# A mathematical miscellany

This is a collection of gems from math, programming, and science, a miscellany in the old fashioned sense.

• You can transpile Python functions on the fly into other languages (in this case, JavaScript).
• Some probability distributions have heavier tails than others, and there’s an obscure way to measure that.
• The naive way to calculate the Golden ratio is slow. You can do it way more efficiently.
• When you show a pagination bar on a web page, calculating the bounds is actually not trivial unless you look at it the right way.
• When I was doing microscopy, I needed to calculate an affine transform from three points to interpolate a grid.
• How apothecary’s balances work is not actually obvious.
• Most classical mechanics books show how to get conservation of energy from Lagrangian mechanics, but I haven’t seen it done from Newton’s laws.
• The material derivative—the derivative used when calculating changes in a thing when that thing is also flowing—can be forced from type-level considerations.
• In a fit of pique about trying to type commutative diagrams from category theory into a computer, I threw together a way to flatten them. John Baez referred to it as “like drying roses.”
• Lockless and Ranganathan published an interesting way of thinking about pairwise correlations in ensembles of related proteins.
• The unit circle in p-norms looks less and less like a circle. It turns out you can do interesting things with that, like estimate the number of components of a vector that are significantly different from zero.
• There’s a cute decomposition to separate measured noise in gene expression into what was inherited and what was is locally random.
• Luria and Delbrück found a way to differentiate random mutation from responding to the environment in populations.
• Koch developed postulates for deciding if something caused a disease or not.
• When you’re trying to approximate functions, it helps to be able to measuring their pointiness.