This article contains a long list of several dozen quotations on "the infinite sphere whose center is everywhere." Many others have gathered similar lists of this quotation over the centuries; as far as I am aware, this present list is the most extensive available online today.
The several-dozen quotes below range from Jorge Luis Borges to the Tao Te Ching, from Joseph Campbell to Nietzsche, from the ancient Greek Empedocles (possibly the first mention) to a scientist talking about the Big Bang (one of the latest), and many in between. I suspect there are at least as many authors and thinkers again, beyond this present listing, who can be added to the growing compendium. I add a new item below every now and then, as I continue to research from time to time.
I've been following this particular idea for a few years, ever since I had a remarkable experience which could hardly be put into words more concise than the title above: "God is an infinite sphere, the center of which is everywhere, the circumference nowhere." For those who want to get right to the list of quotations, scroll down; but for those who are interested in reading about a brief vision I personally experienced, which describes this idea in more detail, click the little arrow to see more:
Seeking references to this remarkable idea
After that experience, I later came upon a mention of this idea (infinite sphere, nowhere, everywhere, etc.) written by Nicholas of Cusa in the 1400s. My heart leaped: I knew exactly what he was getting at. At that time, I did have a vague memory of reading Borge's Aleph story long before, but honestly did not remember the unique phrase from his story: "center everywhere, circumference nowhere." In other words, the first time I read those words in Borge's story (before my vision), they had little meaning, as though they were poetic, a literary device to convey infinity in words -- as they remain for many who encounter them: Simply good poetry, evoking a sense of boundlessness, greatness, immeasurability, perfection. Then I experienced it in person and later realized that his description was technically accurate, not just poetically.
That moment of recognition when reading Cusa's words led me to wonder where else the idea ocurrred in history, which soon led me to Borges, and only then did I begin to get a sense of its place in the history of ideas. This made me even more curious, and I began gathering references to this idea into a single location, not realizing at first how deeply it penetrated into the lives of so many great thinkers. Several papers I recently discovered on this subject go into how Nicholas of Cusa's use of the idea was particularly revolutionary within the long lineage, and it is his framework (not an earlier one) that we mean today when we think of the "infinite sphere with center everywhere, circumference nowhere" in a manner informed by modern scientific insights.
Now I have a couple dozen references [update: now it is over three dozen, with another dozen 'related' references], and expect I will add to this list for years to come, as I get time.
How refreshing it was to find not only Cusa's remarkable thinking in general, but that of many others shown below, as the list has grown and continues to grow. Most people associate the quote with Pascal, but it was old even when he quoted it. Mystics, mathematicians, philosophers, theologians, rabbis, scholars, well-known seekers, and others more obscure have written on this intriguing idea for many centuries.
In the course of collecting the following list of quotations, I found many smaller fragments discussing the idea, but also several larger PDFs and well-researched articles that explore the concept in detail, including one in German: "UNENDLICHE SPHARE UND ALLMITTELPUNKT: Beiträge Zur Genealogie Der Mathematischen Mystik" by Dietrich Mahnke (which has not been translated yet so I want to run it through DeepL Translate one of these days).
Rather than letting this privately-gathered list collect dust in my personal notes which eventually will make their way into a book, I'm publishing this rough compilation today in hopes that it may be useful to others working on the same idea as well.
While we're here, this is the quote from Borges, which remains one of the more compelling images around this concept, so it makes a good introduction:
On the back part of the step, toward the right, I saw a small iridescent sphere of almost unbearable brilliance. At first I thought it was revolving; then I realised that this movement was an illusion created by the dizzying world it bounded. The Aleph's diameter was probably little more than an inch, but all space was there, actual and undiminished. Each thing (a mirror's face, let us say) was infinite things, since I distinctly saw it from every angle of the universe. I saw the teeming sea; I saw daybreak and nightfall; I saw the multitudes of America; I saw a silvery cobweb in the center of a black pyramid; I saw a splintered labyrinth (it was London); I saw, close up, unending eyes watching themselves in me as in a mirror; I saw all the mirrors on earth and none of them reflected me... (Jorge Luis Borges)
So here is the list:
With no further ado, this is the list, in roughly chronological order:
- "The substance of God is spherical, in no way resembling man. He is all eye and all ear, but does not breathe; he is the totality of mind and thought, and is eternal." -- Diogenes Laertius, talking about what Xenophanes believed in Lives of Eminent Philosophers. Xenophanes lived 570-478 BC. Although Xenophanes is generally believed the first to talk about God as a sphere, the idea may go back even further: "It is said that [Musaeus], the son of Eumolpus, was the first to compose a genealogy of the gods and to construct a sphere, and that he maintained that all things proceed from unity and are resolved again into unity." -- Diogenes Laertius, talking about Musaeus in Lives of Eminent Philosophers. It is unknown when Musaeus lived, maybe 700 BC or older.
- "Empedocles quoque sic Deum diffinire fertur: Deus est sphaera cujus centraum ubique, circumferentia nusquam." ("Empedocles defined God as follows: 'God is a sphere whose center is everywhere, circumference nowhere.'") Vincent de Beauvais, Speculum historiale (ca. 1190-1264). This is the first clear reference to the idea, but it is not yet clear where Beauvais got this quote. I first found reference to this quote in Nietzsche and a Platonist Tradition of the Cosmos: Center Everywhere and Circumference Nowhere by Robin Small. Empedocles lived c. 494-434 BC
- "...a few years after he died, the Sicilian Empedocles of Agrigentum plotted a laborious cosmogony, in one section of which the particles of earth, air, fire, and water compose an endless sphere, 'the round Sphairos, which rejoices in its circular solitude.'" -- Jorge Luis Borges, Pascal's Sphere. Also quoted by Borges, but missing the "infinite" aspect, is Parmenides: "Being is like the mass of a well-rounded sphere, whose force is constant from the center in any direction." -- Parmenides of Elea. Parmenides lived around 515 BC, but only a few fragments of his writings exist, so speculation is heavy with this one. On a related note, Permenides is known to be the oldest reference to the sphericity of the earth.
- "The soul is not a circle in the sense of the geometric figure but in that it at once contains the Primal Nature as centre and is contained by it as circumference [... We] hold through our own centre to the centre of all the centres, just as the centres of the great circles of a sphere coincide with that of the sphere to which all belong." -- Plotinus, 3rd Century
- (The following quote is not a direct quote, but regards examples of the close relationship between Plotinus' ideas and those of Marius Victorinus in the 4th century. Victorinus is believed by some to be the original author of the 'infinite sphere' phrase): "I shall mention only one, the geometrical comparison of centre and sphere of which Plotinus is so fond and which appears at least twice in the Adversus Arium -- applied to the Trinity first in its inner life (i. 6), and then in its relation to the world at large. The point or centre gives birth, as it were, to both line (radius) and sphere. Victorinus insists that we should imagine a tridimensional and ever-moving sphere rather than a flat motionless circumference. The centre (i.e. the Father), having no dimensions, is perfectly still, but dynamically present in each moment and movement of the line and sphere which it generates and which revolve around it (Son and Spirit are magis motus); the centre is thus to some extent the whole sphere. Around this divine reality revolves the cosmos, which is not a perfect sphere but some approximate imitation." -- Henry, P. (1950). The Adversus Arium of Marius Victorinus, The First Systematic Exposition of the Doctrine of the Trinity. The Journal of Theological Studies
- "God is everywhere and nowhere in space." (In this quote, although there is no reference to the sphere, the description contains the essential paradox, and Emerson later attributes the sphere to Augustine as well, although apparently mistakenly.) -- Augustine, Confessions, 354-430 A.D.
- "God is an infinite sphere, the center of which is everywhere, the circumference nowhere." -- Hermes Trismegistus or possibly Aristotle, Book of the 24 Philosophers, 12th Century. Marius Victorinus is believed by some to be the author of this book. Others believe Hermes Trismegistus was an actual historical character who appeared in ancient Egypt and perhaps earlier, and is associated with the Egyptian god Thoth, although his name here is obviously Greek.
- "God is an intelligible sphere, whose center is everywhere, and whose circumference is nowhere." -- Alain of Lille, 12th Century
- "For divinity has the form of a wheel, complete and whole, without beginning or end; and it is circumscribed by neither space nor time, but contains all things within itself." -- Hildegard von Bingen, Liber Divinorum Operum (The Book of Divine Works) Part I, Vision 2: The Cosmic Spheres and Human Being, translated by Nathaniel M. Campbell, 12th Century
- "But it is true without fail that she whose womb swelled understood more than Plato, for she knew from the time that she bore Him and rejoiced in doing so, that He was the wondrous sphere that can have no end, that shoots its center through every place and whose circumference has no fixed place. She knew that He was the wondrous triangle whose unity creates three angles, but whose three angles make only one whole. He is the triangular circle, the circular triangle who harbored in the virgin. Plato did not know as much as that; he did not see that the triple unity in this simple trinity, the sovereign deity clothed in a human skin, is God who is called Creator." -- The Romance of the Rose, Guillaume de Lorris and Jean de Meun, 1230-1275
- "With his whole being God is present whole and entire as much in the least thing as in the greatest. Thus the just person who loves God in all things would seek in vain for something more or greater when he has some little thing in which the God whom he loves alone to the exclusion of everything else is totally present. There is no 'greater' or 'less' in God nor in the One; they are below and outside God and the One. And thus someone who sees, seeks, and loves what is more or less is not as such divine. This is the meaning of the axiom in the Book of Twenty-Four Philosophers: 'God is the infinite intellectual sphere with as many circumferences as centers and whose center is everywhere and circumference nowhere. He is entire in his least part.'" -- Meister Eckhart (1260-1328), Commentary on Exodus n. 91, Chapter t6, verse 18 (LWII 94, a7-95); translated in Meister Eckhart: Teacher and Preacher, ed. and trans. Bernard McGinn with the collaboration of Frank Tobin
- "In its depths I saw internalized, bound with love in one volume, what through the universe becomes unsewn quires: substances and accidents and their modes as it were conflated together, in such away that what I describe is a simple light... In that Light one becomes such that it is impossible ever to consent to turn away from it toward any other sight, because goodness, the object of the will, is all gathered there, and what is perfect there falls short elsewhere... In the profound and clear Subsistence of the deep Light I saw three circles, of three colors and of one circumference, and one seemed refected from the other like a rainbow from a rainbow, and the third seemed fire breathing equally from both." -- Dante, Paradiso, Canto 33, 1300
- "By God's power, presence, and essence, God is the One whose center is everywhere and whose circumference is nowhere. God exists uncircumscribed in everything. God is, therefore, all inclusive. God is the essence of everything. God is most perfect and immense: within all things, but not enclosed; outside all things, but not excluded; above all things, but not aloof; below all things, but not debased. Finally, therefore, this God is all in all…. Consequently, from him, through him and in him, all things exist." -- St. Bonaventure, 13th Century
- "God is an infinite circle whose center is everywhere and whose circumference is nowhere." -- Nicholas of Cusa (1401 – 1464)
- "Thus God is the center of all, because He is so in all things that He is more internal to each thing than it is to itself. He is also the world's circumference because, in existing outside all things, He so transcends all things that His dignity immeasurably excels the highest summit of each thing. Again, He is greatest of all in power to the extent He is least of all in quantity, if this is permissable way of putting it. As He is the center, He is in all, but as the circumference, He is outside all; in all, but not included because He is also the circumference; outside all too but not excluded because He is also the center. So what is God? One might call Him a spiritual circle whose center is everywhere, whose circumference is nowhere." -- Marsilio Ficino, Platonic Theology, XVII, 3. 15th Century
- "Now, my friends, you may depart, and may that intellectual sphere whose centre is everywhere and circumference nowhere, whom we call GOD, keep you in his almighty protection." -- Gargantua and Pantagruel, Francois Rabelais, 16th Century
- "Our soul delighteth to disport itself and is well pleased in that frolic to take a review of its native country, which is the heavens, where it receiveth a most notable participation of its first beginning with an imbuement from its divine source, and in contemplation of that infinite and intellectual sphere, whereof the centre is everywhere, and the circumference in no place of the universal world, to wit, God." -- Gargantua and Pantagruel, by Francois Rabelais, 16th Century
- "We can state with certainty that the universe is all center, or that the center of the universe is everywhere and the circumference nowhere." -- Giordano Bruno, 1584
- "The whole visible world is only an imperceptible atom in the ample bosom of nature. No idea approaches it. We may enlarge our conceptions beyond all imaginable space; we only produce atoms in comparison with the reality of things. It is an infinite sphere, the center of which is everywhere, the circumference nowhere. In short, it is the greatest sensible mark of the almighty power of God that imagination loses itself in that thought." -- Pascal, 1600s
- "We naturally think ourselves much more capable of reaching the center of for the visible expanse of the things than of grasping their circumference, world visibly surpasses us; but since it is we who surpass smaller things, we believe ourselves more capable of possessing them. Yet just as great a capacity is needed for reaching the Nothing as the Everything; it must be infinite for both of them, and it seems to me that anyone who had grasped the final principles of things would also have managed to reach the infinite. The one depends on the other, and the one leads to the other. These extremes meet and reunite with each other just because of their distance apart; they rediscover each other in God and in God alone." -- Pascal, Pensees, 129.
- "What Mr. Pascal says about the double infinity, which surrounds us in the increasingly large and the vanishingly small, when in his Pensées (n.22) he talks about the general knowledge of man, is only an introduction to my system. What wouldn’t he have said with that power of eloquence he possessed if he had gone further, if he had known that all matter is organic throughout, and that, however small a portion one takes, it contains representatively, by virtue of the actual diminution to infinity it contains, the actual increasing to infinity that is in the universe outside it. That is, each small portion contains, in an infinity of ways, a living mirror expressing the whole infinite universe that exists with it, so that a sufficiently great mind, armed with sufficiently penetrating sight, could see here everything which is everywhere." Gottfried Wilhelm Leibniz, c 1696. From a manuscript: Double Infinity in Pascal and Monad [LH 1, 20, Bl. 212r]. Leibniz wrote this in response to the Pensee by Pascal which discusses this idea, so even though it's a little opaque, he's talking about this "infinite sphere" idea and diving deeper into it.
- "O God, thou art an intelligible sphere, whose centre is everywhere, whose circumference is nowhere but in thyself." -- Joseph Hall, sermon, 1600s
- "God is a sphere whose center is everywhere and whose circumference is nowhere." The Blessed and Boundless God, George Swinnock, 1600s
- "Let him ask Truth herself where she is.... She will tell him, that if he climb into heaven she is there, and that if he go down to hell, she is there also. And that if he take the wings of the morning, and remain in the uttermost parts of the sea, even there also he shall meet with her, and can never go out of her sphere, whose center is every where, and whose circumference is no where." -- John Norris, An Essay towards the Theory of the Ideal or Intelligible World, (London, 1701)
- "God is that Sacred Circle of All-Being, of Infiniteness, of Eternity, whose Center is everywhere, in the smallest Point of Things; whose Circumference is no where bounded." -- Peter Sterry, The Appearance of God to man, 1710
- "Properly speaking, a mystery is an obviously absurd dogma which nevertheless conceals within itself a sublime truth . . . for example when Pascal, who was at the same time pietist, mathematician, and philosopher, says in this threefold capacity that God is everywhere center and nowhere periphery." -- Schopenhauer, Parerga and Paralipomena, II, 334 (Sect. 174), 1851
- "The eye is the first circle; the horizon which it forms is the second; and throughout nature this primary figure is repeated without end. It is the highest emblem in the cipher of the world. St. Augustine described the nature of God as a circle whose centre was everywhere, and its circumference nowhere." -- Ralph Waldo Emerson, Circles, 1841
- "You are a wheel whose substance alone exists, the diameter of the circle without circumference creating a plane by its rotation around its median point. The substance of your diameter is a Point." -- Alfred Jarry, 1869
- "God is the tangential point between zero and infinity." –- Alfred Jarry, 1898.
- "O Zarathustra... to those who think as we do, all things themselves are dancing: they come and offer their hands and laugh and flee and come back. Everything goes, everything comes back; eternally rolls the wheel of being. Everything dies, everything blossoms again; eternally runs the year of being. Everything breaks, everything is joined anew; eternally the same house is being built. Everything parts, everything greets every other thing again; eternally the ring of being remains faithful to itself. In every Now, being begins; round every Here rolls the sphere There. The center is everywhere. Bent is the path of eternity." -- Friedrich Nietzsche, Thus Spoke Zarathustra, a Book for All and None (1884)
- "Every center of force has a perspective towards the entire remainder, i.e. its own particular valuation, mode of action, and mode of resistance. The 'apparent world', therefore, is reduced to a specific mode of action on the world, emanating from a center. Now there is no other mode of action whatever; and the 'world' is only a word for the totality of these actions." -- Nietzsche, The Will to Power, 305 (Sect. 567). (Couple this quote with the preceding one by Nietzsche for a more complete idea of what he's saying.)
- "The Library is a sphere whose exact center is any hexagon and whose circumference is unattainable." -- Jorge Luis Borges, 20th Century
- "God is an intelligible sphere -- a sphere known to mind, not to the senses -- whose center is everywhere and whose circumference nowhere." -- Joseph Campbell, Power of Myth, 20th Century
- "'God is an intelligible sphere whose center is everywhere and circumference nowhere.' So we are told in a little twelfth-century book known as The Book of the Twenty-four Philosophers. Each of us -- whoever and wherever he may be -- is then the center, and within him, whether he knows it or not, is that Mind at Large, the laws of which are the laws not only of all minds but of all space as well." -- Joseph Campbell, Myths to Live By (p. 274)
- "The center of the world is the axis mundi, the central point the pole around which all revolves. The central point of the world is the point where stillness and movement are together. Movement is time, but stillness is eternity. Realizing how this moment of your life is actually a moment of eternity, and the experiencing the eternal aspect of what you’re doing in the experiences -- this the mythological experience.” -- Joseph Campbell, Power of Myth, 20th Century. (related to the preceding entry)
- "I had a feeling once about Mathematics, that I saw it all -- Depth beyond depth was revealed to me -- the Byss and the Abyss. I saw, as one might see the transit of Venus -- or even the Lord Mayor's Show, a quantity passing through infinity and changing its sign from plus to minus. I saw exactly how it happened and why the tergiversation was inevitable: and how the one step involved all the others. It was like politics. But it was after dinner and I let it go!" -- Winston Churchill, My Early Life, 1930
- "At the center of the universe dwells the Great Spirit. And that center is really everywhere. It is within each of us." -- Black Elk, 20th Century
- "And while I stood there I saw more than I can tell and understood more than I saw; for I was seeing in a sacred manner the shapes of all things in the spirit, and the shape of all shapes as they must live together like one being. And I saw that the sacred hoop of my people was one of many hoops that made one circle, wide as daylight and as starlight, and in the center grew one mighty flowering tree to shelter all the children of one mother and one father. And I saw that it was holy." -- Black Elk, 20th Century
- "Pascal said that God is a circle, of which the center is everywhere and the circumference nowhere. But how is one to imagine a circle apart from its circumference? The Zohar adopts the antithesis of this paradoxical image and in respect of the circle of Pascal would say rather that the circumference is everywhere, while that which is nowhere is the center." -- Manly P. Hall, The Secret Teachings of all Ages, 20th Century
There are other, related lists:
There is another list growing, where various writers have written similar, or related, ideas:
- "The kingdom of heaven is like to a grain of mustard seed, which a man took, and sowed in his field: Which indeed is the least of all seeds: but when it is grown, it is the greatest among herbs, and becometh a tree, so that the birds of the air come and lodge in the branches thereof." -- Book of Matthew, 1st Century
- "Tao is always nameless. Small as it is in its Primal Simplicity, It is inferior to nothing in the world." -- Tao Te Ching, 6th Century
- "By Me, in My unmanifested form, this entire universe is pervaded. All beings are in Me, but I am not in them. And yet everything that is created does not rest in Me. Behold My mystic opulence! Although I am the maintainer of all living entities and although I am everywhere, I am not a part of this cosmic manifestation, for My Self is the very source of creation." -- Bhagavad-Gîtâ
- "I am smaller than the atom. So also I am greater than the Universal Self." -- Kaivalya Upanishad
- "He is Atman within the heart, smaller than a grain of rice, smaller than a grain of barley, smaller than a mustard seed, smaller than a grain of millet; He is Atman within the heart, greater than the earth, greater than the mid-region, greater than heaven, greater than all these worlds." -- Chândogya Upanishad
- "That which permeates all, which nothing transcends and which, like the universal space around us, fills everything completely from within and without, that Supreme non-dual Brahman — that thou art." -- Sankaracharya
- "That in whom reside all beings and who resides in all beings, who is the giver of grace to all, the Supreme Soul of the universe, the limitless being — I am that." -- Amritbindu Upanishad
- "Allah, in the same way as he is 'the First one and the Last one' (El-Awwal wa El-Akher), is also 'the Outside and the Inside' (El-Zâher wa El-Bâten), because nothing that exists can be outside of Him, and in Him only is contained all reality, because He is Himself the absolute Reality, the total Truth: Hoa El-Haqq." -- René Guénon, 20th Century
Believe it or not, empirical science looks at this idea
It looks like there is another category of these kind of quotations, one that is embedded in skeptical, empirical science, rather than arising from faith, religion, spirituality, mysticism, or personal narrative. We begin with a unique entry, about which I've written elsewhere. It's clearly describing the infinite sphere whose circumference is nowhere, but it goes into great detail from a scientific perspective. It also talks about the several dimensions between our normal frame and this "absolute" frame, and even suggests how the absolute frame may be accessed, perhaps through some form of meditation. Because of its great detail on the nature of the infinite sphere in a scientific frame, which is talking about how the infinite sphere permeates everywhere simultaneously as a condition of perfect "rest", it's worth presenting in all of that detail.
The second item, from Brian Murarescu, is the first one to give a clear, experential reference to the infinite sphere which is everywhere and nowhere. It is this simple, accessible, description which makes the other references more real, rather than being just a philosophical or mathematical idea. This reference was one of a few hundred similar experiences well-documented during a study by Johns Hopkins. Johns Hopkins scientists are bringing, in their words, "high standards of scholarly competence" to the unambiguous point that some mind-altering substances in a single experience can cause a profoundly positive transformation in the lives of the person with the experience, with no negative side effects. And further, people with such an experience will remember it years later as one of the most meaningful moments of their entire lives, consistently because it has brought them into awareness with the oneness of everything. Thus there are hundreds of clinically-studied references to this idea of an infinite oneness that is everywhere. It is a strange combination; science and mind-altering substances bringing empirical reproducibility to the study of interacting with the oneness that is everywhere. Note that Murarescu intentionally never used any mind-altering substances himself, because he wanted to remain objective in his research. Also, note the reference to "dissolution of the self," quite similar to what I described above, which appears in the 2nd item. The sixth and seventh items below are perhaps the most remarkable within the scientific context because these are from cosmologists and physicists talking about how difficult it is to describe things like the Big Bang and subatomic quanta of energy. Yet, what they say overlaps what all these mystics have been saying for centuries, speaking with familiar paradoxical phrases like "there is no center or edge to the explosion."
- "Physicists define time as a measurement of energy or force in motion. In other words, it is a measurement of change. However, in order for energy to be in motion it must first be limited in some way within the confines of some sort of vibratory pattern so that its confinement gives it the capacity for being contained at a specific location which is distinguishable from other locations (space). Energy which is not confined is force without limit, without dimension, without the limits of form. It is infinity, cannot move because there is nothing beyond infinity, and is therefore outside of the dimension of time. It is also beyond space because that concept implies that a specific energy form is limited to a specific location, and is absent from other locations. But if energy is in the state of infinity, there are no boundaries, no 'here' to differentiate from 'there', no sense of area. Energy in infinity means energy uniformly extended without limit. It has no beginning, no end, no location. It is conscious force, the fundamental, primal power of existence without form, a state of infinite being. Energy in infinity is said to be completely at rest and, therefore, cannot generate holograms so long as it remains utterly inactive. It retains its inherent capacity for consciousness in that it can receive and passively perceive holograms generated by energy in motion out in the various dimensions which make up the created universe but it cannot be perceived by consciousness operating in the active universe. Energy in this state of inactive infinity is termed by physicists as energy in its absolute state, or simply 'the Absolute.' Between the Absolute and the 'material' universe in which we experience our physical existence are various intervening dimensions to which human consciousness in altered states of being may gain access. Theoretically, human consciousness may continue to expand the horizons of its perceptual capability until it reaches the dimension of the Absolute at which point perception stops because the Absolute generates no holograms of or about itself. Since the Absolute is conscious energy in infinity (i.e. without boundaries), it occupies every dimension to include the time-space dimension in which we have our physical existence but we cannot perceive it. It overlays everything as do many of the intervening gradients or dimensions through which the energies of the universe pass on their way to and from their home in the state of infinity (the Absolute). To enter these intervening dimensions, human consciousness must focus with such intense coherence that the frequency of the energy pattern which comprises that consciousness (i.e. the brainwave output) can accelerate to the point where the resulting frequency pattern, if displayed on an oscilloscope, would look virtually like a solid line. Achievement of this state of altered consciousness sets the stage for perception of non-time-space dimensions because of the operation of a principle in physics known as Planck’s Distance. This is an aspect of quantum mechanics which applies to the fact that any oscillating frequency (such as a brainwave) reaches two points of complete rest which constitute the boundaries of each individual oscillation (i.e. movement up or down). Without these points of rest, an oscillating wave pattern would be impossible since the points of rest are required to permit the energy to change direction and thus continue vibrating between rigid limits. But it is also true that when, for an infinitesimally brief instant, that energy reaches one of its two points of rest it 'clicks out' of time-space and joins infinity..." -- Wayne M. McDonnell, Analysis and Assessment of Gateway Process, US Army Intelligence and Security Command, June 9, 1983. Also available in the CIA library, because of its previous top-security classification. (emphasis added)
- "Dinah is keen that I not misquote her by writing something as sentimental and clichéd as 'being at one with the universe.' So she describes a process in which there was a 'dissolution of the self' and a 'melting away of barriers.' She remembers the moment when concepts like 'internal' and 'external' no longer held true. 'I'm not just standing there, looking out at the world anymore. I'm part of the world.' After a lengthy pause while she harvests the right phrase, Dinah refers to this fleeting moment as 'a state of pure being.' She recalls taking several deep breaths, exhaling with force, just to hear the air escape her chest. She needed to prove that her physical body was still there, that it still existed somewhere in time and space. The source of her awareness, once so easy to locate, was suddenly everywhere and nowhere at once. And then it all made sense. In that unsettling, parallel reality [...] Dinah arrived at the realization that 'birth and death actually don't have any meaning.' When forced to clarify, she adds, 'It's more of a state of always being.' 'Always being?' 'Always being. So being now and always. There's no beginning or end. Every moment is an eternity of its own.'" -- Brian Murarescu, The Immortality Key, the Secret History of the Religion with No Name (emphasis added)
- "Infinity is a mirrored extension from one imagined point in the universe to every other imagined point, and back again to that same point from every other imagined point. Infinity is zero simultaneously multiplied and divided by zero, forever and forever." -- Walter Russell, Mirrors and Lens of Cosmic Cinema, 20th Century
- "When God thinks at any one point of rest in His universe, that point becomes the center of an invisible cube of White Magnetic Light. From there it is harmonically repeated as cube centers throughout His Cosmic Kaleidoscope, at the rate of several hundred billions of cyclic pulsations every second. Their speed of extension into this three dimensional illusion is about 186,400 miles per second." -- Walter Russell, Atomic Suicide, 20th Century
- "...there exists for the first time in thought, not 'a single sphere which expands in size without limit', but an infinite number of infinitely transparent absolute actualities: the sphere of absolute objectivity now existing: the sphere of spheres infinitely newly beginning, the sphere of infinitely new, infinitely separate spheres: the sphere the surface of which is the beginning of an absolutely transparent depth. This is the inception of the infinite proportionality of the body. This is the limit of the infinite expansion of the 'single sphere'. This is the beginning of the circumference of the infinite circle. This is the line for the first time. This is the time of beginning. This is creation displacing the abyss itself: the body of the Living God in the form of the beginning, depth absolutely surface, the infinite identical with the finite: the absolute incompatibility of the infinitely numbered points of the circumference of the circle: the absolutely transparent circle." D.G. Leahy, Foundation: Matter the Body Itself, 20th Century
- "One key point is that the Big Bang was not an explosion of the kind any person has ever witnessed. 'This is a hard concept for people to get their heads around,' says Wendy Freedman, a veteran cosmologist at the University of Chicago. 'The first thing to get rid of is an image analogous to a bomb — which is our first tendency to imagine, and which is wrong — where you have an explosion with matter that flies outward from a center. This is not what happens in space. The Big Bang is an explosion of space, and not into space. There is no center or edge to the explosion.' There was no place outside of the Big Bang, so it was not expanding into anything. Rather, all of space began expanding, everywhere. That is why galaxies appear to be moving away from us in every direction. Any observer, anywhere, would see the same thing. I sometimes think of the Big Bang as a metaphor for human psychology. In a sense, you can think of yourself as the center of the universe, since that’s how it looks to all observers. But in a deeper sense, nobody is at the center, since the expansion is everywhere and all of us are in the same situation." -- Corey S. Powell, Could the Big Bang Be Wrong? Discover Magazine, Jun 15, 2019 (emphasis added)
- "Most fundamental matter particles, such as electrons, muons and quarks, get their mass from their resistance to a field that permeates the universe called the Higgs field. The more the Higgs field pulls on a particle, the more mass it has. When it comes to composite particles like protons and neutrons, which are made up of quarks, most of their mass comes from the pull of the strong force that holds the quarks together. Photons and gluons, two force-carrying particles, are fundamental, so they don’t host the internal tug-of-war of a composite particle. They are also unaffected by the Higgs field. Indeed, they seem to be without mass. Massless particles are purely energy. 'It’s sufficient for a particle to have energy to have a meaningful sense of existence,' says Flip Tanedo, assistant professor of physics at the University of California, Riverside. These quanta of energy don’t have edges, and they don't have surfaces, says Tien-Tien Yu, an assistant professor of physics at the University of Oregon. A better way to think of particles is as ripples on a quantum field, says Natalia Toro, a theorist at the US Department of Energy’s SLAC National Accelerator Laboratory and an associate professor in Stanford University’s theoretical particle physics department. A quantum field has vibration modes like the harmonics on a guitar string. Pluck it with the right frequency and you get a particle. The two particles physicists know to be (at least approximately) massless—photons and gluons—are both force-carrying particles, also known as gauge bosons. Photons are associated with the electromagnetic force, and gluons are associated with the strong force. (The graviton, a gauge boson associated with gravity, is also expected be massless, but its existence hasn’t been confirmed yet.) These massless particles have some unique properties. They are completely stable, so unlike some particles, they do not lose their energy decaying into pairs of less massive particles. Because all their energy is kinetic, they always travel at the speed of light. And thanks to special relativity, 'things traveling at the speed of light don't actually age,' Tanedo says. 'So a photon is actually not aging relative to us. It’s timeless, in that sense.'" July 23, 2019, Symmetry Magazine, by Madeleine O'Keefe. (emphasis added)
Further notes (which I also update over time, so pardon the patchwork of past/present/future references):
A related discovery is an article from 2016 which contains an excellent timeline of many of these quotes and their authors, in a discussion of Marshal McLuhan's idea of acoustic space. This is also an infinite sphere. McLuhan was once asked what he meant by acoustic space. He responded, "I mean space that has no center and no margin, unlike strictly linear space, which is an extension and intensification of the eye. Acoustic space is organic and integral, perceived through the simultaneous interplay of all the senses; whereas 'rational' or pictorial space is uniform, sequential and continuous and creates a closed world." (Playboy, 1969).
McLuhan also talked about the ancient meaning of acoustic space: "Until writing was invented, man lived in acoustic space: boundless, directionless, horizonless, in the dark of the mind, in the world of emotion, by primordial intuition, terror." (McLuhan and Fiore 1967). Years later, McLuhan added more detail: "Acoustic Space has the basic character of a sphere whose focus or center is simultaneously everywhere and whose margin is nowhere... Acoustic space is dynamic; it has no fixed boundaries. It is space created by the method or process itself. In contrast, visual space is static and container-like, with a fixed center and margin." (McLuhan and Powers, 1989). All of this detail is very useful to the larger discussion of what is meant by the key metaphor of "infinite sphere with no circumference." Along those lines, the authors of this paper conclude with a striking point that brings our central metaphor from its ancient past right into today: "As a result, we will never know what motivated the connection he made between the nature of acoustic space and a 12th Century medieval definition of God that seems to work as a description of 21st Century cyberspace." Similarly, a paper on Nietzsche's ideas regarding this metaphor (Nietzsche and a Platonist Tradition of the Cosmos: Center Everywhere and Circumference Nowhere) is very insightful for the larger discussion of meaning.
I came back to this growing compendium after re-reading Jorge Borges The Aleph after twenty years. Even though the closing quote from his book was already included in the list, I made edits to highlight his narrative. Wow, his is an impressive description of something hard to describe!
I also have a brief narrative I've written which approaches that same Aleph from a different angle (from outer space, instead of from a dark basement). I have now included the brief sketch in the sidebar box above.
Borges has a brief essay on the history of this idea, called Pascal's Sphere.
There are a few new names (italicized below) on this list from someone else's similar blog post, which I will research as time permits (italicized items are ones for which I have no quote yet: Empedocles, St. Augustine, Marius Victorinus, Alain de Lille, Hermes Trismegistus, Meister Eckhart, Thomas Bradwardine, Nicholas of Cusa, Giordano Bruno, Baruch Spinoza, Voltaire, Gilles Deleuze, Jorge Luis Borges, Blaise Pascal.
Also finally found a PDF of Mahnke's book mentioned above, but it was not scanned well so will not be a simple thing to translate from German into English. One of these days...
This article received numerous comments over years, but in my transition from WordPress to OctoberCMS, I lost all the comments. My apologies to those whose comments, some of them containing items listed above, were here.
Finally found a Leibniz reference, which I added above, along with one from Hildegard von Bingen, and another reference from science, bringing the total to almost 40 now. It's fascinating going through this article from time to time, because my knowledge of this idea grows deeper over time. For example, I updated the reference above to Hermes Trismigestus and his link to Thoth, because I've learned more about both characters since I first started collecting these quotes years ago.