'F = plaintiff ( Rho) ;

emi) ; ( Quirk)

'aw) ; TRUE = song) ;

\. Natural)

Vehicle

RD = after­It his wit' s

of a pure ut one at a ~d 11 Literal May and Aug­TRG (energy) ,

explained in ent than the

In an alter­v words, as l is applied .omposed to

:ag L)

Treesong) 01)

141

WORD ROOTS AND BRANCHES

A. ROSS ECKLE R Morristown, New Jersey

Take a word, remove a letter, and rear range the remaining letters to form another word; the shorter word is known as a transdeletion of the longer one. Converse~y, the longer word is called a transaddition of the shorter. This process can be continued, and a chain of succes­sive transdeletions or transadditions formed; let us define the roots of a word to be all those words that can be reached by 'successive trans­deletions, and the branche s of a word to be all tho se words that can be reached by succes sive trans additions . Natur ally, the roots and branch­e s depend upon the dictionary specified; the large r the dictionary, the more flourishing the word tree consisting of roots and branches com­bined.

Sometimes it is possible to form a word from another by merely removing 0 r adding a letter; rear r angement of the remaining letter s is not necessary. If an internal letter is removed, the new word has been formed by a deletion; if the fir st letter is removed this is a be­headment, and if the last letter is removed, a curtailment. The cor­responding terms describing the addition of a letter to a word to form another word are insertion, hydration, and caudation. If we form roots and branche s both with and without letter - rear rangement, we have an enlarged word tree (with enlarged roots and branches) .

Root sand branche s can form a lush structure, with branchings and recombinations occurring. On the next page, the word tree for WORD is illustrated, using boldface words (or inferred forms, such as past tenses and plurals) from the Merriam- Webster Pocket Dictionary.

For convenience, the tree is shown on its side, with roots to the left and branches to the right of the word WORD, forming the trunk. Note that it is impossible to go below two-letter words without having beheadment or curtailment; we allow one-letter words as a special case.

There are many words containing the letters of WORD which are not in the tree; for example, TOWA RD cannot be reached because the re are no intermediate words using the letters aWARD or TWORD. Many seven-letter words are unreachable:

forward widower working dowager outward windrow workday towards doorway warlord worldly roadway worried wording bowlder lowered

142

byword rowdy(

d dowry drowsy

" wormed,..... cowered do ~crowed - chowder/ '" f dowrieso rod ? browsed

" / '" /drowse ,wonders -worsened or WORD - dower dowser worsted

/ "'" / rowed ~""worked /powered r row ~pOWder _ prowled

:;:; dewdrop worded --redwood

'drowned ~wronged

wonder ~ broVlIled - rawboned drown " frowned

onward crowned crowd~ coward

The enlarged word tree for WORD is considerably more complex; for example, two new main branches appear, one with WORLD and WORLDS and the other with SWORD, which furnishes a second connec­tion to DROWSY. In addition, numerous inflected forms appear for the first time: POWDERS, POWDERY, DROWNS, CROWDS, CROWED, REDWOODS, ONWARDS, COWARDS, CROWDED. But the most dra­matic change occurs in the many new connecting branches that make the tree resemble a thicket.

Most trees of short words are, in fact, so dense that it is difficult to diagram them. Tree s of long words are far thinne r, and harder to construct. On the next page, I show the enlarged branche s of SIDE R­A TION, based on Webste r I s Second Edition. To make it a bit easier to follow, each added letter is underlined, and insertions/hydrations/ caudations are parenthe sized.

Note that the standard tree contains one branch which extends from SIDERATION to DICTATORlALNESS, a fifteen-letter word. It is not hard to find a root of SIDERATION which goes back to a one-letter word, so that I ha ve exhibited a tree branch (not using insertions /hydrations / caudations) extending from a one-letter word to a fifteen-letter word.

Is it possible to find even longer branches -- or, equivalently, is it possible to find roots extending down to one-letter words for words of sixteen letters or more? This is an example of a logological investi ­gation which is abnost impossible to carry out by hand, but made much easier with the aid of a computer. In particular, I found it feasible to investigate only after receiving a computer printout of the Air Force list (most of the words in We bste r I s Second Edition) ar ranged in ana­grammatic form by word length; I am much indebted to Thomas Kurtz of Dartmouth College for performing the anagr ammatic sorting. (In a list arranged in anagrammatic form, the words are first written with their letters in alphabetic order, as CEORST for ESCORT, and these 11 words " then alphabetized. )

(il >-1 ----­PJ

I§:...... c-.­...... o ~ (fJ

/\'--;10..Ig. ......

(fJ(fJ ...... o 0.. >-1 (lI 0.. ......'1 ll.l ~ ......rl­ PJ ...... (fJrl­ ......

PJo (lI

~ 0.. ~

./side~onat rite ~ endotrachei tis --( endotrachelitis) ~ anthosiderite e:::::::...- thyroadenitis ­

disori~ntate --........... !.ederationist --( federationist~) / ~ ad~no~etritis

L-- inte rmastoid"""" .endaor-.!itis E:::: - ~~derationist - (moderationist~)

~( e nd.2~o rti ti s )< " ,decorationist -- (decorationists)

dissertation~ dissertations) endogastritis - gastroadenitis tradITionle s s dis se rtational . dictato rialne s s

disrelation--- dilatorinessz - rl· ­0

l-i IS C r etional b <t; cG redictations

C""'I ~ derivations "<t' 0r-i defricationsl-iU)

...,0 doetrinai re s CI) discreation~ ­<I)

- ~coad~inister - dosimetrician --( dosimetrician~)..c u ~ ro :Eredications --- predia.B.nosticJ.-< ~

'0 endocarditis ~ <I)Q1) - - endoparasitic -- ( Endoparasitica)J.-< '( eradications / - - ­ror-i ~

~ e radiations deas.Eiration

Tardenoisian

read~itions~~isordinated --- desideration

'0 I <I) ~ ..cC H­

'0 u..c 1 ~ 0 I _ ~ 0 00 .r< ..... uo 'N'0 ro <I) Q) >: <I.>~ ~ro<l.> ;::l ~ cG H [JJ 00 0 I ;::l ~ A' ro ~ ..c <I)2 0 ~ g '0 .r<.r< "" s:: H ~ 00

Q) o .;: H ~.~ ~o ..... s:: .r< H [JJ ~ E~ ~ ro ;::l 5 .~ <I) ~ s:: <I) ..... s:: J.-< 0 H.-!<:

r-i;::S::°u'Oro ..... <1.>1"'\00 J.-< ~ 0 ~'O<I),.D ~-..c[JJ P-r ..... o ..... 1-'-! c ..... '0 f-l ro .r< 00 00 <I.> ro ~ >- J.-< > <I).r< 0 s:: s:: ~ • .-1 H 4-JH ~ ErouJ.-<~~~ 'OHU)<I.>ro '0 .r< ~ H ? ~0S::'OCIl~·r<CIl '<1)'0

00'0 roo o~ ~~.r<roro 'OroQ1)~s::o ro ro H ~~~'OJ.-<~ H CIl..c ..... <I.> l-i r-i >- <I.> Q) S Q) H <I) S s:: ~O·~'Ou~ s:: ~cG E..c .r< ,.D >- ~ ,..c ~ r-i ,. r-i ...... r< hn • r< ro.r< -ro .A'v.v ~J.-<<l.>cG°o.,u ~ ~'OCIl ..c >< <I.>-~ roou~~-""'~OJ.-<~ _J U Q) Q) '0 s:: 00 <I.>~ 0 <I.> ro ..... [JJ .... s:: "I ro_ - ~ ....... > ...... r< :;l'r<", ro~ o;>~

----

144

A nearly complete survey of seventeen-letter and sixteen-letter words in the Air Force list, omitting only those containing the rare letter s FJKQVWXZ, revealed that no seventeen-lette r words exist for which roots can be developed down to one letter with no deletions/ beheadments/curtailments. However, since the Air Force list does not ordinarily contain inflected forms (plurals, past tenses, partici ­ples and the like) , it is not clear from this survey that an enlarged root of this length cannot be found.

A similarly complete survey of sixteen-letter and fifteen-letter words proved too tedious to carry out, but it was possible to examine a substantial fraction of these: all words containing at most one of the letters BDGMY, at most two of the letters CHLNOPRSU, and at most three of AEIT. I succeeded in finding one sixteen-letter word with roots extending to one letter; two of the thousands of different roots are given below:

repre sentational repre s entationa1 transpe ritoneal transperitoneal pre sentational pretranslation septentrional planirostrate steprelation Leptinotarsa inte r septal ae roplani st eternalist senatorial reinstate rationale inte re st oriental entrie s latrine inse rt rental reins later rise rate sir tar is at I a

A full diagram of the uppe r root of REPRESENTATIONAL is given on the next page; to avoid complexities, all deletions / curtailment s /behead­ments have been left out. At the ten-letter level, the root includes the isogram (no repeated letters) INTERPOSAL, and the four-way trans­posal ALPEST RINE/ EPISTERNAL/ INTERLAPSE/ P RESENTIAL.

In searching for my roots, I was able to estimate the probabilities that a seventeen-letter wo rd can be trans deleted to a sixteen-letter one, and a sixteen-letter word to a fifteen-letter one, in the Air Force list:

Prob (1 7 to 16) = 15/1235 = 0.012 Pro b ( 16 to 15 ) = 23/533 = 0.043

The corresponding probabilities for shorter transdeletions are not known precisely, but they i.ncrease rapidly; I estimate that Prob ( 15 to 14) =0.1, Prob(Hto13) =0.25, Prob(13to 12) =0.5, and Prob ( 12 to 11) = 0.8. Multiplying these together, the probability of a seventeen-letter word having roots down to one letter is quite small only 0.000005. However, there may, perhaps, be another sixteen-letter

Upp

"d >-j

o ....... co ,.... \ll >-j..... \ll ,:j

~~

"d/

>-j

(ll

\ll t-' rl ­(ll >-j

III rl ­..... o ,:j Ul

Septent .rlOn

entoretinas> penetrations

inte rpolate "' ­. ~ pretension I '" lnte r septal ~ a /- septentr'lOnal

postenteral'l steprelation

postretinal/ pre sentational

antiapostle \.

...:1 alterat' ~ . Ions ?~ Leptinotarsa~ /0 replantat'IonsH lntraseptal "" /) t-l

<t: stratoplane t-l

\!) Z'<f1 H ~ aeropla .nlst

(f)

~ pretranslation _~transperitoneal __cC transalpine

P-. (..Ll cC nonaspirate ante ro spinal 4-< 0

prenationalen

4-> 0 /

planirostrate0 NeopolitanscC !-< <l) reparations 0.. 0..

::> prerational ~ proletarians

prealte rationsintersporal/

proletariat ~ postarterial

I I !-<

<l) ._ o 'U 1 <l)<l) <tl <l) I 4-> 4->

<l)~4-> en s:: 4-> ...... 4->.-< <l)~ en -en (/).~ s:: 4-> (/) <l) 0 en 4-<r-i<l).., ~ 4-> J:: \!)!-< <l) s:: <l) U 'U !-< • .-< 0 en • ....-1 ...... O<tlr-i o <l) (/) <tl 4->!-<r-i<l) !-< 4-> 0 0''-< <l) <l)C4-<c~4-> H C I

4-> s::; 0 s::; 4-> 0 s:: ,.Q <l) !-< 4-> _ >- s::; J:: ..... 4-> o 4-> en <l):t <tl .~ ~ 'U t tlO 4-> <tl •.-< 0 ~ <l) <l)

<l) !-< >< <l) <tl!-< <l)-'U4->...:1<l) >< <l) 4-> ~ !-< .0 4-> U S::,.Q ~ <l)

...... "' <l) r-i ~ 0.. <tl ...... <l) s:: <tl > en ;:::l >- ....... <tl V !-< o ...... <l) 4-> ..... 4->r-i"' ....... I 0'U'U4-> ,Qr-io <l) !-< 'U ,.Q ..::: ><I '" <l) r-is:: ~ en 'U;'::: ~ s:: tlOS::U"'Hs:: 0 !-< s:: !-< p-. J:: <tl ;:::l ......<l) 4-> 'U en <l) <l) 4-> 4-> J:: 0 <l) <l)S::~t-l o ~ Jii

~) hl'\ s..., 0 <l) <Il m ..... J...4 .~ ~ • .-4 I ........ H t\, ~ <tl <tl "'? 0' (/J

interpenetration - prete rintentional * intermediateness - indeterminateness

physiotherape p

146

word besides REPRESENTATIONAL awaiting discovery in Webster IS

Second, for the co r re sponding probability increas e s to 0.0004, and there are 3374 sixteen-letter solid Websterian words in the Air Force list (however, the transdeletion probability is likely much less than 0.0004 for words containing rare letters or excessive repetition of common letters). If the word Gtock is enlarged by allowing inferred forms, plus words from We bste r I s Third, the OED, the Random House Dictionary, Funk & Wagnalls, and the like, all the se trans dele ­tion probabilities are increased.

One seventeen-letter word in the Air Force list was transdeleted twic e: A NTICEREMONlALIST to NONMA TERlALISTIC to RECIT A­TIONALISM. No fourteen-letter transdeletion of RECITATIONALISM could be found, but three thirteen-letter double transdeletions were located: MATERIALISTIC (lacking n, 0) , ANTIREALISTIC (lacking m, 0) and REMASTICATION (lacking i, 1). Jeff Grant of Hastings, New Zealand searched the OED for a fourteen-letter transdeletion without success, but suggested the plausible coinage RECLAMATION­1ST which in tur!1 transdeletes to REMASTICATION. The Oxford Uni­

versity Press did not have any cita­antic eremonia1i st tion fo r RECLAMA TIONIST in its file, nonmate rialis tic but the G. & C. Merriam Company recitationalism did: an article entitled II What You rec1amationist Can Believe About MVA" by Wesley remastication Price in the January 19 1946 is sue of cremationist the Saturday Evening Post used the c reationis m word twice. remication manticore Tr ouble was, the Ar my didn 1 t want reaction its plan modified by reclamationists certain retain Reclamationists got a special provi­train so putting irrigation first, navigation rant last, in use of water arising tan west of the 98th meridian at a In the article, 11 reclamationists" were

member s of the Reclamation Bureau, various upper Missouri Valley leaders and members of the National Re­clamation Association, all opposing a river modification plan sponsored by the Army Corps of Engineers. If RECLAMATIONIST is admitted as a word, even though it has not appeared in any dictionary, the seventeen~

letter ANTICEREMONIALIST can be successively transdeleted down to a single letter, as demonstrated above.

Since seventeen-letter trandeletions are quite r.are, it 1S worth list ­ing the other fourteen I found:

chorographically - chronographically anopisthographic - anthr opophagistic ':' administrational - maladministration

mic rophot< c ounte rmi~

ultrace rerr e Ie ctro opti contracept uncreditab reconcilial biopsychol biophysiol(

Several of tl probably the transdeletio

electromet psychother palaeodend

As word tailments to scientific te seventeen-l€ for this rea~

down to a on teen-letter \ root of PAL.

p p

Two similar

p

p p

Finally, a sl PHYSICOTH

n Webster IS

0004, and he Air Force h less than )etition of ng inferred Random e tr ans dele­

ransdeleted RECITA­

,TIONALISM :ions were [C (lacking . Hasting s J

,deletion LAMATION-Oxford Uni­

ave any c ita­\I1ST in its file, m Company II What You ,Tl by Wesley 1946 i,ssue of

) st used the

ny didn' t want eclamationists

special provi­irst, navigation arising :lian

ationists II we re ation Bureau, ~ National Re­Ian sponsored , admitted as the seventeen­eted down to

is worth list ­

147

microphotography - chromotypographic * countermigration - untrigonometrical * ultraceremonious - peritoneomu s cular * electrooptically - photoelectrically contraceptionist - antistreptococcin * uncreditablene s s - unp-redictablene s s reconciliability - irreconcilability biopsychological - physicobiological biophysiological - physicobiological

Several of these are only slightly rearranged; the asterisked ones are probably the most interesting. There are a handful of eighteen-letter trans deletions , but none are particularly noteworthy:

electrometrically - thermoelectrically psychotherapeutic - physicotherapeutic palaeodendrologic - paleodendrological

A s words become longe r, the ratio of deletions /beheadments / cur­tailments to transdeletions rise s rapidly in the Air Force list; many scientific terms have slightly variant spellings. For example, for seventeen-lette r words the ratio is 72/15 = 4.8, not counting plurals; for this reason, there is some hope that an enlarged root stretching down to a one-letter word can be found for an eighteen-letter or nine­teen-letter word. A near-miss is provided by the following enlarged root of PALAEONTOGRAPHICAL:

palaeontographic al paleontographical palaeontographic

palaeoanthropic paleontographic pal e oahthr opi c p alae anth rop i c

paleanthropic

Two similar enlarged roots based on the same prefix are:

palaeoe thnolog i st s palaeoethnologi st

palaeethnologist paleoethnologi st paleethnologi st

pala eoethnologi cal paleoethnological palaeethnological

palaeoethnologic paleothnological paleoethnologic palaeethnologic

paleethnologic

Finally, a sho rt but complex root based on the nineteen-lette r word PHYSICOTHERAPEUTICS:

phys icotherapeutic s phys iothe rapeutics phys icotherapeutic psychotherapeutic s

physiothe rapeutic psychotherapeutic