[net.math] \"IBM = HAL + 1\" and other rotation revelations

osman@sprite.DEC (Eric Osman, dtn 283-7484) (03/09/85)

Many of us are familiar with the word-shift puzzle associated with the
movie 2001.  Namely, add 1 to each letter of the "HAL", the name of
the computer in the movie, and you get "IBM".

In a mathematical sense, we can represent this fact like this:

	IBM = HAL + 1

I ran a procedure on our computer to search the on-line dictionary for examples
of sets of English words that are related by shifting letters.  The longest
words that work are:

	SULPHUR = PRIMERO + 3

Here are others I liked.

	KNEE = FIZZ + 5

	GNARL = XERIC + 9	(I haven't looked up XERIC, but assuming it's
				 a word, I like this one because it has my name
				 in it.)

	SATIN = MUNCH + 6

	IRON = FOLK + 3

	TEAR = PAWN + 4

	GROG = WHEW + 10

	GROW = DOLT + 3		("All DOLTS ought to GROW up 3 years !")

	SHALE = LATEX + 7

	LAYOUT = FUSION + 6

	APTLY = TIMER + 7

	ARENA = RIVER + 9

	NEST = HYMN + 6

	ASS = WOO + 4		(I better not say anything about this one)

	BUNNY = SLEEP + 9	(Nor this one)

	PIES = HAWK + 8

	BURY = SLIP + 9

	HAZER = BUTYL + 6

	KEG = ICE + 1		(nice association: icy cold keg of beer)

	FAGOT = TOUCH + 12	(hmmm)

	NOON = DEED + 10

	RUT = ILK + 9 = BED + 16

	LOO = ILL + 3 = BEE + 8 = ADD + 11

	ILLY = BEER + 7

	LOX = FIR + 6

	FIX = BET + 4		(Something about fixing a race ?)

	FROG = COLD + 3

	HUSH = BOMB + 6		(Sort of a gruesome association)

	ONYX = BALK + 13

	SPUR = LINK + 7		(Isn't there some mountain in New England
				 containing two trails with these respective
				 names ?)

	ROUT = LION + 6

	HERO = DANK + 4

	OWL = GOD + 8		(Hey Topher, Toby, you read me ?)

	STOP = HIDE + 11

	JERK = FANG + 4

	LOOP = BEEF + 10

	INGOT = CHAIN + 6

	PEPPER = LALLAN + 4	(I hope LALLAN is a word.  I don't know what
				 it means)

	SEX = OAT + 4		(I liked this because of the "sow your
				 wild oats" loose connection between the words)

	TIGER = PECAN + 4

	JOLLY = CHEER + 7	(My favorite)

	VEX = RAT + 4

	WET = SAP + 4

	SURE = PROB + 3		(Kind of cute, given the meaning of
				 "probably" vs "definitely")

	SUING = MOCHA + 6

	TIE = PEA + 4

	PET = LAP + 4		(Something about a lap dog ?)

	TWIN = LOAF + 8

	STIR = OPEN + 4		(two words from a recipe ?)

	ZOO = PEE + 10 = ADD + 25	(wrap around from Z to A again)

	SHOW = PELT + 3

	TWO = RUM + 2 = LOG + 8

p.s.

	Col. G.L. Sicherman motivated me to make the study.  He pointed
	out the SULPHUR/PRIMERO "rot3" relationship.

p.p.s.

   In case you're wondering how my computer procedure worked, the
   main steps were:

   1) Run a program that takes every word in the dictionary, subtracts
      whatever it needs from every letter such that the first letter
      becomes "A", then outputs both versions as a record.  So JOLLY
      and CHEER will appear in the list as

	AFCCP                                  CHEER
	. . .
	AFCCP                                  JOLLY

   2) Use the dcl SORT command to sort the records.  This causes all the
      ". . ." lines to move elsewhere, bringing the "CHEER" and "JOLLY" records
      together in the file.

   3) Run a program that scans the sorted file and prints out all sets
      of consecutive records that have the same left-hand column.  Hence
      since "CHEER" and "JOLLY" both have "AFCCP" in their left-hand
      column, they get printed out.