Science & education writer · View profile
· 3 min read
For 2, 4, 4, 4, 5, 5, 7, 9 the coefficient of variation is 42.76 %. It is the right tool for comparing spread across different scales — and completely wrong for any scale whose zero was chosen by convention.
· 3 min read
7,000 units made against a capacity of 10,000 is 70 % utilisation. The reflex is to call the other 30 % a loss; queueing theory says it is the reason the line still delivers on time.
· 3 min read
At 85 % monthly retention the average customer stays 6.7 months and is worth 224. At 95 % they stay 20 months and are worth 373. The lifetime is a reciprocal, and reciprocals explode.
· 3 min read
Going from a 95 % service level to 99 % raises the z-score from 1.645 to 2.326 and the safety stock from 346 units to 488. The last few points of availability are the expensive ones.
· 4 min read
Boiling point follows air pressure, so it falls about one degree Fahrenheit every 550 feet. In Mexico City water boils at 198 °F, in Denver at 202 °F, and on Everest at 157 °F — which is why altitude changes cooking times.
· 4 min read
3d6 and 1d20 have almost the same average and nothing else in common. Against a target of 12 the three dice are better, against 18 they are five times worse — and the calculator gives the exact figures rather than a simulation.
· 4 min read
The population barely enters the sample size formula. What does enter it is the margin of error, and halving that margin quadruples the survey — from 385 people to 1,537.
· 4 min read
With a 0.6 % base rate, a soft pity at 74 and a hard pity at 90, the effective chance climbs from 0.6 % to 36.6 % by pull 80 and 90.6 % by pull 89. Without pity, ninety pulls would give 41.8 %.
· 5 min read
Twelve pieces of 46 cm take 1.84 m on a 140 cm bolt. Make them 47 cm and it jumps to 2.82 m — fifty-three per cent more fabric for one centimetre, because the third piece no longer fits across.
· 6 min read
The same Ferguson zone 3 puts a compact lamp 18 to 30 cm above the basking site and a 54 W tube 74 to 127. The zone describes the animal; the distance belongs to the lamp, and a mesh screen moves it again.
· 6 min read
The same 12.7 kg puppy at sixteen weeks predicts a 21.9 kg adult if it is a small breed and 38.5 kg if it is a giant one. The arithmetic is trivial; the class you pick is worth seventy-six per cent.
· 6 min read
Roll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.
· 4 min read
At 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.
· 13 min read
Points over total is trivial. What is not: averaging percentages instead of weighting them can shift a mark by twelve points, negative marking changes when guessing is worth it, and the same 62 % is a fail on one scale and an upper second on another. What the tool does, and the two things it cannot do.
· 12 min read
Twenty-five and five come from Francesco Cirillo's method, not from a trial. What the research actually measured is task switching and the cost of getting back in — and the reason a fixed interval helps is not that 25 minutes is optimal. Plus what the planner really returns, including the long break it quietly leaves out.
· 11 min read
Magnus–Tetens with the Alduchov–Eskridge coefficients, 17.625 and 243.04. Why an absolute number beats relative humidity for judging comfort, what temperature a window has to reach before it runs, and the one input the calculator does not check.
· 12 min read
The calculator runs the 2001 index, not the 1945 one, and refuses to answer above 50 °F or under 3 mph. Here is what its number is a model of — bare skin, in shade, walking — and the two things it says nothing about: a clothed body, and a parked car.
· 11 min read
Lumens are what a lamp emits; lux is what lands on a surface. You cannot convert one to the other without an area, or without a distance and a beam angle. Anything that offers you a bare conversion factor is selling you a fiction.
· 11 min read
Area grows with the square of the diameter, so an 18-inch pizza is not half as big again as a 12-inch — it is more than twice. Price per square inch settles the argument; the crust and the toppings complicate it.
· 15 min read
Series adds, parallel adds reciprocals — that part is easy. The parts that catch people: which member dominates the answer, why two 5 % resistors in parallel are still 5 %, and why the smallest resistor in a parallel pair takes the largest share of the power.
· 15 min read
Vout = Vin·R2/(R1+R2) is only true when nothing is connected to the output. Draw current and the voltage collapses, by an amount that follows one exact law. Here is that law, the ten-times rule checked against it, and why a lower-resistance divider costs you power forever.
· 8 min read
For sound, f' = f(v + v_o)/(v − v_s) — and getting the signs backwards is the classic error. Here is the convention spelled out, a 440 Hz source computed at four speeds, and why light needs a different equation entirely.
· 9 min read
Re = ρvL/μ compares inertia with viscosity, and the units really do cancel. See the number worked out for honey, a household pipe, an artery, a swimmer and a wing — and why the 2 300 threshold belongs to pipe flow alone.
· 8 min read
Hooke's law says force is proportional to stretch — but only below the elastic limit. Here is F = kx with worked numbers, what a 200 N/m spring actually feels like, and how springs combine.