In the thread on Jonathan Bartlett and priorities for Math education, I raised two comments that I think it would be profitable to further reflect on. First, from 33 on how the US National Academy of Sciences tried to classify Mathematics as a “science”: https://services.math.duke.edu/undergraduate/Handbook96_97/node5.html The Nature of Mathematics (These paragraphs are reprinted with permission […]
The panic in sociology, psychology, nutrition science, and pharmacology has been growing as >70% papers with “p-values” smaller than 0.05 are discovered to be unrepeatable.
Our contributor JB asked to have a conversation on what is important in Mathematics, especially Math education. I shared some thoughts. >>Why not, let’s just do that, follow it up and see where it goes? For instance, I think a key insight is to find a useful, powerful definition of what mathematics is. If we […]
History shows that Newton’s own development of the idea of infinite series was exactly as I described. In Newton’s day, polynomials were known to be imperfect stand-ins for transcendental functions.
Referring to calculus textbook author Jonathan Bartlett, he writes, “What surprises me is that even creationists with math or related degrees often have problems with basic mathematics.” Bartlett will answer shortly.
Unfortunately, most mathematics texts teach only the mathematics, never the insights. I felt so frustrated by this gap that I wrote my own textbook, in which I try to teach both.
Edward Feser: When we grasp that formal nature of being a triangle, we are grasping something that is totally abstract. It applies to every single triangle that has existed, does exist, will exist or, for that matter, could exist, whether it is a triangle drawn in ink, whether it is a triangle drawn in sand, whether it is a triangle you construct by putting three sticks together, whether it is a triangle formed by the side of a pyramid, the idea or the concept is entirely abstract.
On August 7th, News started a discussion on time’s arrow (which ties to the second law of thermodynamics). I found an interesting comment by FF: FF, 4: >> It’s always frustrating to read articles on time’s arrow or time travel. In one camp, we have the Star Trek physics fanatics who believe in time travel […]
“Has Darwinism really failed? Peter Robinson discusses it with David Berlinski, David Gelernter, and Stephen Meyer, who have raised doubts about Darwin’s theory in their two books and essay, respectively The Deniable Darwin, Darwin’s Doubt, and “Giving Up Darwin” (published in the Claremont Review of Books). ” When this stuff is happening, Darwinism is on the outs culturally.
In pop science media, the End of All Things is the heat death of the universe, but some opt for stranger fates instead.
Laws concerning the way people behave around numbers mean that quantification itself invites certain types of corruption.
And Alan Turing tried to live with it. Maybe that’s not the story you heard, but …
People forget that finger counting is machine learning too. (as far as your mind is concerned, your fingers are machines.)
One outcome of Simpson’s Paradox is that machines cannot replace statisticians in analysing results. A great deal depends on interpretation, as Marks shows. “Clustering remains largely an art.”
Dr Carol Wood of Wesleyan University (a student of Abraham Robinson who pioneered non-standard analysis 50+ years ago) has discussed the hyperreals in two Numberphile videos: First: Extended: Wenmackers may also be helpful: In effect, using Model Theory (thus a fair amount of protective hedging!) or other approaches, one may propose an “extension” of the […]