Stanford Lecture: Don Knuth-"Hamiltonian Paths in Antiquity" (2016)

Computer Musings 2016
Donald Knuth's 23rd Annual Christmas Tree Lecture: "Hamiltonian Paths in Antiquity"
Speaker: Donald Knuth
About 1850, William Rowan Hamilton invented the Icosian Game, which involved finding a path that encounters all points of a network without retracing its steps. Variants of his game have turned out to be important in many modern computer applications.
The speaker will give evidence that people have been interested in such questions since at least Graeco-Roman times. Furthermore, ingenious Sanskrit and Arabic documents from the ninth century, and continuing through medieval times, also reveal that this is perhaps the oldest nontrivial combinatorial problem in the history of civilization.
About the Speaker:
Donald Ervin Knuth is an American computer scientist, mathematician, and Professor Emeritus at Stanford University.
He is the author of the multi-volume work The Art of Computer Programming and has been called the "father" of the analysis of algorithms. He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces.

[@michakrzak8367]

Thank you, Professor Knuth, for mentioning Sinterit in your lecture. We were more than happy for printing those icosahedrons for you.

[@srinivasakrishnanl2289]

One of the reasons why Sanskrit poets seemed to deal with some of these problems was their habit of doing 'citrakavi' i.e., picture poems or crostics. These involved composing poems whose metrical units (poetical syllables or groups of syllables) could be arranged on a picture so the verse is evocative of the picture. Sometimes the verse had as its theme what's suggested by the picture. Thus they would have cobra crostic, double cobra crostic, bow crostic, double bow crostic, drum crostic, double drum crostic etc etc. One of the popular ones (and maybe of some interest to the audience here) is the chariot crostic. This involved having the words for numbers in each line of the verse. Thus the first line will have '1', the second '121', the third '12321' and so on for a few lines. The subsequent lines could go on a decreasing sequence i.e., 12321, 121, 1 etc. If you arrange these numbers (with the first line on top and the next line below it) it would look like a triangle positioned over an inverted triangle, which is how the canopy of the traditional chariot looks in a line drawing. In temples in South India there are wall paintings which have chariots and words of famous poems inscribed on the chariot. In my native town of Kumbakonam in the state of Tamilnadu, there's a Siva temple with a huge mural of a Tamil poem whose metrical units are painted on parts of a chariot. This is by a famous poet who was a devotee of Siva. And in the next street, there's a Vishnu temple with a chariot mural of an equally famous Tamil poem to Vishnu. This time by a famous poet who was a devotee of Vishnu. This echoes Prof Knuth's remark about competition among poets. Both poets lived in the 7th-8th century CE timeframe.

[@csm-csm]

Thanks for story! This is very interesting, could you provide an example of picture and poem correspondence?

[@ronitdhanphole]

@@csm-csm Vikram Chandra has an excellent lecture on Chitra Kavya (on youtube).

Great professor Knuth! One of the brightest mind of this century

[@ilovemyx1594]

I am not sure if Prof Knuth missed it or not. But both Ratnakara:'s work and Swamy Desika Acharya's work is complete wrt both 4x8 and 8x8 Knight's tour or thuragabanda.

[@juliannevillecorrea]

36:07 thank you sir ❤️

[@jayquelin]

my hero

[@m7mdyahia]

26:23
The arabic manuscript was published KSU faculty of art here
fac.ksu.edu.sa/madwani/publication/144765

[@SaveSoilSaveSoil]

Any Sanskrit-literate person volunteers to comment on how good the Sanskrit poems are? On a different note, I love Prof. Knuth's cute little poems! 😍

[@Akaula1]

Ratnakara was 156 CE and time mentioned in this is wrong.

[@ArunOlappamannaVasudevan]

Please write to Prof. Donald Knuth in paper letter.

[@dufferzafar]

Can you please cite some sources? We could also discuss this on Knight's Tour Wikipedia Page

[@suchoudh]

Thx for Sanskrit session

[@artursafiullin7008]

master yoda prototype

[@50oje]

it turned out to come in Volume 4C ;-)

[@brashcrab]

7217 1:07