Martin Gardner (1914 to 2010) Remembrance
[ Martin Gardner ] [ https://en.wikipedia.org/wiki/Martin_Gardner ] died yesterday, at age 95 (1914 to 2010). He is the one who started me on the path of math. From about 1990 to 1995, i read pretty much all of his recreational math books (collection of his Scientific American column), as well as several of his pseudo-science debunking books. It is him, that made me decided that math is my career. (which turned into programing)
Conway's Game of Life
Of his recreational math articles, the one subject i think that taught me the most is his intro to [ Conway's Game of Life ] [ https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life ] (GoL). It introduced to me, back then a shocking idea, that deterministic behavior does not imply predictability. (in the 1990s, chaos theory, and computer drawing of fractals, run rampant as pop science. It was even highlighted in Hollywood movies such as Jurassic Park.)
I've spent months playing the Game Of Life in 1990s, and every few years i'd re-visit and checkout what's the latest software of it or any theoretical advances. The last i checked, few years ago, GoL has been advanced quite far, to the point that people are starting to construct animated messages like those [ Dot Matrix Displays ] [ https://en.wikipedia.org/wiki/Dot_matrix_display ] that has texts scroll by. (See the logo of the software Golly as a example. You can find Golly at Great Software for Cellular Automata.)
GoL has been proven to be [ Turing complete ] [ https://en.wikipedia.org/wiki/Turing_complete ] in i think late 1990s. Seems trivial now, but wasn't so at the time. Also, [ Rule 110 ] [ https://en.wikipedia.org/wiki/Rule_110 ] has been proven to be Turing Complete, arguably the “most simple” cellular automata to be proven so. Also note, that there are quite a few models of [ Universal Turing machines ] [ https://en.wikipedia.org/wiki/Universal_Turing_machine ], and in 2007, Wolfram proposed a problem with $25k USD award for anyone to prove that a 2-state 3-symbol CA is Turing equivalent. Alex Smith came forward and got the prize, though not without some dispute from a accomplished computer scientist. For detail, see: [ Wolfram's 2-state 3-symbol Turing machine ] [ https://en.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol_Turing_machine ] .
GoL started me a life long interest in Cellular Automata, and have read about it much since. (See: Notes on A New Kind of Science)
Another math area i learned much from Martin is [ Penrose tiling ] [ https://en.wikipedia.org/wiki/Penrose_tiling ]. Its discovery and popularization sent a shock wave in science community. Namely, the concept of aperiodic tiling and quasicrystals, and aperiodic tiling of just 2 prototiles exists.
Tiling and symmetry has also become a life long interest for me. I've spend few years studying it in late 1990s. See:
- The Discontinuous Groups of Rotation and Translation in the Plane
- Plane Tiling Mathematica Package
- Math Tiling Gallery
- Great software for Tilings, Patterns, Symmetry
- Knitting, Chinese Knots, Braid Theory
- Reading Notes on Tilings and Patterns
Martin's writings introduced me into so many math subjects. Math board games, puzzles, fractals, regular polyhedrons, geometric dissections, probability, game theory, number theory, cryptanalysis, graph theory, knot theory, … See Great Math Software for many software i collected mostly in late 1990s related to these topics.
(i despise professional mathematician's sneering attitude toward these recreational math subjects, or discrete math subjects like combinatorics, with their cryptic jargons of topology and analysis faak.)
Other books by Martin Gardner that i remember well are his Annotated Alice In Wonderland Buy at amazon, his book [ The Ambidextrous Universe: Mirror Asymmetry and Time-Reversed Worlds ] [ https://en.wikipedia.org/wiki/The_Ambidextrous_Universe:_Mirror_Asymmetry_and_Time-Reversed_Worlds ] Buy at amazon, and pseudo science debunking book Science: Good, Bad and Bogus Buy at amazon .
The Alice book has become my favorite book of all times, if i can just name one book without any qualifications. I read his annotated version, twice, in separate years, once in ~1988 and once in early 1990s. I made a website of Alice with full text and image galleries: Alice in Wonderland, and Through the Looking-Glass .
The central attraction of Alice to me, besides the math and logic allusions, is that Alice the character, to me represents the epitome of [ logical positivism ] [ https://en.wikipedia.org/wiki/logical_positivism ] attitude and personality. Logical positivism is my philosophy, introduced to me and influenced me by my favorite author Bertrand Russell.
Logical Positivism in philosophy context can be quite technical and mean slightly different things, but to me, it is mostly a combination of empiricism, rationalism, utilitarianism, with emphasis of logic and a positive attitude.
In my teen years and much of early 20s, i have strong interest in paranormal stuff, like ghosts, ufos, bigfoot, psychics etc. My un-informed but studious mind explored these topics thru reading many books, beginning foolishly by reading books of these proponents cranked out, teaching you things such as how crystals emit energy, sitting inside the center of pyramid can heal wounds, how to bend spoons by mind, alien abductions, the mysteries of bigfoot and Loch Ness monsters etc. This beginner reading eventually lead to science readings such as pseudo-science debunking books, astronomy textbooks, as i went thru college at the time. Martin's science debunking book in particular had a impact with my affairs in Scientology. (See: Scientology and Falun Gong)
I discovered that there are quite a lot articles in remembrance of Martin. Of course, but somehow i haven't thought of looking up before:
- Scientific American by Douglas Hofstadter.
- rudyrucker.com by Rudy Rucker.
- richarddawkins.net by Richard Dawkins.
- randi.org James Randi.
- blog.wolfram.com by Ed Pegg Jr.
I particularly enjoyed Douglas Hofstadter's tribute above, and this one: Martin Gardner: Impresario of Mathematical Games by Rudy Rucker. At rudyrucker.com .
These articles didn't just tell what Martin did or how they appreciated him, but contained more a bit info about Martin as a person.
See also: Hermits and Cranks: Lessons from Martin Gardner on Recognizing Pseudoscientists , by Michael Shermer. At scientificamerican.com .
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