First Blog

It may be widely believe that knowledge progresses gradually, in small steps, in gentle increments, or in slight gradations.  It may be not so, even for us as individuals.  New knowledge or understanding often begins with insights.  When you gain an insight, and it is true, it becomes applicable and remains so from then on.     This changes one’s problem solving game. This insight provides a new tool or rule, but importantly   it creates a discontinuity in your problem solving methods.    So, we might ask whether insights can come gradually?   In some cases, probably yes, though examples are difficult to furnish.  The emergence of infinity, often credited to Cantor, took centuries of dancing around the edges by philosophers.  The germ theory of disease so often attributed to Pasteur was anticipated almost with the invention of the microscope.   On the other hand plate tectonics seemed to arise by a simple insight by a single person, Alfred Wegener, in 1912 and took a mere half

Vision for the blind By trade, I am a mathematician.  I can do lots of tricks in math, but only in math.  But there are so many things I just don't know.   Why don't I know?  What prevents me from knowing?  Why can't I answer so many questions?  This has to do with mental capacity, of course.   (See, http://used-ideas.blogspot.com/2012/05/how-to-teach-ant-how-to-read.html )   Still I keep trying.   This is despite the serious models presented to us by scientists and theologians to help me along. Let me explain understanding through the metaphor of sight. We use this metaphor all the time.  "I see it," is the most familiar expression.  Yet the deeper questions are how clearly you may see it, or how deep is your vision.   Vision-type statements involving understanding include. ·          I see what you mean. ·          It is still fuzzy, but I am getting on to it. ·          I saw through it at once. ·          They recognized the facts of the situat