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Traveling around the Ouija board.

Supposedly guided by spirits from another world, the planchette glides from letter to letter on a Ouija board, spelling out words. One can characterize the difficulty of a word by the distance the planchette must travel to spell the words (visiting the letters in the order of their appearance in the word). The table below gives the shortest-travel and the longest-travel words of various lengths, in pixels using the Ouija board at http://www.brainjar.com/dhtml.ouija/graphics/board.jpg. The ratio of the longest to the shortest travel is given in the final column.
4 68 feed 1155 mama 17
5 112 deers 1446 Malay 13
6 126 booboo 1809 malaya 14
7 180 feeders 2034 layaway 11
8 228 deferred 2247 chalazal 10
9 266 deferrers 2892 Malayalam 11
10 323 feedstuffs 2522 amalgamate 7.8
11 441 prestressed 2804 emblazoning 6.4
12 447 dessertspoon 3020 amalgamating 6.8
13 672 preregistered 3042 emblazonments 4.5
14 854 oppressiveness, 3081 unmaintainable 3.6
 stubbornnesses
15 826 dessertspoonful 3155 uncomplainingly 3.8
16 995 suggestivenesses 3286 circumambulating 3.3
17 1090 nonpossessiveness 3362 symptomatological 3.1
18 1310 lightheartednesses 3205 compartmentalizing 2.4
19 1655 antivivisectionists 3422 symptomatologically 2.1
20 1839 representativenesses 3336 microminiaturization 1.8
21 1862 hyperaggressivenesses 3505 microminiaturizations 1.9
22 2495 counterrevolutionaries 3172 electroencephalography 1.9
23 3254 electroencephalographic 3361 disestablishmentarianism 1.0

One can similarly measure the distance traveled on a QWERTY
typewriter keyboard to spell out various words, using http:
//ww.btinternetcom/~bill.furnell/QWERTY.jpg as a guide.

4 52 loll 846 papa 16
5 90 deeds 1101 papal 12
6 105 weewee 1234 jalaps 12
7 134 weeweed 1344 halalah l0
8 149 assessee 1520 palatals 10
9 216 addressee 1750 Malayalam 8.1
10 254 addressees 1776 soapflakes 7.0
11 345 readdressed 1848 Panamanians 5.4
12 454 underdressed 1995 spermatozoan 4.4
13 510 underassessed 2042 legislatorial 4.0
14 682 addressability 2155 paleographical 3.2
15 810 assertivenesses 2217 kaleidoscopical 2.7
16 836 schoolmistresses 2281 parliamentarians 2.7
17 1054 wrongheadednesses 2495 triskaidekaphobia 2.4
18 1028 lightheartednesses 2340 psychoanalytically 2.3
19 1399 disinterestednesses 2552 antiparliamentarian 1.8
20 1450 counterrevolutionary 2697 antiparliamentarians 1.9
21 1526 hyperaggressivenesses 2669 electroencephalograph 1.7
22 1712 counterrevolutionaries 2797 electroencephalographs 1.6
23 2860 disestablismentarianism 2890 electroencephalographic 1.0

The long palindrome Malayalam appears on both lists,
as does counterrevolutionaries, despite the completely
different arrangement of the alphabet.

Logologists may well prefer a distance metric based on position
in the alphabet. Replace the letters of a word with their alphabet
values (A=1, B=2, etc.) and take the sum of the absolute differences
between successive values (for example, FIB's travel is based on 6 9
2 which becomes 3+7 = 10). Here again are the longest-travel and
shortest-travel words sorted by length.

4 2 deed, feed, noon, 68 away
 poon, poop
5 4 ababa 83 braza, rayas
6 4 deeded 101 brazas
7 7 acceded 127 layaway
8 13 cabbaged, pronposs, 33 layaways
 rollmops
9 19 mollified, nonporous 141 graveyard
10 20 nonsupport 156 graveyards
11 21 nonsupports 159 sauerbraten
12 32 opportunists 173 taramasalata
13 43 diffeomorphic 177 bureaucratize
14 51 nonnitrogenous 191 bureaucratizes
15 58 nonproportional 185 bureaucratizing
16 66 monopolistically 200 parameterization
17 71 nonproportionally 218 bureaucratization
18 93 hemorrhoidectomies 197 pseudoaristocratic
19 96 anthropomorphically 192 hydrotherapeutician
20 112 antiinsurrectionists 221 representativenesses
21 122 antiinstitutionalists 211 hyperaggressivenesses
22 178 counterclassifications 186 electroencephalography
23 176 electroencephalographic 203 disestablismentarianism

If you allow for a circular alphabet (for example, A to Z is 1 step,
not 25) you get dramatically different results for the longest-travel
words, since the longest distance between letters in a circular
alphabet gets cut in half. Improved shortest-travel words are
asterisked.

4 2 deed, feed, noon, 39 nana
 pooh, poop
5 4 ababa 51 frere, serer
6 4 deeded 64 manana
7 7 acceded 72 mananas, paperer
8 13 cabbaged, pronposs, 82 frescoer
 rollmops
9 15 succeeded * 91 lapboards
10 20 nonsupport 102 paperboard
11 21 nonsupports 113 paperboards
12 32 opportunists 121 repetitively
13 43 diffeomorphic 123 grandmaternal,
 prerequisites
14 47 monopolization * 131 repetitiveness
15 52 monopolizations * 137 hyperactivities,
 representatives
16 66 monopolistically 155 repetitivenesses
17 71 nonproportionally 148 overargumentative
18 83 hemorrhoidectomies * 165 hypersensitivities
19 96 anthropomorphically 155 antiparliamentarian,
 hyperaggressiveness
20 103 microminiaturization * 179 representativenesses
21 108 microminiaturizations * 179 hyperaggressivenesses
22 148 counterclassifications * 162 counterrevolutionaries
23 191 electroencephalographic * 167 disestablismentarianism


Can one improve the letter layouts on a Ouija board to minimize the average travel distance for a typical word? For the Ouija board, place the letters of the alphabet on a hexagonal grid, adding a position to signal the space between successive words. Calculate the total travel distance for a corpus of common words for this arrangement, and then recalculate the travel distance with a pair of letters interchanged. By successive trial-and-error repetitions of this nature, one can approach that arrangement which minimizes the total travel distance. The pattern below gives the best arrangement found after numerous computer runs; not unexpectedly, the etaoinshrdlu common letters cluster around the space. The total travel distance was 522059582.

What if one uses a checkerboard grid instead? The best arrangement, found by similar trial and error, is given below; it is nearly 3 per cent more efficient than the hexagonal one, yielding a total travel distance of 508196981.

If one merely rearranges the letters to lie on two straight lines, mimicking the two arcs on the Ouija board, the travel distance corresponding to the arrangement ZXVGINAROFUPQ over JKWCHTESDLMYB is increased to 724085201, still much better than the standard arrangement of ABCDEFGHIJKLM over NOPQRSTUVWXYZ with total travel distance of 1082666795. The spacebar is placed under the A in the first arrangement, and the T in the second.

Thinking beyond the Ouija board, one can generalize to any communication task involving a stylus, say on a PDA or on an interface for a disabled person. The total travel distance for similarly-sized squares laid out on a typewriter keyboard is 964564575. After rearranging the letters to QBULCINGVZ on the top row, JPMOATHWK on the second, and XYFRSED on the third, the total travel distance is reduced to 615591269, 36 per cent better than the qwerty keyboard.

[ILLUSTRATION OMITTED]

ERIC IVERSON

Eagan, Minnesota
COPYRIGHT 2005 Jeremiah Farrell
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2005 Gale, Cengage Learning. All rights reserved.

Article Details
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Author:Iverson, Eric
Publication:Word Ways
Date:Aug 1, 2005
Words:1048
Previous Article:Palindromy's unseen "virtual verse".
Next Article:620 7x7 squares with geographical palindromes.


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