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.

f(x) = ½x + 7

it was only yesterday that i realised that the rule of thumb for dating people of different ages (the “half your age plus 7” rule) determines not only the lower bounds for dating but the upper bounds as well—that for each ½x + 7, there is a corresponding 2(x-7). for the last 15 years of my life, i have been ignoring an entire market segment, namely those of the genus cougar.

i decided to graph these equations as a handy pocket guide for when i mack on chicks in the library stacks and a few interesting things soon became apparent. for starters, if one is under 14, it is mathematically impossible to date anybody. let’s say my five year-old nephew wanted to join the scene. according to this rule, he could only date girls older than 7.5 (which he would be down with), BUT the same girls also have to be younger than -4. MATH has prevented my nephew from getting jiggy with anybody!

only when you become 14, does math allow you to begin dating—and then you can ONLY date other 14 year-olds. society will scoff at you if you ask a 15 year-old to your freshman day dance, and don’t even think of approaching a 13 year-old.

from 14 on, your options increase at a linear rate such that by the time you are seventy, you are eligible to date 42 year-olds AND 126 year-olds. so the next time that your seventy year-old auntie introduces you to her 126 year-old paramour, give them each a (gentle) nudge and let them know that you support their union.

fun with authors’ names #2

what’s longer than an 8-author name chain? how bout one that goes on for ∞? and what’s longer than ∞?

3 × ∞, duh.

the adventures of papa and bill continued

i feel that perhaps my post from yesterday has led to the belief that i am of the mindset that papa hemingway and bill faulkner were twins separated at birth. indeed, i do think this and if the rigorous application of statistics to the sublime can’t prove it, our only recourse is exhumation. let us grab some shovels together and get ourselves to work!

the adventures of papa and bill

there are, as far as i am aware, two famous literary disputes about length involving ernest hemingway. the first was with his buddy, f. scott fitzgerald over the length of his wiener. the second was a dispute with his adversary, william faulkner over the length of the words they chose.

faulkner fired the first shot saying, “hemingway has never been known to use a word that might send a reader to the dictionary.” which earned the following riposte from hemingway, “poor faulkner. does he really think big emotions come from big words? i know all the ten-dollar words as he does, but i prefer the older, simpler ones.”

i decided to chart the longest words in each of their major works and see if i could draw a non-scientific conclusion. the longest of all words was faulkner’s cinderstrewnpacked, which only appears in the dictionary of made up words that william faulkner made up.

additional data: the average word length in these three hemingway novels is 3.85 letters; faulkner’s average word length is 3.88 letters, which is statistically the same. 1.08% of hemingway’s words were 10 letters or more whereas 1.56% of faulkner’s were.

conclusion: hype. the top two 20th century american novelists were engaging in a literary pillow fight so they could ride the gravy train of book sales for as long as the public would allow.

stop referencing yourself!

hey mathletes, get this: when the above formula is graphed using a set of predetermined ranges for x and y—it produces itself! it’s called tupper’s self-referential formula and was invented by lee iacocca when he was developing the rack and pinion steering on the dodge caravan (a wildly successful minivan in its day). many years later, a minivan fitting this description ran over my neighbor’s pet snake, betelgeuse. accounts vary as to whether the minivan was swerving to get out of betelgeuse’s way or to hit him (presumably as a social service). no matter the intent, we have the rack and pinion steering to hold accountable for the result (a smear of snake guts along west church street).

see also these robo-jokers.

chaz babbage’s windows error report

ever since i posted the marvelous letter from charles babbage, father of your laptop, to alfred tennyson, i could not shake babbage’s neuroses from my thoughts. the one that struck me the most was that he actually tallied and categorised the causes of 464 broken windows of a nearby factory in a ten month period. what mad mind would do this? whatever the state of his mind, his data was ripe for the pickin’ and plottin’—thus this chart (you can distend it with a well-placed mouseclick).

for the inquisitive: this is the first treemap that i have had occasion to make and i didn’t quite know how to start—my slapdash solution involved these two programs.