Life Essays
24 articlesA photo rotated 90° lies flat again on another device: how the EXIF flag and a real rotation split the work
The rotate you tap in an album writes one Orientation flag and moves no pixel, while a real turn pushes the picture through a hard-coded 0.92 re-encode and zeroes the metadata: 28210 B parked at 0° still downloads as 28003 B, and four download-and-reload rounds never get back to the start.
Same Day Every Month Versus Every 28 Days, 29 Days Apart Within a Year
The same period log is not equivalent under the two rules: starting from 2026-01-31 the 12th entry is 2027-01-31 on the same calendar day but 2027-01-02 every 28 days, 29 days apart. The page only has a day-based addDays and no calendar-month logic at all.
Shuffling with a random sort comparator is already unfair
To decide speaking order, picking one item from the remaining positions each time is uniform; giving a sort a random comparator does not even fix the number of comparisons. Enumerating every path quantifies the bias: with four elements the most and least likely outcomes differ by 12 times.
Two gallons, two horsepower ratings, two byte prefixes: ask which one first
US and imperial gallons, hp and PS, mmHg and Torr, KB and KiB are four pairs of units with the same name but different definitions. Pin down which one applies before converting; even the number of displayed digits is not always eight.
Born on 29 February: which day you turn 18 in a common year
Born on 29 February, which day counts as your 18th birthday in a common year? Using a calculation date of 2026-10-21, this note sets full age, nominal age, total days and two anniversary conventions side by side, then explains leap-year rules and why the page uses 4 February for the zodiac sign.
What pace does a 3:30 marathon need? Nine segments, negative splits and the floor pace
A 3:30:00 marathon goal reduced to just run 5:00 per km? This note lists nine 5 km segments with progressive paces, segment and cumulative times, the first-half and second-half difference, and the extra seconds when segments get so short that pace hits its floor, all matching the page display conventions.
One transcript, five GPAs: weighted averages and working back to a target
The same sample transcript yields five GPAs from 2.943 to 3.394 under five schemes: per-course credit weighting, simple average, weighted average score and arithmetic average. This note also works back to how far a target GPA is.
3,000 a month for 20 years: compound versus simple interest and the rule of 72
With 100,000 principal plus 3,000 a month at a nominal 4% for 20 years, this note compares compound, simple and beginning-versus-end-of-period contributions, measures the rule of 72 error at each rate, and writes out the logarithm.
Up 10% then down 10% loses money: bases, percentage points and stacked discounts
Up 10% then down 10% leaves 99.0000%, and two successive discounts do not simply add. This note uses a break-even drop table to separate three measures, the percentage base, percentage points and cumulative change, and gives a way to check the result.
Equal instalments versus equal principal: a month-by-month comparison on a 1M, 30-year loan
On a 1,000,000 principal over 30 years, this note compares equal-instalment and equal-principal repayment at 3.0% and 3.5%: monthly payment, total interest, monthly decrease, which period the cumulative totals cross at, and how much a 20-year term saves.
What you actually take home from a 10,000 yuan salary: thresholds, brackets and quick deductions
How much tax comes out of a 10,000 yuan monthly salary? Using a 5,000 yuan standard deduction, this note works through the seven progressive brackets, the quick-deduction recurrence and cumulative withholding, and explains why the number does not match your payslip.
Fraction addition and subtraction: seeing every step of the common denominator
When tutoring fraction addition, where the common denominator comes from, when to reduce, and why mixed numbers do not take part: this note works through 3/4+5/6 and 5/8-1/6 step by step on both routes.