Consider the positive integers in base 2, in binary notation. Define prefix: the digits left of the first pair (from the right) of identical digits along with the left digit of that pair. Define tail: the digits to the right of the prefix. Define the Collatz function: Consider the positive integers in binary in countingContinue reading “Collatz Proof”
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The ultimate Nietzsche
“Truths are illusions about which one has forgotten that this is what they are” An apt description of what is at work when mathematicians are in ‘Platonic’ mode…when foundations that in fact are not solid are deemed sufficiently so. A quote: According to Weyl 1946, “Brouwer made it clear, as I think beyond any doubt,Continue reading “The ultimate Nietzsche”
Infinity
Infinity is not a ‘thing’…it’s a relation. Vector Space • The square roots that come out of the tau(p,q) spaces serve as the eigenvectors of an infinite dimensional vector space. That space is founded on a 2D integer lattice, (p,q). • The lattice gives rise to a countable collection of vectors defined via the squareContinue reading “Infinity”
Count and Measure
• There is only one certainty: There is no such thing as a perfectly impermeable boundary (all are conditional, porous) • Sharkovskii’s ordering of N as an example of a porous boundary: an infinity of infinities • The BITXOR/discrete derivative completely changes the order type of the set of infinite binary strings • A favoriteContinue reading “Count and Measure”
Images
Favorite E T Jaynes quote
E T Jaynes ‘The Gibbs Paradox’… “If one is to condemn things that depend on human information, on the grounds that they are “subjective”, it seems to us that one must condemn all science and all education; for in those fields, human information is all we have. We should rather condemn this misuse of theContinue reading “Favorite E T Jaynes quote”
Mathematics is social
Mathematics is social The extent to which that people can ‘get through life’ without mathematics is an indication of its artificiality. Granted, most of those people rely on technology invented or built by others who may ‘get through life’ using more (or less) mathematics. Still, it is clear that “meaning is use” in anything involvingContinue reading “Mathematics is social”
A Manifesto
A Manifesto There is exactly one absolute: There is no such thing as a world without boundaries nor a perfectly impermeable boundary <=> the only absolute is there are no absolutes <=> there are no ‘perfect’ boundaries, there are only filters • The continuum defines all boundaries, not the other way around…echoes of Deluze andContinue reading “A Manifesto”
Set theory, models, and Skolem
Models of ‘Reality’ References: ‘Mathematical Undecidables, Metaphysical Realism, and Equivalent Descriptions’, Hartry Field ‘The Gibbs Paradox’, E T Jaynes The whole discussion of set theory, models and reality on pages 8 and 9 of the first reference is best understood the way E T Jaynes deals with entropy in his work referenced above, in sectionContinue reading “Set theory, models, and Skolem”
Wants and Needs
Wants and Needs One of the weaknesses of capitalism as a means to satisfy ‘wants’ is that instead of satisfying ’wants’ it clearly by its very motivation ends up creating more ‘wants’ in an endless cycle. Thus, if we put ‘wants’ before ‘needs’, then ’needs’, though limited, will never be satisfied. ‘Wants’ are in everyContinue reading “Wants and Needs”
21st Century Paradox 