The Bamboo Annals

Bamboo.JPG

The original Chinese text of the Bamboo Annals

The ancient Chinese text The Bamboo Annals, published around 300 BC, details the events in Chinese history–or mythology–that transpired between around 2700 BC to the time of the text’s publication. Included in the Annals is the story of the legendary Emperor Yao. Yao was a patient and wise emperor, beloved by his constituents. Unfortunately, his talents were not bestowed upon his son. Danzhu, in contrast with his father, was petty and capricious. He was prone to profligacy. As legend has it, Yao invented the game of Go to instill good values into his son. He insisted that the lessons of Go might carry over to real life.

Danzhu took to the game; he even became a good player. But his attitudes never changed. He rejected the notion that a mere game could teach him how to live. Eventually, a weary and crestfallen Yao abdicated the throne, and gave it to Shun, his trusty advisor, instead of his son. Danzhu was furious. He began concocting a plan to kill his father.

Continue reading

Advertisements

Alien Languages

The recent movie Arrival treats an imagined arrival on earth by alien beings. The United States government, at a loss to understand the visitors’ intentions, conscripts the film’s hero—unusually for Hollywood, a linguist—to help understand the aliens’ language, and in turn, their purpose.

arrival-e1504797937710.jpeg

The aliens’ language’s “freedom from time” evokes the functional programming language Haskell.

The linguist, Louise Banks, soon makes headway. She discovers that the aliens’ language “has no forward or backward direction” and “is free of time”. Moreover, in a nod to the (unfortunately, all-but discredited) Sapir–Whorf hypothesis—according to which, as Banks suggests, “the language you speak determines how you think and… affects how you see everything”—Banks soon finds her own cognition shifting:

If you learn it, when you really learn it, you begin to perceive time the way that they do, so you can see what’s to come. But time, it isn’t the same for them. It’s non-linear.

Far from inducing an reaction of incredulity and awe, these descriptions of the visitors’ language provoked in me just one persistent response: “This is just like the programming language Haskell.” Continue reading

Rabbinic Mathematics

יַּ֥עַשׂ אֶת־הַיָּ֖ם מוּצָ֑ק עֶ֣שֶׂר בָּ֠אַמָּה מִשְּׂפָת֨וֹ עַד־שְׂפָת֜וֹ עָגֹ֣ל׀ סָבִ֗יב וְחָמֵ֤שׁ בָּֽאַמָּה֙ קוֹמָת֔וֹ ׳וּקְוֵה׳ ״וְקָו֙״ שְׁלֹשִׁ֣ים בָּֽאַמָּ֔ה יָסֹ֥ב אֹת֖וֹ סָבִֽיב׃
מלכים א 7:23

And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.
I Kings 7:23

This Hebrew Bible passage from I Kings—along with a similar one from II Chronicles—forms the biblical basis for Talmudic scholar Matityahu Hacohen Munk’s suggestion that “some of the geometrical rules did not hold in King Solomon’s temple,” a heavenly ‘‘world of truth’’ beyond our own, mathematical historians Tsaban and Garber write [1].

What’s so heavenly about the Molten Sea, a putative basin created by King Solomon in the ancient Temple of Jerusalem for ritual ablution? And why do the Rabbis Johanan and Papa discuss it extensively in the Babylonian Talmud, bickering in particular about its brim—“[as thin as] the flower of a lily… a handbreadth thick… wrought like the brim of a cup” [2, Eruvin 14a:29-31]?

The simple answer is that this particular snippet of the Word of God contains an oddity, asserting that this circular basin’s circumference is thrice its diameter—or that the geometrical constant π, rather than an irrational number, with an infinite and unpredictable decimal expansion, is in fact rational, and indeed an integer—the number 3, to be exact. Continue reading

Swiss French, Swiss German

Ferdinand de Saussure was a profound linguistic thinker of the early 1900s. During a legendary series of lectures given at University of Geneva, de Saussure, a French-speaking Swiss, introduced to the world many ideas which have since become fundamental — even “self-evident” — within the discipline of linguistics. De Saussure suggested, for example, that the historical and etymological emphases of his day failed to recognize as the central object of linguistics the instantaneous internal structure of a language, to which prior evolutionary contingencies are irrelevant. A language’s internal structure, in fact, exists moreover independently of the writing system it uses, of the concrete sounds of its phonetic system, and even of its words. It consists entirely, de Saussure argued, of an abstract system of so-called signs — each linking an idea to a sound — which subsist only through the network of relationships among them and persist only through the coordinated ativity of a linguistic community. “It is because the linguistic sign is arbitrary that it knows no other law than that of tradition,” de Saussure famously wrote, “and because it is founded upon tradition that it can be arbitrary.” [1, p. 74]

De Saussure’s facility with historical linguistics was, to his credit, uncanny. Discussing the unfortunate common tendency to confuse historical (diachronic) with instantaneous (synchronic) linguistics, for example, he writes:

In order to explain Greek phuktós, it might be supposed that it suffices to point out that in Greek g and kh become k before a voiceless consonant, and to state this fact in terms of synchronic correspondences such as phugeînphuktóslékhosléktron, etc. But then we come up against cases like tríkhesthriksí, where a complication occurs in the form of a ‘change’ from t to th… [1, p. 96]

De Saussure proceeds like this effortlessly, citing detailed examples variously from Sanskrit [1, p. 2], Latin [1, p. 95], Old High German [1, p. 83], Anglo-Saxon [1, p. 83], early Slavonic [1, p. 86], and, of course, French [1, pp. 31, 69, 85, 95, 104, 106, …].

De Saussure’s true genius, however, was evident perhaps most of all in his novel theory of signs, which emphasized the social, conventional, and ultimately arbitrary nature of linguistic systems — and which eventually produced the field of semiotics.

This theory was validated during my recent trip to Switzerland. Continue reading

A Fragile Truth

My four-week psychiatry rotation at Western State Hospital landed smack in the middle of peak general election season. And, oddly enough, these two experiences have yielded remarkable similarities. In both cases, I have been forced to entertain various versions of the truth.

Many of the patients here at Western State are psychotic. Our known and stated goal, then, is to return these patients to reality-based thinking. Only then might they qualify for discharge. This exercise has presented philosophical challenges. Certainly, sometimes, our job is easy. One of our patients, who signs her forms as Michelle Obama Prince Harry Elizabeth Queen Zealand, communicates with Russia, Germany, Berlin, Jerusalem, East Germany, West Germany, South Germany, and Russia, by radio, television, and satellite, including the satellite in the backyard of her palace, which she built, and in which we currently reside. Another patient, though, gave me pause. Continue reading

I Have a Unique Coffee Mug

I’ll attempt to explore a few of the subtleties surrounding the word unique in English.

0505161536_HDR

I’ve drunk too many of these, and this post is how you can tell.

I’ll begin with an exploration of words like the same and different. Sentences containing these words will prove a fertile initial testing ground.

First, an observation. Consider the sentences:

  1. Every coffee mug in my department is brittle.
  2. Every coffee mug in my department is the same.

Though these sentences appear structurally similar, their predicates are deceptively different. Continue reading

Lesson Time

This article is part of a series entitled Everyday Game Theory. See also:
1. The Escalator’s Dilemma; 2. Electoral College; 3. Passing Curiosity; 4. Lesson Time

This is (a slightly modified version of) a text message exchange which recently occurred between my violin teacher and me.

  1. Teacher: “Can we meet today instead of tomorrow?”
  2. Me: “That’d be great!”
  3. Teacher: “Cool, see you this afternoon.”
  4. Me: “Ok.”

It would not have been acceptable for me to fail to respond to my teacher’s message (1). If I didn’t respond, my teacher would have no way to know whether I ever received her message – and, hence, whether to come today or tomorrow.

Neither would it have been ok, for that matter, for my teacher to let the conversation end at message (2). Until I receive her confirmation (3), I can in no way be sure whether she has seen or acknowledged my message (2). In other words, with her message (3) unsaid, it could remain the case, for all I know, that my teacher, as yet unaware of my response (2), imagines me unaware of (1) and still intent to come tomorrow.

Even after I received my teacher’s message (3), though, it was important for me to send the further message (4). After all, until she receives my message (4), my teacher may well imagine me unaware of her message (3). In that situation — her thought process might go — I would, unaware of her confirmation (3), be liable to suspect her unaware of my response (2), and hence unsure of my receipt of (1), and so liable to come tomorrow.

Why doesn’t this continue? Continue reading