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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.) Read the rest of this entry »

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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