R: origin of notion of computable universes
(maybe) just 'a bit ' off topic, but interesting.. Jorge Liuis Borges: "Las Ruinas Circulares" [circa 1941] http://www.sccs.swarthmore.edu/users/00/pwillen1/lit/cruins.htm http://www.bibliotecasvirtuales.com/biblioteca/Borges/ruinascirculares.htm No one saw him disembark in the unanimous night, no one saw the bamboo canoe sink into the sacred mud, but in a few days there was no one who did not know that the taciturn man came from the South and that his home had been one of those numberless villages upstream in the deeply cleft side of the mountain, where the Zend language has not been contaminated by Greek and where leprosy is infrequent. What is certain is that the grey man kissed the mud, climbed up the bank with pushing aside (probably, without feeling) the blades which were lacerating his flesh, and crawled, nauseated and bloodstained, up to the circular enclosure crowned with a stone tiger or horse, which sometimes was the color of flame and now was that of ashes. This circle was a temple which had been devoured by ancient fires, profaned by the miasmal jungle, and whose god no longer received the homage of men. The stranger stretched himself out beneath the pedestal. He was awakened by the sun high overhead. He was not astonished to find that his wounds had healed; he closed his pallid eyes and slept, not through weakness of flesh but through determination of will. He knew that this temple was the place required for his invincible intent; he knew that the incessant trees had not succeeded in strangling the ruins of another propitious temple downstream which had once belonged to gods now burned and dead; he knew that his immediate obligation was to dream. Toward midnight he was awakened by the inconsolable shriek of a bird. Tracks of bare feet, some figs and a jug warned him that the men of the region had been spying respectfully on his sleep, soliciting his protection or afraid of his magic. He felt a chill of fear, and sought out a sepulchral niche in the dilapidated wall where he concealed himself among unfamiliar leaves. The purpose which guided him was not impossible, though supernatural. He wanted to dream a man; he wanted to dream him in minute entirety and impose him on reality. This magic project had exhausted the entire expanse of his mind; if someone had asked him his name or to relate some event of his former life, he would not have been able to give an answer. This uninhabited, ruined temple suited him, for it is contained a minimum of visible world; the proximity of the workmen also suited him, for they took it upon themselves to provide for his frugal needs. The rice and fruit they brought him were nourishment enough for his body, which was consecrated to the sole task of sleeping and dreaming. At first, his dreams were chaotic; then in a short while they became dialectic in nature. The stranger dreamed that he was in the center of a circular amphitheater which was more or less the burnt temple; clouds of taciturn students filled the tiers of seats; the faces of the farthest ones hung at a distance of many centuries and as high as the stars, but their features were completely precise. The man lectured his pupils on anatomy, cosmography, and magic: the faces listened anxiously and tried to answer understandingly, as if they guessed the importance of that examination which would redeem one of them from his condition of empty illusion and interpolate him into the real world. Asleep or awake, the man thought over the answers of his phantoms, did not allow himself to be deceived by imposters, and in certain perplexities he sensed a growing intelligence. He was seeking a soul worthy of participating in the universe. After nine or ten nights he understood with a certain bitterness that he could expect nothing from those pupils who accepted his doctrine passively, but that he could expect something from those who occasionally dared to oppose him. The former group, although worthy of love and affection, could not ascend to the level of individuals; the latter pre-existed to a slightly greater degree. One afternoon (now afternoons were also given over to sleep, now he was only awake for a couple hours at daybreak) he dismissed the vast illusory student body for good and kept only one pupil. He was a taciturn, sallow boy, at times intractable, and whose sharp features resembled of those of his dreamer. The brusque elimination of his fellow students did not disconcert him for long; after a few private lessons, his progress was enough to astound the teacher. Nevertheless, a catastrophe took place. One day, the man emerged from his sleep as if from a viscous desert, looked at the useless afternoon light which he immediately confused with the dawn, and understood that he had not dreamed. All that night and all day long, the intolerable lucidity of insomnia fell upon him. He tried exploring the forest, to lose his strength; among the hemlock he barely succeeded in experiencing several shor
R: origin of notion of computable universes
Karl Svozil, "Randomness & Undecidability in Physics", World Scientific, 1993, [chapters 10.2 - 10.5] also speaks about the simulaton argument. It is not unreasonable - he says - to speculate about the logico-algebraic structure of "automaton" universes (universes "computer" generated). If there is a hidden computing entity, and if this computing entity is "universal", there is no reason to exclude the so called (intrinsic) "calculus of propositions". Physical properties corresponding to _experimental_ propositions are identified - in the quantum domain - with "projection" operators on the Hilbert space. Thus Hilbert "lattice" corresponds to a lattice of experimental propositions. Algebraic relations and operations between these experimental propositions are called "calculus of propositions". Hilbert lattice and calculus of propositions _should_ be equivalent, even in the quantum domain. (Lattice theory is a framework for organizing structures such as experimental or logical statements). There is no _recursive_ enumeration of the axioms of Hilbert lattices. It is not unreasonable asking something like: do we live in a (quantum) universe created by some "universal" computation ? Thus, to test such speculation, we must look for _phenomena_ which correspond to "automaton" calculus of propositions _not_ contained in a Hilbert lattice (or its subalgebras).
R: origin of notion of computable universes
Gottfried Wilhelm Leibniz [The Monadology, 64-66] wrote: But the machines of nature, namely, living bodies, are still machines in their smallest parts ad infinitum. It is this that constitutes the difference between nature and art, that is to say, between the divine art and ours. And the Author of nature has been able to employ this divine and infinitely wonderful power of art, because each portion of matter is not only infinitely divisible, as the ancients observed, but is also actually subdivided without end, each part into further parts, of which each has some motion of its own; otherwise it would be impossible for each portion of matter to express the whole universe. Whence it appears that in the smallest particle of matter there is a world of creatures, living beings, animals, entelechies, souls. Each portion of matter may be conceived as like a garden full of plants and like a pond full of fishes. But each branch of every plant, each member of every animal, each drop of its liquid parts is also some such garden or pond. And though the earth and the air which are between the plants of the garden, or the water which is between the fish of the pond, be neither plant nor fish; yet they also contain plants and fishes, but mostly so minute as to be imperceptible to us. http://testweb.wpunj.edu/cohss/philosophy/COURSES/PHIL312/LEIBNIZ/LEIBNIZ4.H TM http://www.wpunj.edu/cohss/philosophy/COURSES/PHIL399/LEIBNIZ.HTM And Ockam (with Pier Damiani - De Divina Omnipotentia - and Aristotle) states that not even God, who is in possession of "potentia absoluta" - it means: miracles - not just of "potentia ordinata" - usual physical laws, could erase the past, or re-write it. Does it mean that, according to Ockam, simulations are forbidden? It seems that Ockam (as the Aquinas and also Wyclif) thinks that God could create the multiverse, or many universes. Leibniz also wrote: "although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough if, using reason well, we were never deceived by it.".
R: origin of notion of computable universes
- Italo Calvino - 'Invisible Cities' (1972) VI, Cities and the sky. In Eudossia, that extends up and low, with meandering alleys, steps, narrow lanes, hovels, a carpet is kept in which you can contemplate the real shape of the city. At first nothing seems to resemble less Eudossia than the design of the carpet, ordered in symmetrical figures that repeat their patterns along straight and circular lines, woven of needleful of dazzling colors, which alternating wefts you can follow all along the warp. But if you stop to observe it with attention, you perceive that to every place of the carpet corresponds a place of the city and that all the things contained in the city are comprised in the design, arranged according to their true relationships, which escape to your eye distracted from the coming and going from the swarming from the awful crush. All the confusion in Eudossia, the bray of the mules, the spots of lamp-black, the smell of fish, is what appear in the partial perspective that you pick; but the carpet proves that there is a point from which the city shows its true proportions, the geometric outline implicit in its every minimal detail. Getting lost in Eudossia is easy: but when you concentrates staring the carpet you recognize the road that you were looking for in a crimson or indigo or amaranth thread that through a long round lets you enter in a purple fence that is your true point of arrival. Every inhabitant of Eudossia confronts to the immovable order of the carpet his own image of the city, an anguish, and everyone can find hidden between the arabesques an answer, the story of his life, the twists of his destiny. An oracle was consultated about the mysterious relationship between two such different objects as the carpet and the city. One of the two objects, - it was the response, - has the shape that the gods gave to the starry sky and to the orbits around which the worlds spin; the other one is an approximate glare, like every human work. The augurs since so long were sure that the harmonic design of the carpet was of divine nature; in this sense the oracle was interpreted, without giving place to controversies. But in the same way you can draw the opposite conclusion: that the real map of the universe is the city of Eudossia as it is, a spot that spreads without shape, with zigzag roads, houses collapsing above one another in the dust, fires, cries in the dark.
R: origin of notion of computable universes
Try this http://www.nickbostrom.com and the link 'do we live in a [computer] simulation?'. Regards, - Serafino
