An accountant who plays jazz for a hobby??

I've just finished the book "Apprentices of wonder - Inside the Neural Network Revolution". The book was published in 1989. The author is William F. Allman.

This book tells us stories of those pioneers in neural network research and development. The most interesting part of the book is about the fight between symbolic AI and connectionism AI. In the end, the author concluded that neither side won and the future of AI could be some form of the combination of these two. I totally agree with the author on this prediction.

I also liked the part of how our common sense mind is irrational. For example, in order to show that day-to-day human reasoning is not symbolic (totally rely on logic rules), the author gave us a very interesting study by psychologists Daniel Kahneman, Paul Slovic, and Amos Tversky.

In this study, subjects were given a short description of a person and then asked to guess which professions and hobbies the person was most likely to have. Here we have:

Russ is 34 years old. He is intelligent, but unimaginative, compulsive, and generally lifeless. In school, he was strong in mathematics but weak in social studies and humanities.

Please rank in oder the following statements by their probability, using 1 for the most probable and 8 for the least probable.

• Russ is a physician who plays poker for a hobby.
• Russ is an architect.
• Russ is an accountant.
• Russ plays jazz for a hobby.
• Russ surfs for a hobby.
• Russ is a writer.
• Russ is an accountant who plays jazz for a hobby.
• Russ climbs mountains for a hobby.

The results of the study? Most people, quite reasonably, ranked "Russ is an accountant" as most probable. They also ranked "Russ plays jazz for a hobby" as very unlikely. However, most people also said the probability that "Russ is an accountant who plays jazz for a hobby" is higher than the probability that "Russ plays jazz for a hobby." But this violates the laws of probability! It is impossible for a statement combining two unrelated ( Even related - yuz) elements to be more probable than either element alone. The author claimed that even those students trained in probability and decision science made the same mistake!

The current probability theory defines that P(AB)=P(A)P(B|A)=P(B)P(A|B), since any P(X) can never be bigger than 1, P(AB) can never be bigger than P(A) or P(B).

This is really interesting. We are not only having born optical illusions, we also have born mental illusions! This explained a lot about my stupid decisions made in the past:-) What is truly wrong?? Our common-sense neural network or the symbolic probability theory?