Kurzweil’s How to Create a Mind, and mathematics

I listened last week to Diane Rehm’s interview with Ray Kurzweil, author of the book “How to Create a Mind: The Secret of Human Thought Revealed”  A transcript of the interview can be found here.

Published in mid-November, it is already a New York Times bestseller, and some of the responses to it from prominent […]

Infinities, metaphors and being human

Our thoughtful, imaginative worlds are married to our physical experiences but the subtleties of their union are almost impossible to fully appreciate.  Mathematics, I often argue, has the potential to provide a better view of the situation, perhaps because of the inexhaustible depth of its abstraction, together with the precision it brings to a concept, […]

The Irrationality of Mathematics?

When I write, I often choose my words very carefully in order to remove any opportunity the reader might have to make a quick judgment about the content of what I am saying.  I’m hoping they will keep thinking about what I am saying.  The unexpected pairing of words often accomplishes this, and in this […]

A Look Back at Where Mathematics Comes From (reconciling the internal and the external)

I wanted to take a closer look at the Lakoff/Nuñez book Where Mathematics Comes From and its relationship to what has come to be called the embodied mind.  It seems to me that the biologists who pioneered embodiment had a more radical view of cognition than many of the cognitive scientists who use the paradigm.  […]

Imagined Freedom and The Battle for Set Theory

The essence of mathematics lies precisely in its freedom. This statement from Georg Cantor is quoted so very often, and perhaps this is because of the surprise coupling of the words mathematics and freedom, or because of the implications of the word essence, which calls to mind other words like intrinsic, inherent or something that […]

How Far Can Distance Take Us

I would like to follow up on Alain Connes’ statement in my last blog. The weave of mathematical thought is tight.  The seeds of mathematics are found in early explorations of number relationships and in observations of what we call space. But symbol, stripped of content, has led to heightened powers of thought and discernment.  […]

The Origin of Concepts and Some Thoughts on Watson

Quite a lot of work is being produced by cognitive scientists about metaphor – what they are -what they do, how they shape thought – and I find it all interesting and provocative.  The way in which metaphor shapes the way we see the world is the subject of James Geary’s book  I Is an […]

What was Plato Thinking?

Last week I pointed to a few discussions of mathematics I found interesting and this is my first chance to follow up.  One of them took note of the surprising persistence of a platonic view of mathematical objects, a view that inevitably introduces into our scientific culture some version of a metaphysical idea.  Paul Bernays […]

Embodied Cognition

My attention was brought again today to cognitive scientists working in what has come to be called embodied cognition.  My initiation into these ideas happened when I read the book Where Mathematics Comes From by George Lakoff and Rafael Núñez.   The book explores mathematical ideas from the perspective that our bodies, living in their world, […]

The Body’s Thoughts

It has been understood for some time that metaphor provides a sensory anchor to abstract ideas.  But, more recently, cognitive psychologists have looked at how active the role of metaphor may be in thinking.  In a recent article on Boston.com, experiments are cited which explore the extent to which metaphor shapes thought.

The article cites […]