Publisher: Lighthouse Books for Translation and Publishing
Publication Date: September 20, 2017
Binding: Kobo eBook
How this relates to Quantum-TGD
What made me fascinated was how closely the basic hierarchies of Quantum-TGD relate to the objects studies in type theory and Voevoedski's approach.
Let us start with set theory and type theory. TGD provides a non-trivial example about types which by the way distinguishes TGD from superstring models. Imbedding space is set, space-time surface are its subsets. "World of Classical Worlds" (WCW) is the key abstraction distinguishing TGD from superstring models where one still tries to deal by working at space-time level.
What has surprised me against and again that super string modellers have spend decades in the landscape instead of making super string models a real theory by introducing loop space as a key notion although it has very nice mathematics: just the existence of Kähler geometry fixes it uniquely: this observation actually led to the realisation that quantum TGD might be unique just from its mathematical existence.
The points of WCW are 3-surfaces and its sets are collections of 3-surfaces. They are of higher type than the sets of imbedding space. There would be no sense in putting points of WCW and of imbedding space in the same basket. But in the set theory before Russell you could in principle do this. We have got as as birth gift the ability to not put cows and tooth brushes into same set. But the ability to take seriously the existence of more abstract types does not seem to be a birth gift.