Well, no Gordian knot slicing here, but still a great back and forth.

I especially enjoyed Ed Frenkel’s metaphor of Mathematics as an archipelago. Frenkel is an excellent argument for tolerance if ever there was one. If PT could get him on the show to talk about anything – we would all be the better for it.

Note we tried to change Mathematic education in the “New Math” movement. I would have liked to have heard Islami talk to that approach and maybe to the critiques of Morris Kline.

More back and forth between guest, Josh, and Ray might help. I felt pushed by Czar duties, this or that question. More call and response would have helped. I think Islami had more to give, misspoke a few times, and needed push back.

I ordered Yackel’s book. If you can’t cut knots, you might as well make them.

es30,

Arezoo doesn’t specifically address Wigner’s “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” in this discussion but the ideas run throughout the show.

Look to her review of the equally well-spoken Martin Carrier and Johannes Lehnard’s study “Mathematics as a tool: tracing new roles of mathematics in the sciences.” There she summarizes what I believe to be her take on Wigner.

“In an often quoted but not carefully read paper, Wigner (1960) spoke of the unreasonable effectiveness of mathematics in the natural sciences. Mathematics and modern physics in his view presented such fundamentally different branches of knowledge that their close relationship appeared to be puzzling, mysterious and unreasonable.

Missing from Wigner’s analysis is an account of the constitution of mathematics, on the one hand, and its changing relationship with sciences on the other. He adopts uncritically the definition of pure abstract mathematics of the twentieth century and projects it to the mathematics of all areas and all eras. Moreover, the paper is focused almost exclusively on modern theoretical physics (Islami 2016).

Thus, critics of Wigner have focused, and with good motivation, on ineffectiveness of mathematics in other sciences (see, for example, Longo and Monte ́vil 2013; Steiner 1998; Velupillai 2005, for responses).”

I wonder what you might think of that? Would the show have gone there, but it did not.

The recent clash between epidemiologists and virologists about the term “transmission” is an excellent example of where Wigner went wrong with that essay/talk. Arezoo gets into the weeds in her own work, saying Wigner is not to blame for the insult.

Regardless of who said what and when the idea that Math speaks to divinity was a mistake by Dr. Islami. I think she would regret using that phrase if your comment pressed her. Misinterpretation of Math as anything but a tool is a crucial talking point for Arezoo and a cluster for Wigner and most physical scientists today. The world will and has already started to pay the price for computational biologists philosophically getting this wrong.

I like this post.

Why math should ever be considered outside time is a question not asked that needs a response. Discussing infinity and time together is deceptively intuitive. Arezoo Islami is a philosopher of time as well as math. It would have been helpful to hear her talk to both projects and correlate anything.

Infinity is a tool and no enigma, however. It is practical and limiting, both. Limits are the chains, and rigor is the anchor that changed the conception of infinity as we considered both the infinite heaven and the infinitesimal. Math has done a pretty fine job of capturing infinity, for the most part, with the concept of limits. Hilbert's hotel presents a world with many infinities. The Grand Hotel is a world that is useful.

Wild ass guesses (WAGs) should be disambiguated from iWAGs – informed WAGs. Some of the most meaningful and deep anchors and chains of my life and thought, of any one person's thoughts, are WAGs. Some can be dispensed with thought and experience, however, as well as lurking in the unquestioned and pervasive ether of culture.

Yet another vector for caution. We need to be careful to question our wild assery before dismissing someone else's iWAG. The "I" in iWAG can be the source of that dismissal. But to term epistemology, as a WAG doesn't pull power from explanations; it only focuses on their importance.

Zeno's paradoxes are a lark, were dismissed in his lifetime, and have persisted to modern times in those who failed to come to terms with them philosophically. Democritus and Leucippus answered the paradoxes in real-time (in the lifetime of Socrates) but were themselves dismissed by Platonic and later Aristotelian intransigence. Leucippus, a possible student of Zeno's, proposed the atomic theory of matter in Sherlockian fashion. Unfortunately, Josh points to Zeno instead of Democritus, but people still get confused. It is hard to overcome Ancient thought, the Roman and Medieval and predominantly modern, still accepted, Aristotelian world views. Reacting, adjusting, and refuting them is incumbent on philosophers today. Not only to read Plato and Aristotle but to refute and adapt them. Zeno can be dismissed entirely, however, as can much of Parmenides (all Monism aside.)

Democritus and Lucretius, on the other hand, need appreciation. Lucretius has had some rejuvenation, but Democritus wasn't rethought until Einstein considered Brownian motion. This show would have been a great time to refocus on the philosophy of thought experiments, their consequences, and how math can model thought and, thereby, reality.

Ancient Greek life had the conflict of Sophistry (Fake News) and Reason (Math – "Let none ignorant of geometry pass"), but that conflict comes to us by the filtered quill of others who didn't understand or appreciate the thoughts and conflicts. These quills had their own ideas and conflicts, which also WAG the dog.