Purpose of the Compton Lecture Series

April 8The 63rd Compton Lecture Series, 2006 through June 3, 2006, 11:00 a.m.

Sean at cosmic variance point to this series of lectures that are being presented each year and in this series the entitled is called, "String Theory: With a View Towards Reality" which will be presented by Nicholas Halmagyi, McCormick Fellow, Enrico Fermi Institute.

Dear Friends of the Enrico Fermi Institute:

We cordially invite you to join us for the next series of the Arthur H. Compton Lectures. The Lectures are intended for the general public, friends of the Enrico Fermi Institute, members of the University community, and interested citizens of the Chicago area. They provide a descriptive account of some of the frontiers of present-day science. We don’t expect you to have a formal background in mathematics or science, but hope to appeal to your curiosity and to share with you some of the excitement of modern scientific research.

String Theory is an attempt to describe all particles by multi-dimensional objects, such as strings and membranes. These objects propagate in a ten dimensional universe of which four dimensions are visible to us. This rather outlandish conjecture has led a large community of theoretical physicists to hope for a unification of particle physics and Einstein's general relativity.

The rather serious caveat is the difficulty in providing predictions which can be experimentally verified since the physical manifestation of the string hypothesis will be most obvious only at energy scales which far exceed our current experiments.

In these lectures Dr. Nicholas Halmagyi will explain the humble beginnings of String Theory and will detail the staircase of energy scales which climb up to quantum gravity and string theory. No scientific background is required.

Just bring your curiosity. We hope you can join us for the first lecture on Saturday, April 8, 2006 at 11:00 AM in Room 106 of the Kersten Physics Teaching Center, 5720 South Ellis Avenue. Enter through the door at the southeast corner. The series will run from April 8, 2006 through June 3, 2006.

There will be NO lecture on Saturday, May 27th and the Compton Lecture Luncheon will be held on June 3rd.

Sincerely,

James E. Pilcher Director

There is a list of Present and Recent Abstracts, some mentioned in the article presented by Sean Carroll, and many others on the Compton lecture presentation itself.

For me it will be a interesting set of lectures, as I have watched this development for the last couple of years trying to piece togehter the essence of this perspective, about the way in whch one could now percieve a model used to help grow towards a dimensional expression of particle physics in high energy areas.

I would not like one to think that I am without purpose in my attachments to Cosmic varaince, and to those there in cosmic variance without understanding that some in their respective trades, are just as green(e) when it comes to applying their tools of the trade with string theory, while working their specific areas.



Feynman's Rainbow, by Leonard Mlodinow Warner Books 2003

Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace by Leonard Mlodinow FreePress 2001

Also too, having watched a previous writer like Leonard Mlodinow, the quest to pursue science as well as develop the "path with a heart," to me exemplfies the struggle of some science people to find this part of themself. Meanings, to continue in the directions they do. While it might have been a aimless struggle( the recorded history) that apparent at one time as the story unfolds, were the glimpses into other times of people, as the greater teachers of science, like Feynman or Gellman, these insights into their lives present some of the essesnce of what has to be found as motivations needed to develope awareness not only for themself, but in the struggle to move society along with them.

More thoughts on Enlightenment?

While that book is not available there, it has many other books listed for inspection.

Richard Maurice Bucke(pdf) and Cosmic Consciousness was one of the first books that I read about almost 35 years ago. It was long ago assimilated, so I could not tell you much, other then I question now the role might be presented to our awareness, for those developing and being responsive to intuitive moments. Or what, a enlightened individual might be, after having met moments that may correlate to what enlightenment might be, "more then once," for the initiated?

As I said I am not a very good meditator, although I do look quietly and focused in my intentions as to what such quiet moments could produce, after working to understand.


In the Third Person?

It was in the early spring at the beginning of his thirty-sixth year. He and two friends had spent the evening reading Wordsworth, Shelley, Keats, Browning, and especially Whitman. They parted at midnight, and he had a long drive in a hansom. ...His mind, deeply under the influence of the ideas, images, and emotions called up by reading and talk of the evening, was calm and peaceful. He was in a state of quiet, almost passive enjoyment. All at once, without warning of any kind, he found himself wrapped around as it were by a flame-coloured cloud...he knew that the light was within himself. Directly afterwards came upon him a sense of exaltation, of immense joyousness accompanied or immediately followed by an intellectual illumination quite impossible to describe... he saw and knew that the cosmos is not dead matter but a living Presence, that the soul of man is immortal, that the universe is so ordered that without any peradventure all things work together for the good of each and all, that the foundation principle of the world is what we call love and that the happiness of every one in the long run is absolutely certain.

I'm thinking out loud. :)

Does such an elevation really make the individual any different remembering and being respectful, of the life they are currently living/others?

I personally don't think these constructs change in which we had to learn to use in how we assess/work life. Means, that the job is ever more difficult and the responsibility to living life ever more complicated/greater. We are now supposed to be more aware?

We now understand possibly what the emotive development means in how we produce memory and the attitude development granted to reacting in life ( what can be changed in the future). Yet, we are still involved in purifying these emotions, still the uneducated ruler(ego) exists, by the unleashed potentials of a mind who still sleeps, while it should be awake?

Yet, the mind has been synchronized, with the development of the lower centers and the" heart," the place where such development begins? How do all such probabilities come to mind?

Might we now become aware of the responsibility we have for truth to ourselves/others and the illusions we might have perpetuated? The fog and qualities of working towards a "open heart and clear mind" that may be met because of the issues we developed/developing, along in life.

Of course there could be many interpretations caused by my ambiguity of words choosen here, yet, is enlightenment really ever that far away for each of us to experience?

That such potentials could exist if we had thought these things not sacrosanct to mysticism alone, but is really part of developing and working responsibly, in our quest to understand life/science?

Abraham Maslow and Peak Experience

"The worst disease afflicting human kind is hardening of the categories." - Artist Bob Miller.

Well I having been watching the topics ofCategorically Not site created. I see such fine visitations by those who have ventured into the science, asking for responsibility of mind in science, be given to society on a platform, as a fine and ethical reporting/lectures, on where science/other issues, are today?

That they had ventured beyond the safe haven of science, to talk about "intuition of a kind", held to thoughts on subjectivity made me think.

So things less likely to be held in the role of experimental validation( and psychological modelling has learnt to bear the brunt of scorn by many science minds?) that we might like to see physical processes and evidenced to date, also, as a kind of invitation to think about the roles subjectively of modelled thought about intuition worked, revealled as common today in practise?

Peak experiences (wikipedia 17 April 2006)

Peak experience is a term used to describe certain extra-personal and ecstatic states, particularly ones tinged with themes of unification, harmonization and interconnectedness. Participants characterize these experiences, and the relevations imparted therein, as possessing an ineffably mystical (or overtly religious) quality or essence

The question I might have placed up front here, is if such thoughts about intuition are born to what it would constitute, would one have said, a close relation to "Peak experience"? What would any consolidation of the individual represent in it's wholeness, if such an actualization moment was percieved for a short time, that such gains made by the work and study of, found it's application would have been granted in the moment of one's solitude? As one who gazed into the stream, or one who found in such a place that would help the mind in its efforts to raised the packet from the probability of all possibilties, as an enlightening moment?

From whence would all such idealizations emerge, that such an tonality of thought would embrace itself as a self actualized moment in the connection to the value of all probabilites with this peak moment? The probability of all things needed a resource and commonality from which all minds could draw some comparison. Where was this moment of recognition? A harmonical Oscillator of a kind, possibly? The basis of all reality existed in some form self described harmonical expression?


1908-1970
by Dr. C. George Boeree

Abraham Harold Maslow was born April 1, 1908 in Brooklyn, New York. He was the first of seven children born to his parents, who themselves were uneducated Jewish immigrants from Russia. His parents, hoping for the best for their children in the new world, pushed him hard for academic success. Not surprisingly, he became very lonely as a boy, and found his refuge in books.

What I had been working towards here in the pass couple of years is evidence by the archive to the right.

It has been a interestng experience trying as best I can to see where science was going. What was being held at the forefront of science knowledge, in regards to the theoretical idealizations, that were born to push insight, and perception deeper into the coming realities. The cognition of what might be borne in mind, that any emergence might have revealled of itself in the aspect of new geometries formed to consolidate all geometries that currenty exist?

What shall these be in the mind where cognition is born out of the reality about our being?

Surprizingly, as one learns about themself, the life experience seems to become clearer, as we progress along the "road of independance." Learning curves, that keep us so occupied, that the life's lesson might never seem ever finished, as we progress through one goal or another. Find, the mind flowing and growing. IT had a path which we might have never had known, had we not realized what it had amounted to in realization? It's work?

What could the intellect become if it held all it's intention to "abstract form" in mathematics, that it never found the associations it did and were needed in pushing into those deeper realities? There was a point it no longer worked, and such a place held in the microcosmic view, was still part of a much larger cosmological view? Can this not be so?

How can a speck of a universe be physically identical to the great expanse we view in the heavens above? (Greene, The Elegant Universe, pages 248-249).

Above it all, there were ideas in my mind that biased the way I talked and wrote, that I saw beyond what the intentions were about our participation into forging the reductionistic view, as some part of the greater whole? Why, I recognized the probelmatic koan( can I call it that) revealled in Brian Greene's wording that guided my thought process.

This was labelled as an liminocentruc structures, and within the context of this blogger experience of writing, I wrote about them historically, as a place visited, and as images that arise in mind, that could have represented aspects of our wholeness.

The mandala can also be an image of eternity cycling through time and as such images soul's and Nature's circular journeys, as they are reflected in, for example, the Native American Medicine Wheel, in seasonal, rebirth and karmic cycles, in mythic journeys of going out and returning changed to one's point of origin, and in the zodiacal wheel as life's twelve archetypal stages of personal growth.

This cyclic transformation is also at the heart of ancient Chinese meditation. When the spiritual light in the body moves through rhythmical breathing in a circle, all the opposite energies of heaven and earth, sun and moon, light and dark, are crystallised and form what the Chinese called the Golden Flower, an inner mandala imaging the balanced, open and centred heart.

Maybe, mandalic in origins, that such symbols revealled the deeper insight of the soul who had travelled and secured the "parcel of thought gained" as packages to be born in mind, to surface time and time again?

What use to loose our pursuates to self actualization, and immmediate recognitions of that peak experience, to have found Maslow had created a pyramid of a kind? It had already rested deeply in my own mind's creations, as a model formed. Can I progress his thoughts and his models mine. I most certainly can, and I have the history to prove this, as I incinuate from what is baised in my own views. My writing.

Who is Abraham Maslow, that such idealizations would amount to a psychological veiw I engaged in just the last couple of days or so, that I'd found some association too, model depictions, that I myself had created.

Consider this the base of the pyramid and the four faces, and what value this insight that such perfection could have arsien from Maslow's hierarchal renditions towards self actualization, that the lower centers of humanity would have been it's struggle in the heart, to have become actualized in the heart of mind, as a transcendance of thought, gained?

It was with some historical perspective that having spent years studing, that such model was produced. Which guided my own wording and thinking as I developed. Befuddle readers, as to the demands for a more clearer kind of writing.

Asked, if the most predominante language should be, I too had said math, but most will say english. I give my reasons why, for math, yet so inexperienced am I it's many forms:)

The archetype has no form of its own, but it acts as an "organizing principle" on the things we see or do. It works the way that instincts work in Freud's theory: At first, the baby just wants something to eat, without knowing what it wants. It has a rather indefinite yearning which, nevertheless, can be satisfied by some things and not by others. Later, with experience, the child begins to yearn for something more specific when it is hungry -- a bottle, a cookie, a broiled lobster, a slice of New York style pizza.

The archetype is like a black hole in space: You only know its there by how it draws matter and light to itself.

Less comprehensible no doubt, without out the reader having has some idea of where I was speaking from? No, not from some "other worldly" person like PLato, but an "archetype used" to progress the thoughts of many who had themself engaged in science, about the greater perception/inspiration, as we moved back from the Plato's Cave, to gain in light, about man's imprisonment. As we have "unchained the mind" from the links/matter that bind us.

So you might say what changed?

As I read some more on Maslow, I learnt about many things about my own mind that felt true, to what was being read. That I understand now, that the first part of the lesson about self and it's motivation with years of study, might had seen and been lost, had I not now concluded some thoughts about what I have gained in recognition about self? Time in perception about the past allows this recollection and reminincing now focused forward.

What could be added to Maslows hierarchal diagram of thinking mind and about the steps of progression had some kind of self actualization been bound in the determined mind of one who was not a conformist? To any degree, who liken the freedom to study outside all of the rules of engagement, was still very respectful of the halls of higher learning.

Engaging life as a father and husband, the early years and education did not ever reveal that I would be capable less than the man working ever with his hands and mind to be paid? That his family needed to be supported and growth accomplished as any child would in nurture. While amidst this, a experimentor, and philosopher, as student of life in father felt.



You had to be motivated( what kind of motivation is seeking, what is it's base), or why would you waste your time travelling through the idealizations we do encounter. Facing to see what modulation of thought might do in seeing anew? You had to rise above those lower centers. Such a climb, to the heart in mind(some might know of it's truth comparison in images shown here. Was part of the actualization process after attending class?



Alchemcial processes might have shown such step processes engaged in the process of purifying(psychological), as well as leading to the understanding of who the king was(ego) and how mastery would have been gained over?

On Gauss's Day of Reckoning

A famous story about the boy wonder of mathematics has taken on a life of its own -Brian Hayes

Illustration by Theoni Pappas

In a fanciful drawing done in the manner of a woodcut, the young Carl Friedrich Gauss receives instruction in arithmetic from the schoolmaster J. G. Büttner. As the story goes, Gauss was about to give Büttner a lesson in mathematical creativity.

To me the historical significance of this research is important to me. People could chastise me for saying that the research I do has no quality, then what should be assumed with scientific credentials? Still the romance I have for such abstractions and development of thinking is important just the same. It is about creativity to me, and looking back to the ingenuity of thought, is something I can see in everyone. One doesn't have to consider them self less then, just by being the student that would solve the problem, while insight and acute perception, might have been revealed in one who could throw down the slate the quickest.

The story is fascinating tome on a lot of different levels and to tracking down the essence of what we see passed from one hand to another, and how this ambiguity might creep in and additions make there way for added material.

I understand this in our response to writing science, with what language is supposed to be. Sure talk about chinese , Italian, Latin of ole, and we want to know what the truest expression of the language should be?

Of course this is the responsibility of math, that a common basis be found, between all languages, that the source would have described it so abstract/yet closest to the center of the circle) that all would understand and could work the abstract nature of this math.

I feel guilty, that I cannot contribute so well to this math language, that I strive to listen very good to the concepts espoused, as close as possible to the development of this Algebraic way of seeing.

Yes, it is as important, as the geometrical seeing that it be inherent in the way things abstractly can be seen. That both would have supported the continued work fo science.

Mine then is the student's plight in a vast world that I exist away from, yet, try and stay as close as I can to learn.

Do I sanction everyones abilities away from this in character, is no less then the character I assume, and has been treated. That respect be given, might have found the truer calling of sharing the insights, be as truthful as possible. We should all strive to this of course.

What is Swirling in my Mind

As I lay there many things float through my mind about how we are seeing things now.

So the article above sparked some thoughts here about Sylvestor surfaces and B field understandings, that also included Lagrangian perspective along with WMAP polarization mapping. All these things seem so disconnected?

I keep finding myself trying to wrap all of this in a gravitational perspective as it should , no less important then gauss contributions, hidden for a time, while the student of his brings the perspective for us all to see. So how familiar is protege as Riemann that his Hypothesis is so much the like of the numbers apparent, as in the youthful gaze of the student challenged.

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.

Describing the Intuitive Process?

True creativity often starts where language ends-Arthur Koestler

If such a image is recognized in how we attain such clarity, then would such a map be insignificant? What was conducive to the event happening? Fishing the deep waters of our subconcious purposely or with no cause other then to resolve a problem?



As subjective as the topic of intuition might be in regards to each others abilities, I see no reason why such a process should not be explained. People with good science abilities recognize that this process is a valid one regardless of the leanings towards atheistic, or godliness in bias, that I think appropriate that it is taken out of the subjective realm and mysticism? That any good luck, might wane, if all of a sudden talked about.

Clifford:

His was the best single sentence summing up the concept, as we were to use it that evening: Intuition is the process of getting to a destination without knowing the route. He also added: Sometimes you did not even know you wanted to get there. I've modified the words a bit, but that's the essence of what he said. It was a definition that was so appreciated, you could hear several audible hhhhmmmmms of recognition from the audience.

There is a quiet recognition here, of something that touches us all, and trying to explain it does not seem like a inappropriate thing to do. Thus I would try and model a approach no different then the mathematician or scientist who is at a lost for words/math. Thus, Arthur’s quote up top makes some kind of sense.

Now sure the ingenuity of the moment might seem far and in between, but being aware of the day today circumstances in our memories induced created, is a good way of watching how this process might unfold. That they might only be one time of significance, would not dissaude me from stating that it is more likely encounter more then one might think. An example multiplied by the number of people who say ah, yes I see, and we understand that the point about it’s significance, that we are in agreement. Is there some other explanantion, the more the merrier, that we might see the greater detail?

This intuitive process is as applicable to our search for wordings, as it is for science/math.

Where is the most apropriate place for such recognitions, as to when the work ends, and we are at a loss?

A Supersymmetrical idea perhaps, or a potential resource seen in analogy like water, of the subconscious/unconscious? Would we be wise to know when such things are sent to the subconscious, that by such continued recourse in the sameness of experience, such things will arise to the surface time and time again.

Has this emotive experience changed, or, can we assign new attitudes to what we always did uncosciously? By being aware in our daily lives, the forces of violent seas or a messy house in symbolic analogy will we have recognized the warnings from a disorganized mind, or one, that has not paid attention to the experience manifested?

Arthur Koestler and Creativity

True creativity often starts where language ends.
Arthur Koestler

For those who engaged the issue of intuition, can we say that this is very close to what creativity is ,and the quote suplied above, is in essence. Is the mind, having come to a point on the Aristotlean arch, as, having fully understood, that work with reason and insight would have been to see that, the medium what ever it is, is held to this regard?



If the question is held in context of the mind and foci is strong, in what probabilistic venue would we see such events as issuing from someplace? This I would say would be the "unconscious" and in having diagramed this in a schematic way, how is it that such causations, might have been tied to the fisherman's line and lure, that is sent deep into a future for an examination result.

Of Koestler’s many books, his powerfully anti-Communist novel Darkness at Noon (1941) is still the most famous, but he wrote one book that focused squarely on the paranormal – The Roots of Coincidence (1972). Here, he attempts to find a basis for paranormal events in coincidence, or more precisely synchronicity, so that there is only one phenomenon to explain rather than many. He proceeds to seek the roots of coincidence in the Alice-in-Wonderland world of quantum physics, the infinitesimally small subatomic realm where our everyday logic no longer holds sway, where particles can be waves and vice versa, where forces that only mathematical equations can glimpse swim in the dark, unfathomable ocean of probability before the manifestation of either matter or mind. Towards the end of the book, Koestler pleads that parapsychology be made “academically respectable and attractive to students”, otherwise the “limitations of our biological equipment may condemn us to the role of Peeping Toms at the keyhole of eternity”.

So it was gathered all around, everything that we were involved with, and out of it, a solution abstractually engaging the mind in symbolisms of a language not understood. But still relevant. What would this new language be, if it had run it's course previously, and we needed new insight. We were careful then in understanding the porgress can be made in our expectancy, as well as having full confident in the self, to explore these unknown regions.

Who better then to create the dialogue necessary in bringing forth the creative flow, if we had acknowledged the teacher and student, within ourselves?

Art Mirrors Physics Mirrors Art, by Stephen G. Brush

The French mathematician Henri Poincaré provided inspiration for both Einstein and Picasso. Einstein read Poincaré's Science and Hypothesis (French edition 1902, German translation 1904) and discussed it with his friends in Bern. He might also have read Poincaré's 1898 article on the measurement of time, in which the synchronization of clocks was discussed--a topic of professional interest to Einstein as a patent examiner. Picasso learned about Science and Hypothesis indirectly through Maurice Princet, an insurance actuary who explained the new geometry to Picasso and his friends in Paris. At that time there was considerable popular fascination with the idea of a fourth spatial dimension, thought by some to be the home of spirits, conceived by others as an "astral plane" where one can see all sides of an object at once. The British novelist H. G. Wells caused a sensation with his book The Time Machine (1895, French translation in a popular magazine 1898-99), where the fourth dimension was time, not space.

So, would we have recognized some of these features, in the way the words are written, or how the question mark, would transcended the inspiration sought and found from others, who would propel us forward? The conditions then and foundational attitudes had to rely on what history had already gone through, that we might have recognized also the work that Poincare might have relinquished in that dialogue. To have propelled other minds, like Picasso or Einstein forward?

Is this where "time" became something of a issue with the space coordinates, that such resolution might have paved the way for a spacetime? Answered, what the fourth dimension actually was? Such progression then would have been important, as we move forward in society that not only had Poincare provided the prospect, but that also Grossman in the geometrically refined views sought out as well, to contribute to the troubles Einstein was facing?

Where these might have thought to be random, the events are tied together? Are seen in the actualization of what trasncended these two random events? Or were they?



We talk about the historical time and around then, what was happening if we had seen information on Flatland and Abbott? Issues of mysticism held in context of what those extra dimensions might actually mean.

Out of this, a new found responsibility, as to how such mysticism once held in the spookiness of Einstein, has now an explanation that has been further refined in what a Anton Zeilinger might have been doing for us?

Enlightenment of a Kind?

The Structure of Consciousness John Fudjack - September, 1999

By 'dilating' and 'expanding' the scope of our attention we not only discover that 'form is emptiness' (the donut has a hole), but also that 'emptiness is form' (objects precipitate out of the larger 'space') - to use Buddhist terminology. The emptiness that we arrive at by narrowing our focus on the innermost is identical to the emptiness that we arrive at by expanding our focus to the outermost. The 'infinitely large' is identical to the 'infinitesimally small'.

Liminocentric Structure

I wonder if I had related this piece of information that I had gained in my research would have been of benefit here for those who believe in the singularity? If it irrates the conscousness long enough, and hard enough, what will be released in the quiet moment that had been conducive to creativity flowing?


'The Princess & The Pea' from 'The Washerwoman's Child'


If you thought it "the pea" or some object so dense, well I have something else to consider when we see the dynamical way things collapse, and are reborn, to become the motivation let's say, for a inflationary new universe?

But it's more then that, if one considered Brian Greene's quote?

In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above? (Greene, The Elegant Universe, pages 248-249).

That statement in bold troubled me for a long time. There is an image I like to show that describes this breakthrough, not saying whether or not this is a type of enlightenment? I really don't know what that means I think.

In this metaphor, when we are seeing the donut as solid object in space, this is like ordinary everyday consciousness. When we see the donut and the hole at its center, this is like a stage of realization in which 'form' is recognized as 'empty'. When we zoom in extremely closely and inspect the 'emptiness' at the center, or zoom out an extreme distance away from the object and the donut seems to disappear and we have only empty space - this is like certain 'objectless' states of awareness that can occur in meditation. But the final goal is not to achieve the undifferentiated state itself; it is to come to the special perspective that allows us to continue to see all three aspects at once - the donut, the whole in the middle, and the space surrounding it - this is like the 'enlightened' state, in this analogy. 10 The innermost and outermost psychological 'space' (which is here a metaphor for 'concentrated attention' and 'diffused attention') are recognized as indeed the same, continuous.

Click on quote.

Working the Angles UNtil They Add Up Too?

I assume now, you are in the non-eucldiean inferences?

If people had thought "the negative" always evil, then what value any "dynamic of thinking" if we could not resolve what we had been doing by changing the shape of our attitudes? :)



Helen Joyce:

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

Some might have never understood the dynamics going on, and if a "backreaction" was created, what value would this serve in our thinking? I ponder. Some might think of Dirac? Some of anti-matter? In opposition, some might think of Reimann and what was encapsulate in Gauss's Mountain.

So maybe in churches, or concert halls, we might think about the ways "sound reverberates," within an enclosure? The lines in the architecture? How this resonance passes through and changes the very matters in their oscillations?

Hyperbolic Geometry and it's Rise

Omar Khayyám the mathematician(6 april 2006 Wikipedia)

He was famous during his lifetime as a mathematician, well known for inventing the method of solving cubic equations by intersecting a parabola with a circle. Although his approach at achieving this had earlier been attempted by Menaechmus and others, Khayyám provided a generalization extending it to all cubics. In addition he discovered the binomial expansion, and authored criticisms of Euclid's theories of parallels which made their way to England, where they contributed to the eventual development of non-Euclidean geometry.

Giovanni Girolamo Saccheri(6 April 2006 Wikipedia)

Saccheri entered the Jesuit order in 1685, and was ordained as a priest in 1694. He taught philosophy at Turin from 1694 to 1697, and philosophy, theology, and mathematics at Pavia from 1697 until his death. He was a protege of the mathematician Tommaso Ceva and published several works including Quaesita geometrica (1693), Logica demonstrativa (1697), and Neo-statica (1708).

Of course the question as to "Victorian" was on mind. Is non-euclidean held to a time frame, or not?

Victorian Era(wikipedia 6 April 2006)

It is often defined as the years from 1837 to 1901

Time valuations are being thought about here. In regards too, non euclidean geometry and it's rise. Shows, many correlations within that time frame. So that was suprizing, if held to a context of the victorian socialogical time frame. But we know this statement is far from the truth?


Seminar on the History of Hyperbolic Geometry, by Greg Schreiber

We began with an exposition of Euclidean geometry, first from Euclid's perspective (as given in his Elements) and then from a modern perspective due to Hilbert (in his Foundations of Geometry). Almost all criticisms of Euclid up to the 19th century were centered on his fifth postulate, the so-called Parallel Postulate.The first half of the course dealt with various attempts by ancient, medieval, and (relatively) modern mathematicians to prove this postulate from Euclid's others. Some of the most noteworthy efforts were by the Roman mathematician Proclus, the Islamic mathematicians Omar Khayyam and Nasir al-Din al-Tusi, the Jesuit priest Girolamo Sacchieri, the Englishman John Wallis, and the Frenchmen Lambert and Legendre. Each one gave a flawed proof of the parallel postulate, containing some hidden assumption equivalent to that postulate. In this way properties of hyperbolic geometry were discovered, even though no one believed such a geometry to be possible.


History (wikipedia 6 April 2006)

Hyperbolic geometry was initially explored by Giovanni Gerolamo Saccheri in the 1700s, who nevertheless believed that it was inconsistent, and later by János Bolyai, Karl Friedrich Gauss, and Nikolai Ivanovich Lobachevsky, after whom it is sometimes named.