If You Could Design Your Own Numbers

Old intelligence challenge (Steve Smale)

"What are the limits of intelligence, both artificial and human?"

In the best written answer, John Robertson argues that there are indeed limits to artificial and human intelligence, since the physical universe itself is finite, but that these limits are quite high as illustrated for example by mathematics. Then he asks the big question:

"Will we solve the important problems that mankind faces?" As examples, he mentions the questions of why there is something instead of nothing and what the nature of consciousness is.

Robertson argues that artificial (machine) intelligence is at least as great as human intelligence because the brain is a machine. On the other hand, he thinks that brains probably can be genetically engineered to do anything a futuristic computer can do. Mike Jackson wonders why we tend to evaluate artificial intelligence by comparing it to human intelligence in the first place.

Modern mathematics proves results from generally accepted axioms. In 1931, the mathematician Kurt Gdel astonished the world by proving roughly that for any such system, if it is self-consistent, there are truths which cannot be proved. This result dashed all hopes of mathematically deriving all truth from a fundamental set of self-evident axioms.

New number challenge (Jim Henry)

Our Arabic number symbols 1, 2, 3, etc., although superior to Roman numerals, have some disadvantages. The 4 and the 9 can sometimes be confused. The 5 takes two pen strokes. The 1 can be confused with the letters "I" and "l." The zero can be confused with the letter "O."

The challenge is to come up with a completely new set of symbols for the numbers from 0 to 9. "We can aim at having a year 2000 switchover to [the best] new, improved way of writing numbers," Henry says.

Curiously, many Arab countries today use "Indic" numerals as in the illustration above.

* Send answers, comments, and new questions to:

Math Chat, Math Dept, Williams College, Williamstown, MA 01267

or by fax to (413) 597-4061 or by e-mail to Frank.Morgan@williams.edu. Professor Morgan's home page is at www.williams.edu/Mathematics/fmorgan