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Benjamin Wells
University of San Francisco
San Francisco, California
 

For nearly three decades, Benjamin Wells taught mathematics and computer science courses as a member of both departments at the University of San Francisco. He regularly offered freshman seminars that combined science and art. He holds degrees from MIT and UC Berkeley and has worked and studied in several other countries. He won a John Templeton Foundation science and religion course prize for “Infinity, Chaos, and Mysticism in Science and Religion” in 1998 and held the USF Davies Professorship in 1989, teaching a seminar “Approaching Infinity: Mathematics and the Mystic Quest.”

He cofounded the USF Math & Art Fusion Project and serves as its director. It seeks to use the permanent collection of San Francisco’s De Young Museum to teach middle-school mathematics.

Wells has periodically shared mathematical art at Bridges conferences and other exhibitions. His contributions to math and art include explorations of the Klein 4-group and Galois theory in puppet shows, analysis and generation of tongue twisters, a study of 1, and demonstrations of the dualizing Hoberman plastic toys. In the photograph, he holds the Hoberman Switch-Pitch ball, a self-dualizing tetrahedral structure that is the mascot of the Fusion Project.

A fan of fractals, he has studied the fractal arrangement of mineral spherites in a Mono Lake brine fly larval instar and has performed his “Fractal Rap” to OPP at numerous gatherings.

As the last student of noted logician Alfred Tarski, Wells works on the boundary of logic, algebra, and computing. Several papers explore pseudorecursive semigroup varieties. This has led to five contributions to hypercomputation.

He has also published in computer graphics, visual communication (with 22 patents), and classic computers. In particular, he has investigated the universality of the Colossus machines built for Bletchley Park. His collaborative research includes the action of finite state machines on infinite sequences; expert tutoring systems; peer teaching in secondary school; and math education films and videos. He has studied the behavior and application of squarefree sequences, rediscovering a number of great results—the fun of discovery outweighing the tardiness!

He says, “I enjoy reviewing books in familiar and in strange fields. It serves potential readers to outline the material and to suggest the issues covered and the manner of their coverage, forming a preview of style and efficacy as well as contents. If there is a chance for humor, all the better.”

Since retiring in 2011, he spends much time in event planning with his wife; for some of that work, please see: Francis in the Schools and White Pony Express.


     

On k-abelian palindromes
Cassaigne J., Karhumki J., Puzynina S.  Information and Computation 260(C): 89-98, 2018. Type: Article

This paper explores words (finite strings over a fixed finite alphabet Σ with at least two letters) that are k-abelian equivalent to their reversals. Two words are k-abelian equivalent if and only if thei...

 

Languages with membership determined by single letter factors
Higgins P., Alwan S.  Theoretical Computer Science 680 15-24, 2017. Type: Article

This paper continues a previous one [1] by the authors, Higgins and Alwan, expanding on the notion of scan languages that require a word to be read completely before determining whether the word belongs to the language. This applies to every word,...

 

Characterization of context-free languages
Badano M., Vaggione D.  Theoretical Computer Science 676 92-96, 2017. Type: Article

The authors prove that a generalized Greibach normal form (GNF) grammar still generates a context-free language. They expand the left side of GNF-type rules to be any nonempty product of variables (nonterminals), not just a single variable. Then, ...

 

Hamlet on the holodeck: the future of narrative in cyberspace (updated ed.)
Murray J.,  The MIT Press, Cambridge, MA, 2017. 440 pp. Type: Book (978-0-262533-48-5)

Readers of this book are treated to an exploration of how story enlivens new computer-based representational technologies. Taking an incident from the Star Trek holodeck as an initial example, Murray demonstrates that the old method of repr...

 

Digital fonts and reading
Dyson M., Suen C.,  World Scientific Publishing Co, Inc., Hackensack, NJ, 2016. 296 pp. Type: Book

This anthology of 14 papers by 21 authors, including the two editors, focuses on the interaction of vision and type design....

 
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