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Tag: 1946

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: First Attempts at a Content Organization


Athanasius Kircher (1602-80), Frontispiece of Obeliscus Pamphilius, Obeliscus Pamphilius: Hoc est Interpretatio nova & hucusque intenta obelisci Hieroglyphici, eBook courtesy of GoogleBooks, published by Lud. Grignani 1650, held by Ghent University. 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. 

“Probably in 1660, three years before the publication of the Polygraphia, Kircher wrote a manuscript bearing the title Novum hoc inventum quo omnia mundi idiomata ad unum reducuntur (Mss. Chigiani I, vi, 225, Biblioteca Apostolica Vaticana; cf. Marrone 1986).

Schott says that Kircher kept his system a secret at the express wish of the emperor, who had requested that his polygraphy be reserved for his exclusive use alone.

The Novum inventum was still tentative and incomplete; it contained an extremely elementary grammar plus a lexicon of 1,620 words. However, the project looks more interesting that the later one because it provides a list of 54 fundamental categories, each represented by an icon.

These icons are reminiscent of those that one might find today in airports and railway stations: some were schematically representative (like a small chalice for drinking); others were strictly geometrical (rectangles, triangles, circles).

Some were furthermore superficially derived from Egyptian hieroglyphics. They were functionally equivalent to the Roman numbers in the Polygraphia (in both texts, Arabic numbers referred to particular items).

Thus, for example, the square representing the four elements plus the numeral 4 meant water as an element; water as something to drink was instead expressed by a chalice (meaning the class of drinkable things) followed by the numeral 3.

There are two interesting features in this project. The first is that Kircher tried to merge a polygraphy with a sort of hieroglyphical lexicon, so that his language could be used (at least in the author’s intention) without translating it into a natural language.

Seeing a “square + 4,” the readers should immediately understand that the named thing is an element, and seeing “chalice + 3” they should understand that one is referring to something to drink.

The difficulty was due to the fact that, while both Kircher’s Polygraphia and Becher’s Character allow a translating operator (be it a human being or a machine) to work independently of any knowledge of the meaning of the linguistic items, the Novum inventum requires a non-mechanical and quasi-philosophical knowledge: in order to encode the word aqua as “square + 4,” one should previously know that it is the name of an element–information that the term of a natural language does not provide.

Sir Thomas Urquhart, who published two volumes describing a sort of polygraphy (Ekskubalauron, 1652, and Logopandecteision, 1653), noted that, arbitrary as the order of the alphabet might be, it was still easier to look things up in alphabetical order than in a categorical order.

The second interesting feature of Kircher’s initial project is certainly given by the effort to make the fundamental concepts independent of any existing natural language.

Its weakness is due to the fact that the list of the 54 categories was notably incongruous: it included divine entities, angelic and heavenly, elements, human beings, animals, vegetables, minerals, the dignities and other abstract concepts deriving from the Lullian Ars, things to drink, clothes, weights, numbers, hours, cities, food, family, actions such as seeing or giving, adjectives, adverbs, months of the year.

It was perhaps the lack of internal coherency in this system of concepts that induced Kircher to abandon this line of research, and devote himself to the more modest and mechanical method used in the Polygraphia.

Kircher’s incongruous classification had a precedent. Although he regarded Kircher as the pioneer in the art of polygraphy, in his Technica curiosa (as well as in his Jocoseriorum naturae et artiis sive magiae naturalis centuriae tres) Gaspar Schott gave an extended description of a 1653 project that was certainly earlier than Kircher’s (the Novum inventum is dedicated to Pope Alexander VII, who ascended the pontifical throne only in 1655).

The project was due to another Jesuit, a Spaniard (“whose name I have forgotten,” as Schott says on p. 483), who had presented in Rome (on a single folio) an Artificium, or an Arithmeticus nomenclator, mundi omnes nationes ad linguarum et sermonis unitatem invitans (“Artificial Glossary, inviting all the nations of the world to unity of languages and speech”).

Schott says that the anonymous author wrote a pasigraphy because he was a mute. As a matter of fact the subtitle of the Artificium also reads Authore linguae (quod mirere) Hispano quodam, vere, ut dicitur, muto (“The author of this language–a marvelous thing–being a Spaniard, truly, it is said, dumb”).

According to Ceñal (1946) the author was a certain Pedro Bermudo, and the subtitle of the manuscript would represent a word play since, in Castilian, “Bermudo” must be pronounced almost as Ver-mudo.

It is difficult to judge how reliable the accounts of Schott are; when he described Becher’s system, he improved it, adding details that he derived from the works of Kircher. Be that as it may, Schott described the Artificium as having divided the lexicon of the various languages into 44 fundamental classes, each of which contained between 20 and 30 numbered items.

Here too a Roman number referred to the class and an Arabic number referred to the item itself. Schott noted that the system provided for the use of signs other than numbers, but gave his opinion that numbers comprised the most convenient method of reference since anyone from any nation could easily learn their use.

The Artificium envisioned a system of designating endings, (marking number, tense or case) as complex as that of Becher. An Arabic number followed by an acute accent was the sign of the plural; followed by a grave accent, it became the nota possessionis.

Numbers with a dot above signified verbs in the present; numbers followed by a dot signified the genitive. In order to distinguish between vocative and dative, it was necessary to count, in one case, five, and, in the other, six, dots trailing after the number.

Crocodile was written “XVI.2” (class of animals + crocodile), but should one have occasion to address an assembly of crocodiles (“O Crocodiles!”), it would be necessary to write (and then read) “XVI.2′ . . . . . ‘.

It was almost impossible not to muddle the points behind one word with the points in front of another, or with full stops, or with the various other orthographic conventions that the system established.

In short, it was just as impracticable as all of the others. Still, what is interesting about it is the list of 44 classes. It is worth listing them all, giving, in parenthesis, only some examples of the elements each contained.

  1. Elements (fire, wind, smoke, ashes, Hell, Purgatory, centre of the earth).
  2. Celestial entities (stars, lightning, bolts, rainbows . . .).
  3. Intellectual entities (God, jesus, discourse, opinion, suspicion, soul, stratagems, or ghosts).
  4. Secular statuses (emperor, barons, plebs).
  5. Ecclesiastical states.
  6. Artificers (painters, sailors).
  7. Instruments.
  8. Affections (love, justice, lechery).
  9. Religion.
  10. Sacramental confession.
  11. Tribunal.
  12. Army.
  13. Medicine (doctor, hunger, enema).
  14. Brute animals.
  15. Birds.
  16. Fish and reptiles.
  17. Parts of animals.
  18. Furnishings.
  19. Foodstuffs.
  20. Beverages and liquids (wine, beer, water, butter, wax, and resin).
  21. Clothes.
  22. Silken fabrics.
  23. Wool.
  24. Homespun and other spun goods.
  25. Nautical and aromas (ship, cinnamon, anchor, chocolate).
  26. Metal and coin.
  27. Various artifacts.
  28. Stone.
  29. Jewels.
  30. Trees and fruits.
  31. Public places.
  32. Weights and measures.
  33. Numerals.
  34. Time.
  35. Nouns.
  36. Adjectives.
  37. Verbs.
  38. Undesignated grammatical category.
  39. Undesignated grammatical category.
  40. Undesignated grammatical category.
  41. Undesignated grammatical category.
  42. Undesignated grammatical category.
  43. Persons (pronouns and appellations such as Most Eminent Cardinal).
  44. Vehicular (hay, road, footpad).

The young Leibniz would criticize the absurdity of arrangements such as this in his Dissertatio de arte combinatoria, 1666.

This sort of incongruity will affect as a secret flaw even the projects of a philosophically more sophisticated nature–such as the a priori philosophic languages we will look at in the next chapter.

This did not escape Jorge Luis Borges. Reading Wilkins, at second hand as he admits (in Other Inquisitions, “The analytical idiom of John Wilkins“), he was instantly struck by the lack of a logical order in the categorical divisions (he discusses explicitly the subdivisions of stones), and this inspired his invention of the Chinese classification which Foucault posed at the head of his The Order of Things.

In this imaginary Chinese encyclopedia bearing the title Celestial Emporium of Benevolent  Recognition, “animals are divided into: (a) belonging to the emperor, (b) embalmed, (c) tame, (d) sucking pigs, (e) sirens (f) fabulous, (g) stray dogs. (h) included in the present classification, (i) frenzied, (j) innumerable, (k) drawn with a very fine camelhair brush, (l) et cetera, (m) having just broken the water pitcher, (n) that from a long way off look like flies.”).

Borge’s conclusion was that there is no classification of the universe that is not arbitrary and conjectural. At the end of our panorama of philosophical languages, we shall see that, in the end, even Leibniz was forced to acknowledge this bitter conclusion.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 203-8.

Recalculating the Antediluvian Reigns of Sumerian Kings

“At one time the present writer tended to interpret the large numbers associated with the Hebrew exodus from Egypt and also with the census lists in Numbers as “symbols of relative power, triumph, importance, and the like,” a position that can be sustained to a degree from ancient Near Eastern literature but does not account satisfactorily for all the Biblical data involved.

Sensing that there might, after all, be a rationale underlying the very large figures, a few scholars adopted cautious positions reflecting that possibility.

Among all extant exemplars of the Sumerian King List, the Weld-Blundell prism in the Ashmolean Museum contains the most extensive version as well as the most complete copy of the King List. The prism contains four sides with two columns on each side. Perforated, the prism had a wooden spindle so that it might be rotated and read on all four sides.

Among all extant exemplars of the Sumerian King List, the Weld-Blundell prism in the Ashmolean Museum contains the most extensive version as well as the most complete copy of the King List.
The prism contains four sides with two columns on each side. Perforated, the prism had a wooden spindle so that it might be rotated and read on all four sides.

A serious mathematical investigation of the postdiluvian portions of the Sumerian King List was undertaken by D. W. Young (Dwight W. Young, “A Mathematical Approach to Certain Dynastic Spans in the Sumerian King List,” JNES 47 (1988), pp. 123-9), in which he suggested that the total years for certain dynasties utilized squares or higher powers of numbers, perhaps in combinations.

Thereafter his interests shifted to the problem of large numbers in the accounts of the Hebrew patriarchs (Dwight W. Young, “The Influence of Babylonian Algebra on Longevity Among the Antediluvians,” ZAW 102 (1990), pp. 321-5), but his studies in that area are not strictly relevant to the present problem.

His great contribution was to take seriously the numbers of the ancient writings with which he dealt and to attempt to interpret them mathematically.

The ancient Sumerians were innovators in the areas of astronomy and mathematics as well as in other unrelated fields of investigation. It is now known that their arithmetical calculations were based upon the sexagesimal system, and thus when they considered the mathematics of time it was natural to divide the hour up into sixty units, and then to reduce each one of those units to a further sixty components or, in our language, minutes and seconds.

There is still very much to be learned about Sumerian mathematics, but from what is known of the pragmatic nature of the subject it appears increasingly clear that their numerical exercises were organized on the basis of rationality rather than mythology.

Having regard to this situation, scholarship now has the responsibility of investigating the numerical problems of Sumerian times against such a background.

To the present writer it now seems evident that the solution to the large numbers found in the antediluvian Sumerian King List is disarmingly simple. It is obvious that, proceeding rationally, base-60 must be involved in numbers of the magnitude contained on the prism. The list of rulers and regnal years is as follows:

Cf. J. Finegan, Light From the Ancient Past (Princeton: Princeton University, 1946), p. 25.

Cf. J. Finegan, Light From the Ancient Past (Princeton: Princeton University, 1946), p. 25.

An inspection of this table shows two kings credited with reigns of 36,000 years each and three others recorded as having reigned for 28,800 years each. In the case of Alalgar and the divine Dumuzi, the numbers assigned to them contain two factors—namely, 3600 (the square of base 60) and 10 — which when multiplied furnish the large number under investigation.

In the case of the triad comprising Alulim, Enmengal-Anna, and Ensipazi-Anna, the factors involved are the square of base-60 multiplied by 8. When the base is isolated from the calculation, the remaining factor constitutes the actual length of the king’s reign.

This process can be expressed by a formula, as follows:

Formula for Calculating Actual Reignwhere Pr is the prism’s record, B is base-60 raised to the power of 2 to give base-60 squared, and At is the actual length of the king’s tenure. By employing this means of calculation, the above table can be rewritten as follows:

Recalculated Actual Reign of Years and Months

Notice may now be taken of the third century BC list compiled by Berossos. As observed earlier, the names are Greek and the total has been extended to ten rulers by the addition of two names.

Xisouthros, the legendary hero who survived the flood, is one of these. It has also been suggested that Amelon and Ammenon may be corrupt forms of the name Enmenlu-Anna, but this cannot be demonstrated.”

R.K. Harrison, “Reinvestigating the Antediluvian Sumerian King List,” Journal of the Evangelical Theological Society (JETS) 36 / 1 (March 1993), pp. 4-6.

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