Wait, no we don't. Our birthdays are actually 144 (sometimes 145) days apart. But if you read our birthdays as fractions (month/day), then his birthday is the reduced form of mine. What are our birthdays?
BONUS PUZZLE (I thought this would be too obscure for a regular PotD... prove me wrong!):
In the original illustrations for Alice in Wonderland, a certain "fraction" appears on the Mad Hatter's hat. (It's not really a fraction—it's a price tag in shillings and pence.) If you reduce that "fraction", you get the logo of what Cincinnati-based institution with over 1100 branches?
Almost every pair of sounds that English speakers recognize as different have a minimal pair to prove it. But there's one pair of consonant sounds that do not and cannot have a minimal pair in English, because one of the sounds never occurs at the beginning of a syllable, while the other never occurs at the end. Yet no English speaker would confuse these sounds. What are they?
Hint
One of the sounds is typically represented by two letters.
As for the other 't' sounds, the t in art is "unreleased" (notice that you can barely hear a 't' at all, it's more like the t just cuts off your breath) and the t in artery is a "flap", sounding a bit more like a soft quick 'd' than a 't'.
More information about why minimal pairs matter in linguistics (if you're curious!)
Linguists care about minimal pairs because they provide evidence of what sounds are different in a given language.
Whattt? Aren't different sounds... just... DIFFERENT?
It's not so simple! The letter t makes four different sounds in tar, star, art, and artery, but as an English speaker you have to pay close attention to notice the differences (and even then you might not notice). In English, all these sounds are considered variants of a single sound /t/, and we automatically select one based on position in a word. There are no minimal pairs to distinguish them, so understanding what has been said never hinges on hearing which /t/ sound a speaker has used. But some other languages DO make a full distinction between (some of) these sounds.
Wait, I want to know more about those four 't' sounds.
If you say tar and star into the palm of your hand, you'll feel a puff of air with the t in tar that isn't there for star. In English, that puff of air (a.k.a. "aspiration") is automatic when /t/ comes at the beginning of a word. Some languages (like Spanish) do not aspirate /t/ in any position; if you want to speak those languages with a convincing accent, you have to learn to suppress that puff of air! And some languages (like Hindi) have minimal pairs for aspirated and unaspirated /t/, meaning you not only have to learn to turn the puff of air on or off, but you have to learn to hear it in order to identify what has been said.
Solution
The sounds are "ng" (which, in English, always occurs after the vowel in a given syllable) and "h" (which always occurs before the vowel).
Congratulations to yesterday's solvers Jacob C., Charlie, Peter M., Graham, and Kate. Thanks to everybody who made a guess!
Ten years later, Dr. Shapiro revived Puzzle of the Day at Proof School, writing each day's puzzle on a name tag. After 600 puzzles or so, he was just starting to feel normal about students reading his chest all the time when campus closed and the puzzle, like the rest of our lives, moved online. New puzzles are posted daily on school days.
Want to catch up on old PotDs? There's an archive currently containing puzzles from March to June 2020.