Potential Geometry in Quantum Physics, Vision, and Cosmology




LINK to Squaring the Circle post


LINK to Calculus and Infinity / Infinitesimal Conceptions


LINK to Worship of Geometry / Sacred Geometry

Link to Collective Unconscious
Link to Infinite Dimensionality

Link to Infinite Control Theory post
Link to God of Physics post




Ancient Origins of Atom Theory and note the most recent skepticism

Particle Tracks in Bubble Chambers — review saved sessions and download all best ones


Laue Diffraction of Biological Crystals — find all the best ones and embed theme

QUANTUM CORRAL EXPERIMENTS — review saved sessions and download all best ones

LIGHT GEOMETRY / Electromagnetic Field – DIFFRACTION, PROPAGATION, ETC – punctured plan field

God as “Center Everywhere, Circumference Nowhere” – also sphere as a metaphor for “particular intellectual focus” “one potential body of knowledge” “one area of research”

Higher Dimensional Geometrical Constructions with the Circle as its foundation – embed all interesting ones

Embed Protein Spirals in here somewhere …






Consider possible ToE – Hyper-Sphere with Toroidal Deformations – consider rudy rucker quotes

subatomic particle tracks, find best images

smoke particle geometries

ice circles rotation, photo and/or video

herman weyl quotes

Atom and Archetype writings by Jung – find quotes to add

“magic number of electrons” — google for sphere / spherical / sphericity / sphericality comments and analysis


In physics, the “dimensionless point” is the observer.  But this is the center of everything!

If the center is everywhere, here is always there.  But you don’t have to care.

If you aren’t annoyed by this statement, you might be a fan of rainbows.


It’s not what you look at that matters, it’s what you see.  –  Henry David Thoreau.


Reorganize this post into sections dealing with supposedly separate areas, then philosophize about their hidden connections


Center of the Universe is Everywhere  (list all instances of the religious saying that God is a circle whose..)

Fraser Cain explanation of center everywhere



Which post to add Biosphere – Sphere of No Form song video?  This one or another…?


include section on spherical wavefront of inverse square laws of light, and gravity


This isn’t exactly right as a theory of everything, but it’s not completely wrong either.  He’s working with what we have.  ???  Or is this simply one mathematical object which is being fixated on and is obviously not the ToE

Newscientist – E8 Rotations





Tying Quantum Knots – Amherst College and Aalto University

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In physics, circle bundles are the natural geometric setting for electromagnetism. A circle bundle is a special case of a sphere bundle.

(is this because of practicality and wiring setups or is it because of a fundamental property of electromagnetic flow?


In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of very small radius, so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This extra dimension is a compact set, and the phenomenon of having a space-time with compact dimensions is referred to as compactification.

In modern geometry, the extra fifth dimension can be understood to be the circle group U(1), as electromagnetism can essentially be formulated as a gauge theory on a fiber bundle, the circle bundle, with gauge group U(1). Once this geometrical interpretation is understood, it is relatively straightforward to replace U(1) by a general Lie group.

“The main idea which leads to Lie sphere geometry is that lines (or planes) should be regarded as circles (or spheres) of infinite radius and that points in the plane (or space) should be regarded as circles (or spheres) of zero radius.”

add more quotes




“In 1993 the physicist Gerard ‘t Hooft put forward the holographic principle, which explains that the information about an extra dimension is visible as a curvature in a spacetime with one fewer dimensions. For example, holograms are three-dimensional pictures placed on a two-dimensional surface, which gives the image a curvature when the observer moves. Similarly, in general relativity, the fourth dimension is manifested in observable three dimensions as the curvature of path of a moving infinitesimal (test) particle. Hooft has speculated that the fifth dimension is really the spacetime fabric.”


Much of the early work on five dimensional space was in an attempt to develop a theory that unifies the four fundamental forces in nature: strong and weak nuclear forces, gravity and electromagnetism. German mathematician Theodor Kaluza and Swedish physicist Oskar Klein independently developed the Kaluza–Klein theory in 1921, which used the fifth dimension to unify gravity with electromagnetic force. Although their approaches were later found to be at least partially inaccurate, the concept provided a basis for further research over the past century.[1]

To explain why this dimension would not be directly observable, Klein suggested that the fifth dimension would be rolled up into a tiny, compact loop on the order of 10-33 centimeters.[1] Under his reasoning, he envisioned light as a disturbance caused by rippling in the higher dimension just beyond human perception, similar to how fish in a pond can only see shadows of ripples across the surface of the water caused by raindrops.[2]

While not detectable, it would indirectly imply a connection between seemingly unrelated forces. Kaluza-Klein theory experienced a revival in the 1970s due to the emergence of superstring theory and supergravity: the concept that reality is composed of vibrating strands of energy, a postulate only mathematically viable in ten dimensions or more. Superstring theory then evolved into a more generalized approach known as M-theory. M-theory suggested a potentially observable extra dimension in addition to the ten essential dimensions which would allow for the existence of superstrings. The other 10 dimensions are compacted, or “rolled up”, to a size below the subatomic level.[1][2] Kaluza–Klein theory today is seen as essentially a gauge theory, with the gauge being the circle group.

Mathematical approaches were developed in the early 20th century that viewed the fifth dimension as a theoretical construct. These theories make reference to Hilbert space, a concept that postulates an infinite number of mathematical dimensions to allow for a limitless number of quantum states. Einstein, Bergmann and Bargmann later tried to extend the four-dimensional spacetime of general relativity into an extra physical dimension to incorporate electromagnetism, though they were unsuccessful.


add ed witten interview

compare to molecular water clusters and other crystal structures

E8 Lie Group

Garret Lisi responds to refutation


‘Most beautiful’ math structure appears in lab for first time

“A complex form of mathematical symmetry linked to string theory has been glimpsed in the real world for the first time, in laboratory experiments on exotic crystals.

Mathematicians discovered a complex 248-dimensional symmetry called E8 in the late 1800s.

In the 1970s, the symmetrical form turned up in calculations related to string theory, a candidate for the “theory of everything” that might explain all the forces in the universe.”

“Now, physicists have detected the signature of E8 in a very different realm – experiments on super-chilled crystals.”




The Scientific Promise of Perfect Symmetry


Garrett Lisi Through the Wormhole Visualizing Circles

“My work always tried to unite the
Truth with the Beautiful, but when I
had to choose one or the other, I usually chose the Beautiful.”

-Hermann Weyl

“Physics should be beautiful.”

  • Sir Fred Hoyle

“Mathematics possesses not only truth, but also supreme beauty”
-Bertrand Russell

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. – Henri Poincare

Scientific American Article – A Geometric Theory of Everything

Deep down, the particles and forces of the universe are a manifestation of exquisite geometry

add quotes

adding quotes
Follow Link to watch Mpg

Hexagonal Fractal Pattern Formation



search Scripps Research Institute E8 symmetry DNA

“The Golden Ratio, roughly equal to 1.618, was first formally introduced in text by Greek mathematician Pythagoras and later by Euclid in the 5th century BC. In the fourth century BC, Aristotle noted its aesthetic properties.
Aside from interesting mathematical properties, geometric shapes derived from the golden ratio, such as the golden rectangle, the golden triangle, and Kepler’s triangle, were believed to be aesthetically pleasing. As such, many works of ancient art exhibit and incorporate the golden ratio in their design. Various authors can discern the presence of the golden ratio in Egyptian, Sumerian and Greek vases, Chinese pottery, Olmec sculptures, and Cretan and Mycenaean products from as early as the late Bronze Age. The prevalence of this special number in art and architecture even before its formal discovery by Pythagoras is perhaps evidence of an instinctive and primal human cognitive preference for the golden ratio.”

It is in De Divina Proportione that the golden ratio is defined as the divine proportion. Pacioli also details the use of the golden ratio as the mathematical definition of beauty when applied to the human face.

“The Ancients, having taken into consideration the rigorous construction of the human body, elaborated all their works, as especially their holy temples, according to these proportions; for they found here the two principal figures without which no project is possible: the perfection of the circle, the principle of all regular bodies, and the equilateral square.” from De Divina Proportione (1509)


Complexity & Chaos – Part 13b




google Photos of spiral particle paths

Golden ratio discovered in a quantum world
“When applying a magnetic field at right angles to an aligned spin the magnetic chain will transform into a new state called quantum critical, which can be thought of as a quantum version of a fractal pattern. Prof. Alan Tennant, the leader of the Berlin group, explains “The system reaches a quantum uncertain – or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical.”

By tuning the system and artificially introducing more quantum uncertainty the researchers observed that the chain of atoms acts like a nanoscale guitar string. Dr. Radu Coldea from Oxford University, who is the principal author of the paper and drove the international project from its inception a decade ago until the present, explains: “Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture.” Radu Coldea is convinced that this is no coincidence. “It reflects a beautiful property of the quantum system – a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material”, he explains.

The observed resonant states in cobalt niobate are a dramatic laboratory illustration of the way in which mathematical theories developed for particle physics may find application in nanoscale science and ultimately in future technology. Prof. Tennant remarks on the perfect harmony found in quantum uncertainty instead of disorder. “Such discoveries are leading physicists to speculate that the quantum, atomic scale world may have its own underlying order. Similar surprises may await researchers in other materials in the quantum critical state.”

World-Science.net – Golden Ratio hints at atomic symmetry



RA – Creation Of Tefnet


Circles is an essay by Ralph Waldo Emerson, first published in 1841. The essay consists of a philosophical view of the vast array of circles one may find throughout nature. In the opening line of the essay Emerson states “The eye is the first circle; the horizon which it forms is the second; and throughout nature this primary figure is repeated without end”.

link to essay


Optical Nervous System – Alan Watts

The Lie algebra of visual perception.
Hoffman, William C.Journal of Mathematical Psychology, Vol 3(1), 1966, 65-98.

The familiar perceptual constancies of image location in the field of view, image orientation, size constancy, shape constancy, binocular distortion, and motion, have their natural mathematical expression in terms of Lie groups of transformations over the visual manifold. If Lie’s 3 fundamental theorems are to be satisfied, 3 additional perceptual invariances must also be present: time, efferent binocularity, and what apparently constitutes some sort of circulating memory in space-time. This Lie algebra of visual perception admits ready explanations for the following visual phenomena: the developmental sequence of infant vision, orthogonal after-images, after-effects of seen movement, the spiral after-effect and the spiral images sometimes evoked under flicker, reading reversals, and the visual analogue of the Fitzgerald contraction. The theory also predicts certain new complementary (orthogonal) after-images, the existence of which have been verified experimentally.

geometric psychology, google names for further research

“Subjective geometry” is a term coined by Weintraub and Krantz to describe the distortion imposed upon geometric patterns by the visual system itself—so-called optical illusions. The latter are widely regarded as being generated by misplaced “constancy” effects, i.e., they are regarded as stemming from the invariance of an object’s appearance under wide variations in viewing conditions, such as obliquity, rotations, etc. The invariances represented by these constancies—shape constancy, size constancy, etc.—are spatiotemporal invariants of certain Lie subgroups of P4(R) circled plus CO(1, 3) circled plus GL(4, R) that govern Euclidean and non-Euclidean geometry. That Euclidean subgroups describe a Cyclopean visual world; the non-Euclidean, a binocular (bipolar) world of hyperbolic nature, according to the work of Luneburg, Blank, Indow, and others. The visual field of view is itself a geometric object involving not only “figure” and “ground” but also visual contours (orbits of the Lie groups involved), linear perspective, interposition, and contact and symplectic structures. The retina and “cortical retina” are both covered by a family of “circular-surround” cellular response fields (of a “Mexican hat” nature) which constitute an atlas for the visual manifold S. Upon this manifold are defined certain equivariant vector bundles that account for constancy phenomena and certain jet bundles, arising out of the vector bundles by prolongation, that generate the differential invariants characterizing higher form perception. The resultant theory of perceptual-cognitive processing has been termed “geometric psychology,” in analogy to MacLane’s “geometrical mechanics” and Brockett–Hermann–Mayne’s “geometry of systems,” the mathematical structure being very similar in all three instances. Functorial maps from the category GvFB(S) of equivariant fibre bundles to the simplicial category and the category of simplicial objects complete the theory by extending the perceptual system to cognitive phenomena and information-processing psychology.

Constructive Aspect of Visual Perception

Snakes – search files and re-upload

Projections of Mobius Transformations on a Reimann sphere

Wiki Mobius Transformations

Full 20 minute version is on youtube


Mark Otten – Mushroom Therapy (Costa Del Sol Chillout Mix)  (-ADD A MID-BASS TRACK TO THIS, or cut it shorter and use as a backtrack)

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Stereographic Projection of the Riemann Sphere – Möbius Transformations Revealed [HD]


Shpongle – The God Particle [Visualization]   (maybe move to calculus infinitesimal post)

Chronos – Sunset and a Star [Music Video]

Globular – Infinity Inside [Visualization]

Torus Merkaba Meditation Sacred Geometry

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Why is everything so spherical?  bubbles, water drops, flames in outerspace, stars, planets, moons

ScienceatNASA ScienceCasts: Strange Flames on the International Space Station


Shpongle ~ Invocation → Turn Up The Silence ~ ( Posted here mostly for the visualization – ES Fractals — move to other fractal post, or novel considerations for existentialists post)


Find hindu “Mind is the universe” comments..


One of defining characteristics of a circle is perfection.  If a circle is not perfect, it is not a circle.  A sphere is an image of perfection and infinity to many.  How many circles make up a sphere? >is a similar question to: ~how many ways can you divide a circle? or: ~how many sides does a circle have?  Or how many points make up a line?  Or how many lines make up a plane?  It’s arbitrary, infinite, or whatever you say it is.  Or it may be a meaningless question to you.




“The Promised Land of evolution is growth from electron to divinity.”  – Toyohiko Kagawa (pre-1936)


Cosmos: A Personal Voyage (1980)

Episode 12, “Encyclopedia Galactica

Carl Sagan:

The ash of stellar alchemy had emerged into consciousness.
We are a way for the cosmos to know itself.
We are star stuff harvesting starlight.

We humans long to be connected with our origins, so we create rituals. Science is another way to express this longing. It also connects us with our origins, and it too has its rituals and its commandments. Its only sacred truth is that there are no sacred truths. All assumptions must be critically examined. Arguments from authority are worthless. Whatever is inconsistent with the facts, no matter how fond of it we are, must be discarded or revised. Science is not perfect, it’s often misused, it’s only a tool, but it’s the best tool we have: self-correcting, ever-changing, applicable to everything. With this tool, we vanquish the impossible. With the methods of science we have begun to explore the cosmos.

We have learned to value careful observations, to respect the facts even when they are disquieting, when they seem to contradict conventional wisdom.
The Canterbury monks faithfully recorded an impact on the moon and the Anasazi people, an explosion of a distant star.
They saw for us as we see for them.
We see further than they only because we stand on their shoulders.
We build on what they knew.
We depend on free inquiry and free access to knowledge.
We humans have seen the atoms which constitute all of matter and the forces that sculpt this world and others.
We know the molecules of life are easily formed under conditions common throughout the cosmos.
We have mapped the molecular machines at the heart of life.
We have discovered a microcosm in a drop of water.
We have peered into the bloodstream and down on our stormy planet to see the Earth as a single organism.
We have found volcanoes on other worlds and explosions on the sun, studied comets from the depths of space and traced their origins and destinies, listened to pulsars and searched for other civilizations.
We humans have set foot on another world in a place called the Sea of Tranquility, an astonishing achievement for creatures such as we whose earliest footsteps are preserved in the volcanic ash of East Africa.
We have walked far.
These are some of the things that hydrogen atoms do given 15 billion years of cosmic evolution.

It has the sound of epic myth.
But it’s simply a description of the evolution of the cosmos as revealed by science in our time.
And we—we who embody the local eyes and ears and thoughts and feelings of the cosmos—we’ve begun, at last, to wonder about our origins.
Star stuff, contemplating the stars, organized collections of 10 billion-billion-billion atoms contemplating the evolution of matter, tracing that long path by which it arrived at consciousness here on the planet Earth and perhaps throughout the cosmos.


Particle Accelerator Experiments at Large Hadron Collider in CERN Geneva, SW



Brian Greene explains some math behind the Higgs Boson

Why “Change without Change” is One of the Fundamental Principles of the Universe

Brian Greene: The Search For Hidden Dimensions

Brian Greene: How Can We Picture the Fourth Dimension?

String Theory Dimensionality – “A Tree Is to the Universe As a String Is To An Atom” – Brian Greene

The Light that Reveals the Horizon of Unknowing – Terence Mckenna



Quaternion spin half — repeating spherical wave – nested electron model

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Solving the Electron Spin

A Clashing of Waves – Jorge Fuentes

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The world is large-

It contains multitudes.

I look with all-embracing eyes

And I tell you what I see.

Do I contradict myself?

Very well, I contradict myself.

If you are not bedazzled yet:

Look differently, and marvel.

  • Walt Whitman from Leaves of Grass

IBM Atomic Shorts: Ripples on the surface

Particle.Wave – Matter.Energy – Determinism.Indeterminism – Locality.Nonlocality Realism.Nonrealism

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Movement of Single Electrons – captured on video during double slit experiment

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Square Salt Crystals on the Dead Sea Shore


We Plants Are Happy Plants – Life Is Living You

Sonic 3 Music – Blue Spheres – Special Last Stage

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One Single Electron Photo-Video

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The mind, at its deepest organizational level, reflects the geometric principles of the organization of space and time.  –  Terence Mckenna

We Plants Are Happy Plants – Not Waiting For Anything (-reduce treble 2nd half)

There is nothing strange in the circle being the origin of any and every marvel. – Aristotle

The Soul is the form of the body.  – Aristotle

Concentric Circles - Penrose

BBC – Cosmos may show echoes of events before Big Bang

They surveyed nearly 11,000 locations, looking for directions in the sky where, at some point in the past, vast galaxies circling one another may have collided.

The supermassive black holes at their centres would have merged, turning some of their mass into tremendous bursts of energy.

The CCC theory holds that the same object may have undergone the same processes more than once in history, and each would have sent a “shockwave” of energy propagating outward.

The search turned up 12 candidates that showed concentric circles consistent with the idea – some with as many as five rings, representing five massive events coming from the same object through the course of history.

The suggestion is that the rings – representing unexpected order in a vast sky of disorder – represent pre-Big Bang events, toward the end of the last “aeon”.






Similar Ancient Sacred Geometrical Objects:

Metatron’s Cube

Metatron's Cube

Metatron's Cube

Flower of Life


Leonardo da Vinci studied the Flower of Life’s form and its mathematical properties. He drew the Flower of Life itself, as well as various components such as the Seed of Life. He drew geometric figures representing shapes such as the platonic solids, a sphere, and a torus, and also used the golden ratio of phi in his artwork; all of which may be derived from the Flower of Life design.

Leonardo Da Vinci's Flower of Life Drawing

Leonardo Da Vinci Drawings

More Da Vinci Drawings


A Breakthrough in Higher Dimensional Spheres | Infinite Series | PBS Digital Studios



P. Krishna & D. Pandey, “Close-Packed Structures” International Union of Crystallography by University College Cardiff Press. Cardiff, Wales. PDF


“In geometry, close-packing of spheres is a dense arrangement of equal spheres in an infinite, regular arrangement (or lattice).”
“Many crystal structures are based on a close-packing of atoms, or of large ions with smaller ions filling the spaces between them. The cubic and hexagonal arrangements are very close to one another in energy, and it may be difficult to predict which form will be preferred from first principles.”

Close Packing of Spheres - Wikipedia

add gell-mann hexagon and quotes
Quark Model nonet
Quark model octet

Have you ever seen an atom?  (move these blurry atom photos above the more recent better atom/electon photos)




google image
add graphene pics quotes

Ultra-high vacuum scanning tunnelling microscope image of a point defect in graphene (Image: Nathan Guisinger/Argonne National Laboratory/EMMD Group/ShareAlike 2.0)

quotes and diagrams – hexagonal neuron arrays


embed more from
Kenneth Librecht






electrified snow crystals

embed explanation of hexagonal molecular structure leading to macro hexagons

embed snowflake classification diagram

embed video/pics of ICE CIRCLES

bee honeycomb


add links and quotes

Why are most planets, moons and stars sphere shaped

NYT – The Circular Logic of the Universe

“The shape of any object represents the balance of two opposing forces,” explained Larry S. Liebovitch of the Center for Complex Systems and Brain Sciences at Florida Atlantic University. “You get things that are round when those forces are isotropic, that is, felt equally in all directions.”

In a star, gravity is pulling the mass of gas inward toward a central point, while pressure is pushing the gas outward, and the two competing forces reach a dynamic détente — “simultaneously stable and unstable,” you might say — in the form of a sphere. For a planet like Earth, gravity tugs the mostly molten rock in toward the core, but the rocks and their hostile electrons push back with equal vehemence.

In precipitating clouds, water droplets are exceptionally sticky, as the lightly positive end of one water molecule seeks the lightly negative end of another. But, again, mutually hostile electrons put a limit on molecular intimacy, and the compromise conformation is shaped like a ball. “A sphere is the most compact way for an object to form itself,” said Denis Dutton, an evolutionary theorist at the University of Canterbury in New Zealand.

A sphere is also tough. For a given surface area, it’s stronger than virtually any other shape. If you want to make a secure container using the least amount of material, Dr. Liebovitch said, make that container round.

A surface on which light can orbit a black hole is called a photon sphere. The Kerr solution has infinitely many photon spheres, lying between an inner one and an outer one. In the nonrotating, Schwarzschild solution, with α=0, the inner and outer photon spheres degenerate, so that all the photons sphere occur at the same radius. The greater the spin of the black hole is, the farther from each other the inner and outer photon spheres move. A beam of light traveling in a direction opposite to the spin of the black hole will circularly orbit the hole at the outer photon sphere. A beam of light traveling in the same direction as the black hole’s spin will circularly orbit at the inner photon sphere. Orbiting geodesics with some angular momentum perpendicular to the axis of rotation of the black hole will orbit on photon spheres between these two extremes.

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quotes and pics

Computed hydrogen atom orbital for n=6, l=0, m=0. This is the 6s orbital. Note that for n >1, s orbitals also have nodes like p, d and f orbitals. However, only s orbitals invariably have a center anti-node; the other types never do



Chemical bonds between atoms were explained by Gilbert Newton Lewis, who in 1916 proposed that a covalent bond between two atoms is maintained by a pair of electrons shared between them.[42] Later, in 1923, Walter Heitler and Fritz London gave the full explanation of the electron-pair formation and chemical bonding in terms of quantum mechanics. In 1919, the American chemist Irving Langmuir elaborated on the Lewis’ static model of the atom and suggested that all electrons were distributed in successive “concentric (nearly) spherical shells, all of equal thickness”. The shells were, in turn, divided by him in a number of cells each containing one pair of electrons. With this model Langmuir was able to qualitatively explain the chemical properties of all elements in the periodic table, which were known to largely repeat themselves according to the periodic law.

Bohr Model of Atom
add pix and subtext from wiki


“Since the field equations are non-linear, Einstein assumed that they were insoluble. However, in 1916 Karl Schwarzschild discovered an exact solution for the case of a spherically symmetric spacetime surrounding a massive object in spherical coordinates. This is now known as the Schwarzschild solution. Since then, many other exact solutions have been found.”

Bob Gardner’s “Topology, Cosmology and Shape of Space” Talk, Section 7
“Some 200,000 years after the big bang, the universe became transparent to radiation and a shower of light was released. This is seen today as the Cosmic Microwave Background (CMB). This radiation (first detected in the early 1960’s by Penzias and Wilson) is one of the strongest pieces of evidence for the big bang.”
“Today the CMB appears as a giant sphere of radiation with us at the center of it (we are not in a special place – all locations see the CMB as a sphere of radiation with the observer at the center).”

Assuming the Universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction—that is, the observable universe is a spherical volume (a ball) centered on the observer, regardless of the shape of the Universe as a whole. The actual shape of the Universe may or may not be spherical. However, the portion of it that we (humans, from the perspective of planet Earth) are able to observe is determined by whether or not the light and other signals originating from distant objects has had time to arrive at our point of observation (planet Earth). Therefore, the observable universe appears from our perspective to be spherical. Every location in the Universe has its own observable universe which may or may not overlap with the one centered around the Earth.

While special relativity constrains objects in the Universe from moving faster than the speed of light with respect to each other, there is no such constraint when space itself is expanding.

Some parts of the Universe may simply be too far away for the light from there to have reached Earth. Due to the expansion of space, at a later time they could be observed.

Both popular and professional research articles in cosmology often use the term “Universe” to mean “observable universe”. This can be justified on the grounds that we can never know anything by direct experimentation about any part of the Universe that is “causally disconnected” from us, although many credible theories require a total Universe much larger than the observable universe.

‘To a wise man, the whole earth is open, because the true country of a virtuous soul is the entire universe.’ – Democritus of Abdera

Visualizing Earth’s Path – Vsauce Short

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What IS Angular Momentum?

Celestial Sphere and Observable Universe

embed best images

Spherical / Globular Star Clusters

embed best images, VIRGO, MESSIER 15, OMEGA CENTAURI

Misconceptions About the Universe – Veritasium

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Glass Sphere Design in Unreal Engine – Game Graphics

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“Albert Einstein, together with Theodor Kaluza and Oskar Klein, realized that extra dimensions can be used to unify the different fields of physics, as well as unifying the fields with their material sources. In fact, it was Einstein’s dream to transpose the “base wood” of the matter term in his field equations to the “marble” of the geometrical term.”

add quote from intro and elsewhere
embed other pages of weyl

Hermann Weyl and the Unity of Knowledge


Plotinus quotes on sphere

Xenophanes on spheres

rudy rucker on hypersphere


Alain de Lille, a 12th century theologian, borrowing from the Corpus Hermeticum of the 3rd Century:

“God is an intelligible sphere whose centre is everywhere and whose circumference is nowhere.”

While Giordano Bruno wrote:

“We can assert with certainty that the universe is all centre, or that the centre of the universe is everywhere and its circumference is nowhere.”

Pascal used the following words:

“God is a circle; His centre is everywhere, His circumference is nowhere.”

Or in another translation:

“Nature is an infinite sphere whose centre is everywhere, whose circumference is nowhere.”

And in his short story: ‘The Library of Babel’, J.L. Borjes plays with the idea:

“The library is a sphere whose exact centre is in any one of the hexagons and whose circumference is inaccessible.”

Circle and Centre,

“The famous saying that God is “a sphere of which the centre is everywhere and the circumference nowhere” is, in fact, first found in a pseudo-Hermetic treatise of the twelfth century, and was transferred by Cusanus to the universe, as a reflection of God, in a manner which is Hermetic in spirit..This concept was basic for Bruno, for whom the innumerable worlds are all divine centres of the unbounded universe.”

Yates, Bruno, p. 247.

The Liber XXIV philosophorum, published by Clemens Baeumker, Das pseudi.hermetische Buch der XXIV Meister, Beitrage zur Geschichte der Philosophie und Theologue des Mittelalters, fasc.xxv, Munster, 1928.

The source of Cusanus, is: De docta ignorantia, II, cap.2; cf.Koyre, op. cit., pp. 10ff.”


“The Indian term mandala is in Tibetan dKyil-hKhor. It means to surround any prominent facet of reality with beauty.”

“In both psychology and anthropology – the circular structure was of deep significance. In ancient times when a sacred enclosure was being defined, or a grove or piece of land that is set apart and dedicated to a God or Goddess, the first act of the magician or shaman priest was to draw a magical circle as protection.

This old magical device is used universally when a special or secret purpose is intended, or to find/define a holy place. The circle describes the energy of holiness, or wholeness. Though the triangle and the square also features in later aspects of the sacred construction. The circle is a symbol so complete and absolute, cosmically all-embracing – that today all circular designs are termed ‘mandalas’ which is not actually correct.

But one certainty is that throughout the visual literature of all systems, the circle holds the highest honours. In Pythagorian and Platonic ideas, in the Hermetic – Alchemical squaring of the circle (in Michael Maier and countless others), in Raymon Lull – there is a common agreement on this most absolute of shapes. In this, we find relationships to the Mandalas of Tibet.”

C.G.Jung on the mandala:

“They are amongst the oldest religious systems of humanity and may even have existed in Paleolithic times. Moreover they are distributed all over the world.”

Jung gives us a description of a Gnostic Mandala from the Codex Brucianus:

“This same is he (Monogenes) who dwelleth in the Monad, which is in the Sethius and which came from the place of which none can say where it is; From Him it is the Monad came, in the manner of a ship, laden with all good things and in the manner of a field planted with every kind of tree, and in the manner of a city, filled with all races of mankind…This is the fashion of the Monad all these being in it there are twelve Monads as a crown upon its head… And to its veil which surrounds it in the manner of a defense there are twelve gates…This same is the Mother City of the One Begotten.” In Jung, Psychology and Alchemy.

In Jung, Psychology and Alchemy.

Mandalas in the European tradition appear in experiences of the highest intensity, and take on Solar symbolism. Trungpa Rinpoche writes:

“This is the basic mandala principle. The mandala is generally depicted as a circle which revolves around a centre, which signifies that everything around you becomes part of your awareness, the whole sphere expressing the vivid reality of life.”

Lama Govinda writes:

“In other words, the meditator must imagine himself in the centre of the mandala as an embodiment of the divine figure of perfect Buddhahood, the realization of which is the aim of his sadhana.”

This process is a deep cypher on the structure of the psyche itself. By psyche we mean the constellation of data that constitutes the idea of the self, viewed from the position of an ego. By imprinting the memory storage with a Yantra, the psyche is activated, and the calcifications of the ego base are dissolved, or at least temporarily dislodged. This process is well illustrated by the work of the Renaissance magus, Marsillio Ficino:

“Like all his magic, Ficino’s use of talismans was a highly subjective and imaginative one. His magical practices, whether poetic and musical incantations, evolved into beautiful Renaissance forms. This use of magic images was really directed towards a conditioning of the imagination to receive celestial influences. His talismanic images, were intended to be held within, in the imagination of their user. He describes how an image drawn from astralised mythology could be printed inwardly on the mind with such force that when a person, with this imprint in his imagination, came out into the world of external appearances, these became unified through the power of the inner images, drawn from the higher world.”

Frances A. Yates, Giordano Bruno and the Hermetic Tradition.

Here we reminded again of the quote from Mookerjee:

“…the physics and metaphysics of the world are made to coincide with the psyche of the meditator.”

“On what we used to explain away as mysteries, modern discoveries in higher physics has shed new light. For this the Tantric art of India deserves scientific analysis. What is more, while in abstract art we still normally think in terms of space and time, Tantra has gone further and brought in concepts of sound and light, especially in conditioning art forms. This has no parallel elsewhere.”

“In this spiritual process, a new sign language symbolizing the man-universe relation was discovered and used.”

As will be seen, this synchronicity of the psyche and “the world of external appearances” which marks Ficino’s work, is the fruit of research into visual metaphysics, and identical to the Yantra of Tantra Art.

Once again we are confronted with the fact that an Order / Sequence exists in both Eastern and Western procedures. In Ficino:

“Applied to the inner talismanic images of an occult memory system, this would mean that the magical power of such images would consist of their perfect proportion.”


“Renaissance theory of proportion was based on the ‘universal harmony’, the harmonious proportions of the world, the macrocosm, reflected in the body of man, the microcosm.”
Frances A. Yates, Giordano Bruno and the Hermetic Tradition.

add metapatterns quotes + mckenna quote as the sphere of understanding expands
add pics of spheres in nature, volvox, bubbles, galactic bubble

ADD Charles Gilchrist
jung quotes

Flower of Life (Sacred Geometry by ieoie)

Charles Gilchrist 101E – Metatron’s Cube

A regular hexagon is constructible with compass and straightedge. A step-by-step animated method of this, given by Euclid's Elements, Book IV, Proposition 15. ??

http://en.wikipedia.org/wiki/Petrie_polygon Hexagon, Cube

Petrie Polygon Hexagon, Octahedron

Ilya Prigogine – SpaceTime SquareCircle

Cube 2D&3D Camera (Sacred Geometry by ieoie)

Metatron Cube 2D ( Sacred Geometry by ieoie )  MOVE TO METATRON POST!!!!!!!!!!!!!!!

Metatron Cube 3D ( Sacred Geometry by ieoie )  MOVE TO METATRON POST!!!!!!!!!!!!!!!

Torus Fun ( ieoie )

Villarceau circles

A torus is the product of two circles.

Vesica Piscis


The geometric figure of a tube torus represented by the Seed of Life.

Morphing Platonic Solids ieoie

Carl Sagan explains the “geometry of the universe”

Carl Sagan on modern cosmology + Hindu cosmology

Cosmic Crystallography and Spherical Lensing?


Cosmic Topology Physicsweb.org – A Cosmic Hall of Mirrors – Dodecahedron, Octahedron, or Tetrahedron?

Space Seen as Finite, Shaped Like a Soccer Ball
By Robert Roy Britt


excerpts and diagrams

Dodecahedral Honeycomb

“Is the universe a dodecahedron?

The standard model of cosmology predicts that the universe is infinite and flat. However, cosmologists in France and the US are now suggesting that space could be finite and shaped like a dodecahedron instead. They claim that a universe with the same shape as the twelve-sided polygon can explain measurements of the cosmic microwave background – the radiation left over from the big bang – that spaces with more mundane shapes cannot”

“Experience remains, of course, the sole criterion of the physical utility of a mathematical construction. But the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.” – Albert Einstein

“Pure mathematics is, in its way, the poetry of logical ideas.” – Albert Einstein

“Thought is only a flash in the middle of a long night, but the flash that means everything.” – Poincare

“To force the future of mathematics the true method is to study its history and its present state.” – Poincare

Mathematics is the art of giving the same name to different things. – Poincare


Poincare disk with boundary at infinity — embed picture

090613 0900 Susskind DarkEnergy h264 1080p 10mb  — quote this video perhaps..









The Colbert Report Mon – Thurs 11:30pm / 10:30c
Brian Greene
Colbert Report Full Episodes Political Humor & Satire Blog</a> Video Archive

Elusive Proof, Elusive Prover: A New Mathematical Mystery


Carl Sagan on Pythagoras, Platonic Solids

Dodecahedron (Sacred Geometry by ieoie)

Norman Sieroka

3.2 Wheeler’s geometrodynamics

“A prominent attempt to develop pure field physics within the second half of
the twentieth century was John Wheeler’s geometrodynamics. Like Weyl’s
unified field theory of 1918, Wheeler’s project was particularly motivated by
general relativity and also aimed at reducing matter to the geometrical features
of space–time.26 However, it also shares a feature with Weyl’s agent theory
because it assumes that space–time is not a simply connected manifold.27
Let me explain all this in some more detail.
Wheeler claims that ‘in geometrodynamics, mass and charge are not
idealized as properties of point particles, they are, instead, aspects of the geometrical
structure of space’ (Misner and Wheeler [1957], p. 595–6). According
to this view something that appears to us as being matter is just a circulating
lump of electromagnetic and/or gravitational radiation that is kept together
by its own gravitational force. Wheeler calls such lumps ‘gravitationalelectromagnetic
entities’, or ‘geons’ for short. He says: ‘To the outside the
geon manifests mass, but inside there is nowhere that one can put his finger
and say “Here is ‘real’ mass!’’ ’ (Wheeler [1961], p. 65).

Webofstories.com link

Quote from transcripts

Geometry and physics and the future of mathematics

Michael Atiyah – Geometry and Algebra

Possibility of spherical geon; stability and quantum theory; Wheeler-DeWitt Equation

“A spherical geon is, in principle, possible too, where some radiation is going round one circle, other radiation going around another circle, and these various circles with the various items of radiation, these circles are added at random. So you end up with a smooth, spherical distribution of energy. But, again, unstable. Did you hold out the hope that when quantum theory was brought into the picture that it might provide the necessary stability? Yes, I didn’t see how to use quantum theory in the whole story. But it would be marvelous if quantum theory had led to some structure that would keep this thing from collapsing. But I don’t see now any likelihood that that is the case. But at the time, I was hoping that this would be a model for elementary particles. Why dream up something new out of which to make particles when you already have in front of you electromagnetic radiation and gravitational radiation? But we are still struggling with the ultimate constitution of particles today. So I would not want to bet. Dealing with gravitation, I must say that it seemed to me the whole subject fell into order in a new way. There were no great mysteries except at the interface between gravitation and quantum theory. Quantum theory says that a physical system has a certain probability to be in this configuration or that configuration or another. But how would you talk of the probability of a space that’s curved like this and a space curved like that, and so on? Where would you be standing when you were pontificating about this geometry? In which geometry would you be? It’s a ticklish business. Fortunately, we could talk about these things in a seminar and I had a colleague, Valentine Bargmann, who had been an assistant of Einstein at one time. And he saw into some recent work by a colleague at the University of Rochester, saw enough to give some guidance into this. And another student of mine, named Edward Fireman saw how to operate at the semi-classical level, at the level where you almost can use classical concepts. And that was a step on the way to translating this question of the quantum theory of gravitation into a ‘doable’ form. It ended up with an equation which looked mostly symbolic. My Texas colleague, Bryce Dewitt, found a way to translate that symbolic equation into quite concrete mathematical terms, so today it’s called a Wheeler-Dewitt Equation. But it’s one thing to have an equation, another thing to solve it, and so another thing to interpret the solution. A colleague at Pennsylvania State University, Abhay Ashtekar, has found a lovely way to solve this equation. But we still haven’t got a full insight into what the solutions mean and how to speak about them. That’s a continuing enterprise. It’s strange that the two greatest developments of theoretical physics, the quantum theory and relativity, should take so long to come into a union.”

John Wheeler
Thinking behind first major paper on relativity. Geons and the concept of the Geon

“Radiation, a pencil of radiation carries energy with it, and energy has mass, and therefore, a pencil of radiation must exert some attraction on things beside it. What about getting a pencil of radiation curved into a circle so the light goes around and round, then the attraction it exerts is concentrated as if at the center. So what is it that bends this pencil of radiation into the circle is the gravitational attraction of the pencil of radiation itself. That was the idea of the geon. Actually, if you think of different possibilities for the size of that geon, bigger or smaller, you find that if it’s very big, the energy is low, to push the radiation together requires energy. And you climb a hill like the hill of a volcano until you come to a maximum energy, and then, if the pencil of radiation becomes any smaller in size, the energy starts to go down and the thing collapses. So a geon is really an unstable entity. It either blows up into a cloud of radiation traveling away in all directions, or it collapses into a totally collapsed object, something that we today would call a Black Hole. But that stability analysis I didn’t have in mind when I first published this work, only later did I see that that’s a feature that’s dominant. But nowadays, I’m attracted with this idea that this pencil of radiation going around in a circle does not have to be light, it can be gravitational waves. And you can have gravitational waves imploding to make a black hole.” – John Wheeler

Spheres in particle analysis


Is This What Quantum Mechanics Looks Like? – Veritasium


Terence Mckenna – Empower your Mandala

Terence Mckenna – Angels and Demons in Science

Paul Carus wrote, “There is no science that teaches the harmonies of nature more clearly than mathematics, and the magic squares are like a mirror which reflects the symmetry of the divine norm immanent in all things, in the immeasurable immensity of the cosmos and in the construction of the atom not less than in the mysterious depths of the human mind.”

Randy Powell – A Wild Pythagorean on the loose (Claims may not be true, Tech applications I couldn’t verify)



Chronos – Sunset and a Star [Music Video]

Cygnus X-1 by RUSH

<iframe width=”420″ height=”315″ src=”https://www.youtube.com/embed/ZeQLVxBczBY” frameborder=”0″ allowfullscreen></iframe>







“It’s the black hole that forced both astronomers and physicists to take Albert Einstein’s most notable achievement – general relativity – seriously.  For a time the theory had entered a valley of despair.  Einstein was honored as the “Person of the Twentieth Century” by Time magazine (what year), yet such an honor would have been a huge surprise to the scientific community in midcentury.(questionable?)  In that era, few universities in the world even taught general relativity, believing it had no practical applications for physicists.  The best and the brightest flocked to other realms of physics.  After the flurry of excitement in 1919, when a famous solar eclipse measurement triumphantly provided the proof for Einstein’s theory of relativity, the noted physicist’s new outlook came to be largely ignored.  Isaac Newton’s take on gravity worked just fine in our everyday world of low velocities and normal stars, so why be concerned with the miniscule adjustments that general relativity offered?  What was it’s use?  “Einstein’s predictions refer to such minute departures from Newtonian theory,” noted one critic, “that I do not see what all the fuss is about.”  After a while, Einstein’s revised vision of gravity appeared to have no relevance at all.  By the time Einstein died, general relativity was in the doldrums.  Only a handful of physicists were specializing in the field.  As Nobel Laureate Max Born, a longstanding and intimate friend of Einstein, confessed in a conference the year of Einstein’s death, general relativity “appealed to me like a work of art, to be enjoyed and admired from a distance.”

But in reality, what Einstein had done was devise a theory that was decades ahead of its time.  Experimental measurements had to catch up to his model of gravity, which had been fashioned from pure intuitive thought.  Not until astronomers revealed surprising new phenomena* in the universe, brought about with advanced technologies, did scientists take a second and more serious look at Einstein’s view of gravity.   *quasars, pulsars, neutron stars, black holes, titanic energies that can be understood only in the light of relativity.

And what astrophysicists ultimately discovered and came to appreciate was general relativity’s deeper aesthetic appeal, especially when it came to black holes.  “They are,” said Subrahmanyan Chandrasekhar on recieving the Nobel Prize in physics in 1983, “the most perfect macroscopic objects there are in the universe.”  “Beauty is the splendor of truth.”  Black holes offered all that a physicist yearned for in a theoretical outcome: both simplicity and beauty.

The black hole (..) is now a vital component of the universe.  Nearly every fully developed galaxy appears to have a supermassive black hole at its center; it may be that the very existence of a galaxy depends on it.

John Archibald Wheeler, a dean of American relativity, once noted in the dedication of his autobiography, “We will first understand how simple the universe is when we realized how strange it is.”

But arriving at that knowledge took more than two hundred years – from the precursor of the black hole idea in the 1780s to the observational proof in the latter half of the twentieth century. (what year?)







“(In 1919) The German astronomor Karl Schwarzschild arrived at the first full solution to general relativity’s equations. (…)  It was this remarkable achievement, which both surprised and delighted Einstein, that initiated the long march toward our modern conception of the black hole.  Both a practical astronomer and a theorist, Schwarzschild was a stand-out in a multitude of fields.  He made major contributions in electrodynamics, optics, quantum theory, and stellar astronomy: he was a pioneer in substituting photographic plates for the human eye at the telescope: and he could at times be quite bold in his speculations.  Fifteen years before Einstein even introduced the notion of space-time bending, Schwarzschild had pondered whether space was curved rather than flat – either turned inward like a sphere or curved outward like a hyperbola out to infinity.  “We can wonder how the world would appear in a spherical or psuedo-spherical geometry . . . ,” he told a meeting of German astronomers in 1900.  “One would then find oneself, if one will, in a geometrical fairyland; and one does not know whether the beauty of this fairyland may not in fact be realized in nature.”

Schwarzschild wanted to remove all doubt as to the uniqueness of Einstein’s results.  And in aiming for that goal, he ended up devising a method that became a valuable tool for relativists for years afterward.  In carrying out this endeavor, Schwarzschild did what all good mathematicians do – devise a scheme that makes the mathematics of the problem simpler.  He used spherical coordinates, which makes it easier to map the gravitational field around a spherical mass – in this case, a nonspinning star.  To see how this approach can make a complex question simpler, imagine an everyday problem: Take an airplane circling an airport from three miles (almost five kilometers) away.  If you want to describe its path using the geometry of a flat grid, the result is very messy.  If you designate its east-west position x and its north-south position y, then the algebraic equation that describes its entire route is x + y =3(add superscript square).  But let’s say you shift to a different geometry altogether: a graph with radial, or circular coordinates.  In that case you don’t have to worry about x’s and y’s at all.  The plane is always three miles from the center of a circle, and the equation that describes its flight path is no more complicated than r = 3 (radius = 3).  That, in a way, is what Shwarzschild did.  But his new set of coordinates led to a whopping predicament when he looked at the very center of space-time, where his star resided.  As Ralph Sampson, the astronomer royal for Scotland, remarked at the time, “The consequences . . . are so startling that it is difficult to believe they have any relationship to reality.”  To understand this dilemma, picture what happens if all the mass of that star, say the Sun, is squeezed down to a very small size.  Upon doing this, Schwarzschild discovered that, around this hypothetical point, a spherical region of space suddenly arose, out of which nothing – no signal, not a glimmer of light nor bit of matter – could escape.  In its day, it was called “Schwarzschild’s sphere.”  Today we call this boundary the “event horizon.”  That’s because no event occurring within its borders can be observed from the outside.  More than an indentation, space-time in this case becomes a bottomless pit.  Light and matter can go in but never come back out.  It’s a point of no return.  The light and matter get crushed down to a singular point, a condition of zero volume and infinite density called a “singularity.”  It’s where the ordinary laws of physics completely break down.

That is how we currently picture such a singularity.  Schwarzschild and others in his day actually viewed this situation fairly differently: watching how objects, such as light particles, approached Schwarzschild’s sphere, “they got stuck, so to speak,” explains historian Eisenstaedt.  “This was then taken as bona fide evidence that all trajectories ended up or died at the [sphere], where time . . . stopped. . . . The [light’s] trajectory appeared to perpetually approach the magical sphere, as if to vanish there.”  Or maybe they simple piled up on the surface of this magical ball.  It was a strange and weird place.  The “Schwarzschild singularity” (as it was also called) was an impenetrable sphere from their perspective.

Arthur Eddington, in his 1926 book The Internal Consitution of the Stars, was confident that no star could possible collapse to such a compacted state.  So, why worry about it?  As he fancifully put it, “The mass would produce so much curvature of the space-time metric that space would close up round the star, leaving us outside (i.e. nowhere).”  That was one way to look at it.  But despite Eddington’s imaginative description, most relativists at the time did not seriously think that space-time itself was being significantly warped and twisted around Schwarzschild’s singularity.  “They realized that the spatial component might be slightly bent, that time may be a bit out of step, but nobody imagined that Schwarzschild’s solution could represent a space really different, completely different, from Newton’s,” explains Eisenstaedt.  That awaited new mathematical insights in the 1960s.  Relativists needed the ability to map the entire region of space-time around the singularity – a grand, calculation-intensive enterprise impossible for physicists in the 1910s and 1920s to undertake.  The modern-day vision of a “black hole,” a pit in space-time was not yet imagined.  But, still, what was the best way to describe this unusual place?  Schwarzschild used the term discontinuity.  In France and Belgium it became the sphere catastrophique, for it did appear like a catastrophic place where all the laws of physics went awry.  For Eddington, it was the “magic circle.”  Others simply referred to it as a “frontier” or “barrier.”

And how big would that magical sphere be?  That depended on the amount of mass caught inside it.  If our Sun, which is nearly 900,000 miles (1.4 million kilometers) wide, were suddenly squeezed down to a point, its magic sphere would less than 4 miles (6 kilometers) across.  (…)

What happens if the amount is greater, such as the equivalent of ten suns squished down to a point?  In that case, the magic sphere would stretch almost forty miles (around sixty kilometers) across.  The equations showed that the width of the magical sphere (that is, the event horizon) expands as more and more mass is trapped within it.


Speaking now of white dwarf stars, not black holes:

It took quantum mechanics, under development in the 1920s, to solve the puzzle (of how a star could remain stable in the incredibly compressed white dwarf form, with such seemingly impossible densities being continually sustained).  (Sirius B star density calculated to be around 25,000 times more than the sun, but with a size only a little larger than the Earth)  Considering the mass of the entire Sun crushed into an Earth-sized space – creating the densest matter then known in the universe – British theorist Ralph Fowler, in 1926, figured out that pressures inside the compact dwarf star become so extreme that all its atomic nuclei are packed into the smallest volume possible.  Atoms are largely empty space.  But all that extra space is drastically reduced within a white dwarf star.  At the same time, its free electrons generate an internal energy and pressure that keep the atom from collapsing further.  (…)  And that is the key to a white dwarf’s stability: the incredible pressure exerted by the highly confined and fast-moving electrons prevents the star from further compaction.  This pressure exceeds the crushing forces found at the center of our Sun a million times over.  Such a pressure was inconceivable until the arrival of quantum mechanics.


The white dwarf is the luminous stellar core left behind after the star runs out of fuel and releases its gaseous outer envelope into space.  Radiating the energy left over from its fiery past, the white dward, like a dying ember, eventually cools down and fades away.


(In 1931) Chandra’s equations were telling him that past his threshold(of star mass), the star appeared to be headed toward total collapse, with its density going to infinity (a result he deemed “inconceivable”).

Chandra was not alone in his pursuit.  The problem of stellar mass was in the air.  It was a time when astrophysicists were starting to analyse the internal structure of a star – how it was powered, how it was built.


Lev Landau (in the Soviet Union, working with another model of a star’s inner structure) concluded in 1931, that “there exists in the whole quantum theory no cause preventing the system from collapsing to a point,” if the star were heavier than 1.5 solar masses.  But this was obviously a “ridiculous” result, he decided.  He knew there were stars more massive.  What could possibly explain this obvious contradiction?  To answer that, Landau reasoned that the laws of physics must be breaking down within the heart of a star, following up on a thought that the Danish atomic physicist Neils Bohr had earlier expressed.  The stellar core was a “pathological” region, as Landau put it, where matter becomes so dense it forms “one gigantic nucleus.”


Chandra (in 1932) wrote in a journal article “We conclude that great progress in the analysis of stellar structure is not possible before we can answer the following fundamental question:  Given an enclosure containing electrons and atomic nuclei (total charge zero), what happens if we go on compressing the material indefinitely?”  Indeed, what does happen to the star?


Too busy arguing about the exact composition of a star’s innards, the only thing his opponents could agree on was that a star would never collapse to a point.


Chandra wrote in 1934, “It is necessary to emphasize one major result of the whole investigation, namely, that it must be taken as well established that the life-history of a star of small mass must be essentially different than the life history of a star of large mass.  For a star of small mass the natural white-dwarf stage is an initial step towards complete extinction.  A star of large mass . . . cannot pass into the white-dwarf stage, and one is left speculating on other possibilities.”  In other words, low-mass stars would assuredly die as white dwarfs, but what fate befalls a star of higher mass, whose central core steps over the limit?  What could possibly happen to it?



(find graph google image search, embed)

In an eighteen page paper in 1935, a graph he included portrayed his bottom line: as a white dwarf star grew smaller and smaller with increased mass, its radius approached zero.  “When the central density is high enough . . . ,” wrote Chandra, “the configurations then would have such small radii they would cease to have any practical importance in astrophysics.”  Stars were not expected to act like this.  Eddington, not pleased by the paper, is often quoted “there should be a law of Nature to prevent a star from behaving in this absurd way!”  (…) simply overwhelmed by the psychological factor – the preposterous notion that matter could somehow be crushed to oblivion.  (…) it defied common sense.  (…)  Werner Israel writes, “In 1935 the astronomical community was not ready to ‘buy’ the idea of gravitational collapse (…)”  In this era, astronomers were fairly old-fashioned.  Few were trained or even interested in applying the new physics – relativity and quantum mechanics – to astrophysical problems.  Many didn’t even think relativity was even a part of physics but more a branch of mathematics.



copy down page 80 — comparison to division by zero

page 83 about einstein’s spherical/circular excuse against collapse

page 84 about nazis banning einstein’s physics as Jewish, and relativity being taught as mathematics instead of physics..


CONTINUE READING…. go to library, take notes back home to blog














embed photos of spherical star clusters


From Space.com   http://www.space.com/23756-white-dwarf-stars.html

Smaller stars, such as red dwarfs, don’t make it to the red giant state. They simply burn through all of the hydrogen within the star, leaving behind the shell that is a white dwarf. However, red dwarfs take trillions of years to consume their fuel, far longer than the 13.8-billion-year-old age of the universe, so no red dwarfs have yet become white dwarfs.


From here    http://www2.hesston.edu/Physics/StarsAmy/starspaper.htm

Up to this point, most of the events of stellar evolution are well documented. What happens to a star after the red-giant phase is not certain. Physics does show that a star, regardless of its size, must eventually run out of fuel and collapse. In theory, gravity wins. With this in mind the means of a stars death is determined by its initial mass.

Low mass stars, or sun-like stars will go the planetary nebula route (Col). Because of the incredible rate of the helium to carbon burning seen in the helium phase, coupled with a relatively small change in temperature, the star becomes unstable. This causes it to develop a superwind. The superwind gusts rip off the outer shell of the star, leaving a hot core behind. The core never reaches the ignition temperature of carbon burning. The core cannot contract and heat up to a temperature needed to initiate carbon fusion. In about 75,000 years it forms a white dwarf star, composed mostly of carbon. During this process its surface becomes very hot. But without energy, it can’t contain itself. Because the core is out of fuel, the white dwarf will eventually cool to a black dwarf. This will take many billions of years to cool (Star). Black dwarfs do not exist because this process would take longer than the lifespan of the universe (Szeto).


For Albert Einstein, locality was one aspect of a broader philosophical puzzle:  Why are we humans able to do science at all?  Why is the world such that we can make sense of it?  In a famous essay in 1936, Einstein wrote that the most incomprehensible thing about the universe is that it is comprehensible.  Einstein’s point was that physicists really had no right to expect that; the world needn’t have been orderly at all.  It didn’t have to abide by laws.  Under other circumstances, it might have been anarchic all the way down.  When a friend wrote to ask Einstein what he’d meant by the comprehensibility remark, he wrote back, “A priori one should expect a chaotic world which cannot be grasped by the mind in any way.”  Although Einstein said comprehensibility was a “miracle” we shall never understand, that didn’t stop him from trying.

google einstein’s comments on symmetry, locality, and time..




“The description of “color” property spaces (..) involves complex numbers.  The ‘strong color space’ is a property space with three complex dimensions, and likewise for the weak and electromagnetic color property spaces.  In each case the symmetry transformations do not change the overall distance from the origin, so the property spaces of what we’ve called entities (particles related to one another by symmetry transformations) are spheres of various dimensions.  In the case of the strong interactions we start with three complex dimensions, which are six real dimensions, and so the property space of a quark entity is a sphere with five real dimensions.  For electromagnetic charge we have one complex dimension, two real dimensions, and finally a one-dimensional sphere, also known as a circle.  The radius of that circle is the magnitude of the electric charge.

From ‘A Beautiful Question’ by Frank Wilczek   pg. 400 NOTES


Mathematically, the simplest periodic motions are those in which a particle moves at a constant speed around a circle.  If we look at the height of a particle moving that way, we get the simplest periodic motion you can realize on a line.  It is called a sinusoidal oscillation.  (Look up an artistic representation or animation of a sinusoidal wave’s motion to get an idea of it’s relationship to circular geometry.)

If you unfold this motion in time – that is, plot he height as a function of time – you get the sine function.  Sinusoidal waves appear in the description of sound waves associated wit a pure tone and light waves associated with a pure spectral color.

(simplicity and geometric energy efficiency in nature)



pg. 402 NOTES

— review his notes on spinors

— and look up books he recommends, free online — On the Sensations of Ton by Helmholtz and Theory of Sound by Rayleigh


maxwells-equations.com   check it out……………………………………..


https://en.wikipedia.org/wiki/Maxwell%27s_equations    QUOTE parts on infinity and zero


OPAL SCIENCE – The Rainbow Stone

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Are there any perfect circles in nature?  There seem to be circles which come close to perfection.







Is a rainbow a perfect circle?


A rainbow is a perfect circle because the spherical geometry of the raindrops make a circle the most likely constructive interference pattern for the scattered light to show.  Is this true???    or..  simply the angle drives the concentration of the colored waveforms …  or both …


“What we call the rainbow is actually the colored edge of a disc of light,” says Alistair Fraser, coauthor of The Rainbow Bridge: Rainbows in Art, Myth, and Science.

If conceived of in as many dimensions as possible, it may actually be the colored edge of a small field of large spheres of potential viewability.

How many possible angles can a light ray be reflected/refracted when shone into a perfectly spherical transparent surface?

In order to properly conceived of the actual rainbow, one must conceive of an ideal rainbow.  One which could be seen from below, from above, or from any side (one hemispherical projective side still being the brightest)

In reality, this would require an ideally thick and broad field of water vapor, an optimally clear area of the sky for the sun to shine through, and the magical ability to float around like helicopter drone or occupy all viewpoints simultaneously.

I encourage everyone to imagine the ideal rainbow.

There is only one rainbow!  THE RAINBOW!  If anyone told you they saw a different one, they’re lying.

(If the angle of viewing changes, so does the particular relevant section of incident rays, out of the total wall of rays.  The raindrops are always moving and switching out and it doesn’t make any difference.)


What is a rainbow?  Why is it almost always perceived as a perfectly circular curve?

What is the fullest and most accurate description of the physical manifestation of a rainbow? (in it’s natural context arising from water droplets suspended in air) ? Rather than modeling a rainbow from one person’s relative position, consider all possible points of observation.   the fullest reification / physical definition of a rainbow

The rainbow is a property of many things/the total field.  It’s a manifestation of our possible vantage points.  As well as a manifestation of the cloud or water formation, and of the sunlight itself.  It’s a direct bright wavefront hitting complex planes of smoothly curved micro surfaces.  The circularity of the rainbow is conserved from the circularity of the water droplets.  It’s impossible to measure how perfect the circles in nature are.  But they seem pretty smooth.

Do the shape of the sun and the shape of the water both contribute significantly to the shape of the rainbow?

Some people like to assume that the circularity of the rainbow is a result of the circularity of moving photons (?) and the circularity of the image of the sun itself contained in the light beams.

How much of a role does the shape of the sun play in determining the shape of the rainbow?  If the sun were square-shaped, maybe the rainbow would be square with rounded corners, as a combination of the outline of the sun and the round surface of the water.

I wonder, if water droplets were not spherical, what would rainbows look like?  In an alternate universe with cubed rain-drops.. the rainbow would be chaotic, because cube rain-drops are not perfectly symmetrical upon rotation.


A full circle rainbow from below is called a sun dog.


Capturing a full circle rainbow from above is an ideal job for a helicopter drone pilot videographer

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embed heiligenshein as the brightest example of the anti-solar point


A Rainbow is a Natural Phenomenon – Does it tell us anything about nature?


Think back to the last time you thought about rainbows..

Did it tell you more about physics or the mind?

Does rainbow appreciation only have aesthetic value,

Some people think, “a rainbow isn’t really a thing at all, and shame on you for thinking it is.”  Some people like to think they are being physically objective by excluding the observer.  //But in some analytical situations, you have to include every possible observational standpoint//


A rainbow is the same shape as the sun, a drop of water, and your eye.

The largest and most beautiful rainbows are formed by a field of spheres, most often by mist near a rain cloud.  This is the natural occurrence of rainbows, most commonly by weather or waterfalls.

“A rainbow can be seen in other sources of water drops, such as fountains, or even dew drops on grass or spider webs.” – http://optics.kulgun.net/Rainbow/rainbow-faq.shtml

“Artificially” or experimentally created rainbows are not as spectacular.  Glass prisms are created for this purpose.  They are re-creations of a natural phemonenon.  The normal conditions for a rainbow arise from the very complex interaction of fields of elements in the atmosphere.  If you want to study what a rainbow really is, buying a prism isn’t enough.  You must imagine a wall of light coming into contact with a field of spheres, which then constructively refracts and additively amplifies the chaotically scattering field of light in all directions.  To fully capture the physical reality of a rainbow…  you must include all possible viewpoints in your visualization.  In the interest of being thorough / comprehensive… Every possible way that one instance/occurence of a rainbow phenomenon can be perceived, IS what the rainbow truly is, assuming we want the complete description of the rainbow in physical terms.





www.biblicalchristianworldview.net 16

“Because a droplet in sunlight is uniformly illuminated, the impact parameters of the incident rays are uniformly distributed.


The concentration of scattered light is therefore expected to be greatest where the scattering angle varies most slowly with the changes in the impact parameter. In other words, the scattered light is brightest where it gathers together the incident rays from the largest range of impact parameters.”


embed artificially created rainbows


Xingu – Ozric  (this song is funny to listen to when you’re thinking about spherical reflections)

<iframe width=”560″ height=”315″ src=”https://www.youtube.com/embed/egx4Avl_J6o” frameborder=”0″ allowfullscreen></iframe>





Caustic Ray Tracing


Electromagnetic field lines …



Can a rainbow be called a fractal?  The full rainbow being a complete picture of billions of smaller rainbows formed by each singular drop of water in the field of vapor… ?


Can you make a rainbow with one sphere of water?  Newton says yes..

Is is spherical then?  Not with a single beam.

But what if an intense wall of light is allowed to hit the sphere at essentially one angle of approach?

Then would a circular rainbow be able to form from one large singular sphere?

In a hypothetical experiment… If you shoot a photon into a perfect sphere… (or a cylinder)  and assuming it only takes straight paths..  and then is allowed to just keep on bouncing internally to the sphere…

How many unique angles is it possible to bounce at?

The answer seems to be uncountably infinite and unmeasurable.

It is said that light beams enter the raindrop and refract at specific angles.  Most people imagine this only in a simple linear way, because the light source (sun) is shining from one direction, and the rainbow is in one fixed place, and you the viewer imagined to be fixed.

A wall of light, all arriving from the same direction, would hit the field of water drops in a very complex way.

It is not one singular beam of light as in the model/illustrastion typically used to demonstrate the angle.  The model is an simpler idealization which can be generalized to the full field, if you exert your imagination.


The “only perfect angle” for rainbow projection actually happens all around (360 degrees) the inside surface of spherical droplet

The colorfully dispersive refraction actually happens at uncountably many angles (probably) around the full sphere of an idea rain drop, most strongly reflecting individually colored frequencies off the the back interior hemisphere.

First imagine the incoming beam of light as a single linear beam which enters the water drop and reflects back a small broken segment of dispersed color.

-Then imagine the incoming beam as a flat plane of light (approaching the sphere on its edge) instead, entering the drop of water and reflecting back a linear section of dispersed color at the right angles for rainbows (40-42 and 51).  In this scenario, the rainbow is reflected along the whole arc of the back inside surface of a spherical rain drop, in contrast to a singular beam.  I don’t think it’s possible to project a perfect flat plane of light in physical reality, but this is a geometrical thought experiment.

-Then imagine the incoming beam as a flat plane of light which is now approaching and intersecting the sphere on its flat side.  This would be like a wall of light hitting the sphere, but only very thin wall.  This hypothetical configuration would produce the most complex reflections before the real world configuration, which is the most complex.

-Then imagine it as a combination of all these geometric situations. This is the real world.

The light source is large and distant, creating a dense wall of light.  One of the most astonishing things about a rainbow’s form is its perfect simplicity, arising from incalculably complex interactions between three completely different complex fields, one of energy, and one of matter, and one of mind.

Imagine the incoming beam of light as a dense field or wall which enters the spherical water drops (first and most strongly) from one side, hitting half of the sphere directly, then entering the full interior and reflecting off the back surface, to say the least.

-Then imagine that linear arc of dispersed color actually reflecting at every point (multiple times with varying levels of intensity) along the concavely hemispherical circular surface.  The rainbow would be reflected   This is why rainbows can be viewed from several vantage points at once, rather than just one fixed point, distance, height or angle./  The perfect angle for rainbow formation is actually to be found projected from the whole back interior surface of the raindrop.  (Maybe the great circle of the raindrop has something to do with the projection)

The whole rainbow should actually be defined by the totality of all the possible ways of viewing the rainbow.


Some people like to claim that no one ever sees the same rainbow.  This is relatively true.  But on the other hand, it’s bullshit.

(imagine the one actual rainbow to be the physically related phenomenon which would appear to any observer from any relative position)

The good conditions for a rainbow can be considered the whole occurrence, and any phenomena arising from that local area of effect could be considered the same rainbow.

It’s really a matter of semantic description and modeling.

To see the “full rainbow” you would have to occupy every possible viewpoint.


Do the possible reflection paths multiply on a perfectly circular surface compared to a flat surface ???

How much less determistic is its possible motion?

How much more randomness?

How much more chaos?  How much more indeterminacy?  How much more freedom?  (the unmeasurable degree of perfection of naturally occuring spheres?  Are we to assume there no such thing as a perfectly smooth curve actualized in nature)

What higher level of chaos and freedom would the possible reflection paths have if the circular surface were perfectly circular?  It would seem, the flatter the surface is, the more deterministic and determinable(calculable) its resultant path would be.

The idea of a perfect curve has archetypal power for what reason?


How indeterminate or deterministic is the possible path of a photon or any other particle???

Does physics know this ???


The inside of a rainbow is often brighter (whiter) than the space outside the rainbow, which may appear unusually dark.  This could be the result of the collective projection of combined events of total internal reflection.  The brighter the inside of the rainbow, the more fully the individual drops in the field are achieving total internal reflection.


Light resists language’s attempts to describe it fully, because it is very much like the opposite of a simple object with a fixed location.

On the other hand, a drop of water is one nice definition of a simple of object with a somewhat fixed location.  The cloud of water vapor or wall of rain also has a somewhat fixed location for the duration of the viewing of a rainbow.


The field of water drops reveals something about the light, an arguably complete set of it’s possible presentations.

The light reveals something about the water, a projection of its geometry.



Is a rainbow anything like a holographic image?  Or a stereographic projection of a maximally complex reflective situation?  (of one large water droplet, with some level of total internal reflection, surrounded by a wall of dispersed light concentrated into bands of color viewable ‘stereographically’ from any direction as long as the 40-42 reflective angle is still possible)  You can view a rainbow at any angle, theoretically infinite vantage points.



Stereographic projection is:  a one-to-one correspondence between the points on a sphere and the extended complex plane where the north pole on the sphere corresponds to the point at infinity of the plane. 

We have seen that the stereographic projection of any circle of the sphere is itself a circle.

My thoughts… (Concerning rainbows, where is the point at infinity? Is the point at infinity the observer?  Or is the point at infinity the center of the rainbow?)






A great circle is the largest circle that can be drawn on any given sphere.

The great circles are the geodesics of the sphere.

For most pairs of points on the surface of a sphere, there is a unique great circle through the two points. The exception is a pair of antipodal points, for which there are infinitely many great circles. The minor arc of a great circle between two points is the shortest surface-path between them.

Some examples of great circles on the celestial sphere include the celestial horizon, the celestial equator, and the ecliptic. Great circles are also used as rather accurate approximations of geodesics on the Earth‘s surface for air or sea navigation (although it is not a perfect sphere), as well as on spheroidal celestial bodies.

https://en.wikipedia.org/wiki/Circle_of_a_sphere       Small Circle







A coherent wavefront hitting a field of spheres which scatters light in all directions

How many vantage points can a single rainbow be viewed from?


How close to a rainbow can you get?



A rainbow will appear to recede as you approach it, as long as there is still light and water vapor in an effective relative orientation.    ? true ?



What determines the size of a rainbow?


Rainbows are viewable at a particular angle — and within a minimum and maximum distance ?? — from any direction

Bright White Light Source —-> Field of complex reflective surfaces —-> All possible points of observation —> Fullest description of the dispersion of color during a rainbow


A rainbow is a perfect circle because the spherical geometry of the raindrops make a circle the most likely constructive interference pattern for the scattered light to show.  Is this true???    or..  simply the angle drives the concentration of the colored waveforms …  or both …


Rainbow quality –> depends on how perfectly or imperfectly spherical the raindrops are –> how dense the wall of water drops is –> how large or small the water drops are –>


The Double Cone View of Rainbows

In an effort to be total and physically complete in our modeling of what a rainbow is

The rainbow can be conceived physically to be a geometrical cone of colorfully refracted light proceeding from the weather phenomena to the point of your eyes.

(… imagining from above to get the fullest picture …)

The rainbow can also be conceived of as an area of dispersed refraction defined by all possible viewpoints proceeding to converge on the center of the physical field of what is causing the rainbow to form, which is the ideal field of vapor which is necessary to refract the clearest/brightest circularly concentrated dispersion of colored frequencies.

This is an equally realistic conceptualization in terms of the behavior and form of the light.


If light were coming strongly from all directions, you could see a rainbow from all sides.  That would require special reflective situtations which may be rare in nature.  Usually the light is coming strongly from the sun, which is technically from one direction, but it is also very wide and ambient.   (maybe move this statement)

NASA | Anatomy of a Raindrop


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‘Physics of the Air’ – by William Jackson Humphreys


obtain quotes and images   ???



H. M. Nussenzveig, “The Theory of the Rainbow,” Scientific American, vol. 236, no. 4, pp. 116–127, 1977

A caustic surface or “burning curve” in geometric optics is a boundary separating accessible and inaccessible regions for a given family of light rays. The rays within that defined family can “pile up” against the boundary but they never cross it. The boundary, therefore, is an envelope with respect to that family. Caustics are very common in everyday life—for example, the double crescent-shaped cusp of reflected light from a point source at the bottom of a coffee cup or inside a wedding band. Another caustic phenomenon is the rainbow [1], where for a given color the scattering angle from the raindrop assumes a stationary value with respect to the impact parameter or distance that the incident ray makes relative to the center of the raindrop (at a local minimum of about 138 deg for the primary and a local maximum of about 130 deg for the secondary). Since light rays are equally likely to impinge on a raindrop at any impact distance, stationarity of the scattering angle (which occurs for the primary at an impact distance of about 80 percent of the radius of the raindrop) means that the light rays “pile up” at that exit angle. And because their scattering angle and, therefore, their phase at exit from the raindrop are stationary with respect to the impact parameter at this angle, they all are essentially in phase and reinforce each other in the vicinity of this stationary point upon arrival at the observer. This results in the “caustic” phenomenon. Light rays from a raindrop at scattering angles slightly less than the local maximum of the primary rainbow can have impact distances that are slightly higher and lower than the impact distance that provides the stationary scattering angle. Because these higher and lower rays travel through the raindrop along slightly different paths, their travel times to the observer differ, which can result in their arriving at the observer both in and out of phase; both constructive and destructive interference can result. These are the supernumerary bands observed with some rainbows. Supernumerary bands in rainbows are the analog to the amplitude and phase variability that we observe in a radio occultation signal near a caustic.

Supernumerary Rainbow Rings

What Causes Aurora Borealis?




The aurora often appears as curtains of lights, but they can also be arcs or spirals, often following lines of force in Earth’s magnetic field.

Our sun is 93 million miles away.  Great storms are flaring on the sun and sending gusts of charged solar particles across space.  When the Earth is in the path of the particle stream, our planet’s magnetic field and atmosphere react.

When the charged particles from the sun strike atoms and molecules in Earth’s atmosphere, they excite those atoms, causing them to light up.

What does it mean for an atom to be excited? Atoms consist of a central nucleus and a surrounding cloud of electrons encircling the nucleus in an orbit. When charged particles from the sun strike atoms in Earth’s atmosphere, electrons move to higher-energy orbits, further away from the nucleus. Then when an electron moves back to a lower-energy orbit, it releases a particle of light or photon.

The colors in the aurora were also a source of mystery throughout human history.  Science says that different gases in Earth’s atmosphere give off different colors when they are excited. Oxygen gives off the green color of the aurora, for example.  Nitrogen causes blue or red colors.

Most auroras are green in color but sometimes you’ll see a hint of pink, and strong displays might also have red, violet and white colors. The lights typically are seen in the far north – the nations bordering the Arctic Ocean – Canada and Alaska, Scandinavian countries, Iceland, Greenland and Russia.  The lights have a counterpart at Earth’s south polar regions.


study red shift, blue shift, and spectral colors


aurora borealis in mythology..

google it





In this analysis, the light is the thing in itself.  I am that I am.




what is critical opalescence ?? why is the sky really blue

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One thought on “Potential Geometry in Quantum Physics, Vision, and Cosmology”

  1. Here is the 2nd time i had come across your blog in the last few weeks. Appears like I should notice it.

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