The Restored Eye

A Website Devoted to High-falutin Intellectual issues, and other Fun Things
by Jacob T. Schwartz

Jack's final book has been published by Springer.
Domenico Cantone and Eugenio Omodeo, with the help of Martin Davis completed the book they were all working on one month before Jack's death. Jack would be proud.

Computational Logic and Set Theory: Applying Formalized Logic to Analysis

A Biographical Memoir written for the National Academy of Sciences by Martin Davis and Edmond Schonberg (PDF file)

Jacob T. Schwartz - January 9, 1930 - March 2, 2009

A Celebration of the Life of Jacob T. Schwartz - March 27, 2009
Click here to view program

Courant Institute of Mathematical Sciences
251 Mercer Street
New York, NY 10011

Jack's Obituary in the Communications of the ACM - (PDF file)

Slideshow by Diana Schwartz (prepared for Jack's 65th Birthday Symposium at Courant) - (Flash Video)

Jacob T. Schwartz Lipari International School - Thank you, Alfredo Ferro


Posthumously Posted by Diana Schwartz - Posted December 13, 2009
These are projects Jack was working on during his illness. They are being posted as I sort through the gigabytes of works-in-progress he left on his various hard drives.

Work Posted by Jack Schwartz
Basics of Geometric Lens Optics (in progress) - The last work Jack posted on this site.
Mechanics Draft Educational Module

Notes on quantum mechanics
      Bell's inequality and Bell figures

Proof Verification

Introductory material for A set-theoretically based proof verifier and its application to the basic theorems of analysis
Course syllabus for 2002 Computational Logic Course

Educational multimedia: preliminary drafts
Multimedia in Education: What Needs to be Done?
Comments on design of interactive educational materials

Middle-school materials
Sketch plan for middle-school mathematics interactive - Interactive Algebra
Eggs-in-boxes, recursion, and prime numbers

Course syllabus for 2004 Bioinformatics Course
Sample code items for 2004 Bioinformatics Course

A bit of topology

An elementary knot invariant related to edge-colorings by elements of groups

A strange vanity item.

Jack Schwartz' brain, with eyeballs and a bit of nose - JPEG posted by Jack after an MRI

Illusion-based artwork - A Quicktime Movie

Programming in SETL. (Draft in Progress)

Chapter 2 - Elementary Types
Chapter 3 - Operations
Chapter 4 - Control structures
Chapter 5 - Procedures
Chapter 6 - Debugging
Chapter 7 - Packages and Libraries
Chapter 8 - Objects
Chapter 9 - Examples
Chapter 10 - Graphics and Socket Programming
Chapter 11 - Native packages
Chapter 12 - Databases

Studies in visual psychophysics

Study I - Some observations on the psychophysics of Glass patterns and related visual phenomena
Study II - Motion perception in various settings.
Study III - An Analysis of the Cafe Wall Illusion.
Study IV - Homogeneous Textures.
Study V - Motion Edges and Other Edges.
Study VI - Formation of cyclopean images.
Study VII - Formation of gestalts.

Minor psychophysical observations

A curious variant of the Cafe Wall Illusion
An animated version of the Cafe Wall Illusion
Two Cafe Wall Illusions at right angles
Stereo size constancy
An anaglyph demonstrating an amusing binocular effect.
The coupling of binocular depth perception to the perception of size
Doubled anaglyphs and related stereo presentations
A depth illusion seen differently by different viewers

Jack and Diana's Projects

The Electronic Dictionary of Musical Themes based on the Dictionary of Musical Themes by Barlow and Morgenstern
The Glenn Gould Performance Database
Analog and Digital
Animated Relativity based on the book Relativity in Illustrations by Jacob T. Schwartz
Drum Machine


A 3-D paint program for the young at heart of all ages.
Paleolithic stone implements: a tribute to the technological accomplishments of our early relatives (2002)
Ray Tracer (August 2008)
Jacob T. Schwartz Vitae
Do the Integers Exist? The Unknowability of Arithmetic Consistency by Jacob T. Schwartz - PDF file
The New Connectionism: Developing Relationships Between Neuroscience and Artificial Intelligence - by Jacob T. Schwartz
Visual Illusions Artwork Slideshow by Jacob T. Schwartz (2005)
More Visual Illusions (and explanations) by Jacob T. Schwartz (2005)
Genie in the Bottle: What Bioterrorism Might Mean by Jacob T. Schwartz (2002)
Remarks in honor of Gian-Carlo Rota on the occasion of his 60th birthday by Jacob T. Schwartz
The Pernicious Influence of Mathematics on Science by Jacob T. Schwartz
Phylogenator - A Tool for Viewing Molecular Phylogeny Data by Jacob T. Schwartz
Francis Bacon and Galileo Galilei: Two Approaches to Progress in Science (December 7, 1987)


Materials contributed by Eugenio G. Omodeo

And don't forget...


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