The von Neumann-Morgenstern Elephant

I was telling Richard, Ko-Hung, and Joe yesterday about a paper I remembered by Oskar Morgenstern entitled The Collaboration Between Oskar Morgenstern and John von Neumann on the Theory of Games. It’s a nice piece on the writing of one of the economist’s most sacred texts, The Theory of Games and Economic Behavior first published in 1944. The book, spanning nearly 700 pages, was composed over several years, often in von Neumann’s house in Princeton. Morgenstern writes that the meetings were so frequent, von Neumann’s wife, Klari was distressed by the “perpetual collaboration.” He says that to mollify Klari, an avid collector of elephant trinkets, they promised to include a diagram with an elephant for her:

There were endless meetings either at my apartment over the bank or at 26 Westcott Road, where Johnny lived with his wife Klari and his daughter Marina (now Mrs. Marina von Neumann Whitman). We wrote virtually everything together and in the manuscript there are sometimes long passages written by one or the other and also passages in which the handwriting changes two or three times on the same page. We spent most afternoons together, consuming quantities of coffee, and Klari was often rather distressed by our perpetual collaboration and incessant conversations. She was at that time collecting elephants made of ivory, glass, and all sorts of other material. At one point she teased us by saying that she would have nothing more to do with the ominous book, which grew larger and larger and consumed more and more of our time if it didn’t also have an elephant in it. So we promised we would happily put an elephant in the book: anyone who opens the pages can find a diagram showing an elephant if he knows that he should look for one.

I took some time to look for this Easter egg and it is on page 64 (of the third edition) in Figure 4:

Finite Domain, Complexity, and the Turing Test

This post is currently a draft.

Blockhead and Aunt Bertha are part of a class of objections which charge that the Turing test does not constitute a sufficient condition for intelligence on the grounds that there are trivial programs which can pass it through memorization. An example such objection might begin by arguing that it is logically possible to construct a computer program in the following way:

1. Perform a Turing test with a sequence of questions
   with a human (call her Bertha) respondent

2. Record those responses on a hash structure on 

3. Repeat steps 1 and 2 for each possible Turing test
   sequence of questions.

Figure 1. A setup procedure

Once this setup procedure is completed, the objection specifies the following rule for interactions in the interrogation: when posed with a question from an interrogator, have the program look up Bertha’s responses in the hashtable. Because we have enumerated all possible Turing test sequences, the appropriate response should be somewhere in it.

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