4 is the magic number cont’d [spoilers]

yesterday, i made it my bidness to clue you into 4 and why it’s the magic number. today i will tell you why. i will also discuss at length my unabatable zeal for charting the mathematics behind its magic—in a crowded jumbo jet, sipping on campari & o.j., whizzing through the air at an altitude of 39,000 feet, and watching a brendan fraser movie where he can communicate with raccoons.

the solution is frustrating at first but very gratifying once you yourself get to make someone else figure out how every number leads back to 4 just as every road leads to rome. i played a little trick on you yesterday by not writing out the numbers (despite what the chicago manual of style says). if i had, you might have realised that each number is the amount of letters it contains. thus: 3 (three) is 5 (five) is 4 (four). doh! 4 is magic therefore because it has the unique property of being spelled with its own amount of letters.

for every number to be reducible to 4 however, there needs to be additional magic—all numbers have to lead to it, and no other number can be “magic”. if 5 were spelled with two letters, 5 would be 2, 2 would be 3, and 3 would be 5 again— creating an infinite loop that never gets to 4. additionally, only one number can be spelled with its own amount of letters. if 6 were spelled “sihcks”, then the whole delicate balance explodes and the puzzle loses its appeal.

these are the things that were whirling around my brain as woodland creatures were flinging rotten fruit at brendan fraser’s gonads. and as the captain made an announcement in three languages, i realised that 4 is only magic in the english numberverse, who knows what mysteries were yet to be uncovered in foreign alphabets. perhaps 9 was magic in mandarin, maybe 13 in romanian. or maybe—and this is what really revved my turbines: maybe english was the only language which held these three magic properties. maybe english and its numbers are the center of the matho-linguistic universe!

i did some quick counting in different languages and soon realised that cinco was cinco and vier was vier. but did all numbers in spanish lead to cinco? were there other numbers in german that were magic? i mapped out a few languages in my counterfeit moleskine journal.

spanish, it seems, is magic only half the time. 50% of the numbers 1-100 will get stuck in a 6-4 infinite loop. german, like its grandnephew english, has 4 as a magic number (and only 4). what about french? french, like france itself, gets tangled in a vast web of bureaucracy. 6 leads to 3, 3 leads to 5, 5 to 4 and back to 6 and so on and so on to infinity. just by sketching out these four languages, i could see how each chart structure was wildly different than the last. i needed more! i became a data junkie!

i made fast friends with the vietnamese government official sitting next to me. “can you spell out the numbers 1-100 in vietnamese,” i asked over another round of campari & o.j.?”

“huh?!?” he said (the question mark-exclamation point-question mark i added)

but weirdly, he wrote them down without further questioning. “do you know any other languages?” i asked. perhaps he anticipated what i was going to ask him to do and responded in the negative. so i set about the plane querying people on what languages that they knew and then prodding them to write out every number in that language from 1-100. it was actually a pretty good icebreaker and people were oddly compliant. perhaps everyone was bored with watching brendan fraser tongue kiss brooke shields, or perhaps people were just excited to showcase their language. for whatever reason, i soon had myself a dozen cocktail napkins with over 1,000 handwritten numbers scrawled all over them.

as i always do when overwhelmed with a sudden influx of correlatable data, i got out my laptop, closed my redtube.com tab, and opened up my charting program so i could chart the tar out of these numbers and their relationships.

the images above are from this feverish, 39,000 foot high charting session. you will notice how the structure of numbers and how they are spelled in each language is as different as the languages themselves. and yet similar languages do have similar structures. the longest number in portuguese, spanish, and italian is 54, yet italian has a magic number, spanish is half magic and portuguese is only a quarter magic.

consider also vietnamese in which half of all numbers are ten letters long. in malay, not a single number is spelled with 6 letters. in polish, it takes 24 letters to spell out the number 99. in typical german efficiency, it takes just four maximum steps to arrive at the magic number while it takes 7 steps in italian. these are just a few of the highlights, the rest i leave in your intrepid hands.

in the end: english’s four, german’s vier, and italian’s tre were the only fully magic numbers in my pool of 10 languages but that does not take away from the other languages and the beauty of their relationships in this odd intersection of number and letter and language and math.

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props to my fellow passengers on thai air who answered my out-of-nowhere request for written numbers (and now know why i was badgering them): mr. binh, hugh, almas, weronika, jordan, that guy with the jason mraz hat who was reading the entertainment section of usa today, and phillip—you guys, please consider yourself members of the mile high club for polyglots.

disclaimer: i couldn’t read everybody’s handwriting, and don’t know every language (yet), so there will doubtlessly be some mistakes in these charts—perhaps even some large and embarrassing ones.

4 is the magic number

before i clue you in on 4 and why it’s the magic number, let me first digress a little bit and tell you about the river of 1,000 penises.

on my last full day in cambodia, i thought it would be a real gas to tour phnom kulen and explore the linga 1,000—a gushing stream which flows over hundreds of stone phalluses. the problem was that nobody wanted to go on the 2 hour drive with me to see such a marvel, “we don’t want to see 1,000 stone phalluses,” they said.

finally, i bumped into a german rugby player named otto who was receptive to my invitation. before he had a chance to second guess what he was signing up for, i hailed us a tuk-tuk and we were soon speeding down a 50 kilometer stretch of dirt road and screaming rugby hakas into the dust.

in the end, the stone phalluses weren’t really phallusy enough for either otto or i, though that is not the point of this post. the point of this post is to clue you into 4 and why it’s the magic number, and i’m getting to that.

we spent our time on the return voyage giving eachother puzzles to solve. i busted out this classic, which otto made short work of before i had really finished asking. then he told me about 4. “4 is the magic number,” he said. “5 is 4 and 4 is 4.”

“huh?”

“give me another number,” he said.

“6”

“6 is 3, 3 is 5, 5 is 4 and 4 is 4” he said. “give me another.”

“13”

“13 is 8, 8 is 5, and 5 is…”

“4 and 4 is 4. so every number can be reduced to 4 in some way? how about 4,032?” i said, ever the smartass.

otto rolled his eyes in his head as if under a voodoo jinx. a few seconds later: “4,032 is 21, 21 is 9, 9 is 4 and 4 is 4.”

“scrotumburgers,” i thought, “this is a grand puzzle.” by the time that we got back to homebase, i had cracked it, though the insidious mathematics behind the thing soon drove me to complete mania as i spent an 11 hour (11 is 6, 6 is 3, 3 is 5, 5 is 4, 4 is 4) plane ride from bangkok to rome haranguing 9 (9 is 4, 4 is 4) passengers about their thoughts on the puzzle and charting the output to a ridiculously obsessive degree. that story, the charts, and the answer to how 4 actually is the magic number, i shall reserve for tomorrow.

[the solution can be found here]

beta-testing a new puzzle

many are the puzzles that i attempt to solve, far fewer are the ones that i actually do solve—but a still smaller category are the puzzles that i write myself. i developed the following puzzle last night while suffering from insomnia and staring at a digital clock.

the setup: each numeral on a clock is composed of digital sections (eg. 8 has seven sections; 9 has six). using the 12-hour clock…

easy: determine the difference (in minutes) between the time with the fewest total sections and the time with most total sections.

hard: determine the time with the single greatest net change in sections from the minute before it (e.g. the net change between 3:34 and 3:33 is 1 section).

comments are now enabled (for 1 day only) in anticipation of the avalanche of answers, feedback, and derivatives that you might have.

UPDATE: the correct answers to both the easy and hard questions appear in the comments, so if you want to submit your solution without reading anyone else’s you can always email me via email.

opposite day

mike from the internet has sent me the above sentence (to which i added a calming grey-pink gradient and then typeset it in rustika). it is part grammar lesson, part logic riddle, and part buddhist kōan. mike writes:

I think the sentence should be read front to end as normal, and the resulting instruction would be nonsensical, like if somebody said to “Stop at green traffic lights, go at red traffic lights.”

since i am a reader (and unabashed abuser) of parentheses (and nested parentheses (like this one)) i default to reading parentheses. therefore, i would read this sentence as “do not read words inside of parentheses” and then, (providing i always did what imperative verbs told me) i would disregard all future parentheses. supposing i was then to read the sentence over again, i would trip the gate in the opposite direction (do read words inside of parentheses) and get stuck in an infinite loop. if it weren’t for that soothing grey-pink gradient, i would soon luze my marbles (marbles is a metaphor for sanity).

finally, mike mentions that i may refer to him as mike but that i don’t need to. therefore, i will refer to him as kilroy. so readers, how do you interpret kilroy’s sentence?

in honour of coining -or- the mile high club for logicians

i mentioned yesterday that i spent a good deal of my return flight questioning sachiv about his father’s reverse-œdipus issues. but what of my other flight? well, i WAS going to watch the benjamin button movie starring danny devito BUT on the day that i left, my father sent me this puzzle which i decided to work on instead.

you are given 12 coins. 1 of the coins is irregular and weighs either slightly more or slightly less than the other 11. you are also given an old-fashioned scale of the type that has come to symbolise the legal profession. your challenge is to determine which of the coins is irregular and if it weighs more or less than the others IN ONLY 3 ROUNDS OF WEIGHING ON THE SCALE.

it seemed easy enough but it took almost the entire 4 hour flight to arrive at an answer that still needed further retooling once i made it to a beach. if you can’t take the suspense, my solution is here [warning: the solution is A LOT more complicated than i originally thought].