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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 […]

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 […]

Foraging for food, remembering, and mathematics

On April 16 Scientificamerican.com reported on research that links hunting for words with foraging for food.

Our brains may have evolved to forage for some kinds of memories in the same way, shifting our attention from one cluster of stored information to another depending on what each patch has to offer. Recently, Thomas Hills of […]

Worms, promiscuous connections and autistic savants

If you’ve been reading my posts, you’ve probably figured out that this blog is motivated, to a large extent, by my fascination with what mathematics can help us see about the source, targets and bewildering range of human cognition. My expectations rest on the idea that what we have come to call the human mind […]

The Stream of Consciousness, Connectomes and Mathematics

I asked myself a naive question just the other day: “What is a thought?” I wondered about it when, during a workout, I saw my mind drift, and a chain of unrelated memory fragments were brought to my awareness through spontaneous, even nonsensical associations. Their shared presence was prompted, perhaps, by words or by something […]

SEEING, TOUCHING AND DOING MATHEMATICS

Hearing about visual processes, from neuroscientists and artists alike, consistently brings mathematical thoughts to mind for me – like Samir Zeki’s descriptions of how visual images are constructed, or the Impressionist painters’ attention to the sensations in the eye rather than the subject of the painting, and, of course, Poincaré’s suggestion that visual space has […]