Visualizing 1 x 2
I used to think, thanks to Prof. Ronnie Brown‘s patient tutoring over the past couple of decades, of a function f: A -> B as a process of transforming A into B. Times change, or containing that incessant itch to sound profound: I got bored with verbs. I think of a function f: A -> B as an Abbildung (Conceptual Mathematics, page 245; yes, I like German), as a picture of A in B, and then use that thought to explain everything on either surface of the star-studded skies in terms of pictures. PRODUCT of the present note is past night’s catch.
P.S. Shape and Color is tonight’s scheduled bed-time story. Cast members include Extensive, Intensive, Quantity, and of course Quality. There are other characters: Sampling aka Exemplification, Sorting alias Classification, both of which are somewhat slick in that they surprise me with the things they pull out of their hats that keep changing (see page 81 of Conceptual Mathematics if you dont believe me). Not to be forgotten are Covariant, Contravariant, Linear, and Multiplicative. Make sure your parents don’t get mad if you stay up all night, listening to my silly stories, during a weekday; please don’t blame me if you doze off in the class (in grad school I used to go to class to sleep—no lullaby is as sedative as lectures by Nobel laureates).