Guide to the Thomas Banchoff papers on the fourth dimension , 1843-2013

(bulk 1970-2007)

John Hay Library, University Archives and Manuscripts
Box A
Brown University
Providence, RI 02912
Telephone: Manuscripts: 401-863-3723; University Archives: 401-863-2148
Email: Manuscripts: hay@brown.edu; University Archives: archives@brown.edu

Published in 2022

Collection Overview

Title:	Thomas Banchoff papers on the fourth dimension
Date range:	1843-2013, (1970-2007)
Creator:	Banchoff, Thomas
Extent:	13 Linear Feet 12 records center boxes, 3 letter-size document cases
Abstract:	The Thomas Banchoff papers on the fourth dimension (1843-2013) contain his research and writing on the mathematical and philosophical theories of the fourth dimension, its visualization, and historical conceptions of it. Included are correspondence, conference proceedings, articles, manuscripts, clippings, CD's, and DVDs. The material covers mathematical, artistic, religious, and philosophical concepts of hyperspace and the higher dimensions from the mid-nineteeth century to the present, along with Banchoff's research on Edwin Abbott Abbott and his nineteenth-century novella, Flatland. Also included are audiovisual materials in a number of formats representing film and musical interpretations of Flatland, teaching materials, class recordings, and geometry and calculus texts and presentations.
Language of materials:	English
Repository:	John Hay Library, University Archives and Manuscripts
Collection number:	MS.2015.001

Scope & content

The Thomas Banchoff papers on the fourth dimension represent Professor Banchoff's teaching, research, and writings on the higher dimensions, in both a mathematical and an imaginative context. The papers are arranged in seven series:

Series 1. Correspondence and personal (1970-2010) contains personal and professional correspondence relating to Banchoff's research and writing on the higher dimensions, Edwin A. Abbott, and his novella Flatland, as well as particulars of Banchoff's annual research trips to England. Most of the correspondence is arranged by year, but several individual correspondents have their own folders; the series also contains biographical and personal media in the form of CDs, DVDs, audiocassettes, and videocassettes;

Series 2. Writings, teaching, and conferences (1978-2013) includes material relating to teaching the fourth dimension, especially to primary and secondary school students. Also included are class and conference materials, clippings, miscellaneous notes and articles by Banchoff about teaching mathematics and the fourth dimension with computer animation, models, and multimedia resources;

Series 3. Fourth dimension (1856-2010) includes material relating to the idea of the fourth dimension in both modern and historical contexts, and from both scientific and imaginative viewpoints; the series also includes material about its influence on literature, art, and architecture; there are also numerous media resources concerning the visualization of higher dimensions in mathematics, puzzles, and art, including the work of Salvadore Dali.

Series 4. Spiritualism, transcendentalism, religion (1871-2001) contains material about philosophically and spiritually related influences on, and offshoots of, the idea of the higher dimensions, from the nineteenth century to the present. Included are essays by and about George Stuart Fullerton, Charles Webster Leadbeater, and P. D. Ouspensky;

Series 5. Edwin Abbott Abbott (1843-2002) includes biographical and historical research, social and religious influences, and transcriptions of Abbott's correspondence, along with Banchoff notes on his research and an extensive E.A. Abbott bibliography;

Series 6. Flatland (1882-2008) contains annotated versions, commentary, and contemporary reviews of E. A. Abbott's novellaFlatland; Banchoff articles and talks on Flatland; notes about related versions of the novella, such as the film, hypertext project, and interactive CD-ROM; there are also multiple media interpretations of the novella;

Series 7. Miscellaneous media (1991-2013) comprises DVDs, CD-ROMs, videocassettes, and audiocassettes containing ideas and references relating to hyperspace.

Access Points

Subject Names

• Abbott, Edwin Abbott

Subject Organizations

• Brown University. Department of Mathematics
• Brown University--Faculty--Archives

Subject Topics

• Theosophy
• Spiritualism -- 19th century
• Computer science
• Computer graphics
• Computer art
• College teachers -- United States -- 20th century
• Graphic arts
• Mathematical literature
• Mathematics -- Study and teaching
• Occultism
• Hypercube
• Hyperspace -- Study and teaching
• Fourth dimension
• Geometry, Differential
• Fourth dimension -- History

Occupations

• Educators
• Teachers
• Mathematicians

Document Types

• Research (function)
• Videocassettes
• slides (photographs)
• Scripts (documents)
• Reviews (book)
• DVDs
• Correspondence
• color photographs
• Color slides
• Clippings (information artifacts)
• CD-ROMs
• Book catalogs
• Audiocassettes
• Floppy disks
• Instructional materials
• Lecture notes
• Manuscripts (documents)
• Notes

Arrangement

• Series 1. Correspondence and personal
• Series 2. Writings, teaching, and conferences
• Series 3. Fourth dimension
• Series 4. Spiritualism, transcendentalism, religion
• Series 5. Edwin Abbott Abbott
• Series 6. Flatland
• Series 7. Miscellaneous media

Biographical Note

Although the concept of higher dimensions has existed since Descartes, not until the nineteenth century was it more fully explored. These early intellectual explorations took the forms of both mathematical and imaginative enquiries, such as Charles H. Hinton's "scientific romance" titled "What Is the Fourth Dimension?" (1888) and Edwin Abbott Abbott's novella Flatland (1884). Both Hinton and Abbott built their works on a mathematical foundation, subsequently developing them into moral and social commentaries that reflected a Victorian preoccupation with religion and social class. This Victorian "geometry of higher dimensions" referenced Plato's shadows, Kant's transcendental idealism, Gauss's curved surfaces, and Zollner's four-dimensional spirits.

In his article "From Flatland to Hypergraphics: Interacting with Higher Dimensions" (1990) Thomas Banchoff outlines the evolution of the idea of the fourth dimension expressed in Abbott's Flatland. Edwin Abbott was a headmaster, educator, and theologian, but not a mathematician. He was certainly influenced by the contemporary concept of higher-dimensional ideas, but Banchoff links Abbott's primary interest in the higher dimensions to his exposure to the writings of the younger scientist Charles Hinton. These writings gave Abbott the framework for his novella about "a two-dimensional universe inhabited by flat beings." But, according to Banchoff, Abbott "seems to have been the first to have developed it into a social allegory and the first to treat the possibility of an encounter between beings of different dimensions, with all its challenges and frustrations." Abbott's fourth dimension suggests the divine space that challenges mortal understanding and expression.

Computers have expanded our ability to visualize the higher dimensions by way of both mathematics and popular culture. According to Professor Banchoff, "As we watch images moving on the screen of a graphics computer, we are faced with challenges like those of the first scientists to make use of telescopes or microscopes or X rays. We are seeing things now that have never been before, and we are just learning how to interpret these images. It is literally true that we are in the first stages of a new era when it comes to visualizing dimensions."

Banchoff, Thomas F. "Introducing dimensions and scaling and measurement." Chap. 1 in Beyond the third dimension: geometry, computer graphics, and higher dimensions. Scientific American Library, 1990-1996. http://www.mathaware.org/mam/00/master/essays/B3D/1/technology.html

Banchoff, Thomas F. "From Flatland to hypergraphics: interacting with higher dimensions." Updated version of what was originally published in Interdisciplinary Science Reviews, 1990. http://www.math.brown.edu/~banchoff/gc/ISR/ISR.html

Access & Use

Access to the collection:	There are no restrictions on access for non-digital materials, except that the collection can only be seen by prior appointment. Some materials may be stored off-site and cannot be produced on the same day on which they are requested. Advance notice is required to view born-digital records. Born-digital materials in this collection have not been reformatted yet. Researchers may request access to copies by contacting the John Hay Library with the collection name, collection number, and a description of the item(s) requested. Access to original physical digital media is restricted.
Use of the materials:	Researchers are advised that express written permission to reproduce, quote, or otherwise publish any portion or extract from this collection must be obtained from the Brown University Library. Although Brown University has physical ownership of the collection and the materials contained therein, it does not claim literary rights. It is up to the researcher to determine the owners of the literary rights and to obtain any necessary permissions from them.
Preferred citation:	Thomas Banchoff papers on the fourth dimension, Ms.2015.001, Brown University Library.
Contact information:	John Hay Library, University Archives and Manuscripts Box A Brown University Providence, RI 02912 Telephone: Manuscripts: 401-863-3723; University Archives: 401-863-2148 Email: Manuscripts: hay@brown.edu; University Archives: archives@brown.edu

Administrative Information

ABOUT THE COLLECTION
Acquisition:	Donated by Thomas F. Banchoff on January 20, 2015 and on August 22, 2016.
ABOUT THE FINDING AID
Author:	Deborah Peterson.
Encoding:	This finding aid was produced using ArchivesSpace on 2022-11-23.
Descriptive rules:	Describing Archives: A Content Standard

Additional Information

Related material:

Related Materials Papers related to Thomas Banchoff's research in mathematics and Banchoff-Strauss Productions records are at the Archives of American Mathematics, Briscoe Center for American History, University of Texas at Austin. Papers relating to Thomas Banchoff's presidency of the Mathematical Association of America (1999-2000) are with the Mathematical Association of America, Washington, D.C. Thomas Banchoff collection of materials relating to Edwin Abbott, Ms.2011.0016, Brown University Library Thomas Banchoff papers, OF.1UF.2015.003, Brown University Library

Inventory

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