Author: Abbott, Edwin A.
Title: Flatland: A Romance of Many Dimensions
Description: Flatland is one of the very few novels about math and philosophy that can appeal to almost any layperson. Published in 1880, this short fantasy takes us to a completely flat world of two physical dimensions where all the inhabitants are geometric shapes, and who think the planar world of length and width that they know is all there is. But one inhabitant discovers the existence of a third physical dimension, enabling him to finally grasp the concept of a fourth dimension. Watching our Flatland narrator, we begin to get an idea of the limitations of our own assumptions about reality, and we start to learn how to think about the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England.
Author: Borges, Jorge Luis
Title: Collected Fictions
Description: Undeniably one of the most influential writers to emerge in this century from Latin America or anywhere else, Borges (1899-1986) is best known for his short stories, all of which appear here for the first time in one volume, translated and annotated by University of Puerto Rico professor Hurley. Many of the stories return to the same set of images and themes that mark Borges's best known work: the code of ethics embraced by gauchos, knifefighters and outlaws; labyrinths; confrontations with one's doppelganger; and discoveries of artifacts from other worlds (an encyclopedia of a mysterious region in Iraq; a strange disc that has only one side and that gives a king his power; a menacing book that infinitely multiplies its own pages; fragmentary manuscripts that narrate otherworldly accounts of lands of the immortals). Less familiar are episodes that narrate the violent, sordid careers of pirates and outlaws like Billy the Kid (particularly in the early collection A Universal History of Iniquity) or attempts to dramatize the consciousness of Shakespeare or Homer. Elusive, erudite, melancholic, Borges's fiction will intrigue the general reader as well as the scholar.
Author: Hofstadter, Douglas R.
Title: Gödel, Escher, Bach: An Eternal Golden Braid
Description: Douglas Hofstadter's book is concerned directly with the nature of "maps" or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel Escher and Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.
Author: Paulos, John Allen
Title: Beyond Numeracy
Description: Beyond Numeracy by bestselling author John Allen Paulos is, according to the introduction, "in part a dictionary, in part a collection of short mathematical essays, and in part the ruminations of a numbers man." This book is genuinely different from other books on mathematics intended for a wide audience as the essay topics are indisputably diverse. (Titles include "Human Consciousness, Its Fractal Nature" and "Mathematics in Ethics.") Furthermore, Paulos's unique sense of humor and ability to intelligently editorialize are delightful--especially in a book on such a dry subject.
Author: Petroski, Henry
Title: To Engineer Is Human: The Role of Failure in Successful Design
Description: The moral of this book is that behind every great engineering success is a trail of often ignored (but frequently spectacular) engineering failures. Petroski covers many of the best known examples of well-intentioned but ultimately failed design in action -- the galloping Tacoma Narrows Bridge (which you've probably seen tossing cars willy-nilly in the famous black-and-white footage), the collapse of the Kansas City Hyatt Regency Hotel walkways -- and many lesser known but equally informative examples. The line of reasoning Petroski develops in this book were later formalized into his quasi-Darwinian model of technological evolution in The Evolution of Useful Things, but this book is arguably the more illuminating -- and defintely the more enjoyable -- of these two titles. Highly recommended.