Conference rusure::math

234.0. "IBM = HAL + 1" by SPRITE::OSMAN () Fri Mar 08 1985 14:29

Many of us are familiar with the word-shift puzzle associated with the
movie in 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.

	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.

   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 smallest 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.

net.map on USENET had a recent posting asking what English words
were transformed into other English words by the UNIX rot13
algorithm (i.e. WORD1+13=WORD2).

Whoops !  Due to a bug in my algorithm, my procedure missed a bunch.
I discovered this because a few weeks ago I published a study of those
words whose "difference" is 13, a study motivated by the common practice
within USENET news files of "rot13"ing potentially offensive material.

At that time, the largest example discovered was

	NOWHERE = ABJURER + 13

I happened to notice just now that this example was missing from my
original list.

The bug was that I shouldn't have subtracted whatever makes the
SMALLEST letter be "a".  I should subtract whatever makes the FIRST
letter be "a".

Anyway, having fixed the problem, I can now offer the following:

	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)

Correction to .1: "net.map" should read "net.math".

Sorry. [Response .2 came in before I had a chance to correct this typo.]

Re .2
	This doesn't sound like a bug to me -- you should end up with the
	same results either way.  Consider the simple case of IBM and HAL.

	With the first method you'd get:
		HAL		HAL
		HAL		IBM

	With the second method you'd get:
		A:E		HAL
		A:E		IBM

	In either case, these still map 'together', and would be recognized
	as word-shifts of each other by the final pass.

Yes, it was indeed a bug !  If you use my original algorithm, you miss
the gem

	NOWHERE = ABJURER + 13

Now I leave it to you to describe the characteristics of the set of
words that the bug leaves out.

(The bug being normalizing to smallest letter instead of first letter)

Ah!  Wrap-around.  Z + 2 = B.

You still have a bug. Else how did you get ZOO = ADD + 25?

				Uh . . .





			. . . er . . .





			. . . Oh !



		It should be "ODD" instead of "ADD".  My mistake.



sorry :(