The Fruits of Plasticity

I like the word plasticity, the idea that something would be capable of being shaped or formed.  It’s an optimistic word, pointing to the promise of change, or transformation (another word I like).   Today I happened upon some of the work of Nancy Nersessian, Professor of Cognitive Science at the Georgia Institute of Technology.  She’s written about how scientists think, or how analogies lead to conceptual breakthroughs.  She uses the term generic abstraction which she defines as selectively suppressing information in a representation so as to make inferences that pertain only to the generic case.  This is exactly what mathematics accomplishes as it finds the largest generalities within which particulars fit.  And it accomplishes this by exploring the implications of its very carefully constructed symbolic representations.

One can see the effect of symbols moving thoughts in an early and seemingly simple step in algebra’s development.  Francois Viete, a sixteenth century Frenchman, imagined writing equations using consonants to represent known quantities and vowels to represent the unknowns.  He may not have done this for the first time, but he made it a popular habit.   Removing the numbers was actually like pulling back the curtain for the mind’s eye.  We circumvented our expectations.  When you look at something like a = 5b,  you may be expecting that a is some multiple of 5.   But given a = xb, the lack of specifics compels a symbolic solution.  We can see the potential for numeric relationships better when we take the numbers away.

In Nersessian’s study of creativity, the brain’s own plasticity is also under investigation.  In the development of a generic abstraction, she speaks of hybrid analogies that go through several iterations before a working model is constructed, and in one paper in particular (“Hybrid Analogies in Conceptual Innovation in Science,” Cognitive Systems Research, Special issue 2009), she argues that visualization helps direct the iterations.  All problem solving relies on the brain’s own constructive agility, and in this discussion, visualization seems to play a crucial role.

This also reminds me of the work of Samir Zeki, whose work on the visual brain was discussed in an earlier post.  Rather than rewrite it let me just copy it:

He explains that abstraction is an essential characteristic “imposed upon the brain by one of its chief functions, namely the acquisition of knowledge.” Looking for the essence of things by using abstraction is what the brain is built to do. This looking for the essence, he argues, is what creative work is about.

One more thing.  According to Colin Blakemore, Professor of neuroscience at the University of Oxford,  the force that drove the dramatic increase in human brain size is neuroplasticity.  Blakemore maintains that the change was sudden, and not accomplished by natural selection. The mutation is traced to the brain of a single early human referred to as Mitochondrial Eve!