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Structure, structure and more structure

I was expecting to write about a paper I found recently by Oran Magal, a post doc at McGill University, On the mathematical nature of logic. I was attracted to the paper because the title was followed by the phrase Featuring P. Bernays and K. Gödel

I’m often intrigued […]

Wigner, Persig, Leibniz and the nature of reality

I saw an opinion piece by Stephen Ornes, in the March 16 issue of New Scientist which ties the ongoing debate about the nature of mathematical ideas, to a modern one about money and ownership. Ornes argues that patentability is one of the most hotly contested issues in software development. The problem, as many see […]

Are we finding the mathematical structure of reality?

I’m intrigued by Max Tegmark’s conviction that the universe is, itself, a mathematical structure. He presented his ideas, again, on February 15 at the recent annual meeting of AAAS, in a symposium called Is Beauty Truth? He said that he has just completed a book on the same topic. I listened to the entire session […]

Chaitin, creativity, biology and mathematics

I was looking today, once again, at Gregory Chaitin’s most recent work which is described in his book Proving Darwin. I realized that much of what has been written about this work (even what I have written) doesn’t give adequate attention to the crucial shifts in perspective that metabiology proposes. Chaitin says concisely:

According to […]

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, […]

Embodied and dis-embodied meaning

I found a short paper today by Mark Andrews, Stefan Frank and Gabriella Vigliocco focused on reconciling two trends in the study of meaning in cognitive science. These two trends are represented by embodied cognition theories (which treat meaning as a simulation of perceptual and motor states) and by computational or distributional accounts of meaning […]

Infinities, Tolstoy, dreams and Nabokov

My interest in mathematics is more personal than it is academic. I learned what I know formally, in the usual sequence of undergraduate and graduate math courses. But it has penetrated my personal life, and I have come to see mathematics as deeply rooted in a fundamental human drive to live more, or to live […]

Finger counting, finger gnosia and cerebral structures

In June The Guardian posted an interesting piece on finger counting and numbers. The main content of the article concerns the work of cognitive scientists Andrea Bender and Sieghard Beller which explores the cultural diversity in finger counting. It tells us that if asked to use you hands to count to 10, these variations will […]

Birds and the number 0

I’ve been working on an article that has me thinking about neuroscientifc studies on the cerebral representations of magnitude and it happened to be brought to my attention today that Irene Pepperberg spoke at the 2012 Francis Crick Memorial Conference on Consciousness in Animals.

Pepperberg is famous for having worked for many years with […]