Cooking Slowly – A Tale of Ever-Changing Times

There is an old adage that if you put a live frog in a pot of water and heated it gradually, that frog would just sit in the water and not jump away (even though it could) until the water boils and it is thoroughly cooked.  It may or may not be true (no one has really tried it since the late 1880s), but either way it is an excellent metaphor for certain things. Some authors have been concerned about the replacement of people with robots, automatic tellers, and other types of automation in the workplace because of the associated loss of jobs (1).  This is one concern, but I want to focus on another.  It is about humanity and interpersonal connection and how dealing with machines instead of people all day may be changing us and our culture.  Changes slowly creep into our lives unnoticed, and before we realize it, like the proverbial frog in a pot of slowly warming water, we become cooked (or otherwise harmed). Ten years ago, when I first occupied the office I am in now, I would drive to the parking garage and greet the guy in the booth who handed out tickets to…

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Hyperbolic Geometry and Daily Life

This story begins with an almost unbearable 10th grade Geometry class — unbearable because of the attitude of the teacher. He shall remain nameless, but if he reads this (unlikely to say the least), I’m hoping he will recognize his part. It was 1963 and I was a good and reasonably devoted student. Our teacher, however, stated often that girls just couldn’t learn math very well, so he walked around the class during exams whispering hints and answers to them. However, the powers of the universe (whatever you believe them to be) provided, as they often do, recompense for this disaster of a learning experience in the form of a Mr. Peter Drees (whose name I shall happily mention). Mr. Drees was, I believe, the math coordinator for the school district, and he got it into his head to discover whether he could teach a group of undistinguished 15-year-olds Hyperbolic Geometry. Mr. Drees was successful at getting a few of us to entertain the concept of a non-Euclidean universe with curved space. He didn’t get many of the details across, but, to my mind he taught something even more important. The geometric version goes like this (with apologies to any…

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