List of Illustrations
Cover: A "GEB" and an "EGB" trip-let suspended in space, casting their
symbolic shadows on three planes that meet at the corner of a room.
("Trip-let" is the name which I have given to blocks shaped in such a way
that their shadows in three orthogonal directions are three different
letters. The trip-let idea came to me in a flash one evening as I was trying
to think how best to symbolize the unity of G6del, Escher, and Bach by
somehow fusing their names in a striking design. The two trip-lets shown
on the cover were designed and made by me, using mainly a band saw,
with an end mill for the holes; they are redwood, and are just under 4
inches on a side.)
Facing Words of Thanks: The beginning of Genesis, in ancient Hebrew. xviii
Part I: The "GEB" trip-let casting its three orthogonal shadows.- Johann Sebastian Bach, by Elias Gottlieb Haussmann. 2
- Flute Concert in Sanssouci, by Adolph von Menze!. 5
- The Royal Theme. 6
- Bach's acrostic on 'RICERCAR'. 7
- Waterfall, by M. C. Escher. 11
- Ascending and Descending, by M. C. Escher. 12
- Hand with Reflecting Globe, by M. C. Escher. 13
- Metamorphosis II, by M. C. Escher.^14
- Kurt COde!. 16
- Mobius Strip I, by M. C. Escher. 30
- "Tree" of all theorems of the MIll-system. 40
- Sky Castle, by M. C. Escher. 42
- Liberation, by M. C. Escher. 57
- Mosaic II, by M. C. Escher. 61
- "MAIL BOX". 67
16 Tiling of the plane using birds, by M. C. Escher. 68 - FIGURE-FIGURE Figure, by Scott E. Kim. 69
- Diagram of the relationships between various classes of TNT
strings. 71 - The last page of Bach's Art of the Fugue. 80
20; Visual rendition of the principle underlying G6del's Theorem. 84 - Tower of Babel, by M. C. Escher. 89
- Relativity, by M. C. Escher. 98
- Convex and Concave, by M. C. Escher. 107
- Reptiles, by M. C. Escher. 117
XlV Illustrations