Hexagonalis Borges De Bibliotheca Limes Stabilitu Mirabile. Hanc Marginis Exiguitas not Caperet. " The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries. [...]. Each wall of each hexagon are five
shelves, each shelf contains books thirty-two of uniform size, each book is four hundred and ten pages, each page, of forty lines, each line of forty black letters .[...] The number is twenty-five orthographic symbols. [...]
the Library is total and that its shelves register all the possible combinations of twenty-five symbols spelling (number, though vast, is not infinite), that is all that is given to express, in all languages. " ---------------
[ ...] And you could still continue, said the Buddha, by calculating the number of atoms in the whole kingdom in our world and in the three million worlds contained in the Universe. " How many books made up the 'universe? How many hexagons are used to contain the whole?
A book contains 40 * 40 * 410 = 656,000 points.
The number of all possible books is the combination with repetition of the 25 elements of the alphabet, I began to 656000 time.
Although high, this number and it is still conceivable
65040681423512750823940476214542846900710367529944916190963221641673934662757798746545042627736017598465767752165001.
call this number L. The book contains babel. Each hexagon contains 6 * 5 * 32 = 960 books. The number of hexagons is therefore
L/960 = about 6775 * 10 ^ 112 We'll call him E. Unfortunately, the number is not whole, but we can think of some arbitrary hexagons (the final one, in fact, a true end if you can talk, given the postulated periodicity of the Library) as not completely filled, constructed to allow the Universe to reach L.
Now, how much space would to fulfill to Babel? Suppose, again arbitrarily, that a hexagon is actually a hexagonal prism-based
(There are in fact regular solids, Plato, who have faces like hexagons.) With 3 m side, slant 3sqrt (3) / 2 m (so that the triangles that form the basis of the hexagon is equilateral, for the sake of symmetry) and height 3.5 m. The volume of a hexagon is therefore approximately
81.84 cubic meters. Entire Babel therefore occupies a volume of
* E 81.84 cubic feet = approx 5:54 * 10 ^ 114 cubic meters.
call this volume V
This volume is equal to that of a sphere has a radius of about
(3V/4pigreco) ^ 1 / 3 = 1.1 * 10 ^ 38 meters. Now, given that the observable universe (ours, not books) is equivalent to a sphere of radius 10 ^ 26 m, Babel would be comfortable in 10 ^ 12 (one million) of our universes, or, if you like Moreover, in a universe of one million times greater than our (very elegant hypothesis, given the practical impossibility of proving the infinitude of the World: an endless world is philosophically and physically difficult to sustain and characterize, whereas a finite world, but sufficiently large to contain ALL would be fairer and elegant. The law wants the most beautiful equations, the most concise and simple, would also that in the absence of gods powerless or cruel, the universe is at least as great Babel ...)
Like Archimedes, who in his attempts to calculate Sandstone many grains of sand can hold the Universe (inventing this order a separate numbering system), the sense of calculation is not so much the number itself, but what it leads us to understand. The arbitrary locations, size or location, are only useful for a precise result. But little of what we are interested in the number of hexagons. We like to Archimedes matters most to conclude that what may be the high number of combinations, it will inevitably end, resulting from transactions between finite numbers and non-zero (a hexagon of size nothing, a book of the infinitesimal thickness ... the inconceivable middle page would not reverse). The Universe (literary, but as to what other field would not fit such reasoning?) Is reduced to a number, albeit high, not endless possibilities. The literature of combinatorial Queneau, the hundred thousand billion poems ... pale or mirages examples of the true meaning of letterautra, which is to make Babel. Despite their small units are already included in the Bibliotheca, the total ex ipothesi.
The same reasoning (already used by the same Borges, History of Eternity it) can lead us to say that the known number of atoms in the universe consists observable, without too much difficulty we calculate the number of possible combinations (or chemical bonds, or physical reactions or changes of state, etc.) or the Universe as a whole is intended to make recurrence before, inevitably, in a new ekpìrosis. Will immediately spring to mind that however you take, the number of permutations that the universe is destined to make is certainly limited by the fact that the atoms are bound to react only with certain other atoms (not all possible compounds of the 92 natural elements are achievable, because physically impossible). Better yet, for the purposes of this discussion: that number is all the more finished, though immeasurable beyond imagination.
Already Borges wrote that in a world of infinite (eternal and must be) everything happens, and worse, everything happens in every moment. The life acquires a sense of vague and acted, if any act done was is and will be made infinite and infinite times. Countless times go up to the Masters of the Universe, countless times allepistole die in a duel on the morning after spending sleepless our last hours to outline the theory of revolutionary groups. Countless times we are born and die and infinite number of times we realize that countless others look at us while we watch endless further argues that we take note that this giant domino tiles from simultaneous will never end ... This hypothesis, however, is far more elegant, and not uncomfortable difficult concept of infinity, which has shaken more than one soul in the past (the irrational and aperiodic unraveling of the decimal expansion of the diagonal of one side of a Qudrat has cost an "accident water "to a follower of Pythagoras, a not-too-innocent.) Infinity has in it all and as such carries the weight of the contradiction: take zero times infinity (zero multiplied by infinity). What do you hold? How do you "take zero time" something that can not by definition be "closed" to have "fine"? Although interesting, this is another story ... Why
goes on all conceivable let there be space enough to give rise to all possible permutations, combinations and recombinations that the number of atoms (in the sense of ultimate components of reality under study) allows. Again, this number is, though huge, not infinite, then possible, in particular LIABLE analysis.
Archimedes and his huge (but finite!) Sandstone proved it. Everything is to give a name to the numbers that should be used, and we will have in hand a new unit of measure (for comparison, mens-Mensura-mensis-metron-mann all have the same root: for humans, the measure of all things, there is what has so far, which is under the graspable) useful to establish the bases on which the universe rests undisputable. Once again, the infinite is to be different from us, is to lie between the natural numbers, Kronecker divine work, and together on the Mandelbrot set, a divine work to Penrose.
trillion Universes like ours contain large Babel. What Babel (referring to all possible books, as all possible combinations of atoms, as in all possible qualsiasicosa) is then defined as the unit of the world in question, as is the Avogadro's number is unity business of chemistry.
Our little world is a PicoBabele. No doubt language has its own charm.
