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The Ludic fallacy is the fallacy of mistaking the model/map for the reality/territory. Check out this one-paragraph short story from Jorge Luis Borges, “On Exactitude in Science”:
. . . In that Empire, the Art of Cartograhy attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.
– Suárez Miranda, Viajes de varones prudentes, Libro IV, Cap. XLV, Lérida, 1658
[Translated by Andrew Hurley, in a compilation of Borges' fiction titled Collected Fictions, published by Penguin in 1998.]
Using Borges’ short story as a starting point, Jean Baudrillard discusses the inversion of the relationship between models and reality in “The Precession of Simulacra”, the opening chapter from his book, Simulacra and Simulations. The following are the first two paragraphs:
If once we were able to view the Borges fable in which the cartographers of the Empire draw up a map so detailed that it ends up covering the territory exactly (the decline of the Empire witnesses the fraying of this map, little by little, and its fall into ruins, though some shreds are still discernible in the deserts — the metaphysical beauty of this ruined abstraction testifying to a pride equal to the Empire and rotting like a carcass, returning to the substance of the soil, a bit as the double ends by being confused with the real through aging) — as the most beautiful allegory of simulation, this fable has now come full circle for us, and possesses nothing but the discrete charm of second-order simulacra.
Today abstraction is no longer that of the map, the double, the mirror, or the concept. Simulation is no longer that of a territory, a referential being, or a substance. It is the generation by models of a real without origin or reality: a hyperreal. The territory no longer precedes the map, nor does it survive it. It is nevertheless the map that precedes the territory — precession of simulacra — that engenders the territory, and if one must return to the fable, today it is the territory whose shreds slowly rot across the extent of the map. It is the real, and not the map, whose vestiges persist here and there in the deserts that are no longer those of the Empre, but ours. The desert of the real itself.
[Translated by Sheila Faria Glaser in Baudrillard's Simulacra and Simulations, published by the University of Michgan Press, 1994.]
Human beings in today’s society succumb to countless forms of hyperreality, as this is a reflection of an innate human desire to pervert the Ludic “fallacy” of the mind into the Ludic “fellatio” of the mind.
J. S. Bach’s masterpiece for keyboard, the Goldberg Variations (published in 1754), was originally titled (in 18th-century High German) by the lengthy and unassuming:
Clavier Ubung bestehend in einer Aria mit verschiedenen Veraenderungen vors Clavicimbal mit 2 Manualen
[Keyboard Practice consisting of an Aria with diverse variations for the harpsichord with 2 manuals]
This pedantic title together with the apocryphal story that Bach wrote this piece for an insomniac Count (to be performed by a certain Johann Gottlieb Goldberg) did not help its popularity, as this piece did not enter the concert pianist/harpsichordist repertoire until the 20th-century, when Wanda Landowska, Rosalyn Tureck, and (most notably) Glenn Gould prominently featured the Goldberg Variations in their concerts and recordings. Like Bach’s music in general, the Goldberg Variations became quite attractive to transcribers. Notable examples of transcriptions of Bach’s music include:
- Ferruccio Busoni’s transcription of the Chaconne in D minor (solo violin) for piano. Here is a performance of the original piece for solo violin by Arthur Grumiaux (part 2). Now here is a performance of Busoni’s transcription for piano by Hélène Grimaud (part 2).
- Wendy Carlos’ transcriptions of selections of The Well-Tempered Clavier and The Brandenburg Concertos (as well as other Bach “hits”) for the Moog synthesizer! Here is the first movement of the Brandenburg Concerto No. 3 performed in its original instrumentation by the Freiburg Baroque Orchestra. Now here is a performance of the same piece transcribed for Moog synthesizer.
- The Swingle Singers, an a capella jazz singing group formed in Paris in 1962, has transcribed Bach to great success. Here is a performance of the same 1st movement of Brandenburg Concerto No. 3 by the Swingle Singers.
- Catrin Finch transcribed the Goldberg Variations for harp! Here is her performing the Aria. (Behind the scenes.)
Notable composers who have transcribed Bach’s music include Mozart, Schoenberg, Stravinksy, and Webern.
The Goldberg Variations in particular have been transcribed for (amongst other instrumentations): harp (above), classical guitar, string trio, string orchestra, and brass quintet. Of the transcriptions for strings, Dmitry Sitkovetsky’s transcriptions for string trio and string orchestra have been highly successful:
- Julian Rachlin (violin) with Nobuko Imai (viola) and Mischa Maisky (cello) performs the Aria and Variations 1-4.
- The Stuttgart Chamber Orchestra performs the Aria and Variations 1-2.
The following are selected exemplary performances of the Goldberg Variations on its original instrumentation, the keyboard (harpsichord/piano):
- Glenn Gould performs the Aria and Variations 1-7 on the piano.
- Pierre Hantaï performs the Aria and Variations 1-8 on the harpsichord.
In addition to studying the Goldberg Variations on piano, I have also made some attempts at transcribing the piece for both string trio and and string quartet. Each ensemble poses unique challenges, as the string trio often has the viola sharing melodic lines with both the violin and cello, and the string quartet has the addition of another violin, which is often redundant unless one transcribes more creatively. So far I have only worked on the Aria and Variations 1-4 (out of 32 variations).
The transcriptions are roughly straightforward as the viola is the only part that has any double-stops. The trio and quartet are almost identical in that the first and second violins in the quartet alternate in sharing the violin line in the trio. This is not a very creative solution, and hence I will have to come up with a better attempt.
This is a two-part invention straightforward to play on the piano (or harpsichord), so one problem is dividing up the bass-line into two parts for the viola and cello. This requires a kind of re-interpretation of the bass line by introducing counterpoint where there isn’t explicit counterpoint.
(A good example of this kind of contrapuntal interpretation is found in Glenn Gould’s recording of the C minor prelude from the Prelude and Fugue No. 2 in C minor, BWV 847 from Book I of The Well-Tempered Clavier; 1963, Sony Classical. This recording was used in one of the “short films” from François Girard’s excellent movie, 32 Short Films About Glenn Gould.)
Another problem for the string trio is in the transition line in bars 21-22, where the viola has to play fourths, which apparently is an awkward interval for string players. Also the first and second violins in the quartet alternate in sharing the violin line in the trio. Not a good solution.
I had major difficulty here, and this will be a work in progress. I will post any decent transcriptions in the future.
This variation is a canon at the unison, so for the quartet it is natural for the first and second violin to play the two voices in the right-hand part of the keyboard. The harmonic bass line can be entirely played by the cello, however the viola can be integrated into the bass line in the second section if desired. I will provide alternate versions of the quartet, one incorporating the viola and one leaving it out.
Transcribing for string trio however is a major challenge, as the range of the canon at the unison, though perfect for two violins, is quite difficult for a violin and a viola since the canon is out of the range of the viola. Thus the counterpoint must be broken up. Thus the problem is splitting up the canon so that it gives the illusion of making musical sense to the listener though the violin and the viola must engage in a kind of contrapuntal alchemy to create this illusion of a canon at the unison.
This variation in four-voices is like a four-part chorale, so for the quartet there is virtually no transcribing to be done, just simple separation of the voices. The easiest variation to transcribe so far.
For the trio on the other hand, there are major challenges, as all three instruments must perform a lot of double-stops in order to share the inner voices. Needless to say the trio transcription needs to be vastly improved.
Ever wondered what urban-transit systems look like in its geographical scale? Neil Freeman’s website contains an excellent page that depicts the lines of various transit systems in the world in the same geographic scale.
Now how does the geographical depiction compare with its cartographic depiction? The following are the comparisons of selected transit systems in geographical scale alongside its respective current transit map design. (I will be periodically updating this post to include more systems.)
Note: Due to size restrictions on this blog (and in viewing web pages in general), the geographical scale for each transit system depicted below is different from one another. For example, the size of the Paris Métro is in reality a lot smaller than the London Underground, whereas the depiction below displays the opposite.
^ New York City Subway
Technically the lines extending west of Midtown and Lower Manhattan belong to New Jersey’s Path system, and are not apart of the MTA NYC Subway system. So you would have to buy two separate tickets to ride in both systems. Also there are other variations of the current transit design that does depict the Staten Island Railway line that is missing above. (Also missing are the AirTrain lines from JFK to the E and A trains in the above transit map that more current versions depict.)
This current map design is geographical in nature that stresses function over form, as opposed to geometrical like Massimo Vignelli’s iconic 1972 design and his 2008 update. In particular, this map design is the most geographical out of most other current transit maps in the world. (Other geographical designs include the San Francisco Bay Area’s BART system.)
^ London Underground
^ Paris Métro
^ Tokyo Metro
^ Berlin U-Bahn
^ Moscow Metro
^ Madrid Metro:
^ Stuttgart VVS
In his book The Black Swan, Nassim Taleb introduces a term that embodies the fallacy of mistaking mathematical models for that of reality: the Ludic fallacy. Certain practitioners in the mathematical sciences are often guilty of succumbing to this fallacy, with the highest concentration of offenders coming from the fields of finance, economics and statistics. (Even being awarded a Nobel Prize does not grant one immunity from the Ludic fallacy, e.g. the spectacularly epic failure of Myron Scholes and Robert Merton with LTCM.)
An even more spectacular failure (partially stemming from Wall Street financial “engineers” operating under the Ludic fallacy) is the 2008 financial crash. This is just one of countless examples of the arrogance of human beings to presume to “understand” and “tame” complexity. The ancient Greeks have a term for this kind of arrogance: hubris.