Pythagoras' Dream

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The Monochord

Pythagoras in School of Athens

  

A monochord is an ancient musical and scientific laboratory instrument. It is also the class-name for any musical stringed instrument having only one string (such as the Vietnamese Đàn bầu). The word "monochord" comes from the Greek and means literally "one string." In a true monochord, a single string is stretched over a sound box. The string is fixed at both ends while one or many movable bridges are manipulated to demonstrate mathematical relationships between sounds.

[Slide 3-3: Closeup of Tablet, Bouleau. Janson, H. W. History of Art. (Fifth Edition.NY: Abrams, 1995). p.497
Raphael’s School of Athens shows Pythagoras is explaining the musical ratios to a pupil. Notice the tablet. It shows the words diatessaron, diapente, diapason. The roman numerals for 6, 8, 9, and 12, showing the ratio of the intervals, same as in the music book frontispiece.The word for the tone, ΕΠΟΓΛΟΩΝΕΠΟΓΛΟΩΝΕΠΟΓΛΟΩΝΕΠΟΓΛΟΩΝ, at the top. Under the tablet is a triangular number 10 called the sacred tetractys]

 The monochord can be used to illustrate the mathematical properties of musical pitch. For example, when a monochord's string is open it vibrates at a particular frequency and produces a pitch. When the length of the string is halved, and plucked, it produces a pitch an octave higher and the string vibrates at twice the frequency of the original (2:1)  Play (help·info). Half of this length will produce a pitch two octaves higher than the original—four times the initial frequency (4:1)—and so on. Standard diatonic Pythagorean tuning (Ptolemy’s Diatonic Ditonic) is easily derived starting from superparticular ratios, (n+1)/n, constructed from the first four counting numbers, the tetractys, measured out on a monochord.^{[citation needed]}

The Divine Monochord, from Fludd’s Utriusque Cosmi Maioris Scilicet et Minoris Metaphysica (1617)

The name "monochord" is sometimes incorrectly applied to an instrument with one open string and a second string with a movable bridge; however, such a two-string instrument is properly called a bichord. With two strings you can easily demonstrate how various musical intervals sound. Both open strings are tuned to the same pitch, and then the movable bridge is put in a mathematical position to demonstrate, for instance, the major third (at 4/5th of the string length)  Play (help·info) or the minor third (at 5/6th of the string length)  Play (help·info).

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SEE:Infinite Fire Webinar II - The Emblemata of the Atalanta Fugiens by Dr. Peter J. Forshaw



See: Atalanta fugiens

The Quantum Harmonic Oscillator

Quantum Harmonic Oscillator

 

Here are a series of written Blog entries by Matt Strassler from his Blog, Of Particular Significance.

1. Ball on a Spring (Classical)
2. Ball on a Spring (Quantum)
3. Waves (Classical Form)
4. Waves (Classical Equation of Motion)
5. Waves (Quantum) 
6. Fields
7.  Particles are Quanta
8.  How fields and particles interact with each other 
9.  How the Higgs Field Works

Given a preceding map  by Proffessor Strassler according to what has been gain in finality views requires this updating in order to proceed correctly in the views shared currently in science. So that lineage of thought is important to me.

Probability Distributions for the Quantum Oscillator

At the same time one cannot be held back from looking further and seeing where theoretical views have been taken beyond the constraints applied to the science mind.:)

Pythagoras could be called the first known string theorist. Pythagoras, an excellent lyre player, figured out the first known string physics -- the harmonic relationship. Pythagoras realized that vibrating Lyre strings of equal tensions but different lengths would produce harmonious notesratio of the lengths of the two strings were a whole number. (i.e. middle C and high C) if the......

   Pythagoras discovered this by looking and listening. Today that information is more precisely encoded into mathematics, namely the wave equation for a string with a tension T and a mass per unit length m. If the string is described in coordinates as in the drawing below, where x is the distance along the string and y is the height of the string, as the string oscillates in time t, 

See: Official String Theory Web Site

Measure and Half Measures

Pythagoras, the man in the center with the book, teaching music, in The School of Athens by Raphael

Most of  you will recognize the partial image of the much larger I have used as the heading of this blog.

The Greek Pythagoras, for instance, was able to use abstract but simple mathematics to describe a natural phenomenon very precisely. He discovered the fractions that govern the harmonious musical notes. For example, a stretched string on a violin that produces a C note when you strike it, will give a C an octave higher when you divide its length by two. (Similarly, when we cut of a quarter of the length of the original string, the new string will sound like an E note) This is a famous early example of the use of mathematics to describe a physical phenomenon accurately. Pythagoras used the mathematics of fractions to describe the frequency of musical notes. In the ages that followed, of Galilei, Kepler, Newton and Einstein, mathematics became the prime language to depict nature. The mathematics of numbers, sets, functions, surfaces et cetera turned out to be the most useful tool for those people that felt the urge to understand the laws governing nature. See: Beyond String Theory-Introduction-Natural Language

However esoteric the following may seem to you, I was always enchanted with the idea of sound  as a manifestation of the world we live in, or, as color,  as a meaningful expression of the nature of the world we live in. Not really the artist of sound and color, but much more the artist in conceptual makings of the relation of the world with such ideas, hence, the idea of "Color of gravity."

Hence my interest in gravity, and what we as human beings can gather around our selves, in the ever quest for understanding the consequences of our causal relations to the events that follow us in the making of the reality we live.

The future consequences of probabilistic outcomes according to those positions adopted....can we say indeed that we are predictors of our futures and that at some level this predictability is a far reaching effect of understanding our choices and positions in life? We know this deep down within ourselves, "so as we think" we may become some "ball bouncing on the ocean of life?" Emotive consequences, without recourse to our choosing to excel from the primitive natures of our being in the moment?

Major scale

In music theory, the major scale or Ionian scale is one of the diatonic scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octavesolfege these notes correspond to the syllables "Do, Re, Mi, Fa, Sol, La, Ti/Si, (Do)", the "Do" in the parenthesis at the end being the octave of the root. The simplest major scale to write or play on the piano is C major, the only major scale not to require sharps or flats, using only the white keys on the piano keyboard:

Could we every conceive of the human being as being one full Octave? I thought so as I read, and such comparisons however esoterically contrived by association I found examples to such "predictable outcomes" as ever wanting to be "divined by principle by such choices we can make."  However unassociated these connections may seem.

I mean,  if one was a student of esoteric traditions and philosophies, it might have been "as traveling through a span and phase of one's life time"  leads us to the issues where we sit,  where we are at,  in the presences of the sciences today. We demanded accountability of ourselves in  that presence within the world as to being responsible and true to ourselves on this quest for understanding.

So if I had ever given the comment as to some iconic symbol as the Seal of Solomon, not just on the context of any secular religion as ownership, it is with the idea that representation could have enshrine the relationship between what exists as a "trinity of the above"  with that of "the below,"  when we are centered as to choice being the position with that of the heart.

See also:New Synesthete Character on Heroes


It was with this understanding that the full Octave could be entranced as too, resonances in the human being, that we could be raised and raise ourselves from such a position, so as to be freed from our emotive and ancient predicaments arising from evolutionary states of beings of the past.

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Monochord is a one-stringed instrument with movable bridges, used for measuring intervals. The first monochord is attributed to Pythagoras. 

The story is told that Pythagoras wished to invent an instrument to help the ear measure sounds the same way as a ruler or compass helps the eye to measure space or a scale to measure weights. As he was thinking these thoughts, he passed by a blacksmith's shop. By a happy chance, he heard the iron hammers striking the anvil. The sounds he heard were all consonant to each other, in all combinations but one. He heard three concords, the diaspason (octave), the diapente (fifth), and the diatessaron (fourth). But between the diatessaron (fourth) and the diapente (fifth), he found a discord (second). This interval he found useful to make up the diapason (octave). Believing this happy discovery came to him from God, he hastened into the shop and, by experimenting a bit, found that the difference in sounds were determined by the weight of the hammers and not the force of the blows. He then took the weight of the hammers and went straight home. When he arrived home, he tied strings from the beams of his room. After that, he proceeded to hang weights from the strings equal to the weights he found in the smithy's shop. Setting the strings into vibration, he discovered the intervals of the octave, fifth and fourth. He then transferred that idea into an instrument with pegs, a string and bridges. The monochord was the very instrument he had dreamed of inventing. See: String Instruments including Oud, Folk Fiddle, and Monochord, dan bau, from Carousel Publications Ltd

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Pythagoras could be called the first known string theorist. Pythagoras, an excellent lyre player, figured out the first known string physics -- the harmonic relationship. Pythagoras realized that vibrating Lyre strings of equal tensions but different lengths would produce harmonious notesratio of the lengths of the two strings were a whole number. (i.e. middle C and high C) if the

   Pythagoras discovered this by looking and listening. Today that information is more precisely encoded into mathematics, namely the wave equation for a string with a tension T and a mass per unit length m. If the string is described in coordinates as in the drawing below, where x is the distance along the string and y is the height of the string, as the string oscillates in time t, 

See: Official String Theory Web Site

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

Whose who, in the School of Athens

I was over visiting Clifford's blog called Asymptotia this morning and notice a blog entry called, Heretics of Alexandria. Of course, what first came to mind is the "Library of Alexandria."



Clifford writes and paraphrases:

This full length drama, set in Alexandria Egypt, 415 A.D. features the infamous Philosopher Hypatia, who has come into possession of a document that threatens the very basis of the new religion called Christianity; a document that some would do anything to destroy. Hypatia and a powerful Christian Bishop wage a fierce struggle for the soul of a young priest and for a document which tells a very different version of the life — and death — of Jesus. A true story.

The writing was excellent as was the cast, and Bastian should be extremely proud of himself. (It is a mistake to call it “a true story”, though. It is a story based around historical events, which should absolutely not be confused with being a “true story”. Writers of synopses should not encouarge people to mix up the two.

So I started to do some research on the link offered by Clifford. All of a sudden I could see the many connections bringing "Hypatia of Alexandria" into the fold.


Hypatia of Alexandria (Greek: Υπατία; c. 370–415) was an ancient philosopher, who taught in the fields of mathematics, astronomy and astrology. She lived in Alexandria, in Hellenistic Egypt.

Hypatia was the daughter of Theon, who was also her teacher and the last fellow of the Musaeum of Alexandria. Hypatia did not teach in the Musaeum, but received her pupils in her own home. Hypatia became head of the Platonist school at Alexandria in about 400. There she lectured on mathematics and philosophy, and counted many prominent Christians among her pupils. No images of her exist, but nineteenth century writers and artists envisioned her as an Athene-like beauty.

Many of you who visit here know how much the "School of Athens" picture means to me?

That there was only one woman here named "Hypatia of Alexandria" of course sent me off to have a look. AS well, "more of the meaning" with regards to the Library of Alexandria.


9.Francesco Maria I della Rovere or Hypatia of Alexandria and Parmenides


The frescoe of the "School of Athens" has been a haunting reminder of the many things that Raphael "enclosed in meaning."


School of Athens by Raphael

That I could then give numbers and names to person's within the picture was equally exciting. I started to dissect parts of this picture quite a while back, opening of course with the "very centre of that painting." The labels supplied on this post entry should give links to farther posts about this.


1: Zeno of Citium or Zeno of Elea? – 2: Epicurus – 3: Frederik II of Mantua? – 4: Anicius Manlius Severinus Boethius or Anaximander or Empedocles? – 5: Averroes – 6: Pythagoras – 7: Alcibiades or Alexander the Great? – 8: Antisthenes or Xenophon? – 9: Hypatia or the young Francesco Maria della Rovere? – 10: Aeschines or Xenophon? – 11: Parmenides? – 12: Socrates – 13: Heraclitus (painted as Michelangelo) – 14: Plato holding the Timaeus (painted as Leonardo da Vinci) – 15: Aristotle holding the Ethics – 16: Diogenes of Sinope – 17: Plotinus? – 18: Euclid or Archimedes with students (painted as Bramante)? – 19: Strabo or Zoroaster? – 20: Ptolemy – R: Raphael as Apelles – 21: Il Sodoma as Protogenes

I now realize that with one comment entry gone( maybe both) that I really was not so out of tune. What was Plato's influence on Hypatia of Alexandria?

Letters written to Hypatia by her pupil Synesius give an idea of her intellectual milieu. She was of the Platonic school, although her adherence to the writings of Plotinus, the 3rd century follower of Plato and principal of the neo-Platonic school, is merely assumed.

See also:

No Royal Road to Geometry?

Euclid belonged to the persuasion of Plato and was at home in this philosophy; and this is why he thought the goal of the Elements as a whole to be the construction of the so-called Platonic figures. (Proclus, ed. Friedlein, p. 68, tr. Morrow)

The Mathematikoi had Synesthesia?

Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a main inspirational source for Plato and platonism.

Later resurgence of ideas similar to those held by the early Pythagoreans are collected under the term Neopythagoreanism.

The Pythagoreans were called mathematikoi, which means "those that study all^1"

To say it is easy in knowing where to begin, is a understatement of what has been an enormous struggle to define the world around me. Indicative of the complications of how one may have seen this world in regards to the "views of a Synesthesist," would have taxed most "science minds" if they had "this inkling" of the complexity this brings to science. Think about what is implied here when one refers to "studying it all?"

So as I lay in the twilight hours of the mind's rest period, there are these things that I am asking of myself, as to how I may point to what is comparative in the "geometric views of science" and what is comparative to the views of that science in relation to examples given of the Synesthesist who sees from a certain position.

Again, my mind falls back in the history of humanities evolution and while the distinctiveness of sectors of that past history, it would not be unkind to draw from that history and present the question of what a Synesthesist might have seen in relation to the numbers?


Create and play with the most beautiful, hypnotic light illusions you have ever seen.

I seen the above in relation to Lubos's post. It would be nice to offer the "equation correlations" to these "colour displays" in string theory?:)

Numbers

Are you quicker then I then to see that numbers may have had the colour attached to their very nature, that "all things" then my have had this basis of "music" and "colour association" thrown "into the mix/cross over points"" to call it the Pythagorean?

So imagine being strapped with the job to start from some place, and move any mind to consider the complexity of "departing euclidean views" to meld with the "non-euclidean reality" assigned our everyday species to "what is natural" from straight lines and such. Has now moved to a dynamical world of "Faraday lines" Gauss's role as "teacher of Gaussian Co-ordinates" to views of his student, "Riemann?"


This equation provides a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found.

Should one be so crude as to see that straight lines can have a "greater implication of design" that one would not have seen, had they not understood Gauss's work? That if you moved yourself to natures's domain, how many lines are really that straight?

Ask your self then what is natural and what was man-made? That these straight lines are indeed an order to mankind's "ode to building and living," while there are these "other worldly visions" supplied in the "non euclidean realm" existed free from man's definition of nature.

8.6 On Gauss's Mountains

One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean. It's certainly true that Gauss acquired geodetic survey data during his ten-year involvement in mapping the Kingdom of Hanover during the years from 1818 to 1832, and this data included some large "test triangles", notably the one connecting the those three mountain peaks, which could be used to check for accumulated errors in the smaller triangles. It's also true that Gauss understood how the intrinsic curvature of the Earth's surface would theoretically result in slight discrepancies when fitting the smaller triangles inside the larger triangles, although in practice this effect is negligible, because the Earth's curvature is so slight relative to even the largest triangles that can be visually measured on the surface. Still, Gauss computed the magnitude of this effect for the large test triangles because, as he wrote to Olbers, "the honor of science demands that one understand the nature of this inequality clearly". (The government officials who commissioned Gauss to perform the survey might have recalled Napoleon's remark that Laplace as head of the Department of the Interior had "brought the theory of the infinitely small to administration".) It is sometimes said that the "inequality" which Gauss had in mind was the possible curvature of space itself, but taken in context it seems he was referring to the curvature of the Earth's surface. ²

The Interior Probabilities Manifests as Colour

How foolish would I be then to tell you that "Heaven' Ephemeral Qualities," are coloured to the degrees that "gravity defines itself in time?" That "model building" had to take place, so that the understanding of where this gravity explains itself, could find correlations to humans experiencing "durations of time" within in the living of day to day.

Again I move one back to what this "egg of fluttering does" as of physiological consequent, as the correlations of those same colours manifest in the qualities of those same thought patterns. Those experiences mapped to MRI imaging are condensible features "in the physical" do not explain the "Ephemeral Quality" assigned to each of these regions. Had one knew how to switch around the "value of consciousness" to the condensible feature as brain matter, one would have known about the happenings taking place "outside" of our bodies.

It is here to then that I take from the "metaphysical realm" and bring it into the relations of what is happening in the physical brain. While history has shown groups who gathered to see what was happening, saw "human experiencing" as they went through these colour modes.

¹ Hemmenway, Pryia – Divine Proportion pp66, Sterling Publishing, ISBN 1-4027-3522-7
² Reflections on Relativity8.6 On Guass's Mountain

Pythagoras Could be Called the First Known String Theorist

Pythagoras could be called the first known string theorist. Pythagoras, an excellent lyre player, figured out the first known string physics -- the harmonic relationship. Pythagoras realized that vibrating Lyre strings of equal tensions but different lengths would produce harmonious notes (i.e. middle C and high C) if the ratio of the lengths of the two strings were a whole number. Pythagoras discovered this by looking and listening. Today that information is more precisely encoded into mathematics, namely the wave equation for a string with a tension T and a mass per unit length m. If the string is described in coordinates as in the drawing below, where x is the distance along the string and y is the height of the string, as the string oscillates in time,