Guides
Plain-language explainers on the ideas behind our tools. Where the numbers come from, what they mean, and where they fall short.
What BMI Actually Measures (And What It Doesn't)
A 19th-century population statistic became a personal health number. Here's what it's good for and what it misses.
How Mortgage Amortization Really Works
Why your early payments are mostly interest, and how extra principal payments actually save you money.
Password Strength: Length Beats Complexity
The math behind why a longer passphrase beats a short jumble of symbols.
What Actually Moves Currency Exchange Rates
Interest rates, inflation, trade flows, and central banks. How each one pushes a currency up or down.
WCAG Contrast Ratios Explained
The luminance math behind the 4.5:1 rule, and the color-blindness cases it doesn't catch.
Why Date Math Is Harder Than It Looks
Leap years, a 1582 calendar reform, and why DST transitions can make "tomorrow at this time" ambiguous.
How Diff Algorithms Actually Find Differences
The shortest-edit-script problem behind git diff, and why two "correct" diffs of the same text can look different.
Lossy vs Lossless: What You're Actually Trading Away
How JPEG decides what detail to discard, why PNG can't, and which one actually fits your image.
Percentage Points vs Percent Change
Why 5% to 10% is both a 5-point move and a 100% increase, and how basis points avoid the ambiguity.
The Science (and Myth) Behind the Pomodoro
Cirillo picked 25 minutes by feel, not research. Here's what attention science actually supports.
How QR Codes Survive Damage
The Reed-Solomon error correction that lets a QR code lose up to 30% of itself and still scan.
Screen Recording Codecs Explained
Why the same recording length can produce wildly different file sizes depending on codec and content.
How Spreadsheet Data Gets Corrupted
Why Excel renamed real gene names, and the delimiter and encoding gaps still catching CSV files today.
Unix Time, Timezones, and Leap Seconds
Why Unix timestamps ignore leap seconds entirely, and why the world is retiring them by 2035.
What WPM Actually Measures
Why a "word" in a typing test is defined as five characters, and the gap between gross and net WPM.
Costly Unit-Conversion Mix-Ups
How a mismatched unit system destroyed a Mars orbiter and nearly downed a passenger jet.
Why Word Counts Vary Between Tools
Why "word," "page," and "reading time" are all softer definitions than they sound.
Where Tipping Culture Actually Came From
America's tipping norm was once banned as un-American. And it's still built on top of a wage system from 1991.
Why GPA Scales Don't Actually Compare Across Schools
Weighted scales, grade inflation, and international differences all mean a 4.0 doesn't mean the same thing everywhere.
Gross Pay vs Net Pay
The deduction stack, taxes, payroll tax, and pre-tax benefits, is what explains why your paycheck is smaller than your salary.
Why Calorie Counts Are Approximate
Nutrition labels run on a 130-year-old formula, and US law allows them to be off by up to 20%.
The Rule of 72 and Compound Interest
A centuries-old mental-math shortcut, and why compound growth always looks unimpressive right up until it isn't.
Why Stacked Discounts Don't Add Up
Sequential discounts multiply against a shrinking price, not add. The real math behind "50% off, plus extra 50% off" signage.
Sales Tax vs VAT
Why over 170 countries run on VAT while the US ended up with more than 10,000 overlapping local sales-tax rates instead.
Why Few Babies Arrive on Their Due Date
A due date is the center of a five-week-wide normal range, not a prediction. Real birth data backs that up.
True Randomness vs Pseudorandomness
Most software randomness is a deterministic formula. The real difference, and a 1995 case where it broke encryption.
How Browsers Throttle Background Timers
Browsers deliberately slow JavaScript timers in inactive tabs. Why a countdown can jump, and how it should self-correct.
Why We Still Memorize Times Tables
Multiplication tables trace to Babylonian clay tablets. And cognitive science has a specific reason schools kept drilling them.
Why Designers Use Nonsense Placeholder Text
"Greeking" text is deliberate. Eye-tracking research on reading explains why real words get in a designer's way.
Why Computers Use Binary, Not Decimal
A 1703 essay on binary arithmetic and a landmark 1937 thesis explain why every computer counts in two digits.
JSON's Surprisingly Personal Origin Story
Douglas Crockford says he didn't invent JSON. He noticed it was already hiding inside JavaScript's own syntax.
Regular Expressions Predate the PC
Regex started as 1950s formal logic. And grep's very name is a fossil of how it became a real programming tool.
Why Base64 Makes Files Bigger
Base64 reliably inflates file size by about a third. A deliberate fix for 7-bit email transport from the early internet.
Why Substituted Passwords Are Weak
Cracking tools ship with letter-to-symbol substitutions built in as a default, automated first step. Not a real obstacle.
What a Hash Actually Guarantees
Hashing isn't encryption. What a hash function actually promises, and MD5's real, documented (and narrower) weakness.
camelCase vs snake_case History
Naming conventions trace to Smalltalk, PEP 8, and old terminal limitations. Inherited history, not technical necessity.
Why Every Solvable Sudoku Needs At Least 17 Clues
In 2012 a supercomputer proved no 16-clue puzzle can ever have exactly one solution. Here's why, and where Sudoku actually came from.
Why "Two Sides and an Angle" Can Have Two Right Answers
Trig's "ambiguous case": why the same two sides and angle can describe two genuinely different, equally correct triangles.