Turing, bombs, and the nervous system

When I first became interested in studying mathematics an artist friend of mine expressed his disapproval by characterizing mathematicians as people who made bombs.  Although I didn’t know very much mathematics at the time, I knew enough to know that he was wrong.  But I was reminded today of one of the ways his mistake […]

The seen and the unseen: abstraction and the senses

I listened to three short talks today and found that they had something nice in common – they each show us how sensory experience (often vision) gives rise to mathematics that provides access to what cannot be seen, and clarifies what is seen.

The first of these talks was called Symmetry, reality’s riddle presented by […]

Number Sense: What we can’t do? or What we can see

A number of websites have reported on a recent study, that correlated innate number sense with mathematical ability.  A concise report of the study can be found in the Johns Hopkins University Gazette, published by the institution where the study was done.  The study’s results confirm a correlation between the strength of ones number sense […]

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 […]

Neuroscience and Riemann

I would like to go back today to Riemann, and the significance of his generalized notions of space and magnitude, but with an eye on what neuroscience may be adding to how mathematics gains its effectiveness.

In a recent post, I pointed to the influence the philosopher Herbart had on Riemann’s 1854 lecture in which […]

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 Expressiveness of Number

For me, one of the more intriguing things that happened in mathematics is what is called the arithmetization of the Calculus.  This is not because it contributes to my understanding of fundamental concepts (because it doesn’t).  Nor is it because the ideas are exotic (they’re not). I’m captivated, instead, by what it may demonstrate about […]

Plato And Fish That Count

In a recent post I said that one of the things that dissuades us from accepting the existence of a truly Platonic mathematical world, or believing in the timeless existence of its forms independent of human minds, is the habit we have of distinguishing ourselves from the rest of nature, despite all the evidence we’ve […]

Reimann’s Defense of Conceptual Definitions, Modern Mathematics, and Platonism

Many of this week’s circumstances are limiting the time I have to write but I would like to point to a few sources that contain very nice accounts of what is known as the foundational crisis in mathematics. One of them was written by Paul Bernays in 1935.  Understanding the nature of some of the […]

Archetypes, Image Schemas, Numbers and the Season

Let’s ask again, “What is the nature of the bridge between sense perceptions and concepts?  It’s a simple question to ask, but a fairly difficult one to answer.

Raphael Nunez contributed a chapter to the Springer book, Recasting Reality: Wolfgang Pauli’s Philosophical Ideas and Contemporary Science.  A pdf of the chapter can be found here.  […]