Albrecht Durer's Magic Square

Albrecht Dürer (/ˈdʊərər, ˈdjʊərər/;[1] German: [ˈalbʁɛçt ˈdyːʁɐ]; 21 May 1471 – 6 April 1528)[2] was a painter, printmaker, and theorist of the German Renaissance. Born in Nuremberg, Dürer established his reputation and influence across Europe when he was still in his twenties due to his high-quality woodcut prints. He was in communication with the major Italian artists of his time, including Raphael, Giovanni Bellini and Leonardo da Vinci, and from 1512 he was patronized by emperor Maximilian I. Dürer is commemorated by both the Lutheran and Episcopal Churches. The Expulsion From Paradise by Albrecht Dürer Dürer's vast body of work includes engravings, his preferred technique in his later prints, altarpieces, portraits and self-portraits, watercolours and books. The woodcuts, such as the Apocalypse series (1498), are more Gothic than the rest of his work. His well-known engravings include the Knight, Death, and the Devil (1513), Saint Jerome in his Study (1514) and Melencolia I (1514), which has been the subject of extensive analysis and interpretation. His watercolours also mark him as one of the first European landscape artists, while his ambitious woodcuts revolutionized the potential of that medium. Dürer's introduction of classical motifs into Northern art, through his knowledge of Italian artists and German humanists, has secured his reputation as one of the most important figures of the Northern Renaissance. This is reinforced by his theoretical treatises, which involve principles of mathematics, perspective, and ideal proportions.

Melencolia I 1514

Albrecht Dürer's magic square

Detail of Melencolia I

 

The order-4 magic square Albrecht Dürer immortalized in his 1514 engraving Melencolia I, referred to above, is believed to be the first seen in European art. It is very similar to Yang Hui's square, which was created in China about 250 years before Dürer's time. The sum 34 can be found in the rows, columns, diagonals, each of the quadrants, the center four squares, and the corner squares (of the 4×4 as well as the four contained 3×3 grids). This sum can also be found in the four outer numbers clockwise from the corners (3+8+14+9) and likewise the four counter-clockwise (the locations of four queens in the two solutions of the 4 queens puzzle^[36]), the two sets of four symmetrical numbers (2+8+9+15 and 3+5+12+14), the sum of the middle two entries of the two outer columns and rows (5+9+8+12 and 3+2+15+14), and in four kite or cross shaped quartets (3+5+11+15, 2+10+8+14, 3+9+7+15, and 2+6+12+14). The two numbers in the middle of the bottom row give the date of the engraving: 1514. The numbers 1 and 4 at either side of the date correspond respectively to the letters "A" and "D," which are the initials of the artist.

How Observant is your Science Mind?

This image above I have discussed before on this website. It is also in the legend on the right hand side of this web page. Maybe you can see the "symmetry at play?":)

Dürer Magic Square with Lines






Albrecht Durer and His Magic Square

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For those scientifically minded you must see the outlay and thesis adaption of Prof.dr R.H. Dijkgraaf as he demonstrated the totality of the illumination of his thinking? While I captured a small part of it by referencing the magic square, there is lots more there for the observant eye to take hold of.

Melencolia II
[frontispiece of thesis, after Dürer 1514]by Prof.dr R.H. Dijkgraaf

Nature is the Architect

.....and we are it's builders?



So beyond indeed, is the static realization of the structure of things. This is a more definable recognition of something that is very fluid and expressive. It is by our own humanistic natures that we like to compartmentalize?

"There comes a time when the mind takes a higher plane of knowledge but can never prove how it got there. All great discoveries have involved such a leap. The important thing is not to stop questioning." Albert Einstein (1879- 1955)

While this quote of Einstein is somewhat revealing of what can flash across the mind, it is by intense work that such a time allows for things to gather, and in this work, it will inevitable makes sense. Such cultivation allows for new things to be born and in such nurture and contemplation, something will eventually emerge.

A picture of flux lines in QED (left) and QCD (right).

Although it didn't properly describe strong interactions, in studying string theory physicists stumbled upon an amazing mathematical structure. String theory has turned out to be far richer than people originally anticipated. For example, people found that a certain vibrational state of the string has zero mass and spin 2. According to Einstein's theory of gravity, the gravitational force is mediated by a particle with zero mass and spin 2. So string theory is, among many other things, a theory of gravity!

See: Why Strings

This points to a reductionistic view about the nature of reality. That we are part and parcel creating the constituents of the reality that we see, has a glue that binds, and keeps it together. For each this glue is a process that has meaning for each of us. While one would wonder where such motivation would allow each to perceive it as so one might ask what value is assign each stage of expression to see that such a scale has been reduce to a quality of a kind? It's music?


Cover of Hiding in the Mirror: The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond by Lawrence M. Krauss
Viking Press

Guide Review - Hiding in the Mirror by Lawrence Krauss
In Hiding in the Mirror, astrophysicist and cosmologist Lawrence M. Krauss addresses the concept of extra dimensions, from its appearance in popular culture such as Alice in Wonderland and The Time Machine to theoretical physics areas such as the theory of relativity and string theory. In fact, I would say that the book splits roughly 50/50 between cultural and scientific topics, which is part of the point of the book (that extra dimensions are tied to both areas), but for those who are specifically interested in the scientific aspects there are other books (such as Lisa Randall's Warped Passages) which address the scientific aspects in far more depth.

According to Krauss, extra dimensions have captured the human imagination well before it entered into exploration by physics in the last century or so. The book covers how the concepts were viewed by those in the past, as well as more recent science fiction, such as Star Trek (one of Krauss' favorite topics, as author of the bestselling The Physics of Star Trek). Much of this material is entertaining, but for those who are wanting to get to the heart of the physics, it can feel like filler.

About 100 pages of the book focuses on the recent work to find a unified theory of quantum gravity, focusing predominantly on string theory (with some mention of predecessors). This has been one of the areas where extra dimensions have become extremely dominant. Though Krauss exhibits some genuine skepticism about the track string theory is on, I think calling the book a criticism of string theory would be going a bit far. Krauss is placing string theory within a larger framework of extra dimensional movements in the past, many of which have proved incredibly enlightening and some of which have not done much. It's left to other books to determine whether string theory has any scientific merit.

See:Book Review: Hiding in the Mirror

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See Also:

Where are my keys?

So string theory is, among many other things, a theory of gravity!

EOT-WASH GROUP(4)

Melancholia Magic Square

The most famous 4 x 4 magic square is the so-called Melancholia magic square. In 1514, Albrecht Dürer used the square in his engraving Melancholie which depicts the indecision of the intellectual. The two numbers, 15 and 14, in the centre of the bottom row date the engraving.

This image above I have discussed before in this website. It is also in the legend on the right hand side of this web page.

See:Number Patterns-Fun with Curves & Topology-Jill Britton

Hermetic Ties: Art to Esoteric Form

The father of all perfection in the whole world is here. Its force or power is entire if it be converted into Earth. Separate the Earth from the Fire, the subtle from the gross, sweetly with great industry. It ascends from the Earth to the Heavens and again it descends to the Earth and receives the force of things superior and inferior. By this means you shall have the glory of the whole world and thereby all obscurity shall fly from you. Its force is above all force, for it vanquishes every subtle thing and penetrates every solid thing. So was the world created. From this are and do come admirable adaptations, whereof the process is here in this. Hence am I called Hermes Trismegistus, having the three parts of the philosophy of the whole world. That which I have said of the operation of the Sun is accomplished and ended.Sir Isaac Newton-Translation of the Emerald Tablet

See: Newton on Chymistry

Again I open this blog post with the understanding that what an artist like Raphael may try to do? May include, much of the philosophy of the times, and have these things descriptively enclosing processes indicative of what they had known, but also of what these things could hide within the self.


In center, while Plato - with the philosophy of the ideas and theoretical models, he indicates the sky, Aristotle - considered the father of Science, with the philosophy of the forms and the observation of the nature indicates the Earth. Many historians of the Art in the face correspondence of Plato with Leonardo, Heraclitus with Miguel Angel, and Euclides with Twine agree.

If we watched of distant spot, of century XX aC emphasizes Hermes Trismegisto, - tri three, megisto megas, three times great; perhaps the perception of infinite older than we have and takes by Mercurio name - for Greek and the Toth - for the Egyptians. Considered Father of the Wisdom and Sciences in Greece, in the cult to Osiris it presided over the ceremonies as priest and he was Masterful in Egypt like legislator, philosopher and alchemist during the reign of Ninus in the 2270 aC.

Etimológicamente speaking, of Hermes, the gr. hermenéuiein, “hermetic” - closed, “hermenéutica” - tie art to the reading of old sacred texts talks about so much to the dark as to which it is included/understood in esoteric form. Part of saberes that it accumulated transmitted through the Hermetic Books that only to the chosen ones between the chosen ones could be revealed. As much Pitágoras and Plato as Aristotle and Euclides were initiated in the knowledge of the Hermetic School.

In Man looking into Space, I wanted to show how casual our science has used these images and not realized the context to which the greater meaning had laid hidden, all the while it is used to "describe cosmology" and the science thereof.

A banner has been been written across these times to which scientists hold to all that is true. In this, the reasons to dismiss any implications of history assigned along side, is asking "what validation" can be given to anything that is spoken from our times now.

I went on in that post, "man looking into space," to explain something about the woodcuts. The art form produced, grabbed my thinking in relation to the "alchemical art forms" and grabs my thinking in regards to the "School of Athens picture."


The Yorck Project: 10.000 Meisterwerke der Malerei. DVD-ROM, 2002. ISBN 3936122202. Distributed by DIRECTMEDIA Publishing GmbH.

I just wanted to say that the essence of this blog post is about "the arches," and I am moving toward that description, and what is happening when we take a picture of them. Look at the "design inherent" and "dynamics" as held to gravity in it's construction. Look at what it can signify in it's "internal expression" about our contact with the world around us. The bridging that it can signify.

I would apologize for leaving this post undone, while views pass by the essence of this post. I am indeed busy with life. So I wanted to clarify this push toward the internal dynamics, while speaking to the psychology of this work.

A scientist may side step this look, while quoting the hermetical values of what may be said by the previous first lady Hillary Clinton. In itself, an empty page, only leaves room for what had to be expressed if it was not gotten the first time? Her attempts at humour, are the attempts to break the "rigidity of the personality?"

The Psychology

Myths and metaphors, like dreams, are powerful tools that draw the listener, dreamer, or reader to a character, symbol, or situation, as if in recognition of something deeply known. Myth's bypass the mind's efforts to divorce information. They make an impression, are remembered, and nudge us to find out what they mean, accounting for the avid interest that Ring audiences have in the meaning of the story.¹

Who has been so colourful in your journeys across the internet to include a wonderful language that takes you into this world of discovery of self? You had to know something about the "psychology of people" in order to give a story by nature, it's mythic description, and "most artful" to draw attention to what lies underneath.

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 experiements. However, while the alchemists spoke in terms of chemcials, furaces , flasks, and beakers, they were really talking about the changes taking place within their own bodies, minds, and souls.²

Thus I have given two examples that I had promised sometime back to illustrate some of the "compelling work" that while ancient indeed, is not without it's efforts in todays world. It is the attempt to cross all boundaries, race, gender, and help one to recognize the diversity of the soul with out it's jacket. Shall we call your soul male or female, black or white?

So I am bypassing this, and that has been my message, while the efforts to climb out of the constraints that we have come to recognize within the boundaries of self. Are the realization of the diversity of "all souls" and their time in expression.

Shall we find the excuse to hold ourselves to the thoughts, that while overcoming, the constraints which still exist "within" had to be continually challenged? We have to break the "chains that bind us."

The Arches


Golden Rectangle

I took the picture at a time of day when the tide was at exactly the right place to create this image: when the surface of the water reflected the underside of the bridge and they combined, together they produced what I named the Golden Rectangle as a nod to Pythagoras (my hero). The sensation I experienced at the time was of balancing consciousness and feeling.

It probably seems that it is taking time to get to the essence of this post. IN order to get to the "psychological effect" that I am getting too it important to think of the images of these arches. It is about "each of us" and how we relate to the world. How, the "teacher and student" can exist within the same person.

I point to the Heaven's in the case of the "school of Athens, while Aristotle points to what is on Earth?" Shall we leave no doubt of the "physical things" while we understand that there are more ephemeral qualities to these matter states? That we move continuously between them?



The Inner/Outer World

The drawn of our focus is the external world, but, if we were to connect the internal world with that "external view" how shall we do that. How shall we describe the whole being in this exercise?

Part of this "exchange with reality," is that we can know by continually moving this information "through us" and creating "the space around us," we add to the total view "beyond what was apparent" with just the brain's condensible qualities in neurological display?

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'.The Structure of Consciousness John Fudjack - September, 1999

While I quote above, the second part of the quote adds directly to the understanding. Not only are we "crossing the wires here," we are identifying "a aspect of consciousness" that is continuous.

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.

So given "this relationship" on what we can build within self, then what use all this knowledge if we cannot grow with it? What of Plato's and Aristotle, as figures within the "centre of" Raphael's painting. Their perspective, "as positions in relation too," the "questioning stance" about this "unity of the circle" in our exchange with reality?



So how would you exemplify "this exchange" with reality while "below the surface" all these "probable outcomes" are the manifestation of that which is real? You extend yourself "out there" while you also extend yourself inside? The "infinite regress," is to find oneself, with all that is "past" in front of you, can allow you to stand on what of, "the future" will pass through?

First Principle saids that you acknowledge your place in the scheme of things as you "stretch" the thinking of the mind? Increase the "neurological frontier" in those neurological connections? Increase, the fluttering of the egg's feature, of that condensible brain/body.

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.

But, Aristotle thinks that knowledge begins with experience. We get to first principles through induction. But there is no certainty to the generalizations of induction. The "Problem of Induction" is the question How we know when we have examined enough individual cases to make an inductive generalization. Usually we can't know. Thus, to get from the uncertainty of inductive generalizations to the certainty of self-evident first principles, there must be an intuitive "leap," through what Aristotle calls "Mind." This ties the system together. A deductive system from first principles (like Euclidean geometry) is then what Aristotle calls "knowledge" ("epistemê" in Greek or "scientia" in Latin).

From here it would not be to unlikely that such dealings with the "reality of the world" would ask that we experiment and from such experiment, we learn the truth of the reality. While what the past is "in front" of us, to what goes beyond to it's future would be like asking the very nature of expression to manifest as this universe and laws of thermodynamics that the arrow of time only moves one way.

"The future" arises from within then? We'll move forward by what choices we make? About our conclusions, about reality?


¹ Ring of Power, Jean Shinoda Bolen, M.D. Page 3

²The Emerald Tablet, Dennis William Hauck, Chapter 10, Page 151

Man Looking into Outer Space

"We all are of the citizens of the Sky" Camille Flammarion

In 1858, by the set of its relations, it will allow Camille Flammarion, the 16 years age, to enter as raises astronomer at the Observatory of Paris under the orders of Urbain the Glassmaker, at the office of calculations.

I was over at Cosmic Variance for a visit, and commented on the "woodcut" which is title by the name of the post above given by Camile Flammarion? Below a caption is produced with a



While Daniel ask spyder what the source of this was, I am quietly doing my own research, because I have used this image myself. What did it mean?



This picture is a copy of a "16 century woodcut" copied by Camille Flammarion in 1888.


The Flammarion woodcut. Flammarion's caption translates to "A medieval missionary tells that he has found the point where heaven and Earth meet..."

The widely circulated woodcut of a man poking his head through the firmament of a flat Earth to view the mechanics of the spheres, executed in the style of the 16th century cannot be traced to an earlier source than Camille Flammarion's L'Atmosphère: Météorologie Populaire (Paris, 1888, p. 163) [38]. The woodcut illustrates the statement in the text that a medieval missionary claimed that "he reached the horizon where the Earth and the heavens met", an anecdote that may be traced back to Voltaire, but not to any known medieval source. In its original form, the woodcut included a decorative border that places it in the 19th century; in later publications, some claiming that the woodcut did, in fact, date to the 16th century, the border was removed. Flammarion, according to anecdotal evidence, had commissioned the woodcut himself. In any case, no source of the image earlier than Flammarion's book is known.

See here for larger version "with caption" that has been translated above.

Now the interesting thing about woodcuts and what was found in my research, had to do with how "alchemical texts" can embody the "psychological process" that lent itself to the display the evolution in humanities thoughts.


Splendor Solis ("The Splendour of the Sun") is a well-known colorful alchemical manuscript. The earliest version, written in Middle German, is dated 1532-1535 and is housed at the Prussian State Museum in Berlin. It is illuminated on vellum, with decorative borders like a book of hours, beautifully painted and heightened with gold. The later copies in London, Kassel, Paris and Nuremberg are equally fine. In all twenty copies exist worldwide.

I will give an examples that have been retained by me, for understanding that allow me to speak on this. While I referred to the "enlightenment" and gave this answer above, I used it in context of how we see the cosmos now, given the understanding of the physics we are engaged in science.

While relativity was applied to the cosmos at large, now, quantumly defining the nature of this cosmos, is part of this achievement that I refer too in terms of enlightenment.

What are Woodcuts

In Europe, Woodcut is the oldest technique used for old master prints, developing about 1400, by using on paper existing techniques for printing on cloth. The explosion of sales of cheap woodcuts in the middle of the century led to a fall in standards, and many popular prints were very crude. The development of hatching followed on rather later than in engraving. Michael Wolgemut was significant in making German woodcut more sophisticated from about 1475, and Erhard Reuwich was the first to use cross-hatching (far harder to do than in engraving or etching). Both of these produced mainly book-illustrations, as did various Italian artists who were also raising standards there at the same period. At the end of the century Albrecht Dürer brought the Western woodcut to a level that has never been surpassed, and greatly increased the status of the single-leaf (ie an image sold separately) woodcut.

As woodcut can be easily printed together with movable type, because both are relief-printed, it was the main medium for book illustrations until the late-sixteenth century. The first woodcut book illustration dates to about 1461, only a few years after the beginning of printing with movable type, printed by Albrecht Pfister in Bamberg. Woodcut was used less often for individual ("single-leaf") fine-art prints from about 1550 until the late nineteenth-century, when interest revived. It continued to be important for popular prints until the nineteenth century in most of Europe, and later in some places

I refer to the psychological basis of what these woodcuts can mean from an early historical perspective. By studing methods used I came to learn of what this could mean "not from producing gold from lead" but of what this could mean in terms of applying ourselves and conducting our selves, as a commitment to being better human beings.

This new compound of thought is difficult to understand and apply in our everyday affairs. The Swiss psychiatrist C. G. Jung went perhaps further than any other researcher to extract the psychological wisdom embedded in alchemy and make it available to the modern world. Through his work we learn how alchemy can be used as a powerful means of psychological transformation, personal empowerment and spiritual adventure. Individuation is the real gold sought by true alchemists. Yet, for all his genius, Jung's writings are complex and oftentimes as difficult to read as the alchemical literature. A thorough knowledge of analytic psychology, theology, symbolism and mythology is required to appreciate the depth of Jung's insights. Adding to this challenge is the rapid rate that science and technology have advanced since Jung's death. We live in a New World. Especially with the findings of quantum physics -many of which validate old philosophical truths- the time is ripe for a fresh interpretation of alchemy and how we can apply its powerful recipes to the challenges of contemporary life.

Images or Numbers By Themself

“Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate” (cited by Ivars Peterson in Science News, 5/4/2002).

I have an idea in mind here that will be slow to show because I am not sure how it is supposed to be laid out. So maybe by showing these numbers by them self? What use, if one did not, or was not able to see in another way?


Figure 22.10: Double slit diffraction


I looked at the "straight lines" of Thomas Young's trajectories of photon emission and while quite understandably shown to be of consequence in this post "Interference." I was more interested in how something could start off in one place and do this rotation of sorts, and then come back for examination again in the real world. The Spectrum

Plato:

What a novel idea to have the methods used by the predecessors like Maxwell, to have been united from Faraday's principals? To have Maxwell's equation Gaussian in interpretation of Riemann geometry, somehow, united by the geometries of Einstein and defined as gravity?

But it is also in mind "that the image" has to be put here also before the numbers can show them self. What use these numbers if I do not transcend them to what they can imply in images, to know that the thinking here has to be orientated in such a way that what was simple and straight forward, could have non-euclidean orientations about it?


Michael Faraday (September 22, 1791 – August 25, 1867) was a British scientist (a physicist and chemist) who contributed significantly to the fields of electromagnetism and electrochemistry.

So one reads history in a lot of ways to learn of what has manifested into todays thinking. What lead from "Gaussian coordinates in an "non-euclidean way" to know that it had it's relation in today's physics. To have it included in how we see the consequences of GR in the world. It had been brought together for our eyes in what the photon can do in the gravitational field.

Our Evolution to Images


The Albrecht Durer's Magic Square


Ulam's Spiral


Pascal's Triangle

Evolve to What?

Who was to know what Leonard Susskind was thinking when his mathematical mind was engaged in seeing this "rubber band" had some other comparative abstraction, as something of consequence in our world. Yet, people focus on what they like to focus on, other then what "lead the mind" to think the way they do?


Poincaré Conjecture

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut......

I have to rest now.

Symmetries Can be Chaotically Complex

Imagine in an "action of a kind" you start off from one place. A photon travelling through a slit of Thomas Young's, to get through "a world" to the other side. Sounds like some fairy tale doesn't it? Yet, "the backdrop" is where you started?


Thomas Young (June 14, 1773 – †May 10,1829)

was an English scientist, researcher, physician and polymath. He is sometimes considered to be "the last person to know everything": that is, he was familiar with virtually all the contemporary Western academic knowledge at that point in history. Clearly this can never be verified, and other claimants to this title are Gottfried Leibniz, Leonardo da Vinci, Samuel Taylor Coleridge, Johann Wolfgang Goethe and Francis Bacon, among others. Young also wrote about various subjects to contemporary editions of the Encyclopedia Britannica. His learning was so prodigious in scope and breadth that he was popularly known as "Phenomenon Young."

Simplistically this "massless entity" is affected by the "geometrics of gravity?" Is affected from it's "first light." All the way to some "other point in reality" to some image, called the spectrum.

I am dreaming. I am walking down the street and there is this "N category cafe."

Imagine walking off the street into this very public venue and seeing the philosophy shared is also held to certain constraints. :)Philosophy? Yes, we all have our "points of view."

Travelling the Good Life with Ease

So in this travel how is one to see this "curve of light" or "slide" and we get this sense of what gravity can do.

Imagine indeed, "a hole cosmological related" in the three body problem, it has to travel through, and we get this sense of "lensing and distortion," abstractually gravitationally induced?



So as we look at the cosmos what illusion is perpetrated on our minds as we look into the "great distance of measure" that somehow looking to the journey of "an event local," from our place on and about earth, has not been "chaotically entrained in some way, as we look deep into space?


The Magic Square

Plato:Like Pascal, one finds Albrecht has a unique trick, used by mathematicians to hide information and help, to exemplify greater contextual meaning. Now you have to remember I am a junior here in pre-established halls of learning, so later life does not allow me to venture into, and only allows intuitive trials poining to this solid understanding. I hope I am doing justice to learning.

Moving in abstract spaces

It was necessary to explain why I added "the image" to the right in my index.

Some would think me so "esoteric" that I had somehow lost touch with the realities of science? That to follow any further discussion here "has to be announced" to save one's dignity? What ever?:)I am esoteric in that my views of the world come from a different place, not unlike your expression of where you had come from living your life. How would I come to know all that you are in a "single sentence." A single and very short equation? It's really not that easy is it?:)

So I read you from all the things that you say and get the sense of who you are no different then what is implied in the language of poetic art implied carefully from choosing your words?

Artistically Inclined?

I tried to give some hint of the "ideas floating" around in my head. I understand quite well that my challenge has been to get those "images in my head" transmitted onto paper, in a way that one would not become confused as to what is being implied.

So a good writer I may not be, a "not so good scientist" whose mathematics very ill equipped.

Thus I am faced with these challenges in the new year? A "recognition" of trying to produce that clarity. Whether in "latex" the symbols of mathematics, it is quite a challenge for me, whilst all these things are still engaged in abstract views of reality.

So someone like Clifford, may look at Robert by what he has written and say, "hey, my fellow scientists are indeed in trouble" from what Robert has learnt. So I Clifford will provide "the latex sandbox" for you to play in?

It "appears" I am not alone. My struggle, are to be many a struggle.

Art and the Abstract

But to my amazement this morning in checking up the links associated of Clifford's, I was amazed to see the article of, Hooking Up Manifolds

Now how interesting that what is being displayed there in terms of fun, mathematics, art, could have been so abstractly appealing? "Moving over these surfaces" in ways that one might never appreciated, had you not known about how one can look at the universe in the "two ways mentioned previously," and by simple experiment, transcend such things to art.

Undercut Philosophical basis , "What have you?"

In "Beyond the dance of the sun" I show what we take for granted from a "observational standpoint," and try to increase perception, based on the quantum views.

Is mathematics Invented or Discovered?

"Philosophy In The Flesh"

LAKOFF:

When you start to study the brain and body scientifically, you inevitably wind up using metaphors. Metaphors for the mind, as you say, have evolved over time -- from machines to switchboards to computers. There's no avoiding metaphor in science. In our lab, we use the Neural Circuitry metaphor ubiquitous throughout neuroscience. If you're studying neural computation, that metaphor is necessary. In the day to day research on the details of neural computation, the biological brain moves into the background while the Neural Circuitry introduced by the metaphor is what one works with. But no matter how ubiquitous a metaphor may be, it is important to keep track of what it hides and what it introduces. If you don't, the body does disappear. We're careful about our metaphors, as most scientists should be..

So I asked myself a question.

What if the condensation of the human brain was the reverse, of Damasio's First Law. I mean we can train the neuron pathways to be reconstructed, by establishing the movements previously damaged by stroke. What is the evolution of the human brain, if "mind" is not leading its shape? A newly discovered ability called "Toposense," perhaps?

Okay now, what came first, "chicken" or "egg?"

If one had never read Kuhn, how would one know to respond in kind to the philosophical basis a David Corfield might in sharing perspective about abstractness in mathematical models?

The thesis of 'Proofs and Refutations' is that the development of mathematics does not consist (as conventional philosophy of mathematics tells us it does) in the steady accumulation of eternal truths. Mathematics develops, according to Lakatos, in a much more dramatic and exciting way - by a process of conjecture, followed by attempts to 'prove' the conjecture (i.e. to reduce it to other conjectures) followed by criticism via attempts to produce counter-examples both to the conjectured theorem and to the various steps in the proof.J Worrall and E G Zahar (eds.), I Lakatos : Proofs and Refutations : The Logic of Mathematical Discovery

Okay so you understand as a layman I like to see what is going on out there in the blogger world of mathematicians, I thought I would listen here, and do some research. I had to started out with the presumption that one may encounter and be moved from any positon.

I has to philosophical understand it first.

I have enjoyed both participating in a mathematical dialogue and, as a philosopher, thinking about what such participation has to do with a theory of enquiry. The obvious comparison for me is with the fictional dialogue Proofs and Refutations written by the philosopher Imre Lakatos in the early 1960s. The clearest difference between these two dialogues is that Lakatos takes the engine of conceptual development to be a process of

conjectured result (perhaps imprecisely worded) - proposed (sketched) proof - suggested counterexample - analysis of proof for hidden assumptions - revised definitions, conjecture, and improved proof,

whereas John, I and other contributors look largely to other considerations to get the concepts ‘right’. For instance, it is clear that one cannot get very far without a heavy dose of analogical reasoning, something Lakatos ought to have learned more about from Polya, both in person and through his books.

I was quick to point out what I say about "Observation pays off," and it quickly recieved the trash box. That's not dialogue. :)

Albrecht Dürer(self portrait at 28)

It's about paying carefull attention as to what is created for us in images and paintings. Noticing the "anomalistic behavior" that might be brought forth for our human consumption. It required a metamorphsis for change.

Prof.dr R.H. Dijkgraaf

In that case I pointed out the work of Melencolia II
[frontispiece of thesis, after Dürer 1514]by Prof.dr R.H. Dijkgraaf showing Albrect Durer's images repainted to suit his thesis? So I delved deeper into the image portrayed.

On the surface this information is about what we see, yet below it, it is about seeing in ways that we are not accustom. So, the journey here was to show the nuances that invade perception, and then show what leads further into the understanding of what happens out there in the physics world in regards to the summation of Prof.dr R.H. Dijkgraaf's picture of the original.

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Basis of Reality by Geometric Design?

I would like to continually like to remind one of Plato's cave. If the sun is behind us, how do you relate what is seen dimensionally, and describe it from first principles? The shadows are used in a way to draw our attention to our limitations of thinking.



So I moved this internally, and the sun behind, becomes the sun from a center realized inside. Circles within circles, topologically and constructively asking, which way are we seeing now?

I was thinking here that to get to the "truer source of reality" what underlies our basic intepretations of such "thought constructs," would be to defined essentially in a geometric way, first. This is how first principle is established, as observation to a "geometric way" leads all concepts from this beginning?

Man ponders shadow, or shadow ponders itself?

So let's say you are this fellow sleeping on the bus, and he is having deep suttle thoughts about life. He generalizes what he might see of "mass psychosis" in a geometical way, as well as, see science, necessary as the basis of this expression?

You also hads to know where the beginning of all expression arose from, so this defintion is very important in that respect?

Although theoretical, it establishment with the basis of science would be very important. As Feynman diagrams are.

Example here given with Dirac?

Paul Dirac:

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

Picture is link :)

So the thought construct is very dependant on how we would look at reality and this might inject various geometric processes, yet, we are very aware of the timeline, and where this expression arose from. This is what first principle must do?

While we like to think of the "building blocks of matter" you may of liked to call them strings in the first microseconds, this still does not take you to the source of the expression of what is now geometrically enhanced? So one siads there is no geometry? And of course the Pizza Guy is amazed at how all this could exemplify itself in some way in which the false vacuum and the true vacuum can tunnel from one to another.

So definition of "brane thinking" here encases a lot of information conceptually, as we speak about the reality of such things, and how they arose? These are contained in the most simplfied picture forms. It is necessary to see into how the workings of all "thought constructs," will manifest. Why pictures beomes links to a much more detail way of thinking geometrically.

I gave Dirac as a example.



I also link Albrect Durer for a example as well.

Strange Abstract Movements

When one is engaged in the strange world of the abstract, Quark to Quark measures left me in a strange state. Lines having been given values in distance. That were not readily available to the eye. These lines are happening in spaces, that give "energy values" to that every distance? Gausssian coordinates. The metric.


The Clebsch Diagonal Cubic Surface. It is smooth and all its different 27 lines are real. There are 10 so-called Eckardt points, i.e. points in which three of the lines meet.

So this is a preview to me while working in these abstract spaces, I wanted to make sense of it all, and how such expressions that arise in the standard model, had some framework in which it can follow.




Dürer Magic Square with Lines

A new perspective hidden in the Prof.dr R.H. Dijkgraaf second rendition, and thesis image, reveals a question mark of some significance?:) So how would we see the standard model in some "new context" once gravity is joined with some fifth dimensional view?

What gravity would imply if all dimensional relations are introduced to the entropic models of matter states, while this energy valuation to determination, using information gathered are forcing us to see in ways in regards to those same energy density states?

So you look for these things, in model approaches like, the first three minutes of Steven Weinberg's or even further yet into model approaches given here.


Big Bang Nucleosynthesis Edward L. Wright



OKay. So You Say the Beginning

As can be seen from the curves, at the higher temperatures only neutrons and protons exist, with there being more protons than neutrons. But, as the temperature decreases, there is an increase in the amount of deuterium and helium nuclei. Just below 1 billion degrees there is a significant increase in deuterium and helium, and a decrease in the abundance of protons and neutrons. This is the deuterium "bottleneck" mentioned previously. This uses up the all the free neutrons and some protons, and causes the neutron line to drop off, and the proton line to dip (relatively few protons are used up). The deuterium abundance only increases to a point because it is an intermediate to the formation of helium. So as it is created, it is quickly consumed to complete the process of helium nucleosynthesis. Once all the neutrons have been used up, its presence drops off.

So while you are intrigued by this beginning, something happens that confronts the rational, of how you ever got to this point. Does it matter? I think it does, and if you to are ever to conlucde this assertion of a cyclial nature, you need foundational perspective that helps recognize why string theorist's abhor infinities. What the heck do they mean?

In fact, the temperatures and densities reached in these collisions are similar to those found in the early universe a few microseconds after the Big Bang.

So how much closer can you be taken to the beginning? You need an overview for this cyclical nature to make sense of it.