About Logic Interview with Urs Schreiber

See Assumptions of Physics - Symplectic Group and Uncertainty. 

Subscribe to About Logic. 

Lawvere on the Dialectic of the Continuous and Discrete. Talk given at Nancy, France 26-29 July 2011.

See Lawvere's 1966 The Category of Categories as a Foundation for Mathematics. 

See Lawvere's Cohesive Toposes and Cantor's 'iaufcer Einsen' (cf. my "vague inkling" about cardinality in Frederic Schuller on Metric and Topological Spaces) and cohesive topos in nlab. 

16:57 On structures and cohesion, with Lie groups as an example. See Anthony Bordg and Nicolò Cavalleri Elements of Differential Geometry in Lean. 

1:03:12 On applications to dynamical theory. See Toposes of laws of motion in nlab and this transcript of a 1997 lecture given in Montreal.

1:08:54 He goes back to Frege and the idea, from correspondence with Peano, that certain minimal atomic subsets have properties completely independent of the structure they were abstracted from. This became, via Zermelo and Von Neumann, the "semi-lattice of sets" modeled by the cumulative hierarchy. 

Subscribe to Matt Earnshaw. 

On adjoint modality and the resolution of opposites:

Subscribe to The Wacky Neighbor. 

Comments

Post a Comment

Popular posts from this blog

Steven Johnson - So You Think You Know How to Take Derivatives?

Image
A derivative is linearisation, and differential calculus is essentially linear algebra, ...  See  Freya Holmér - Why Can't You Multiply Vectors?  and  Freya Holmér on Continuity of Splines . See also the MIT OCW page:  Matrix Calculus For Machine Learning And Beyond  (Alan Edelman, Steven G. Johnson) Subscribe to The Julia Programming Language . Alan Edelman talking about expressing mathematics as computer code. The idea is that you can use computer languages to communicate mathematical ideas precisely to other people. See my comments about functional programming languages here:  https://prooftoys.org/ian-grant/hm/ Subscribe to TEDx Talks .
Read more

Tensor Fields and Simplicial Complexes

Image
Listening to Freya Holmér last night I started to get glimmers of an idea I had long ago about how to represent vector spaces in computational processes using this recursive abstract type :  abstype 'a point = POINT   of {getx :  'a vector,       diff :  'a point -> 'a point,       move :  'a point -> 'a point,       scale : 'a -> 'a point,       proj :  'a point -> 'a} with    fun new i (op +) (op -) (op * ) dot =    let fun self x =  POINT       {getx = x,        move = fn (POINT pr) =>           (self (x + (#getx pr))),        diff = fn (POINT pr) =>          self (x - (#getx pr)),        scale = fn i =>          (self (x * i)),        proj = fn (POINT pr) =>     ...
Read more

Hitachi HD44780U LCD Display Fonts

Image
I finally got the bit-mapped fonts from the Hitachi "1602" display :  Here's some JavaScript: const HD44780U01ASCII=[ [],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[], [],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ], [4, 4, 4, 4, 0, 0, 4, 0, 0, 0, ], [10, 10, 10, 0, 0, 0, 0, 0, 0, 0, ], [10, 10, 31, 10, 31, 10, 10, 0, 0, 0, ], [4, 15, 20, 14, 5, 30, 4, 0, 0, 0, ], [24, 25, 2, 4, 8, 19, 3, 0, 0, 0, ], [12, 18, 20, 8, 21, 18, 13, 0, 0, 0, ], [12, 4, 8, 0, 0, 0, 0, 0, 0, 0, ], [2, 4, 8, 8, 8, 4, 2, 0, 0, 0, ], [8, 4, 2, 2, 2, 4, 8, 0, 0, 0, ], [0, 4, 21, 14, 21, 4, 0, 0, 0, 0, ], [0, 4, 4, 31, 4, 4, 0, 0, 0, 0, ], [0, 0, 0, 0, 12, 4, 8, 0, 0, 0, ], [0, 0, 0, 31, 0, 0, 0, 0, 0, 0, ], [0, 0, 0, 0, 0, 12, 12, 0, 0, 0, ], [0, 1, 2, 4, 8, 16, 0, 0, 0, 0, ], [14, 17, 19, 21, 25, 17, 14, 0, 0, 0, ], [4, 12, 4, 4, 4, 4, 14, 0, 0, 0, ], [14, 17, 1, 2, 4, 8, 31, 0, 0, 0, ], [31, 2, 4, 2, 1, 17, 14, 0, 0, 0, ], [2, 6, 10, 18, 31, 2, 2, 0, 0,...
Read more