The problem is that the Church-Turing thesis is not rigorously defined, and it was in the attempt to rigorously define the parameters that the research in the v

The problem is that the Church-Turing thesis is not rigorously defined, and it was in the attempt to rigorously define the parameters that the research in the video was done. I think that qualitatively we can agree that the ruler-and-compass construction of the square root of two is an algorithm. It's a repeatable procedure that can be described in a finite set of steps, and will always yield a provably correct answer. Whereas "waving a hand" is not an algorithm, but the same qualitative definition. The speaker wrote a paper that proved the Church-Turing thesis for sequential algorithms, primarily by defining in strict terms what a sequential algorithm is. Ruler-and-compass constructions are not sequential algorithms by this definition, and the difficulty in specifying the parameters for a generalized "algorithm" is apparently what leads him to the conclusion that the Church-Turing thesis cannot be true in general.