Thursday, 30 April 2020

John Horton Conway and LUX

Introduction


On the 25th April 2020, I came across a newsletter of the French magazine "Tangente" announcing that, despite the ongoing COVID-19 difficulties, their next issue n° 194 would still be published at the end of May. They stated that this future magazine would contain a main section dedicated to the late John Horton Conway, famous for his "Game of Life" (a cellular automaton in which cells live, die and are born). Having been previously unaware of Conway's death, I immediately wished to inform the fellow members of a magic square circle of the sad news, and sent them the following e-mail: 

Dear all,
I have just learnt that John Horton Conway passed away on the 11th April in New Brunswick, New Jersey, at the age of 82, after complications from COVID-19. I did not know him personally, but I expect that some of you did. His well-known LUX method for magic squares is an algorithm for creating magic squares of order 4n+2, where n is a natural number, and his "lozenge" method is another method of construction of magic squares. So this is a considerable loss to the magic square community, and goes to show that the virus is indiscriminate and dangerous.

Here's hoping that a cure will be found soon.

Stay safe!

William 

I rapidly received replies from Peter Loly, Bob Ziff, Awani Kumar and Miguel Angel Amela:

Peter Loly stated that Conway's passing away reminded him of his colleague Richard Guy who had passed away aged 103 on the 30th September 2019, and also of the losses of John Hendricks and Harvey Heinz, both of whom he had met. He asked if I could send this information out on the blog.

Bob Ziff replied to say that Conway had had the bad luck of being in a nursing home for some other health problems, and concluded by writing "Let’s all hope that we stay healthy!"

Awani Kumar replied with a simple "So sad. RIP."

Miguel Angel Amela then replied with a photomontage of a very fitting "in memoriam" plaque: He proposed that John Horton Conway's name could be inscribed above a 6x6 magic square constructed with Conway's LUX method, and that the Spanish words "descansa en la LUX" could be inscribed below. The Spanish text "descansa en la LUX" means "rest in the LUX" or "rest in the LIGHT." Miguel stated that in Latin, the inscription would be R.I.L. or "REQUIESCAT IN LUX," and he suggested a poem written by Art Durkee, entitled "requiescat in lux." 

An "In Memoriam" plaque for John Horton Conway

Miguel Amela's idea of an "in memoriam" plaque in homage of John Horton Conway and his LUX method for constructing magic squares
Adaptation of Miguel Angel Amela's idea of an "in memoriam" plaque for John Horton Conway

Perhaps, one day, a plaque like this will be placed at Cambridge or Princeton, or at another of Conway's haunts.

John Horton Conway's LUX Method


Martin Erickson has already described Conway's LUX method in page 98 of "Aha Solutions" (published by the Mathematical Association of America in 2009), and he even used the same "in memoriam" square of order-6 as a base array to construct a LUX square of order-18! However, here it is useful to examine how the LUX method can be used to construct the "in memoriam" square itself, and the following pdf file explains the construction steps:



The "in memoriam" magic square can also be programmed, for example using languages such as Elixir, Haskell and Ruby, as shown in "Magic squares of singly even order," edited by the programming chrestomathy site "Rosetta Code."

Conclusions


This short article only intends to commemorate a small part of John Horton Conway's work on magic squares. Because I myself have never had the pleasure of meeting him, those who did are far better placed to write about his other accomplishments, and about his life in general. The obituary written by Catherine Zandonella for Princeton University gives us a good insight, not only of his many achievements, but also of his mathematical playfulness and of his kind attention to others that made him many friends. Another source of information with useful external links is John Horton Conway's biography written by John Joseph O'Connor and Edmund Frederick Robertson for the MacTutor History of Mathematics Archive at the University of St Andrews. 

Acknowledgements


I wish to thank Peter Loly, Bob Ziff, Awani Kumar and Miguel Angel Amela for replying to my e-mail. Their messages and contributions have inspired me to write this post.

With COVID-19 still active and dangerous at the time of writing, I urge you all to take heed of the social distancing guidelines, and keep safe!