This time from Erich

The rules:

• Grab the nearest book.
• Open the book to page 56.
• Find the fifth sentence.
• Post the text of the next two to five sentences in your journal along with these instructions.
• Don’t dig for your favorite book, the cool book, or the intellectual one: pick the CLOSEST.

And my entry:

In other words, it would seem that there really is no such thing as a free lunch, since even this hypothetical computer has its own infinite set of problems that are incomputable.

The moral of the story is that Gödel’s incompleteness result applies to all mathematical formalisms that are so complicated they can make statements about mathematics. Thus, no sufficiently complicated (or interesting) model of computation will ever be free of these basic limitations.

“Discrete versus Continuous,” from Chapter 4, “Postscript: Computation,” in Gary William Flake’s The Computational Beauty of Nature (1998) sitting on the credenza next to my desk.

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