From the paper by Paul Cohen…”Skolem and pessimism about proof in mathematics“ “Skolem, in his papers, was so struck by the existence of non-isomorphic models ofall but the most trivial axiom systems that he was led to doubt the relevance ofany mathematical axiom system to the philosophical questions concerningfoundations of mathematics. For example, he pointedContinue reading “Skolem was right”
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The dream is real
We live in an enchanted world. The dream is real….the interpretations not so much.
The Gist of It
Aristotelian logic is nothing more (nor less) than a path through a binary tree. Change the structure of all the paths and all the “conclusions” follow that change. Arguments in mathematics can take one of two forms: proof by contradiction or by “showing” (a la Wittgenstein) via construction. I have shown (the “Real deal” andContinue reading “The Gist of It”
The Real deal, too
To clarify… Just to make sure it is clear, let me say that the main point of the first “Real deal” is this: the discrete derivative is about transforming the entire standard Binary tree by “twisting” every other pair of branches across every row in the tree….it is about transforming the tree, about an automorphismContinue reading “The Real deal, too”
A Few Favorite Sources
Pessimism by Paul Cohen Naming by Haim Gaifman E. Artin Geometric Algebra https://archive.org/details/geometricalgebra033556mbp Anything you can find by E.T. Jaynes…it’s all great…a good start is… Freiling…Throwing Darts at the Real Line https://www.jstor.org/stable/2273955 https://arxiv.org/abs/1311.0545 ….Funny remark about “intuitive justification for the Axiom of Choice”…he must have been referring to the Banach-Tarski Paradox. Stern-Brocot tree info: ContinuedContinue reading “A Few Favorite Sources”
Connections
The goal of this site is to illuminate the vast web of connections that is our world.
The Real deal
Below are clips of an Excel file that gives a definition of the discrete derivative via an algorithm by which it operates on an infinite binary string….by what it does to an individual string. It also shows how the anti-derivative operates. The discrete derivative is the operator that yields Gray’s code used in porting analog to digital.Continue reading “The Real deal”
A Manifesto
Time is real There is only one perfectly, absolutely impermeable boundary: the Horizon There is no such thing as a completed infinity A completed infinity is a contradiction To every Thing there is a Dual There exist things that are self-dual They possess features of both singularity and duality The features observed depend on theContinue reading “A Manifesto”
21st Century Paradox 