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Mathematical life forms and really big numbers

I finally got hold of a copy of Gergory Chaitin’s latest book, Proving Darwin: Making Biology Mathematical. The thesis of the book is very appealing to me, since it equates mathematical creativity with biological creativity. And, I would say that Chaitin’s work is a captivating experiment. He is, as he says, “attempting to find the […]

Order, computation and creativity in biology

Current research into the neuroscience of our visual system tells us that what we see is constructed through the coordinated effect of cells sensitive to particular aspects of a visual scene. Attributes such as motion, form and color are processed in individually specialized areas, along paths that lead to the primary visual cortex, creating what […]

Pollock, fractal expressionism and a mathematical thought

In a blog back in January, I referenced a talk given by David Deutsch in which he made the argument that, while empiricism has been the basis of science, empiricism alone is inadequate because scientific theories explain the seen in terms of the unseen.

What we see, in all these cases, bears no resemblance to […]

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 […]

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 […]

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 […]

Anosognosia, Consciousness and Mathematics

In last weeks post, I reported on the work of a computer scientist (Jürgen Schmidhuber’s artificial curiosity) and neuroscientist Gerald Edelman. I would like to follow-up a bit with more about Edelman’s work and perspective, in part because I was captivated by a story he told (in more than one venue) to illustrate the fact […]

Compression, meaning, and mathematics

One of the more interesting applications of algorithmic action can be seen in Jürgen Schmidhuber’s work on artificial curiosity.

Schmidhuber has been building what he calls ‘artificial scientists and artists’ that possess an algorithmic mechanism for motivating invention. He provides a brief and fairly straightforward description of his creative machines in the transcript of a […]

Seeing, dreaming and mathematics

I was struck by the clarity of statements made about perception in a recent Mind Hacks blog. When Tom Stafford reports on a talk he just gave in Berlin he says this:

Perception is the production of meaning, not the production of images. Our associations and experience are incorporated in the act of perception, so […]

Sounds of space-time, cross-modal sensory experience, and the developing nervous system

I’ve spent a considerable amount of time thinking about how, if mathematics grows out of fundamental cognitive mechanisms, it provides opportunities for seeing more. It is mathematics that allows for the tremendous expansion of empirical study – what we call science. I had the opportunity, last week, to listen to a talk given by Craig […]