Archive for Language and mathematics

Coined Chinese characters: The 24 solar terms, part 4

As is usually the case, the Wikipedia article on the Chinese calendar is comprehensive and built on consensus.  It states:

The Chinese calendar, as the name suggests, is a lunisolar calendar created by or commonly used by the Chinese people. While this description is generally accurate, it does not provide a definitive or complete answer. A total of 102 calendars have been officially recorded in classical historical texts. In addition, many more calendars were created privately, with others being built by people who adapted Chinese cultural practices, such as the Koreans, Japanese, Vietnamese, and many others, over the course of a long history.

A Chinese calendar consists of twelve months, each aligned with the phases of the moon, along with an intercalary month inserted as needed to keep the calendar in sync with the seasons. It also features twenty-four solar terms, which track the position of the sun and are closely related to climate patterns. Among these, the winter solstice is the most significant reference point and must occur in the eleventh month of the year. Each month contains either twenty-nine or thirty days. The sexagenary cycle for each day runs continuously over thousands of years and serves as a determining factor to pinpoint a specific day amidst the many variations in the calendar. In addition, there are many other cycles attached to the calendar that determine the appropriateness of particular days, guiding decisions on what is considered auspicious or inauspicious for different types of activities.

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Coined Chinese characters: The 24 solar terms, part 3

The chapter on "Calendar and Chronology" in Brill's Encyclopedia of China Online (2009) was authored by Ho Peng Yoke (1926-2014), who was the Director of the Needham Research Institute from 1990-2001.  The first two paragraphs of Ho's chapter begin as follows:

The traditional Chinese calendar is lunisolar, i. e. it is based on both the movement of the moon and on what seems to be the orbit of the sun around the earth. The incommensurability of the lunar synodical period of 29.530587… days and the equinoctial year's 365.2421… days has always been the cause for numerous difficulties with respect to the establishment of a calendar in China. In order to replace the former calendars which after a time had lost their validity, roughly 100 different types of calendars were devised over a period of about 2000 years, many of which were never officially adopted. According to Joseph Needham, the history of calendar making is the consequence of attempts to "make the incompatible compatible."

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Coined Chinese characters: The 24 solar terms, part 2

The calendrical system used for defining the dates of traditional Chinese festivals such as ‘Chinese New Year’ (The first day of the first lunar month, now called 'Spring Festival’ Chun jie 春節 in the PRC), the mid-autumn festival 中秋 (full moon of the 8th lunar month) and so on is the last of the many versions of the Chinese luni-solar calendar that were adopted by successive imperial governments until the fall of the empire in 1911.  It is in fact the system adopted by the Qing dynasty in 1644.

Christopher Cullen’s book Heavenly Numbers: Astronomy and Authority in Early Imperial China (Oxford, 2017) gives a detailed account of the successive systems of mathematical astronomy that were used by Chinese astronomical officials in early imperial times to produce the annual luni-solar calendars that were promulgated by imperial authority. The following explanations are taken from Cullen’s book.

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Zipf genius

I have always been deeply intrigued by George Kingsley Zipf (1902-1950), but Mark's recent "Dynamic Philology" (5/24/25) rekindled my interest.

Put simply,

He is the eponym of Zipf's law, which states that while only a few words are used very often, many or most are used rarely,

where Pn is the frequency of a word ranked nth and the exponent a is almost 1. This means that the second item occurs approximately 1/2 as often as the first, and the third item 1/3 as often as the first, and so on. Zipf's discovery of this law in 1935 was one of the first academic studies of word frequency.

Although he originally intended it as a model for linguistics, Zipf later generalized his law to other disciplines. In particular, he observed that the rank vs. frequency distribution of individual incomes in a unified nation approximates this law, and in his 1941 book, "National Unity and Disunity" he theorized that breaks in this "normal curve of income distribution" portend social pressure for change or revolution.

(Wiktionary)

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The mathematics of kana vs. kanji usage over time (1879-1968)

In the fourth comment to "Striving to revive the flagging sinographic cosmopolis" (4/26/25), I stated my observation of morphosyllabic kanji usage is that it has been declining over time at the expense of kana and other phonetic elements of the writing system, and I expressed the wish that a quantitative study of the actual usage be carried out.  It turns out that we already do have this information, and it is visually evident in these graphs which were called to my attention by Jim Unger.

They are from:

Zusetsu nihongo: Gurafu de miru kotoba no sugata kotoba o hakaru keiryō kokugogaku (Kadokawa ko jiten 9), Hayashi Ōki.

図説日本語: グラフで見ることばの姿 ことばを計る計量国語学 (角川小辞典 9), 林大.

Illustrated Japanese: The appearance of words in graphs, Quantitative Japanese linguistics to measure words (Kadokawa Small Dictionaries), Hayashi Ōki, ed. and comp. (1982), pp. 276-277.

The graphs are derived from a 1969 book by Morioka Kenji on Meiji period language.  Both graphs cover the years 1879-1968.

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Logos: The sacred phonology, mathematics, and agriculture of the alphazodiac

[This is a guest post by Brian Pellar]

. . . the consonants are the letters or ciphers which assemble around the vowels to form the words, just as the constellations assemble around the Sun, image of the Divinity, and compose the community of stars over which it presides.                                                                        — Hebreu Primiti

The Consonants of Command

Dear Professor Mair,

In regard to your question, “Is there some sense in which we could think of the 12 aspects/signs/symbols of the alphazodiac as comprising/encompassing the basic sounds of the universe?” I’ve dabbled a bit with some intriguing answers in my papers. For instance, in my very first paper, SPP 196, I placed in the endnotes a very interesting reference from the Gospel of the Egyptians (a Nag Hammadi text) that I feel might bear a relationship to the structure and the underlying “sacred” vowels that comprise the Logos/Word — the breath of God — of the alphazodiac. More specifically,

the “three powers” (the Father, Mother, and Son) give praise to the unnamable Spirit — and the “hidden invisible mystery” that came forth is composed of seven sacred vowels (i.e., the Son “brings forth from the bosom/the seven powers of the great / light of the seven voices, and the word/[is] their completion”), with each of those seven vowels repeated exactly twenty-two times (“iiiiiiiiiiiiiiiiiii[iii]/ ēēēēēēēēēēēēēēēēēēēēēē /oooooooooooooooooooooo/uu[uuu] uuuuuuuuuuuuuuuuu/eeeeeeeeeeeeeeeeeeeeee/aaaaaaa[aaaa]aaaaaaaaaaa/ ōōōōōōōōōōōō ōōōōōōōōōō”) (Robinson 1990: 209–210). [SPP 196, pp. 38-39].

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Roman dodecahedra between Southeast Asia and England, part 5

Spotted on the counter for tea/coffee service at the Residence Inn in Omaha, Nebraska:

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Roman dodecahedra between Southeast Asia and England, part 4

Wherein we embark upon an inquisition into the divine proportions of the dodecahedron and its congeners, take a peek at the history of accounting, explore the mind of Leonardo da Vinci, and examine the humanistic physics of Werner Heisenberg*.

[*Heisenberg's father was a professor of medieval and modern Greek studies at the University of Munich in Germany. Heisenberg had more a “humanistic” education, i.e. more Latin and Greek than in natural sciences.  One morning the young Werner Heisenberg discovered reading Plato's Timaeus a description of the world with regular polyhedra. Heisenberg could not understand why Plato being so rational started to use speculative ideas. But finally he was fascinated by the idea that it could be possible to describe the Universe mathematically. He could not understand why Plato used the Polyhedra as the basic units in his model, but Heisenberg considered that in order to understand the world it is necessary to understand the Physics of the atoms. (source)  He contributed to atomic theory through formulating quantum mechanics in terms of matrices and in discovering the uncertainty principle, which states that a particle's position and momentum cannot both be known exactly. (Britannica | Apr 23, 2024)

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We have had an exciting, joyful journey through dodecahedra land, from the archeological discovery of a new specimen in England, to deep, dense discussions about the meaning and purpose of these mysterious objects, to scampering through and clambering over a playground installation of a related form.  In this post, I would like to return to the essential twelveness of the dodecahedra.

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Roman dodecahedra between Southeast Asia and England, part 3

I stopped short when I passed by this piece of gym equipment in a kindergarten playground near my home.

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Fast talking

The topic of this post is one that deeply fascinates me personally, but also has a bearing on many of the main concerns of the denizens of Language Log:  information, efficiency, density, complexity, meaning, pronunciation, prosody, speed, gender….

It was prompted by this new article:

What’s the Fastest Language in the World?
Theansweriscomplicated. [sic]
by Dan Nosowitz, Atlas Obscura (April 2, 2024)

The article is based upon the work of François Pellegrino a senior researcher in linguistics and cognitive science at the Centre National de la Recherche Scientifique (CNRS), Paris and Université Lumière Lyon II, France.

Francois Pellegrino is mostly a quantitative linguist, meaning his work often includes measuring differences among languages and hunting for explanations behind those differences. He’s worked on language speed a few times, including on one study that compared 17 different languages in a variety of metrics.

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Axing languages and linguistics at West Virginia University

From M. Paul Shore:

Article that appeared on the Washington Post website this morning (and is therefore likely to appear in tomorrow's print edition) about the recently proposed demise of, among other things, the Department of World Languages, Literatures and Linguistics at West Virginia University's flagship Morgantown campus (note that that department name really should be something like "Department of World Languages and Literatures and of Linguistics", since "World" doesn't really apply to "Linguistics"):

Recently proposed demise of languages, linguistics at WVU (Morgantown)

WVU’s plan to cut foreign languages, other programs draws disbelief

Academic overhaul at West Virginia University, in response to budget deficit, outrages faculty and students

Nick Anderson , WP (8/18/23)

A proposal from West Virginia University would discontinue 32 of the university’s 338 majors on its Morgantown campus and eliminate 7 percent of its faculty.  As of 6:30 PM, the article had attracted more than 900 comments, which I'm fairly sure is well above average for the Post website.  By 11 PM, it had garnered 1,400 comments.

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Learning sinitic and sinoglyphic "zero"

Plus Indic, plus Arabic, Korean, Vietnamese, Hokkien (Taiwanese), Hakka, and Fuzhou (Eastern Min).

For an exciting read / ride, be sure to follow the whole thread, travelling through time and space.

Courtesy of Egas Moniz-Bandeira ᠡᡤᠠᠰ ᠮᠣᠨᠢᠰ ᠪᠠᠨᡩ᠋ᠠᠶᠢᠷᠠ

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Mathematical parking

Sign on the campus of Zhōngguó kēxué jìshù dàxué 中国科学技术大学 (University of Science and Technology of China) telling people how to park:

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