Burkard Polster Trying to Start a Revolution

My comment:

40:42 This is fun. I once spent some happy time in 2011 playing around with lambda calculus and normal order reduction which allows one to normalise expressions including subexpressions like YI which is like an infinite list. I was looking for ways to extend numbers so they included solutions to equations like x=x+1 which I was using to represent "infinity". This suggests that there might be a way to do this sensibly using some geometric argument approximating perfect circles by regular n-gons for n=1... and connecting this with nth roots of unity. I did at one point in this process find some sort of numbers which were like conjugate pairs of complex numbers and which were solutions to z=z+1. Unfortunately I lost all my notes and all of my computer backups,... But I recall that a key step was replacing addition by multiplication so that the equations z=z+1 were easier to solve. The idea a was that you invent a magic sort of number C such that Cz = z+1 and then z=Cz is easy to solve [and I think at some stage in this a differential equation appeared], but C has to be a kind of "unity" for all points in the series,... Sounds like nonsense when I put it like this, but it made sense to me at the time and produced some very interesting results when I tried to compute rational approximations to high precision, I never got to the bottom of that but I wonder whether maybe the library (PolyML) I was using for arbitrary precision integer arithmetic used Fourier series to do fast multiplication and I tickled some sort of numerical instability because my series where close to the basis it was using to represent integers.

See The Golden Trisection and Peter Steinbach's papers Sections Beyond Golden and Golden Fields: A Case for the Heptagon. 

See also Mura Yakerson on Algebraic Geometry and Ravi Vakil. 

Subscribe to Mathologer. 

Ben Sparks on rational approximations

Subscribe to Numberphile.

See also Toby's short: Toby on Braids and the Golden Ratio. 

Subscribe to Tibees. 

A recurrent theme I keep coming across these days is one where a series of finite approximations is taken to an infinite limit, then some result is produced and that is in turn developed by another series of finite approximants. See for example Moshe Vardi talking about LTLf.

That pattern appeared here in the thing I wrote without using the letter ν: On Mathematics and Abstract Language.

Here is : On Tarski's Semantic Definition of Truth "Convention T". 

It's important that you print this document double-sided, so that it is on a single sheet of paper, as Putnam will explain in this excellent documentary:

The Origins of Logic in The Organon of Aristotle 

See Andrej Bauer's "Five Stages of Accepting Constructive Mathematics" and also Thomas Forster on Stratification and Simon Peyton-Jones on impredicativity and Hindley-Milner type inference in Stephanie Weirich Hunting Dragons. The latter is this idea of top-down type inference (QL) which seems to correspond a limited form of intensional typing. 

This was my homework today:

I may have overdone it a bit,...