?

The Magic Square



The picture below was arrived using the applet given from that site. What did you have do to change, in order to get the image I did? We are given possibilties?



But of course I am held by the physics of the world we see. As small as, might have exemplified itself in some larger cosmological imagery of a kind, can it be suited to topological features spoken too in string theory?

We know Max Tegmark has refuted the soccerball universe, and bazeian valuation of a quantum gravity model, that seem to good to be true? PLato, still felt that this soccer ball represented God? So maybe baezian, interpretaion, although derived from archimeadean, was more then the models through which they were precribed in Wunderkammen. Something ancient has been brought forward again for the mind bogglers that like to paly in these abstract spaces?

Mathematical Teaching Tools

Introduction: Lost Geometry

When I was small, growing up in Wisconsin, I loved to walk along the railroad tracks. As I walked, I would watch the steel rails grow from a point in the distance ahead of me, sweep around me, and then disappear again in the distance over my shoulder, converging slowly back to a point. The pure geometry of it was breathtaking. What impressed me the most, however, was the powerful metaphor that it suggested: How wide the present seemed, simply because of my presence there; how small the future and the past. And yet, I could move along the tracks, imagining myself expanding and contracting the infinite timeline of history. I could move ahead until any previous place along that continuum had shrunk to insignificance, and I could, despite the relentless directionality that I imagined moving along the tracks like so many schedule-bound trains, drift backwards as easily as I could let myself be carried forward.


The wonderful stories exemplifed by human experience, places me in states of wonder. About how processes in geometry could have engaged us in a real dialogue with nature's way around us. To see these stories exemplified above. One more that quickly came to mind, was Michio Kaku's view from the bridge, to the fish in the pond. Looking at the surface from two perspective sseem really quite amazing to me.

Such exchanges as these are wonderful exercises in the creation of the historical abstract. A Lewis Carroll in the making? An Abbotsolutely certainty of math structures, that we would like to pass on to our children and extend the nature to matter of the brain's mass?

Sunday, February 13, 2005

HIgher Dimensions Without the Geometry?



In Illusions and Miracles I became concerned with what the mind's capabilties which could encounter fifth dimensional views. That such examples were needed, and found in relation to Thomas Banchoff.

Having understood the early development from Euclidean perspective, our furthered evolutionary developement of the geometries, were gained by moving beyond the fifth postulate. I became comfortable with a dynamical realization about our universe(Omega), and about the idealization of curvature in dynamical fields of supergravity.

I made the statement that GR is reduced from the higher geometries and along with that view the understanding that things existed in earliers states of being. Robert Laughlin's views of complexity and symmetry breaking would reveal to me, that the matter states of form, were derived from "other states of existance". This is a fundamental realization of higher dimensional attributes revealled in the topologies/geometries. So from higher, and the continuity of, topological considerations to the firmly fixed realms of geometries in the forms? So from early universe to now, what views allow us to consider that symmetical breaking that has gone through phase transitions, to get from the planck epoch phase of our universe to today?

Having come in contact with a new type of thinking in the realm of the geometries, it became very important to me to understand how this could have manifested early in our historical background? I followed it through GR in order for this to make sense, I continued to move and consider the higher dimensional relevance new models might use in their move to the abstracts realms of thinking.

Here I would interject the realization of string theory, and ask why such a rejection mathematically, would dimiss the subject of strings based on this dimensional realization, and then quickly disperse, string's relevance because of the higher dimensional significance brought to bear on the attribtues of the minds capabilties? Part of the develpement of the brains compacity was the realization that such images produced(higher topological math forms), could indeed symmetryically break to forms within the world. Forms within mind, that could lead to solification in the math? When is a Pipe a Pipe?:)

This is what had troubled me most, noting Peter Woit's rejection of the value of his "anti" campaign of string theory evolution. Maybe, it was more then the idea of the subject and it's established views that he felt were as much part of the illusion as any other theory, that found itself unscientifically determined? Based on the constructs string theory developed? Maybe it was the funding biased felt towards this subject, and lack of, somewhere else. We wouldn't know this, because he had no alternative?

Wednesday, January 26, 2005

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

Thursday, January 20, 2005

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!