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Letter substitution ciphers are more secure in languages that are less compressible.
Which is farther away?
27 vote · Final results
A 1-Lipschitz function *:C×C→C (where C is Cantor space with d(x,y)=2^-n when x & y have the first n but not n+1 bits in common, and C×C carries the L∞ metric), such that x*(y*z) = (x*y)*(x*z), and ∃1∈C: f(x):=x*1 satisfies d(x,fⁿ(x))=2^-ν₂(n), where ν₂ counts factors of 2
Placebo AI alignment: Convince the action predictor that you've aligned it (nevermind how) when it's predicting what actions it will take.
Averting the Oxygen Catastrophe with a Pigouvian tax on oxygen emissions
The L1 norm of (1 meter, 1 kilogram) is 1 meter + 1 kilogram. Its L2 norm is sqrt(1 meter^2 + 1 kilogram^2). Its L infinity norm is... wait, that can't be right.
Finitely-generated torsion modules over a discrete valuation ring are classified by partitions.
The probability that a random n by n matrix over the field with q elements is invertible converges as n goes to infinity to a power series in q^-1, with most coefficients 0, and the rest +/- 1.
Extrapolating from the use of copper, silver, and gold for coins of increasing value, it was proposed to mint coins of even higher value from roentgenium, though this was eventually rejected as impractical.
The more finely you categorize something, the rarer it becomes.
Historian in the setting of a science fiction novel: "Weird how this early twenty-first century science fiction novel so accurately predicts current events."
left-adjoint to the forgetful functor from finite groups of exponent n to finite sets
Hello. My name is Inigo Montoya. You- oh, the AI just rendered your hand wrong? Okay, nevermind. We're cool.
A valued field induces a functor from a linear order to the category of totally disconnected topological spaces. The linear order is the space of Dedekind cuts of the value group.
the smallest sigma-algebra containing the open sets and closed under forward images under Borel functions
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