March 26, 2026
Pi fights and petty digits
How much precision can you squeeze out of a table?
Digits at dawn: math nerds feud over how many decimals you can “squeeze”
TLDR: The post says you can’t beat a table’s own precision and warns that using too many points can backfire, so pick a modest interpolation. Comments split: one camp cheers simplicity, while a nitpicker argues you can “squeeze one more digit” by averaging many entries, turning math tables into a mini soap opera.
A quiet explainer on interpolation — basically guessing numbers between entries in a printed table — turned into a tiny decimal drama. The post argues there’s a hard limit: you can’t get more accuracy than the table’s own digits, and using too many points can actually make things worse as the error grows fast (see the “lambda” constant in the next post). It even name-drops classic tables for logs, sine, and Bessel functions, saying the sweet spot is modest: think 4th–7th order for tight spacing, higher only when points are far apart.
The comments? Pure internet. One nostalgic fan dropped an old-school numerical analysis textbook link and declared it “so much fun,” summoning retro calculator vibes. Then came the nitpickers: one sharp commenter pounced on the “you’re stuck at 15 digits” claim, insisting you can “squeeze one more digit” by combining many entries — imagine repeating a rounded value a hundred times and averaging the rounding noise. Cue the peanut gallery debating whether that trick is genius or just cute math cosplay.
Humor flew as folks joked about arguing at the 15th decimal place and playing “random rounding roulette” with π. Verdict from the crowd? Split between Keep It Simple, Nerds (don’t overfit!) and Squeeze Every Last Digit (clever averaging FTW). Either way, it’s the most drama you’ll see over a log table this week.
Key Points
- •Interpolation error can be bounded by c·h^(n+1) + λ·δ, combining spacing and tabulation precision.
- •Accuracy cannot exceed the precision δ of tabulated values; choose n so c·h^(n+1) ≤ δ.
- •Higher interpolation order can be harmful as λ (Lebesgue constant) grows exponentially with n.
- •In A&S log tables (h=10^-3), linear error ~10^-6; 5th-order gives ~10^-8, near the practical limit.
- •A&S examples: sine table (h=0.001) benefits up to ~7th order (nine figures); Bessel J0 (h=0.1) needs ~11th order for four decimals.