Intelligence, artificial and otherwise

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 […]

The fluency of geometry

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 […]

Proofs, the mind, and mathematics

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 well-known and prolific mathematician Paul Erdős, who traveled the world, participating in countless collaborative efforts, and who would say of proofs that he […]

Mathematical hybrids and the like

My attention was just recently brought to the work of philosopher and poet Emily Grosholz.  It’s rare to find an individual so steeped in the ways of poetry and mathematics, and the desire to explore how and what they express about us.  What I would like to consider here, in this particular post, is really […]

Information and questions of consciousness

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 […]

Probabilities and hallucinations

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 that […]

I spy the confluence of mathematics, psychology, and physics

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 […]

Locating Meaning

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 […]

Spaces

I read about the sad passing of Maryam Mirzakhani in July, and the extraordinary trajectory of her career in mathematics. But I did not know much about what she was actually doing. A recent post in Quanta Magazine, with the title: Why Mathematicians Like to Classify Things, caught my attention because the title suggested that […]

Self-organizing, art, and mathematical mutants

Deciphering the principles of self-organizing systems is often at the heart of new ideas in biology, including neurobiology. A complex, self-organizing 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 well-understood local events. This […]