Archive for Language and mathematics

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)


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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Liuzhou Snail Rice Noodles

Liuzhou Snail Rice Noodles from China. (Facebook, Li Chong-lim photo)

The photograph is from this article:

China’s ‘propaganda noodle soup’ ordered off the market in Taiwan

Noodle packaging has ‘You are Chinese, and I am too’ emblazoned across it

By Huang Tzu-ti, Taiwan News (1/17/23)

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What do the Friedmann equations have to do with the student protests in China?

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The paradox of hard and easy

If you're interested in one-way functions and Kolmogorov complexity, you'll probably want to read this mind-crunching article:

"Researchers Identify ‘Master Problem’ Underlying All Cryptography", by Erica Klarreich, Quanta Magazine (April 6, 2022)

The existence of secure cryptography depends on one of the oldest questions in computational complexity.

To ease our way, here are brief descriptions of the two key terms:

In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. Not being one-to-one is not considered sufficient for a function to be called one-way….


In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963.


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Kurt Reillag and House of Cats and Dogs

A recent email from my colleague Jean Gallier explains why the new edition of Discrete Mathematics is available on his website:

A bit more that three years ago, Springer suggested that I revise my
“Discrete Mathematics” (published in 2010).
Unfortunately, Jocelyn and I
waited too long and now that we are done
Springer no longer wants it.

I added a chapter on probability theory and made some
significant changes (improvements!). I also changed the title.
There is even an intro to the simply-typed lambda-calculus!
In any case, temporarily I am falling back on the little known publisher
“Kurt Reillag and House of Cats and Dogs”.

Interested readers may observe a certain relationship between "Reillag" and "Gallier", and in any case web search will turn up Reillag's home page — which provides this post's main linguistic relevance.

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