The Synapse is a Portal of the Thinking Mind

Life must be understood backwards; but... it must be lived forward.
Soren Kierkegaard

Penrose's Bermuda Triangle?

A long time ago I learnt about using avenues to free the mind by doing different things in the face of adversities. One can not always gauge their reaction to what life throws at them. I found this for me most certainly, and in face of the understanding of the "emotive struggle," it is moving "clarity to such thinking" of the thinking mind, that one would like to at least understand what influences these emotive consequences have on their thinking space.

The brain is a matter defined state of existence and is furthest from the source of expression. Yet, it houses avenues within the very nature of it's structure, to allow processes that may be comparative to me of what spaces can be created, as we create an open portal for all thinking minds avenues to new possible changes.




So I of course like to use a bubble in this context to to display the field around that thinking brain/Body to know that the emotive consequences lie within this field of expression.

It wasn't enough then that what was apparent to me, that the continued struggle I have of dealing with these emotive fluctuations is in our thinking minds, that the reactive states, were held in a place of a deeper repose while the collection of these things come from a history of living.

It was not enough that I knew of a map created by another of psychological stature and lead by scientific valuation, that it would lead to the understanding of Penfield's work on the structure of the brain.

Source:McGill University ArchivesWilder Graves Penfield, OM, CC, CMG, MD, FRS (January 25/26, 1891 – April 5, 1976) was an American-born Canadian neurosurgeon. See also:Wilder Penfield

So while I had given Stefan of Backreaction "a brief summary of it" there in the following quote below, it is in such a way this unfolds I had developed this understanding of "historical context" and now, work toward the future. This is why I like history, and why I used David Hilbert's quote. It signals "advancements in thinking" as we explore history in not only the context of who we are, but of our predecessor's mathematical development as well. The "gap created for such ingenuities" had to realize a "stop off point" for further developments. So we develop from that point, forward.

At 11:08 AM, March 13, 2008, Blogger Plato said. Historical Meme: Seven Things about Richard Carrington

Often we say things in our own lives not aware of the context and influence our parents have on us, yet, such concepts themself are transmitted and unknowingly we become the parent of our raising.

To change the cyclical nature of such events, and move to our own adult situations requires a deeper insight into who we are, that we might change the circumstance and reveal who it is, is talking, when acting in this role of our day to day.

That you may not have children now is not the issue and any young person might know then that we are also our parent, as well as, the child of that experience. It is how we shall choose as an adult to address society, each other, in these ways, that we change the future.

A lot of time if you are not aware of the internal structure this information is transmitted how would you know that it follows "another's mindmap" and you were not aware of it? So as glossy as this sounds "my writing" about our individual histories, we now know that we transmit part of our histories into the future.

Parent ego state


This is a set of feelings, thinking and behaviour that we have copied from our parents and significant others.


As we grow up we take in ideas, beliefs, feelings and behaviours from our parents and caretakers. If we live in an extended family then there are more people to learn and take in from. When we do this, it is called introjecting and it is just as if we take in the whole of the care giver. For example, we may notice that we are saying things just as our father, mother, grandmother may have done, even though, consciously, we don't want to. We do this as we have lived with this person so long that we automatically reproduce certain things that were said to us, or treat others as we might have been treated.


As we grow up we take in ideas, beliefs, feelings and behaviours from our parents and caretakers. If we live in an extended family then there are more people to learn and take in from. When we do this, it is called introjecting and it is just as if we take in the whole of the care giver. For example, we may notice that we are saying things just as our father, mother, grandmother may have done, even though, consciously, we don't want to. We do this as we have lived with this person so long that we automatically reproduce certain things that were said to us, or treat others as we might have been treated.


Adult ego state


The Adult ego state is about direct responses to the here and now. We deal with things that are going on today in ways that are not unhealthily influenced by our past.


The Adult ego state is about being spontaneous and aware with the capacity for intimacy. When in our Adult we are able to see people as they are, rather than what we project onto them. We ask for information rather than stay scared and rather than make assumptions. Taking the best from the past and using it appropriately in the present is an integration of the positive aspects of both our Parent and Child ego states. So this can be called the Integrating Adult. Integrating means that we are constantly updating ourselves through our every day experiences and using this to inform us.


In this structural model, the Integrating Adult ego state circle is placed in the middle to show how it needs to orchestrate between the Parent and the Child ego states. For example, the internal Parent ego state may beat up on the internal Child, saying "You are no good, look at what you did wrong again, you are useless". The Child may then respond with "I am no good, look how useless I am, I never get anything right". Many people hardly hear this kind of internal dialogue as it goes on so much they might just believe life is this way. An effective Integrating Adult ego state can intervene between the Parent and Child ego states. This might be done by stating that this kind of parenting is not helpful and asking if it is prepared to learn another way. Alternatively, the Integrating Adult ego state can just stop any negative dialogue and decide to develop another positive Parent ego state perhaps taken in from other people they have met over the years.


Child ego state


The Child ego state is a set of behaviours, thoughts and feelings which are replayed from our own childhood.


Perhaps the boss calls us into his or her office, we may immediately get a churning in our stomach and wonder what we have done wrong. If this were explored we might remember the time the head teacher called us in to tell us off. Of course, not everything in the Child ego state is negative. We might go into someone's house and smell a lovely smell and remember our grandmother's house when we were little, and all the same warm feelings we had at six year's of age may come flooding back.


Both the Parent and Child ego states are constantly being updated. For example, we may meet someone who gives us the permission we needed as a child, and did not get, to be fun and joyous. We may well use that person in our imagination when we are stressed to counteract our old ways of thinking that we must work longer and longer hours to keep up with everything. We might ask ourselves "I wonder what X would say now". Then on hearing the new permissions to relax and take some time out, do just that and then return to the work renewed and ready for the challenge. Subsequently, rather than beating up on ourselves for what we did or did not do, what tends to happen is we automatically start to give ourselves new permissions and take care of ourselves.


Alternatively, we might have had a traumatic experience yesterday which goes into the Child ego state as an archaic memory that hampers our growth. Positive experiences will also go into the Child ego state as archaic memories. The positive experiences can then be drawn on to remind us that positive things do happen.


The process of analysis's personality in terms of ego states is called structural analysis. It is important to remember that ego states do not have an existence of their own, they are concepts to enable understanding. Therefore it is important to say "I want some fun" rather than "My Child wants some fun". We may be in our Child ego state when we say this, but saying "I" reminds us to take responsibility for our actions.

Transactional Analysis theory was developed by Dr Eric Berne in the 1950's.

Intuitive Light Switches

So you can start off with thinking all about what Penrose had to say, and Max may have pushed this further, to wonder, how his structural interpretation may be compared to what the actual Mathematical Universe is saying. A Square? A soccer Ball. So today, it may be some Easter Egg interpretation?:)





See:

Venn Logic and TA

The Plato’s Cave Study: Does Bullshit Truly Baffle Brains?”

The Continuum: The Interior of the Blackhole

The surface of a marble table is spread out in front of me. I can get from any one point on this table to any other point by passing continuously from one point to a "neighboring" one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing "jumps." I am sure the reader will appreciate with sufficient clearness what I mean here by "neighbouring" and by "jumps" (if he is not too pedantic). We express this property of the surface by describing the latter as a continuum.Albert Einstein p. 83 of his Relativity: The Special and the General Theory

How is it that time could have been a emergent process knowing full well that the measure, and the continued "half measure" we loose perspective on that space. So given the nature of the blackhole, how is it we see such smoothness geometrically developing, as the temperature values increase, according to the nature of the gravitational collapse? An energy valuation according to this radius allows one to think that "somewhere in this creation" the relativistic nature of the fluidity is taken to a point of that "emergent process." One had to account for the developing nature of the dark energy.

Phil Warnell:

If time is an emergent entity, rather then fundamental, then is perplexing why the universe had a beginning. For if time is both infinite and eternal and the universe is neither, it might be of reason to be limited in magnitude and yet why the wait? This also must form to be part of the explanation.

String theory and it first Three Microseconds by it's very nature pushes back perspective beyond Steven Weinberg's First Three Minutes. Consider Before 1 Planck Time

Before a time classified as a Planck time, 10-43 seconds, all of the four fundamental forces are presumed to have been unified into one force. All matter, energy, space and time are presumed to have exploded outward from the original singularity. Nothing is known of this period.

The Foundations of Mathematics, Invented or Discovered?

Mathematical ProblemsLecture delivered before the International Congress of Mathematicians at Paris in 1900By Professor David Hilbert

While insisting on rigor in the proof as a requirement for a perfect solution of a problem, I should like, on the other hand, to oppose the opinion that only the concepts of analysis, or even those of arithmetic alone, are susceptible of a fully rigorous treatment. This opinion, occasionally advocated by eminent men, I consider entirely erroneous. Such a one-sided interpretation of the requirement of rigor would soon lead to the ignoring of all concepts arising from geometry, mechanics and physics, to a stoppage of the flow of new material from the outside world, and finally, indeed, as a last consequence, to the rejection of the ideas of the continuum and of the irrational number. But what an important nerve, vital to mathematical science, would be cut by the extirpation of geometry and mathematical physics! On the contrary I think that wherever, from the side of the theory of knowledge or in geometry, or from the theories of natural or physical science, mathematical ideas come up, the problem arises for mathematical science to investigate the principles underlying these ideas and so to establish them upon a simple and complete system of axioms, that the exactness of the new ideas and their applicability to deduction shall be in no respect inferior to those of the old arithmetical concepts.

The original address "Mathematische Probleme" appeared in Göttinger Nachrichten, 1900, pp. 253-297, and in Archiv der Mathematik und Physik, (3) 1 (1901), 44-63 and 213-237. [A fuller title of the journal Göttinger Nachrichten is Nachrichten von der Königl. Gesellschaft der Wiss. zu Göttingen.]

Phil Warnell:For if time is both infinite and eternal and the universe is neither

So current understanding has been pushed to consider that there is no geometry which can be seen inside the blackhole? If this is not possible, then the very nature of the geometry is existing at "another level" has to be part of an "emergent process" before it manifests from it's previous state?

So what is that previous state that this universe came from? This universe then, is part and parcel of an "existing universe." While you may consider time as eternal, then what would allow for such a space to emergent within that universe to create a new beginning and another offshoot of it?

See:
What is Happening at the Singularity?

A New Cosmological View?

Glaucon

Glaucon (Greek: Γλαύκων) (born circa 445 BC) son of Ariston, was the philosopher Plato's older brother. He is primarily known as a major conversant with Socrates in the Republic (Plato), and the questioner during the Allegory of the Cave. He is also referenced briefly in the beginnings of the dialogues of Plato Parmenides (Plato) and the Symposium (Plato).

While I of course understood this conversation between Plato and Glaucon, there is a statement of reference that needs to be explained. So that it is not misunderstood that "the object" and "state of the one who questions and the one questioned," are shown to be like "God as the Geometer?" It is an "innate feature to the state of enquiry." That it follows alongside mapping, which advanced my own position of "methodology by intuition." An accumulated to a state called"Correlation of Cognition."

So by introducing "this brother"( a figure in mind to advance the developmental methodology,) to create this "state of being" within us, is much like an artistic endeavour of a plot, a writer, since one may not have had this conversation other then to move this story forward. How?:)

So I am glad there is a Glaucon who would move the conversation for advancement.

As Socratic method requires both a questioner and one questioned to move forward, Glaucon, who is the most honest about his ignorance amongst the friends, will help “build” the ideal philosophical city by engaging Socrates without fighting his ideas.

Self Evident

We hold (they say) these truths to be self-evident: That all men are created equal. In what are they created equal? Is it in size, understanding, figure, moral or civil accomplishments, or situation of life?Benjamin Franklin-The Gentleman's Magazine, vol. 46, pp. 403–404)

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

"Deduction" is an interesting thing left on it's own. While we think it only as one avenue to the methodology of approach, it is not without pointing out that the "inductive part" is part of this philosophical adventure too. That it should leave one to understand that the "infinite regression" leaves one on a precipice of change. That what is self evident, becomes the "new stepping stone for advancement."

A VIEW OF MATHEMATICS by Alain CONNES

Most mathematicians adopt a pragmatic attitude and see themselves as the explorers of this mathematical world" whose existence they don't have any wish to question, and whose structure they uncover by a mixture of intuition, not so foreign from poetical desire", and of a great deal of rationality requiring intense periods of concentration.

Each generation builds a mental picture" of their own understanding of this world and constructs more and more penetrating mental tools to explore previously hidden aspects of that reality.

.......and again.

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.

God the Geometer

Let proportion be found not only in numbers, but also in sounds, weights, times and positions, and whatever force there is.Leonardo Da Vinci

Vitruvian Man by Leonardo da Vinci.

Leonardo is clearly illustrating Vitruvius De Architectura 3.1.3 which reads:

The navel is naturally placed in the centre of the human body, and, if in a man lying with his face upward, and his hands and feet extended, from his navel as the centre, a circle be described, it will touch his fingers and toes. It is not alone by a circle, that the human body is thus circumscribed, as may be seen by placing it within a square. For measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that lines at right angles to each other, enclosing the figure, will form a square.

De Architectura, VitruviusFirst Milanese period 1481/2 - 1499

The first printed edition of the De Architectura (On Architecture) by the ancient Roman architect, Vitruvius, appears.

It is never easy sometimes to know what direction to go with these blog posts. What is being shown on the "screen of my mind" is a painting of Leonardo, and along with this idea about Coxeter's insight into what the geometer is really doing when he discovers aspects of what exists before it's manifestation in reality. As if, it is not enough to know what the Higg's is doing as it crosses the room in analogy with the great Professor Einstein.

Science takes us back to the very beginnings of the universe and how it is we know that such phases and transformational changes can be described, and behind it all, there is not some existing geometrical nature to the forms that manifest?

So from an historical perspective, the image set the pace for what discoveries become part of the blog entry. Who is to know what direction this may take me as I scour the internet and find the following.

Fol 79v-80r-Acoustics. Photo RMN © René-Gabriel Ojéda

Music

According to Leonardo, the musician composes harmony by the simultaneous conjunction of its “proportional parts”. The painter “grades the things before the eye as music grades the sounds that meet the ear”. On Ms. L. Fol 79v. Leonardo investigates sound and tries to establish strict mathematical proportions between the loudness of a sound at its origin and its range, the point in space up to which it can be heard. This “pyramidal law” was seen as a universal law of proportion that could be applied to other natural phenomena such as light, perspective and even mechanics.

Leonardo’s pyramidal law of proportional diminution did not always lead to fruitful conclusions. In the absence of knowledge of advanced mechanics, he attempted to apply it to the investigation of gravity, noting that every falling object acquires increments of impetus. He was obviously unaware of the Merton “mean speed theorem” which states that a body traveling at constant velocity will cover the same distance in the same time as an accelerated body if its velocity is half the final speed of the accelerated body.

Undeterred, Leonardo investigated the actions of levers, pulleys and balances at length according to medieval proportional laws, illustrating endless demonstrations of harmonic equilibrium. While most of the results had no practical purpose, Leonardo seems to have taken delight in demonstrating the certainty of proportional law for its own sake. Perhaps it confirmed his view of the inter-connectedness of all things in nature, which he so often disproved in the course of testing theory with experiment.

See Divine proportions as well.

Pyramidal colourings of our Emotive States

Photo RM -Hervé Lewandowski / Thierry Le Mage- Make Mona Smile here.

As you know I am using a comparative view of emotions which are much more subtle then the matter to which we assign our body. Earth is square. Plato points to heaven for a reason, and all things descend according to those things we assign emotive value which return to the matters defined. Alas, the human experience is emotive determined and our lives set in the direction we send it. All matters of due course, are heralded from a much finer level of thought.

See: The Triangle Descends into the Square

As many of you know I am not the great scientist that so many I follow are. Who have spent their times in the higher halls of learning. It is no less important to me that I work to the same vein of truth that they do in their pursuances for understanding and implementation of science under it's laws.

So too I work an area that would have been the decline of our scientist's credibility. The scientists who have suffered under the scorn of their own colleagues because of this divergence from what is known and understood. I do not have to worry, because I already work the lower echelon of the thoughts and feeling about those scorned. My immaturity perhaps and wonderment as to what purpose this lone blogger attempts, and I could be past off as some kook. I persevere, as we all do to understand life, reality and it's truths.

Mind Map: The Medicine Wheel

The Power of Myth With Bill Moyers, by Joseph Campbell , Introduction that Bill Moyers writes,

"Campbell was no pessimist. He believed there is a "point of wisdom beyond the conflicts of illusion and truth by which lives can be put back together again." Finding it is the "prime question of the time." In his final years he was striving for a new synthesis of science and spirit. "The shift from a geocentric to a heliocentric world view," he wrote after the astronauts touched the moon, "seemed to have removed man from the center-and the center seemed so important...

God as Architect/Builder/Geometer/CraftsmanEarly science, particularly geometry and astronomy/astrology, was connected to the divine for most medieval scholars. Notice, even, the circular shape of the halo. The compass in this 13th century manuscript is a symbol of God's act of Creation, as many believed that there was something intrinsically "divine" or "perfect" that could be found in circles The Circle

Going from 2 dimensional drawing to 3 dimensions has spherical relations in terms of it's mathematical development?

While I present a hint to the "explosion of the thinking mind," how is it such a transference to the actual processes in life could have equalled a "mathematical construct" that one might contend exists at the very beginning of this universe?




An Historical Version

Medicine Wheel Teachings by Thunderbird

The term "Medicine" as it is used by First Nations people does not refer to drugs or herbal remedies. It is used within the context of inner spiritual energy and healing or an enlightened experience, in other words, "spiritual energy." The Medicine Wheel and its sacred teachings assist us along the path towards mental, spiritual, emotional, physical balance and enlightenment.

A good starting point is to determine where you are on the Wheel by your birth date. The Medicine Wheel is walked in a clockwise direction (the direction of the Sun). The time needed to walk a complete circle is whatever time it takes - time, in other words, is relative to the process.

Now of course some feel very funny about using such things to represent something about themselves. Develop a map, that indicates some of one's own history according to someone's else method. What I mean here is that what you see of use in a historical method as per the Native Americans, then how would this apply to your own life?

I present this "from my own experience." How such ideas behind the mapping and mandalic interpretations are evidence for me of the complexity of the human mind. How is it we can create such a maps from the experience? One that can unfold for and from another more subtle recognition of the depth our natures. I believe that this process is inherent in each of us. The complexity of our human experiential existence makes this difficult to see. It is as if you "live a dream" and what does it mean at some other level? So you are confused about the chaoticness of the dream state?

A Tibetan interpretation of the Book of the dead would have it seem that confusion shall be the fog, our fog and any clarity of seeing would be to know what it is that causes this fog. Is it our emotive states of existence? Our emotive contaminants of the mental and spiritual state? What colour would these be if we had thought about what an emotive inflection had been given to an experiences of our own, as we speak and think about life?

So this journey of course took me back to Tibetan images, as well as Jung's interpretations of mandalas as expressions of the soul. The construction method and meanings associated with geometrical proportions to the division of the person. In terms of directions, north, south, east or west. These can have meanings to the idea of "seasons to our life" and this is, what going in a circle may mean in terms of the "totality of the life" of one person, from birth to death.

Does any of this seems familiar to you as it did to me. My natural inclination to mind mapping my experiences and developments of a philosophy according to what was being constructed, just arose from developing a "methodology to approach" intuitively.

See:

Mapping the Pathway Inside

The center and the whole-what it means?

Inside the Mathematical Universe

Tipping LightCones and the Escape Velocity of a Photon

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

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


Figure 2. Clebsch's Diagonal Surface: Wonderful.

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

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

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

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

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

Gravity and the Photon

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

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

The gravitational potential energy is then

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

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

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

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

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

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

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

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

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

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

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

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

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

Brain Matters

Felix Christian Klein1849 - 1925

"Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs."

We know the substance of the matters that house our thinking minds. How much more ethereal is the "thinking mind" if it is only subject to the neuronic thinking brain? The "field of endeavours and thoughts" could be moved to geometrical thinking of a kind that would measure the surface of abstract thinking model Earth?



The dimensional thinking here shows the depth of the thinking mind from it's matter to that of something more profound. Einstein revealed this thinking in an accumulative effect of incorporation, not only the Gaussian Arcs, but of what our thinking could mean in terms of the "lensing quality of planets in space."



So you look at the earth in a new way. This elevation of thinking is what general relativity has done when we think of the abstract geometrical modelling produced for our consumption. Sets the mind to thinking in terms of new paradigms.

Klein's Ordering of 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.

It is the elevation in thought of what gravity can mean when it is very strong, that, what was satisfiable in the euclidean realm, is not so good anymore for looking at what the non-euclidean could represent. Then, a progression of the geometries into new realms of thinking. How so, if gravity is so strong inside the blackhole? There currently no geometries at present that can speak to the nature of the blackhole?

On planet Earth, we tend to think of the gravitational effect as being the same no matter where we are on the planet. We certainly don't see variations anywhere near as dramatic as those between the Earth and the Moon. But the truth is, the Earth's topography is highly variable with mountains, valleys, plains, and deep ocean trenches. As a consequence of this variable topography, the density of Earth's surface varies. These fluctuations in density cause slight variations in the gravity field, which, remarkably, GRACE can detect from space.Gravity 101

So the journey here is to define the space of thinking mind that while ethereal in it's production of matter orientated functioning, is subject to a much finer mode of measure.

For instance energy at any one point could have been define on the basis of 1R, but on a surface what value this energy if it does not describe that surface in space as a dynamical feature beyond the matter s defined?

See:Time-Variable Gravity Measurements

Stringy Geometry

fancier way of saying that is that in general, it's okay to model the space around us using the Euclidean metric. But the Euclidean model stops working when gravity becomes strong, as we'll see later. The Euclidean model for space

The magic square of "Albrect Durer" located in my index on the right is fascinating from the point of view that such a symmetry can be derived from the view of moving in an abstract space.

Trying to understand the implication of what is happening in a stronger gravitational field is an abstract journey for me as well, while I hold "thoughts of lensing" in my mind as a accumulative effect of something that is happening naturally out in space.

The move to Lagrangian points out in space is also an accumulative effect of thinking in this abstract way.

I not only think of the "magnetic field as as an associative value for that abstractness," it is a geometry that is the same for me, as I try to unravel the energy valuation of points(KK Tower) of any location in space. While the valuation of a circle on a 2 dimensional screen sees a string vibrating, I am moving this perception to valuations onto mathematical models.

I have nobody to help this way I have to push forward, knowing there will be mistakes, and that hopefully I am grasping the full scope of seeing in a abstract way.


Figure 2. Clebsch's Diagonal Surface: Wonderful.

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

Dr. Kip Thorne, Caltech 01-Relativity-The First 20th Century Revolution

It was the beginning of what might be called (and in fact is called) Stringy Geometry. The point is that strings are not points, and specifically, their extended nature means that in addition to being able to see the usual geometrical properties of a space that the theory like General Relativity can see, the strings can see other, intrinsically stringy, data. There is a quantity in the theory that is called the Kalb-Ramond field (or just the “B-field”) that can be used to measure how much the string can winds on or wraps a piece of the geometry, in essence. The parameter a that measures the size of a piece of the space that collapses when the geometry becomes singular, is essentially joined by another parameter, b, that sort of measures how much the strings have wound or smeared themselves on that piece of the space. The upshot is that a and b naturally combine themselves into a complex parameter that naturally describes the resolution process, solving the puzzle that the Mathematicians faced.

Beyond Einstein: Fixing Singularities in Spacetime

I am always trying to get the "visual models" of such proposals in terms of the B Field. Nigel Hitchin

Can you tell me, if the Dynkin diagrams and the points on a Sylvestor surface/ Cayley model have some value when looking at this subject?

Also, if it would be wrong to see "UV coordinates of a Gaussian arc" can be seen in this light as well?

I am recording this to help me understand how energy windings of the string may be seen as points on the Sylvester Surface?

See: What is Happening at the Singularity?

What is Happening at the Singularity?

WEll, some of the commentors like myself are not worth counting?:)Thanks for keeping it interesting Clifford of Asymptotia. I hope you won't mind the following quotes for consideration.( it was considered spam) so I reprint it here.

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

Is there not some way presented by Susskind which can help one approach understanding of what is going on in the blackhole by incorporating his "thought experiment" in relation to the entanglement process?

So of course questions about "the horizon" are interesting.

Consider any physical system, made of anything at all- let us call it, The Thing. We require only that The Thing can be enclosed within a finite boundary, which we shall call the Screen(Figure39). We would like to know as much as possible about The Thing. But we cannot touch it directly-we are restricted to making measurements of it on The Screen. We may send any kind of radiation we like through The Screen, and record what ever changes result The Screen. The Bekenstein bound says that there is a general limit to how many yes/no questions we can answer about The Thing by making observations through The Screen that surrounds it. The number must be less then one quarter the area of The Screen, in Planck units. What if we ask more questions? The principle tells us that either of two things must happen. Either the area of the screen will increase, as a result of doing an experiment that ask questions beyond the limit; or the experiments we do that go beyond the limit will erase or invalidate, the answers to some of the previous questions. At no time can we know more about The thing than the limit, imposed by the area of the Screen. Page 171 and 172 0f, Three Roads to Quantum Gravity, by Lee Smolin

TWO UNIVERSES of different dimension and obeying disparate physical laws are rendered completely equivalent by the holographic principle. Theorists have demonstrated this principle mathematically for a specific type of five-dimensional spacetime ("anti–de Sitter") and its four-dimensional boundary. In effect, the 5-D universe is recorded like a hologram on the 4-D surface at its periphery. Superstring theory rules in the 5-D spacetime, but a so-called conformal field theory of point particles operates on the 4-D hologram. A black hole in the 5-D spacetime is equivalent to hot radiation on the hologram--for example, the hole and the radiation have the same entropy even though the physical origin of the entropy is completely different for each case. Although these two descriptions of the universe seem utterly unalike, no experiment could distinguish between them, even in principle. by Jacob D. Bekenstein

The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did. Black Holes and Beyond: Harvard's Andrew Strominger on String Theory

So we have these diagrams and thought processes developed from individuals like Jacob D. Bekenstein to help us visualize what is taking place. Gives us key indicators of the valuation needed, in order to determine what maths are going to be used? In this case the subject of Conformal Field Theory makes itself known, for the thought process?

Holography encodes the information in a region of space onto a surface one dimension lower. It sees to be the property of gravity, as is shown by the fact that the area of th event horizon measures the number of internal states of a blackhole, holography would be a one-to-one correspondence between states in our four dimensional world and states in higher dimensions. From a positivist viewpoint, one cannot distinguish which description is more fundamental.Pg 198, The Universe in Nutshell, by Stephen Hawking

So we are given the label in which to speak about the holographic notions of what is being talked about in the case of the blackhole's horizon.


Campbell's Soup Can by Andy Warhol Exhibited in New York (USA), Leo Castelli Gallery

Spacetime in String Theory-Dr. Gary Horowitz, UCSB-Apr 20, 2005

This year marks the hundredth anniversary of Einstein's "miraculous year", 1905, when he formulated special relativity, and explained the origin of the black body spectrum and Brownian motion. In honor of this occasion, I will describe the modern view of spacetime. After reviewing the properties of spacetime in general relativity, I will provide an overview of the nature of spacetime emerging from string theory. This is radically different from relativity. At a perturbative level, the spacetime metric appears as ``coupling constants" in a two-dimensional quantum field theory. Nonperturbatively (with certain boundary conditions), spacetime is not fundamental but must be reconstructed from a holographic, dual theory. I will conclude with some recent ideas about the big bang arising from string theory.

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.Gary T. Horowitz and Juan Maldacena,

See: Stringy Geometry

The Triangle Descends into the Square