Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, experiment with new situations. Occasionally, we as individuals, in a complicated cognitive and sometimes fortuitous process, come up with something that is not only new to us, but to our entire society so that what is a personal novelty can turn into an innovation at a global level. Innovations occur throughout social, biological and technological systems and, though we perceive them as a very natural ingredient of our human experience, little is known about the processes determining their emergence. Still the statistical occurrence of innovations shows striking regularities that represent a starting point to get a deeper insight in the whole phenomenology. This paper represents a small step in that direction, focusing on reviewing the scientific attempts to effectively model the emergence of the new and its regularities, with an emphasis on more recent contributions: from the plain Simon's model tracing back to the 1950s, to the newest model of Polya's urn with triggering of one novelty by another. What seems to be key in the successful modelling schemes proposed so far is the idea of looking at evolution as a path in a complex space, physical, conceptual, biological, technological, whose structure and topology get continuously reshaped and expanded by the occurrence of the new. Mathematically it is very interesting to look at the consequences of the interplay between the "actual" and the "possible" and this is the aim of this short review.
Bookmarked after reading Mathematical Model Reveals the Patterns of How Innovations Arise.
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Imagine you had to take an art class in which you were taught how to paint a fence or a wall, but you were never shown the paintings of the great masters, and you weren't even told that such paintings existed. Pretty soon you'd be asking, why study art?
That's absurd, of course, but it's surprisingly close to the way we teach children mathematics. In elementary and middle school and even into high school, we hide math's great masterpieces from students' view. The arithmetic, algebraic equations and geometric proofs we do teach are important, but they are to mathematics what whitewashing a fence is to Picasso — so reductive it's almost a lie.
Most of us never get to see the real mathematics because our current math curriculum is more than 1,000 years old. For example, the formula for solutions of quadratic equations was in al-Khwarizmi's book published in 830, and Euclid laid the foundations of Euclidean geometry around 300 BC. If the same time warp were true in physics or biology, we wouldn't know about the solar system, the atom and DNA. This creates an extraordinary educational gap for our kids, schools and society.
An interesting train of thought to be sure. I should post in response to this, or at least think about how it could be structured. I definitely want to come back to write more about this topic.
For several years, I’ve hosted my personal blog at http://chrisaldrich.wordpress.com. This week I’ve moved everything over to a new address at http://boffosocko.com.
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Thanks for reading!
Her impact was both literal and figurative: It wasn’t just having read several of her books in high school at the behest of Ken Proctor, but on my way to listen to a lecture she was to present at Johns Hopkins School of Medicine c. 1993.
I was a few minutes late, and apparently she was a few minutes later. While rushing around a corner to get to the auditorium, she came around the other side moving even faster than I. She easily maintained her footing while I landed quite soundly on my back side. Her companion, the terrifically imposing Dr. Levi Watkins, Jr., leaned over, picked me up completely off the ground and set me gently back on my feet. Her gracious apologies extended to a far nicer seat for the event than I could have deserved being about 15 minutes late. She not only let loose my “caged bird,” she signed my printed copy as well. R.I.P.
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