Ralph Dumain

Martin Gardner, Mathematical Games, & the Fourth Dimension

On this site

Dumain contributions

Mathematical Games: Counting Systems and the Relationship between Numbers and the Real World” by Martin Gardner, Scientific American, “Mathematical Games” column, June 1968 [Excerpt including acknowledgments of R. Dumain et al for solutions to Baker’s Solitaire problem, not included in the anthologies]

The fourth dimension

Black mystic in hyperspace by R. Dumain

Gustav Spiller Against the Fourth Dimension

Frank Blighton & the Fourth Dimension

Into the Fourth Dimension” by Frank Blighton

Into the Fifth Dimension” by Frank Blighton

The Hop on Hyperspace” by Frank Blighton

Friedrich Engels on Empiricism, Spiritualism, Science, Mysticism, and Philosophical Naivete

La naturesplorado en la mondo de la spiritoj de Friedrich Engels, elgermanigita de Vilhelmo Lutermano (in Esperanto)

Web guides & bibliographies

Board Games & Related Games & Recreations: Web Guide

Homage to Martin Gardner (October 21, 1914 – May 22, 2010) [all links incorporated into the present web page]

Bibliography of Board Games & Related Games & Recreations (As of 30 August 1994) in the collection of Ralph Dumain

Bibliography & Catalog of Board Games & Related Games & Recreations: Games Collection of Ralph Dumain: Supplement # 1 (1994-2008)

Algorithmic Puzzles: Selected Bibliography

Mathematical Fiction & Related Works: A Guide

Vladimir Nabokov: Science Fiction, Artificial Languages, Ars Combinatoria, Narrative Structure, Martin Gardner, Play: An Arbitrary Bibliography

Ramon Llull & His Influence: Select Bibliography & Web Guide

Doubt & Skepticism: A Directed Minimal Bibliography & Web Guide

Enrique Gaspar y Rimbau: El anacronópete — The First Time Machine

H. G. Wells’ The Time Machine: Selected Bibliography

Selected Non-fictions: Table of Contents by Jorge Luis Borges; Eliot Weinberger (ed.,tr.), Esther Allen (tr.), Suzanne Jill Levine (tr.)

Jorge Luis Borges: Selected Study Materials on the Web

The Cavalier: Covers & Contents

J. U. Giesy (John Ulrich, 1877-1948) & His Collaborators

Science Fiction & Utopia Research Resources: A Selective Work in Progress

On other sites

Dumain contributions


Martin Gardner @ Reason & Society

Testimonials (includes history of my engagement with Martin Gardner)

Martin Gardner Dead at 95

Testimonial 55: Ralph Dumain (Martin Gardner Testimonials)


Martin Gardner - Wikipedia, the free encyclopedia

List of Martin Gardner Mathematical Games columns - Wikipedia, the free encyclopedia

Martin Gardner bibliography - Wikipedia, the free encyclopedia

Essential web sites & bibliographical guides

Martin Gardner Home Site (Martin Gardner Centennial 1914-2014)

Martin Gardner Testimonials

Gathering for Gardner

Gardner Index by Carl W. Lee

Martin Gardner's Collections of "Mathematical Games" Columns by Brian Raiter

Martin Gardner: Mathematical Games

Martin Gardner's Mathematical Games: The Entire Collection of His Scientific American Columns (CD-ROM)

The New Martin Gardner Mathematical Library (Cambridge University Press)

Autobiography & documentary

A Quarter Century of Recreational Mathematics, by Martin Gardner, originally published in Scientific American,  August 1998; reprinted May 29, 2010

Martin Gardner Mathemagician,” episode of “The Nature of Things,” CBC, 1996 (YouTube, 46:04)

Miscellaneous tributes

Martin Gardner Communications Award, July 1994, with Gardner interview (YouTube, 14:08)

Game Inventor: Martin Gardner (a tribute from Kadon Enterprises, Inc.)

John Conway Reminiscences about Dr. Matrix and Bourbaki, by Colm Mulcahy, Scientific American blog, April 1, 2015.

Inspired by Martin Gardner

The Lives and Games of Martin Gardner - Numericana

Bulgarian Solitaire

Ask Dr. Matrix

The Mathemagician and the Pied Puzzler: A Collection in Tribute to Martin Gardner, edited by Elwyn Berlekamp & Tom Rodgers (Natick, MA: AK Peters, 1999)

The fourth dimension (hyperspace) & Flatland(s)

The Unexpected Hanging And Other Mathematical Diversions by Martin Gardner (1991 ed.) *

Martin Gardner | The Church of the Fourth Dimension by Giulio Prisco, October 13, 2012

Fourth dimension - Wikipedia, the free encyclopedia

Four-dimensional space - Wikipedia, the free encyclopedia

Fourth dimension in literature - Wikipedia, the free encyclopedia

Hyperspace - Wikipedia, the free encyclopedia

Johann Karl Friedrich Zöllner - Wikipedia, the free encyclopedia

Spiritualism - Wikipedia, the free encyclopedia

Gustav Spiller - Wikipedia, the free encyclopedia

Edwin Abbott Abbott - Wikipedia, the free encyclopedia

Flatland - Wikipedia, the free encyclopedia

Charles Howard Hinton - Wikipedia, the free encyclopedia

Sphereland - From Wikipedia, the free encyclopedia

Flatterland - From Wikipedia, the free encyclopedia

Rudy Rucker - From Wikipedia, the free encyclopedia

Flatland: A Romance of Many Dimensions, with Illustrations by the Author, A SQUARE [Edwin Abbott Abbott]

Flatland 1965 [film: YouTube]

Flatland: The Film (2007) [YouTube]

Flatland (2007 film) - Wikipedia, the free encyclopedia

The Flatland Store (Flatland: The Movie)

Flatland: The Movie - Wikipedia, the free encyclopedia (2007)

Flatland 2: Sphereland (2012) [IMDB]

Flatland — more YouTube video & audio

C4D | The Church Of The Fourth Dimension

Llull, Bruno, Borges, and the fourth dimension

Borges on Hinton

Charles Hinton and His Cubes by David Auerbach

Deflating Hyperspace” by David Pacchioli

Natural Science and the Spirit World in Dialectics of Nature by Friedrich Engels

Blindness (1977) by Jorge Luis Borges (mentions Spiller)

Mathematical Fiction: Motif=Higher/Lower Dimensions: Search here

Assorted references

Abbott, Edwin Abbott. The Annotated Flatland: A Romance of Many Dimensions; introduction and notes by Ian Stewart. Cambridge, MA: Perseus Publishing, 2002. (Re-published: New York: Basic Books, 2008.)

Gardner, Martin. “The Puzzles in Ulysses,” Semiotica, vol. 57, nos. 3-4 (1985), pp. 317-330. Also in Gardner, The Night is Large: Collected Essays, 1938-1995 (New York: St. Martin’s Press, 1996), pp. 354-367.

* Gardner, Martin. The Unexpected Hanging And Other Mathematical Diversions. 2nd ed. Chicago: University of Chicago Press, 1991. With updated chapters & bibliography, and an afterword. The original edition: New York: Simon & Schuster, 1969.

“The Church Of The Fourth Dimension,” 1969 ed., Chapter 6, pp.65-75; 1991 ed., same +  pp. 246-247 (in Afterword) + Bibliography, p. 256.

“An adventure in hyperspace at the Church of the Fourth Dimension,” “Mathematical Games” column, January 1962.

“Flatlands,” 1969 ed., Chapter 12, pp. 136-146; 1991 ed., same + p. 249 (in Afterword) + Bibliography, p. 259.

“Fiction about life in two dimensions,” “Mathematical Games” column, July 1962.

See also: “The pleasures of doing science and technology in the planiverse” [Dewdney], “Mathematical Games” column, July 1980.

And see also other columns & chapters:

“Is it possible to visualize a four-dimensional figure?”, November 1966.
“The orders of infinity, the topological nature of dimension and "supertasks",” March 1971.
“Hypercubes,” in Mathematical Carnival (1975)
“Spheres and Hyperspheres,” in Mathematical Circus (1979)

Note: I read The Unexpected Hanging in 1969, my likely introduction to Flatland and the fourth dimension.

Pickover, Clifford A. Jews in Hyperspace. Kindle Edition, 2009.

Pickover, Clifford A. Surfing through Hyperspace: Understanding Higher Universes in Six Easy Lessons. New York: Oxford University Press, 1999.

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Uploaded 14 December 2021
Last update 28 July 2022
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