
I didn’t know anything about topology before I entered graduate school, but I continue to see it as one of the more provocative specialties in mathematics and an important transition of thought. Most definitions of the subject describe it as the study of the properties of objects that are preserved through deformations like stretching and […]
A recent post on scientificamerican.com got my attention – no surprise given its title, Could Multiple Personality Disorder Explain Life, the Universe, and Everything. It was coauthored by three individuals: computer scientist Bernardo Kastrup, Psychotherapist Adam Crabtree, and cognitive scientist Edward F. Kelly. The article’s major source is a paper written by Kastrup, published this […]
Earlier this month, Nature reported on Artificial Intelligence (AI) research, where deep learning networks (an AI strategy) spontaneously generated patterns of computations that bore a striking resemblance to the activity generated by our own grey matter – namely by the neurons called grid cells in the mammalian brain. The patterned firing of grid cells enable […]
My thoughts started jumping around today, trying to land on what it was that I found so fascinating about a recent article in Quanta Magazine. This is one of the statements that got me going:
…Numbers emerging from one kind of geometric world matched exactly with very different kinds of numbers from a very different […]
A recent article in Quanta Magazine anticipates the publication of the 6th edition of Proofs from The Book, collected by Martin Aigner and Günter Ziegler. The original volume was inspired by the wellknown and prolific mathematician Paul Erdős, who traveled the world, participating in countless collaborative efforts, and who would say of proofs that he […]
I have been particularly concentrated on whether mathematics can tell us something about the nature of thought, something that we have not yet understood about what thought is made from, how it happens, how it is connected to everything else in the universe. These questions inevitably point me in the direction of research in cognitive […]
I’ve written before about how probabilities are used to understand human perception, understanding, and learning. Joshua Tenenbaum uses probabilistic inferencing to account for how we come to learn concepts, acquire language, and understand the world around us quickly, and with very little information (How to Grow a Mind). Optical illusions are created by statistical judgments […]
I find the relationship between mathematics and vision fascinating. Even within mathematics itself, seeing how the geometric expression of ideas can clarify or further develop countless mathematical thoughts is always worth noting – like the graphs of functions, or the projections of figures. I’ve written before about the relationship between the brain’s visual processes and […]
Recently I became particularly sensitive to discussions that address ‘meaning’ as an emergent property of both biological and formal systems (of which mathematics is one). And this is because it is the meaning of symbols in mathematics that is the source of its power. But it is not at all clear that the meaning of […]
Deciphering the principles of selforganizing systems is often at the heart of new ideas in biology, including neurobiology. A complex, selforganizing system contains a large
number of elements that have predictable, local interactions with each other, but these local interactions create global properties that cannot be predicted from even the most wellunderstood local events. This […]


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