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

Mapping the Pathway Inside

Although [God] did make use of the relevant auxiliary causes, it was he himself who gave their fair design to all that comes to be. That is why we must distinguish two forms of cause, the divine and the necessary. First, the divine, for which we must search in all things if we are to gain a life of happiness to the extent that our nature allows, and second, the necessary, for which we must search for the sake of the divine. Our reason is that without the necessary, those other objects, about which we are serious, cannot on their own be discerned, and hence cannot be comprehended or partaken of in any other way.

Plato



I am not in any way here to argue the historical context that the image above has taken in all that we see in National Geographic or in the articles of archaeological significance. I am using this image in another way that you might not of considered before.

I have given concepts with which one can entertain ideas in relation to what happens from a mandalic, Liminocentric and Mind Mapping sequence of events that will allow certain things to unfold within one's own life? A foundational approach to see the circumstance of life beyond what is just found in the physical reality of the body. Beyond the workings of the physiological sequences of emotive and mental happenings, that "these could have amounted to beyond the realm of the understood."



Imagine for one moment, that the very surface of this sphere, is the sudsy oil based colourations, shimmering from one place to the next, is our mental and emotive states. Our mind (The brain), and it trappings hold the colouration of our reality in way that is not understood. But that colouration is beyond the matters that define the mind itself. Beyond the matters of the brain itself.

So I will "paint the colours of my reasoning for you" to understand the concepts I am putting forth. The conceptual valuations are a culmination of the person trying to organize all that they know in a pictorial sense, that we could see the mind of a Feynman or Dirac, whose skill had come forth? Can come forth in any of you.



It is important then that what you had always seen of earth from space, is more the truth of it, that the gravity now takes hold of this vision and helps you to understand it's place in the universe? While we focus on it's matters we see Grace has been mapped according to the measures used in that sense. I find this correlation of significance when we learn to see the emotive and mental states as such. I still recognize the matter the brain as I do the earth as a matter of fact too.

Is it organizational then that we might reveal aspects within one's own self that we learn to discover certain things about our very own nature. It does not exult us in any way to realize that when you had decided to become comfortable with who you are, that you get the thread that runs through all things for you. That you learn to see who you are in face of all the circumstances that unfold within the span of years from one place to the next? Life continues as it always has. We are just trying to perfect our understanding of who we are in face of all that has to take place for our living in this world.

Where is my home? Why all this travelling from one place to the next, and not finding who it is that speaks through all the information and meetings that take Place. What value all of this and we see we are the accumulation of time spent here and there.

So I gave a structure of a kind to help you understand something about the way I have learnt to see life. It is only a map given that saids what you have to do may have been found useful to help continue your own journey. Something that awakens something in you to say I am happy now that I have found who it is through those times. How I am through all the adversities of living that at the end of that day, who is it that sums all that had taken place?



That is your last judgement of things, that the weight of the feather and heart become symbolized in the scale weighting the feather of truth to your very own heart. Truth then becomes something of a clarifier to what you hold most dear at the same time, put in front of you the ideal with which you shall live. If you can honestly say you have lived your life to your expectations, then what had you accomplished?

Removing the Veil

"Death, so called, is but older matter dressed
In some new form. And in a varied vest,
From tenement to tenement though tossed,
The soul is still the same, the figure only lost." Poem on Pythagoras, Dryden's Ovid.

Benjamin Franklin in his epitaph call it an overcoat we put on, and the summation of this is the accumulation of life and all it trappings and wondering. How simple of any of us to think it is the "actual overcoat" when we know the deeper resonance such epitaph can make of one's entire life. As if, the life were a "book of a kind." With death to come the realization of an worn out cover.

"As to you, Life, I reckon you are the leavings of many deaths, No doubt I have died myself ten thousand times before." "Leaves of Grass" by Walt Whitman

So while the understanding prevails us, what use this metaphorical language for any of us but to see that what starts off as the matter and order of things, had some geometrical presence before it become the model it did.

So you see the brain in the sphere. You see the "gravitational model of the earth" within the confines of of the sphere of development. No where had I yet explained the triangle and face of the pyramid. Should one use it as vertical line of reasoning, that the top of that line should direct the mind to a heaven, or for those of lore to the stars above?

Listen careful then as to the face of the pyramid shown. The foundational aspect is it's base, and, is earth. The face of this pyramid is used to colour the valuations of gravity in it's strength and weaknesses. Is used, to describe the mental and emotive states of being, from a matter orientated understanding of the matter( that based) to the every colouration of the mental and emotive states themself.

Mandalas as Mind Maps

While I respect Carl Jung and his thought on the personality, it would have made more sense to me that at death "perfection would be as best the soul is in it's attempts." To discover, one's nature and recognize that the living and working to perfect, "is the real success" for the work and perfection the soul quests for in attaining the clear light, instead of the fog.

CARL JUNG by Dr. C. George Boeree

The most important archetype of all is the self. The self is the ultimate unity of the personality and is symbolized by the circle, the cross, and the mandala figures that Jung was fond of painting. A mandala is a drawing that is used in meditation because it tends to draw your focus back to the center, and it can be as simple as a geometric figure or as complicated as a stained glass window. The personifications that best represent self are Christ and Buddha, two people who many believe achieved perfection. But Jung felt that perfection of the personality is only truly achieved in death

This blog entry is very important to me for a number of reasons. There is something very natural that can arise from a person's "subconscious state" that can explode(fire all the neurons) to become a person's paradigm change for their waking life. As if, the change and time according to the progression of a soul, is timely at a certain point in one's life. You had to make it happen yourself. No body told me about this, as I came to discover the deeper significances of the change that occurred.

It's also of wonder to me that this progression is signalled, and mark by the individual themself. That it had to come from a "previous existence." You had to used this "Mind Map" in previous circumstances unwittingly, by being a participant in the way this mandalas is set to ignite the soul with that new energy.

Of course you understand what a Mind Map is? Of course you understand what a mandala is? You understand what a liminocentric structure is?

What are Mind Maps?

The Alchemists attempted to perfect the One Thing of Hermes, what they called the First Matter, by using specific physical, psychological, and spiritual techniques that they describe in chemical terms and demonstrated in laboratory experiments. However, while the alchemists spoke in terms of chemicals, furnaces , flasks, and beakers, they were really talking about the changes taking place within their own bodies, minds, and souls.2

The Emerald Tablet, Dennis William Hauck, Chapter 10, Page 151

While I give a woodcut image of historical relevance, it is made to help one remember. The alchemist notion of distilling and perfecting one's very nature in life. Of course, there are current scientist perceptions that speak to the alchemist notions of Newton. I would again have to remind the good scientists about the alchemical nature being more then just the chymstry in a lab. The alchemist body was also a lab. It deals with the psychological aspects of our emotive and mental states.

If the context of these were understood as valuations measured in terms of the "circle within the circle" a topological review was done by me on how determinations of which line is which, arises as we look to unfold the "colour and valuations of being" at one time or another. While I place our individuality at the centre, it is around you that I speak to the unfolding, all the while a physiological process is unfolding in the states of those emotive and mental ventures. The outer most circle is the spiritual domain of our journeys.

Splendor Solis ("The Splendour of the Sun") is a well-known colorful alchemical manuscriptThe symbolic process shows the classical alchemical death and rebirth of the king, and incorporates a series of seven flasks, each associated with one of the planets. Within the flasks a process is shown involving the transformation of bird and animal symbols into the Queen and King, the white and the red tincture. Although the style of the Splendor Solis illuminations suggest an earlier date, they are quite clearly of the 16th century See:Newton the Alchemist

A mind map is a diagram used to represent words, ideas, tasks or other items linked to and arranged radially around a central key word or idea. It is used to generate, visualize, structure and classify ideas, and as an aid in study, organization, problem solving, decision making, and writing.

It is an image-centered diagram that represents semantic or other connections between portions of information. By presenting these connections in a radial, non-linear graphical manner, it encourages a brainstorming approach to any given organizational task, eliminating the hurdle of initially establishing an intrinsically appropriate or relevant conceptual framework to work within.

A mind map is similar to a semantic network or cognitive map but there are no formal restrictions on the kinds of links used.

The elements are arranged intuitively according to the importance of the concepts and they are organized into groupings, branches, or areas. The uniform graphic formulation of the semantic structure of information on the method of gathering knowledge, may aid recall of existing memories.

You would have to understand some of the blog posts I have done, in order to see that mathematical structures are derived from images, however they are described to take us as close as possible to the very "essence of the idea" being translated? This, is a universal language for scientists

Are mathematical truths invented or discovered? This is an age old question that I have seen around for some time. If you believe that every thing has already been thought of, then it would mean, that it is only to be discovered.

The Space you Provide

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.

How quiet do we have to be to recognize "that place" from which such ideas will emerge. A space and place from inside of you.

We can read all our lives and study, but what is it we will take from it all. What will we move forward that will become profound for you to realize all things become anew. Ideas change who we are. Ideas worked can become the ideals, and it this translation in our work, that such things become possible.

Ancient Dwellings

It was around 2002 my wife and I took a trip to Phoenix Arizona, and went to Sedona. We took in some of the sites as shown by the pictures of the dwellings once inhabited by different Indian tribes.



While extremely hot at the time we went, it of course brought wonderment to me how anyone could live in heat like that, even though the areas of Sedona are much higher. The very idea that they were set back into the cliffs was a very good idea in terms of temperatures so this was an ingenious way to stay warm and keep cool.



One of the things that we tend to now on our trips is try and takes in ancient places like these, or other sites like the large Medicine wheels at Bighorn that we travelled to a couple of years ago.

There are deeper reasons that we take on these journey's, that at a time in our lives with our children grown we can now take to to this. The cliff dwellings were drawn on a piece of paper many years ago when I awoke from a weird dream. It was as if I was travelling and came into to look at the cliff dwelling. I was wondering when on our journey whether I would see what I saw, before ever being there.

The Medicine Wheel is actually one of those Mind Maps I talked about, that was used by the Native Americans to house a lot of information about nature and the dealings Native Americans had with that Nature.

That particular model I also dreamt of, and had a profound experience that became part of the connection to the deeper understanding I have about the earth from a native perspective. A deeper understanding about how one comes so very close to one touching the very souls energy. This is why liminocentric structures are of such importance to me. Developing such maps are an important aspect of using the mind map to built this connection to what exists and our very centres.



I'll put a picture here from my trip(it is taken from the board located at the site). It's the Bighorn Medicine Wheel located by Sheridan Wyoming. It is about 9642 feet up and on Medicine Mountain. The walk was about a mile and half in and was about a 100 degrees that day.