21st Century Paradox
Collatz Decoded 17-12-25
A presentation in Word… An analysis of the Collatz function in Excel…
Decoding Collatz
Have a look at the spreadsheet…it should be self explanatory. If not, then send a question.
Collatz Proof
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 counting…
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,…
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 square…
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21st Century Paradox 