The following are the opening paragraphs to selected posts.
on category theory in math (most visited post)
The Avatar Perspective
It’s about to be baby chipmunk season, and (oh, no!) the things get in the street and panic when they see a car coming. They run all over in a frenzy, including going off the road and back on, making it nerve-wracking to try to avoid hitting them. It is especially uncomfortable with a little girl in the car with you, (“Oh, little guy,” she cries). Or it is difficult for a young man trying to impress his date. (To paraphrase Oscar Wilde, she says, “Please don’t run over the rodent. He’s trying his best”).
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on the invention of MRI’s
When Logic Says It Is Impossible
“You could write the entire history of science in the last 50 years in terms of papers rejected….” –Paul Lauterbur, inventor of the MRI, about being told his idea could not work
Lauterbur always comes to my mind whenever the question becomes, “Do all scientists understand their subject matter in the same way?” That question arises because
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on the equivalent for light of what transistors do for electrons
Photonic Crystals
Photonic crystals are lattices of molecules that have special light properties. They occur in nature (peacock feathers) but in the lab are used in such sci-fi sounding ways as invisibility, entangled photons, and logic gates. Also, they are a good example of what in organic chemistry is called “symphony,” which is when outcomes happen only when multiple circumstances come together in just the right way. (To switch our metaphors, we might think of it as “a perfect storm”)
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on Tegmark
Is the Universe a Mathematical Structure?
Much has been written on this subject, but since science is about demonstration, not just analysis, here is a home experiment to help you decide for yourself.
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on comparing causality with cluster kinds
An Example of Plasticity in Causality
Have you ever noticed that the word “cause” has different meanings in the present, conditional, and past tenses? I have been discussing Ben-Menahem’s suggestion that causality is a cluster concept and that that might rescue it from Norton’s argument that causality is a folk science. Norton’s argument is that causality is too “plastic” a notion to be of practical use for judging other phenomena. And now, in providing my own take on that issue, I find it informative to discuss an example of that plasticity.
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just for fun (but true)
The Secret of the Saguaros
Hey, someone stole my saguaro cacti. And I know what you’re thinking. Wouldn’t that require a crane, a heavy-duty truck, multiple people shouting orders, and hours? Where was I when all of this was happening? And my neighbors? What kind of person lets a saguaro cactus get stolen out from under them?
Souls of Lagrange 