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Tag: Infinity

On the Ineffable


This 18th century depiction of Yamantaka, a violent expression of the Bodhisattva Manjushri, defeats Yama, god of death, and demolishes the cycle of samsara on the path to enlightenment. This painting, in the collection of the Metropolitan Museum of Art, was purchased in 1969 courtesy of a bequest by Florence Waterbury. Its Accession Number is 69.71. This is a faithful photographic reproduction of a two-dimensional public domain work of art. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years.

This is my review of Nick Stockton’s “Time Might Only Exist in Your Head. And Everyone Else’s.” From Wired, 26 September, 2016. Published at 0600 hrs. I later modified this piece on 17 October, 2016. It keeps bothering me like a splinter in my mind. In its current revision, it comprises 2,537 words.

“Some physicists blame gravity for time. Others blame observers. Time, the arrow of time, the linearity of time flowing from the infinite past through the present into the indefinite future, cannot exist unless an intelligence, something sentient, exists to observe it, they say.

The moment when particle physics and classical mechanics merge is called “decoherence,” and it also happens to be the moment when time’s direction becomes mathematically important.

Mr. Stockton’s article points out that superposition in quantum mechanics means that an electron can exist in either of two places, a property called probability, but it is impossible to say where an electron is until that electron is actually observed.

Some physicists also say that what matters is not whether time exists, but what direction that time flows. (Claus Kiefer, “Can the Arrow of Time Be Understood From Quantum Cosmology?” in L. Mersini-Houghton and R. Vaas, The Arrow of Time, Springer, Berlin, 2010.)

I marvel that anything can move at all, as any distance can incorporate an infinitude simply by holding your fingers a centimeter apart.

Your fingertips are not necessary, of course. You can imagine an infinite digression between any two points. You can even imagine the digression without the points, which is where things get interesting for me.

Not surprisingly, this reminds me of Jorge Luis Borges (1899-1986), in the academic tradition of droll footnotes, citing “the last magician,” Isaac Newton, saying that “Each particle of space is eternal, each indivisible moment of duration is everywhere.” Principia, III, 42. (Isaac Newton, Newton’s Principia, New York: Daniel Adee, 1846. Borges wrote his 1946 revision of “A New Refutation of Time” in Sur, 1944. Jorge Luis Borges, Selected Non-Fictions, Penguin, 1999.)

How anything can leap across the infinitudes separating all things from everything else mystifies me, and how we can imagine infinity without beginning or without end leaves me without words.

Miraculously, everything in this multiverse can leap infinities, and so we have progression, which is synonymous with time. Even using a term like “infinity” forces a compromise upon us, it is a convention, and these are the paradoxes that compel some physicists to suspect that time emerges from decoherence.

Mr. Stockton’s article explains that the most prominent theory addressing decoherence is the 1960’s-era Wheeler-DeWitt equation, by Dr. Bryce DeWitt and Dr. John Archibald Wheeler. Dr. Wheeler claimed that this equation “erases the seams between quantum and classical mechanics.”

Then Mr. Stockton acknowledges the weirdness underlying decoherence and “so-called quantum gravity.” I love the fact that physicists use a term like “weird” and nobody thinks that it is strange. Because these matters are supremely weird.

The second law of thermodynamics ordains that the amount of disorder, or entropy, in our multiverse will always increase. In 1865 Rudolf Clausius (1822-1888) infamously observed: “The energy of the universe is constant; the entropy of the universe tends to a maximum.” This is the source of the directionality of time: disorder always increases, so time can only move in one direction.

The Wheeler-DeWitt equation notoriously does not include a variable for time. Time, it says, is something that cannot be measured in terms of itself: in physics it is measured as correlations between an object’s location.

In this article, however, the writers (Dr. Robert Lanza and Dr. Yasunori Nomura) insist that gravity is too slow to account for a universal arrow of time.

Worse, because the Wheeler-DeWitt equations do not explain why time moves from the past through the present to the future–in other words, the directionality of time is not explained by the Wheeler-DeWitt equations–all that remains to be examined is us, meaning we, the observers.

One of the writers, Dr. Robert Lanza, founded biocentrism, a theory that space and time are constructs of biological sensory limitations.

Dr. Lanza speculates that time moves as it does because humans, and other sentient beings, for that matter, are biologically, neurologically and philosophically hardwired to experience time in that way.

In fact, Dr. Lanza says, “In his papers on relativity, Einstein showed that time was relative to the observer.”

I do not see how it could be otherwise. While you can claim that mathematics exists independently of human perception, because equations do not depend upon witnesses to observe them, we obviously only know about mathematics because we perceive such equations.

I will go one step further and say that equations, all the equations in an infinitude of mathematics, already exist, and merely await a conjunction of time and sentience to be discovered. But they are already there. We are just not yet smart enough to discern them.

Tibetan Buddhism, in fact, features a category of knowledge of this kind, calling it terma. It refers to objects or ideas which are surfaced to human knowledge when we as a species are ready for them. Some believe that we knew this information in earlier incarnations, and we forgot it, as we submerged into ignorance and amnesia. Now we are gradually, slowly, reawakening.

Dr. Lanza, this article says, goes even further, saying that we the observers create time and its directionality. This is actually a very old idea, and I discuss it in an article that I published on this site almost a year ago, Smoke Signals: Borges, Tzahi Weiss, Kabbalah.

Is it possible to say that there is an independent time, a time that exists without anyone or anything to perceive it? I suppose so. Is there also a time that exists because we perceive it? I think that this is inescapable.

Borges says:

” … Denying temporal succession, denying the self, denying the astronomical universe, are apparent desperations and secret consolations.

Our destiny (as contrasted with the hell of Swedenborg and the hell of Tibetan mythology) is not frightful by being unreal; it is frightful because it is irreversible and ironclad.

Time is the substance I am made of. Time is a river which sweeps me along, but I am the river; it is a tiger which destroys me, but I am the tiger; it is a fire which consumes me, but I am the fire.”

(Jorge Luis BorgesSelected Non-Fictions, 1999, p. 290.)

The time that you experience is not the same time that I experience. Neither of us experiences time as Borges did. Can “the concept of time be defined mathematically without including observers in the system?”

One stance says no, as there is no way to subtract observers from the equations, as equations by default, almost by definition, you could say, are performed by sentient intelligences.

Dr. Yasunori Nomura states that these equations also fail to consider that the entire multiverse as we perceive it exists in a medium that we call spacetime.

By definition, when you talk about spacetime, he says, “you are already talking about a decohered system.”

This article concludes, like most interpretations of spacetime, that everything is relative, everything is subjective.

We are in self-defined prisons of perception, but we imagine paradises where we share the same perceptions, the same spacetime, and we perceive the same physics. The sad thing is, this is maya, or illusion. Some of us know better, and we have been told.

We do not need these physics, not for awakening from the stupor of the mind to anatta, the emptiness of the self, the realization of the non-duality of the absolute and the relative.

Think on this for a moment. The absolute and the relative form a duality that is artificial, this is a construct that we create to help us understand what we perceive. It is, in a sense, a filter. We need no such filters.

Borges, in the quote above, in a denial of denial, refused to renounce temporal succession, rejected the renunciation of the self, repudiated the rejection of the astronomical universe, and dismissed the effort as an “apparent desperation,” slyly condemning it as a “secret consolation.”

It was long a secret, as Tibet was closed to mankind for centuries, but Borges understood what he was rejecting. Borges referred to “the hell of Tibetan mythology” for precisely this reason, and that is why I illustrated this article with a painting depicting Yamantaka, just one aspect of the Bodhisattva Manjushri, vanquishing Yama, the god of death. Borges was telling those of us with eyes to see that he was an idealist, not a nihilist. Borges concluded that we manifest everything.

It is useful, I think, to consider Borges’ reference to fire by juxtapositioning it to this excerpt from the Buddha’s Fire Sermon:

Bikkhus, form is burning, feeling is burning, perception is burning, volitional formations are burning, consciousness is burning. Seeing this, bikkhus, the instructed noble disciple experiences revulsion towards form … feeling … perception …. volitional formations … consciousness …Through dispassion [this mind] is liberated…”

Adittapariyaya Sutta, or the Aditta Sutta, aka The Fire Sermon

In Theravada Buddhism, anatta is considered the no-self or no-soul doctrine. In Mahayana Buddhism, true knowledge is comprehending emptiness.

It is not understood by laymen, much less by our physicists in this article, but Buddhism is inimical to the concept of a soul. Nirvana is the state attained when the practitioner realizes that he has no self, and he has no soul. Self-negation attains its ultimate realization as it vanishes.

In Sanskrit and Pali, nirvana means “blown out,” in the same sense that a candle flame is snuffed. I am certain that Borges knew. Borges knew everything, he read all books, and he made few mistakes.

These ideas contradict the Western philosophical tradition, our mathematics, our physics, our spacetime, even though Hinduism insists that there is an eternal atman, and an ultimate metaphysical reality. Contradictions and confusions abound.

In the Brihadaranyaka Upanishad 1.4.1, the atman is expressed as “I am” at an eternal moment when nothing existed at the beginning of the multiverse. Because we built the Hubble telescope, we estimate that this eternal moment transformed into the Big Bang and this multiverse approximately 13.7 billion years ago.

Using Hubble, we can measure the speed and distances of galaxies, and hence how fast our multiverse is expanding. Comparing these measurements to the age of the oldest globular star clusters gives us a figure of 13 billion years, which compares favorably to the 14 billion years of our observable multiverse.

Due to the speed of light, Hubble cannot see further than 14 billion years away. When the James W. Webb telescope comes online, we expect to confirm that our observable multiverse represents a tenth of the theoretical galaxies on the near side of our cosmological horizon.

But when you consider that the Big Bang might have been just the latest in an infinite series of singularities, interspersed by an unknowable number of periods of quantum potential, the possibility that the multiverse is infinite, literally without end, looms.

So is consciousness 14 billion years old? The Brihadaranyaka Upanishad is one of the oldest, dated to approximately 700 BCE, but this is a compromise, as scholarly estimates range between 900 BCE to 600 BCE, preceding Buddhism.

Human consciousness is very young, even assuming that the priests of Neith who admonished Solon in the Timaeus were correct, the Timaeus is dated to 360 BCE, and I am mindful that when the Temple of Neith in Sais was excavated no records of ancient conflagrations or deluges were recovered. But how old is cosmic consciousness? It is absurd that we even imagine the question.

When the atman awakes, the Hindu say, it is synonymous with Brahman, the basis of everything, indistinguishable in my mind from God, and this is the path to liberation, or so they say.

It is helpful to cite this Upanishad’s verse 1.4.1 in its entirety, as it redolently presages Genesis.

“In the beginning, this (universe) was but the self (Virāj) of a human form. He reflected and found nothing else but himself. He first uttered, ‘I am he.’ Therefore he was called Aham (I). Hence, to this day, when a person is addressed, he first says, ‘It is I,’ and then says the other name that he may have. Because he was first and before this whole (band of aspirants) burnt all evils, therefore he is called Puruṣa. He who knows thus indeed burns one who wants to be (Virāj) before him.”

(Brihadaranyaka Upanishad 1.4.1.)

As perplexed as I am by yet another reference to fire, the Buddhist Suttas, or Sutras, as I prefer, insist that everything, especially nirvana, is non-self, total non-attachment. The Suttas in Pali refer exclusively to the scriptures of the early Pali Canon, the canonical works of Theravada Buddhism, which are said to be the oral teachings of the Buddha.

The Buddha himself admonished the Sangha not to deify his person, so I prefer the Sutras, the less exclusive, more encompassing genre of ancient Indian texts, which include the foundational works of Hinduism, Buddhism and Jainism.

The Buddha started the Wheel of Karma turning as he preached his first sermon at  the Deer Park in Sarnath near Benares, early in the 5th century BCE. It was in his second sermon that he expounded on the no-soul thesis, anatta-vada, which some Western academics criticize as “an extreme empiricist doctrine.” (Brian Morris, Religion and Anthropology: A Critical Introduction (London: Cambridge University Press, 2006, p. 51.)

Anatta is one of the three characteristics of existence in Buddhism, with anicca, or impermanence, and dukkha, or suffering. The three comprise the samsara cycle of existence, addressed in canonical Buddhist texts like the Dhammapada.

The Four Noble Truths insist that there is a way out of samsara. I interpret spacetime as samsara, yet another filter created by subjective consciousness, to help us make sense of our multiverse.

In anatta, the mind returns to its original prelinguistic emptiness of non-attachment, non-discrimination, and non-duality, and the awakening, as it is described, entails the absorption of cessation: it is tantamount to the dissolution of the self.

This “pure consciousness event” is wakeful, without content, and completely non-intentional. It goes without saying that our spacetime and our cosmological horizon are irrelevant to it: It is ineffable. (Yaroslav Komarkovski, Tibetan Buddhism and Mystical Experience, (London: Oxford University Press, 1995, p. 28.)

As Borges said, we are indistinguishable from spacetime. We do not need eyes to see, so death, transformation, is dissolution into nothingness, which many religious traditions summarize as the godhead.

Ironically, it was William James who said:

“The subject of it immediately says that it defies expression, that no adequate report of its contents can be given in words.”

(William James, The Varieties of Religious Experience: A Study in Human Nature (New York: Penguin, 1982.)”

Estéban Trujillo de Gutiérrez, “On the Ineffable”

Bangkok, 17 October, 2016

Eco: Infinite Songs & Locutions, 2


Ramon Llull (1232-1315), La Tercera Figura, from Ars brevis, Pisa, 1308. This illustration is hosted on the net by the Centre de Documentacio de Ramon Llull, while the original is held in the Escorial, MS.f-IV-12, folio 6. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

Mersenne and Guldin were anticipating Borge’s Babel Library ad abundantiam. Not only this, Guldin observed that if the numbers are these, who can marvel at the existence of so many different natural languages?

The art was now providing an excuse for the confusio linguarum. It justifies it, however, by showing that it is impossible to limit the omnipotence of God.

Are there more names than things? How many names, asks Mersenne (Harmonie, II, 72), would we need if were to give more than one to each individual? If Adam really did give names to everything, how long would he have had to spend in Eden?

In the end, human languages limit themselves to the naming of general ideas and of species; to name an individual thing, an indication with a finger is usually sufficient (p. 74).

If this were not so, it might easily “happen that for every hair on the body of an animal and for each hair on the head of a man we might require a particular name that would distinguish it from all others. Thus a man with 100,000 hairs on his head and 100,000 more on his body would need to know 200,000 separate words to name them all” (pp. 72-3).

In order to name every individual thing in the world one should thus create an artificial language capable of generating the requisite number of locutions. If God were to augment the number of individual things unto infinity, to name them all it would be enough to devise an alphabet with a greater number of letters, and this would provide us with the means to name them all (p. 73).

From these giddy heights there dawns a consciousness of the possibility of the infinite perfectibility of knowledge. Man, the new Adam, possesses the possibility of naming all those things which his ancestor had lacked the time to baptize.

Yet such an artificial language would place human beings in competition with God, who has the privilege of knowing all things in their particularity. We shall see that Leibniz was later to sanction the impossibility of such a language.

Mersenne had led a battle against the kabbala and occultism only to be seduced in the end. Here he is cranking away at Lullian wheels, seemingly unaware of the difference between the real omnipotence of God and the potential omnipotence of a human combinatory language.

Besides, in his Quaestiones super Genesim (cols 49 and 52) he claimed that the presence of the sense of infinity in human beings was itself a proof of the existence of God.

This capacity to conceive of a quasi-infinite series of combinations depends on the fact that Mersenne, Guldin, Clavius and others (see, for example, Comenius, Linguarum methodus novissima (1648: III, 19), unlike Lull, were no longer calculating upon concepts but rather upon simple alphabetic sequences, pure elements of expression with no inherent meaning, controlled by no orthodoxy other than the limits of mathematics itself.

Without realizing it, these authors are verging towards the idea of a “blind thought,” a notion that we shall see Leibniz proposing with a greater critical awareness.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 141-3.

Eco: Bruno: Ars Combinatoria & Infinite Worlds, 2


Ettore Ferrari (1845-1929), Giordano Bruno Burned at the Stake, a bas relief on the plinth of the monument to Bruno in Campo de’Fiori square in Rome. This photo by Giovanni Dall’Orto © 2008. The copyright holder of this photo allows anyone to use for any purpose, provided that the copyright holder is properly attributed. Redistribution, derivative work, commercial use, and all other use is permitted.  


“Thus this language claimed to be so perfect as to furnish the keys to express relations between things, not only of this world, but of any of the other infinite worlds in their mutual concordance and opposition.

Nevertheless, in its semiotic structure, it was little more than an immense lexicon, conveying vague meanings, with a very simplified syntax. It was a language that could be deciphered only by short-circuiting it, and whose decipherment was the privilege only of the exegete able to dominate all its connections, thanks to the furor of Bruno’s truly heroic style.

In any case, even if his techniques were not so different from those of other authors of arts of memory, Bruno (like Lull, Nicholas of Cusa and Postel, and like the reformist mystics of the seventeenth century–at whose dawn he was to be burnt at the stake) was inspired by a grand utopian vision.

His flaming hieroglyphical rhetoric aimed at producing, through an enlargement of human knowledge, a reform, a renovation, maybe a revolution in the consciousness, customs, and even the political order of Europe. Of this ideal, Bruno was the agent and propagandist, in his wandering from court to European court.

Here, however, our interest in Bruno is limited to seeing how he developed Lullian techniques. Certainly, his own metaphysics of infinite worlds pushed him to emphasize the formal and architectonic aspects of Lull’s endeavor.

One of his mnemonic treatises, De lampade combinatoria lulliana ad infinita propositiones et media inveniendi (1586), opens by mentioning the limitless number of propositions that the Ars is capable of generating, and then says: “The properties of the terms themselves are of scant importance; it is only important that they show an order, a texture, an architecture.” (I, ix).

In the De umbris idearum (1582) Bruno described a set of movable, concentric wheels subdivided into 150 sectors. Each wheel contained 30 letters, made up of the 23 letters of the Latin alphabet, plus 7 letters from the Greek and Hebrew alphabets to which no letter corresponded in Latin (while, for instance, A could also stand for Alpha and Alef).

To each of the single letters there corresponded a specific image, representing for each respective wheel a different series of figures, activities, situations, etc. When the wheels were rotated against each other in the manner of a combination lock, sequences of letters were produced which served to generate complex images. We can see this in Bruno’s own example (De umbris, 163):

Giordano Bruno, De umbris, 163

Reproduced from Umberto Eco, The Search for the Perfect Language, James Fentress, trans., Blackwell: Oxford, 1995, p. 136, from Giordano Bruno, De umbris idearum, 1582, p. 163. 

In what Bruno called the “Prima Praxis,” the second wheel was rotated so as to obtain a combination such as CA (“Apollo in a banquet”). Turning the third wheel, he might obtain CAA (“Apollo enchained in a banquet”). We shall see in a moment why Bruno did not think it necessary to add fourth and fifth wheels as he would do for the “Secunda Praxis,” where they would represent, respectively, adstantia and circumstantias.

In his “Secunda Praxis,” by adding the five vowels to each of the 30 letters of his alphabet, Bruno describes 5 concentric wheels, each having 150 alphabetical pairs, like AA, AE, AI, AO, AU, BA, BE, BO, and so on through the entire alphabet.

These 150 pairs are repeated on each of the 5 wheels. As in the “Prima Praxis,” the significance changes with every wheel. On the first wheel, the initial letter signifies a human agent, on the second, an action, on the third, an insignia, on the fourth, a bystander, on the fifth, a set of circumstances.

By moving the wheels it is possible to obtain images such as “a woman riding on a bull, combing her hair while holding a mirror in her left hand, accompanied by an adolescent carrying a green bird in his hand” (De umbris, 212, 10).

Bruno speaks of images “ad omnes formationes possible, adaptabiles” (De umbris, 80), that is, susceptible of every possible permutation. In truth, it is almost impossible to write the number of sequences that can be generated by permutating 150 elements 5 at a time, especially as inversions are allowed (De umbris, 223).

This distinguishes the art of Bruno, which positively thirsts after infinity, from the art of Lull.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 135-7.

Is the Universe Infinite?

“…one of the continuing debates among astrophysicists regards whether or not the universe is closed i.e. will not expand forever.

On the one hand, the model of a closed universe holds that there is sufficient mass in the universe so that the Big Bang explosion will gradually slow down and reverse due to the pull of gravity. In this model, all the mass of the universe involutes back into its unimaginably small and dense original condition until another quantum shift precipitates another explosion.

On the other hand, there are those who contend that the supernova data on distant galaxies confirms that there is insufficient mass for the reversal to occur, and that the negative expansion energy of space is causing our universe to expand forever.”

–Daniel Feldman, Qabala: The Mystical Heritage of the Children of Abraham, 2001, pg.  131.

Zelazny on Infinity

“Can life be counted upon to limit itself? No. It is the mindless striving of two to become infinity.

Can death be counted upon to limit itself? Never. It is the equally mindless effort of zero to encompass infinity.”

–Anubis, God of Death, in Roger Zelazny, Creatures of Light and Darkness. Pg. 10.

The Leap into Infinity

“Each step that it takes, however, crossing from nothing to nothing, carries it twice the distance of the previous step.

Each stride also takes the same amount of time as the prior one.

Suns flash by, fall behind, wink out. It runs through solid matter, passes through infernos, pierces nebulae, faster and faster moving through the starfall blizzard in the forest of the night.

Given a sufficient warm-up run, it is said that it could circumnavigate the universe in a single stride.

What would happen if it kept running after that, no one knows.”

–Roger Zelazny, Creatures of Light and Darkness. Pg. 20.

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