Showing posts with label hadamard. Show all posts
Showing posts with label hadamard. Show all posts

Tuesday, September 30, 2008

The Creative Mind: Myths and Mechanisms - Margaret Boden

Professor Margaret Boden is a cutting edge thinker in the fields of Artificial Intelligence and creativity. Recently I stumbled upon her recent publications which prompted me to re-examine some ideas about creativity. I was fascinated to find that even to this day she sets as required reading the above text. For a preview of The Creative Mind: Myths and Mechanisms click here.

This is a legendary text that should be read by all who are interested in the nature of creativity. Be warned though, this book will not provide prescriptions or rules for being creative; the author is far too intelligent and wise to lead her readers into nonsense. I read this text in 1998, it is one of the few books I have kept in my once extensive library. In these days I prefer everything to be computer based because with Google Desktop search and the brilliant Infoselect program I never loose information on my computer. The ability to track down and quickly access information is an important component of creativity.

One of the most striking concepts to emerge out of this text is that of "conceptual space". While doing some research for this post I noted that Boden is still invoking this concept in her recent books and lectures. It is a wonderful little concept that is part and parcel of my arsenal of cognitive tools. That is somewhat paradoxical because in my areas of interest there are so many conceptual spaces that I can and will keep wandering across for the rest of my days. Over recent years I have come to appreciate that creative thinking in this Big Land is 99.999999% blood, sweat, and tears and the rest is luck. That is quite common, in fact creative thinking in many realms is incredibly difficult and time consuming.

One of the fascinating aspects of the concept of "conceptual space" is that it provides insight into how discoveries can quickly proceed and then come to a standstill. As new spaces are opened up discoveries can happen quickly because there are so many good opportunities to be had. It is like a gold rush, the first in pick up the nuggets lying here there and everywhere, those following behind have to search much more harder to find the nuggets. This also explains why "mavericks" can, early on, make such huge gains. If you look at the history of science mavericks tend to succeed early in the development of the science, as the field matures mavericks, lacking the training, knowledge and expertise that comes with years of education, tend to fade into the past.

Conceptual spaces are bounded. This is a very important point. The boundaries specify the search radius and also determine the types of solutions that can be found. Einstein touched on this when he stated:

You can't solve a problem on the same level that it was created. You have to rise above it to the next level.
Note his use of the word "level". In physics that is important because they are seeking a Theory of Everything. In most domains however the idea of "levels" is misleading, Boden's concept of space is much more appropriate. Interestingly, as the physicists Lee Smolin and Paul Davies have stated, the idea of a "Theory of Everything"is eerily reminiscent of God.

There is a tendency for people to speak about creativity as "pushing the envelope". This is also misleading. In many intellectual domains we don't have to push anything except our perseverance, there is plenty of unexplored territory. Phrases like "pushing the envelope" encourage a view that creativity is about breaking the rules and being extreme. Genuine creativity is something entirely different. As Boden states:

But far from being the antithesis of creativity, constraints on thinking are what make it possible. In short, to drop all current constraints and refrain from providing new ones is to invite not creativity, but confusion.
It is the partial continuity of constraints which enables a new idea to be recognized, by author and audience alike, as a creative contribution.
Her comments here touch on what I was referring to earlier. As a conceptual space is explored it soon emerges that there are constraints on one's thinking. One cannot abandon previous concepts simply to be creative, one must have very good reasons for abandoning long held concepts. It is not enough to abandon an idea simply because it gets in the way of creative thinking.

Boden also strongly emphasises the need for persistent effort and patience:

Even Mozart needed twelve years of concentrated practice before he could compose a major work, and much the same seems to be true of other composers.
This commitment involves not only passionate interest, but self-confidence too. A person needs a healthy self-respect to pursue novel ideas, and to make mistakes, despite criticism from others. Self-doubt there may be, but it cannot always win the day. Breaking generally accepted rules, or even stretching them, takes confidence. Continuing to do so, in the face of scepticism and scorn, takes even more.


However she does not exclude the need for the right attitude towards creativity:

Like much play, creativity is often open-ended, with no particular goal or aim.
... Likewise, the artist or scientist may explore a certain style of thinking so as to uncover its potential and identify its limits.
This reminds of a wonderful quote from that wise old Greek Heraclitus:

Man is most nearly himself when he achieves the seriousness of a child at play.
The above is not intended to suggest that creativity is solely about hard work and learning. It is obvious that Eureka! moments are important and most of us have experienced the same at various times during our lives. At least I hope most of us have. When seeking creative ideas it is important to maintain a balance. There are times when no amount of further study and conscious thinking will lead us to a solution. The mathematician Hadamard claimed that were 4 stages in his problem solving: preparation, incubation, illumination and verification. Surely all of us have experienced those occasions when the solution to a problem arises in the most unexpected circumstances. I remember an interview with the Nobel Laureate physicist Roger Penrose. He had been struggling with a particularly difficult problem for a long time. Walking with a friend on the street, the solution came to him just as he stepped off the curb to cross the street.

Such anecdotal stories are too common to dismiss as mere co-incidence, there are too many stories of people finding solutions to problems in such a manner. A word of caution though: Revelation comes only to the prepared mind. Forget that "muse" nonsense, people who experience Eureka moments have almost invariably been working long and hard on the problem. Often they have completely explored the available conceptual space, the breakthrough comes when they stumble upon undiscovered country. So it is not surprising that Einstein once quipped:

How do I work? I grope.
The important thing is not to stop questioning. Curiosity has its own reason for existing. One cannot help but be in awe when he contemplates the mysteries of eternity, of life, of the marvelous structure of reality. It is enough if one tries merely to comprehend a little of this mystery every day. Never lose a holy curiosity.
The below statement is from: Cracking Creativity: The Secrets of Creative Genius, Michael Michalko

When someone asked Einstein what was the difference between him and other people he replied that if other people were asked to find a needles in haystack they would find one then give up, but he would keep looking."
Creative people tend to be like that. Show them something new under the sun and you can almost see the cogs start turning. They are quizzical, fascinated by new things, want to understand these, what these things can be used for, sometimes just to understand why something works. Not all of us can be like that. In my opinion too many of us are often forced to be too practical and too concerned with outcomes rather than play. It is tragic to see so many people have lost their sense of childish fun and enthusiasm. We are taught to "grow up", "behave", and "be sensible". All that reminds me of Eric Olthwaite in Ripping Yarns when his neighbour said to him, "You're a boring little tit."

As to why some people have have retained that sense of fun and exploration I do not really know, though the work of Frank Sulloway may provide some insight into this matter, the truth is education can damage our curiousity. Too much of modern education is conducted in a highly competitive environment where wrong answers are punished. Yet creativity invariably involves making lots of mistakes, sometimes disastrous ones. Fear of being wrong kills creativity.

So if you are interested in improving your creative potential this book is certainly a good starting point. The text is still available and you should also consider her recent texts on the subject. I would love to add those to my reading list but I have already downloaded research articles with circa one hundred unread. Hmmm, now what was that about perseverance?