Wasps, bees, faces and mathematics

An article in the December issue of Scientific American gave me a new insect behavior to ponder and one that might reveal, in the insect’s biology, a distant cousin to the mathematical idea we call mapping.  It seems that there are insects that have a talent for recognizing faces. Their talent has much in common […]

Numerosity, vision, language and mathematics

Understanding the neural functions that contribute to the birth of mathematical structure and meaning is an active subject of research in cognitive science.  A significant amount of work has been done to identify an innate ability we share with other creatures, namely the ability to perceive quantity.  This is sometimes called our approximate number sense.  […]

The geometry of hallucinations

A recent blog from Jennifer Ouellette (from the Scientific American Blog Network)  brought my attention once again to how mathematics is related to the structure-building functions of the brain. As I followed up on some of the references in her post, I found myself on a little journey through hallucinatory experiences that I really enjoyed.

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Daniel Tammet and imagination

I recently got a copy of Daniel Tammet’s latest book, Thinking in Numbers. As you may know, Daniel Tammet has been described as a high functioning autistic savant.   He gained some notoriety in 2004, when he recited the decimal expansion of pi to 22,514 places in just over 5 hours.  You can see him do […]

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 […]

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 […]

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 […]

Fractals, vision, and golf

I came across an article on vision at Physicsworld.com that is concerned chiefly with how digital imaging technology may and may not be able to provide a fix for damaged retinas.  While digital cameras can better mimic the human eye, the gaze of the camera, unlike the eye, is static and uniform.

As sensors in […]

Archimedes, particle accelerators and being visual

I feel like I was pulled into a little whirlpool of interesting bits of info this morning.  I was attracted to the title of David Castelvecchi’s blog: Archimedes and Euclid?  Like String Theory versus Freshman Calculus.   The blog reports the opening of an exhibition at the Walters Art Museum in Baltimore, showcasing one of three […]