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‘The Bell System Technical Journal Vat XX ly 204 Nog Industrial Mathematics By THORNTON ©. FRY The pert exosts of thre major sections, The fixe discuss smaenatieal specie aust als tention co dh ceeutay fasalativeshaacer of ther wtiy ald uaker see cheats Sein te etn, np apn Ge Teor sen daly wot withthe we of th pec, set wy ahr tosh atts pt a Ce bad of ake (others gen, the vate ways Eiht cuties to the Teoowuy aot eGeelvenss of memth, aod the Ais of athens {hat ar est uss. A'mumtero:dinstans ae gives, tosther th Ul arvee of Ca aaa of uate oe pena ia [ls ents dos lead nner, pelea abd eu "The Guadsstion devoted to sats, toucber Incl 1p at phe erent pont, and enes cui nat eomtenety be loca in dh gene ews Iernanncriow MSTHEMATICAT tie used i ef i mt reste ‘rl development setivitiey but ta mee who se Cem lecniquee ‘would no: uualy be ealed machesaticians. “Mathersatrians als play an Hnporiant role fn indueral reware, at ‘hele servies are ofa spell character and do not touch the develope program at near a mary pots “Because of the eoncuat becwewn the ubiquity of mathenates and the ferness of the mathematicians, chis separ is vised into sbarply fdernceted parte. Under “Mathematicians ia Industry” an ettexpt Js male ta explain what sor. of service may be expos! of Indu ‘mathematisens, and to davciop some principles af pimery imporcance ix feoploying and manoging the, An attempt ie also made to apprise future demand for men of this type, and to dlecuss the soures from Which they car bo dorwn. Under Matheraten ix Init” appr bret fnrveye af the rete and chara of Oe wisn of matheralee fn fen special indetries, and examples of specie problems inthe sation of which rather el maa eve been neeshty or advatgeons, aera aa cone de ae hc eR BCL Ln cece it ee aR ing Otis. 7 memes 2s 26 BELL SYSTKM FRCKMIEAL JOURIAE Tn these two sections mathesatis is interpreted beady to include sot only the fundamental sabes, algebra, geometey, analysi, ee, Sut alo their wanfesations ia applioe form as wechanies, chsticty, slectromagaetic theory, hydadyamcs, etc. Stalls, however, touches industrial nctvity in x caer diferent may, and is therfore devs fcpacely uvler 4 hid beading, “Tosti Stasis owl Statens.” ‘One ebvervtéon which wil Be made in mone deal eter is worthy of mention ere, bees of Ue pase and prospective sarc of stay Uiained nena) mathesnaticane Thowge the United Seates nls position of ont ng leadership fa pare theres thee is no vckool SBhich provides nv wleguate methematia] axing for the elect who tse foie the shel inthe fald of ingostrl aplication rather than Ceultivate tos nerd fn ill. Hoth sence generally nd its costal tpptcatins in pacisla, would bo adc ia group of suitable aches free brought together 1a an Seetiation where tere was elo 0 steong ‘beers in the bale ieneos and in enginceing ‘Mammainicians 14 Tsou What ise Matematica? "every man wo now and then comptes the avetge of a set of instru rmeosalroulings ur solves dierent eealion ja mataceatica, thee Ure fey research wotcere who aze not, Hl ua che othe: eel, anly those ‘pho ere primarily engaged in ming additions to materiel k-mslege dre mathernatiins, there ae almost none fa industry. Neither definition issound, The re sabsurd th cond rot cezely seat to Pe esnts] ture of mathenatiealthongh Ths repect scopes a denitivy base Spon the character ofthe man's thinking lather thon the ulimate use t2 which his thieing e pat. Sorce ti voukl be called wathemetihire in ary man's lengua: others phyeiis or ener, ‘Ie fypial men aro difereatited artaiaeaential rempects! "The typical ratlnwatcian ele great dence ina caelsion reach vy aarefal meworing, Her nat convince! tn Ube sac degree by exper Zonal evidesoe, Fur the types! engineer these statements ray be roverscd, Conirase by @eatflly thsgh-out they which predicts a Ervin rely nl cetfaly performed experiment which fal to produce it the tied eather asks Set, “What 5 wrong wih he exper fuento” abd tke typeal engineer, “What fe wrong wth to azgumen: Because of this conidence in tought proceses Uae mathomtcn (urns ratory to paper and peel io many Hurtin is whieh the engineer or physicist would resort othe laberatory. Far the sume rer the mate: satici ix bs "pur form delights fa bur lagen etrctues, sch a5 Aopology ov abetect algsbe, which Lave uu apparent connec'on ith the sword if psi ely and whieh would et laterest the typ engineer, wile conversely the engineer of plyiitfs Iis “pure” lorry takes great Incerst in such vf information a3 tsb of hardaea data which may, so foray he are, be totally snrelted t0 ay tory, ad which he {pital mathemticinn would fad quite boring “Asean charter ofthe typical rather eh highly eis) aude toward the dese of x demonstration, or alticet ay uiher flea of men ct argumen: mye gooe enough, even thougi ser rinar ‘question remsins apen. Far the mathematician au agutteut i ees petfect i every Heal inform x8 wel nein sbetenc, of eae fis wrong ‘Thete are vo intermediate elses, He celle this igarous thinking,” and say I i necessary If ie eoreeslons 20eto be of pemanent value The Iyplclenginer alls it "haf pliting,” net nye thet fe alge ia he ould never ge anything done ‘The mathematician alto tende to iealoe any sittin with which he is confronted. His yatea are “idesl" hs condactors "perfect" his rusface “moot.” He adie this process and ele geting doma ta the engees or yict Ila to duh it somewhat co texprcousy “iguting te facts” ‘Atourth and costly related chameceritic 5 the dase for gently Contented wilh the prosiem of saving the simple egunticn #1 — 0, he solves = — 1 = 0 ington! Or asked stout the torsional vibration fs galvsnometer suspension, he studies a Siber loaded with any auzaber ff mirrors at arbitrary pola along it length. He allt thie “eomercing bis energy": beis solving whole elas problesat sce nse of dealing with them piosemenl, "The engineer clef “ating his time”; of what te ta anemeter ith more than one miro? Ta the vast army of wientie workers whe cansot bo ragged so easly wlth the tage nse ne pro‘euon, tose my open be cle uate avian” sewer dominated by thee four enracctiais of getter onbdence in lng than experimental poof, severe cits of deta, Wellzton, and evento. The bourtarice of the profetion att pethape uot ade harper by Ue deft, otf as the merit of being sed upon typeof mind, which san allie of ie man all ud not ‘pon such superficial and frequently acigeatal matters as the courses he took in ellege or the sot of job he hod Te b moreover, = more fondamental Aistnction thew caw be diawa hetneen, 2a, lyse chert and astronomer. "Takt fe my the sate matic olds toed industry's ferent relationship thom aber slenti, {relaionhip wich must he eleely woleriond by macogercent if his teavies are wo be sueselully exploited "he Place ofthe Mastamatici in Toso Nessrck “the typieal matbettiian desrihed above i mot the sl of man to canyon an ilustiah project. He is eames, not much iaterested [Brings or the dole they eaa bol for. He sa periectionst,unling to compromiar ealizes tothe paint of impractical; fas roncerned with She bro orion that be cen! Kosp his eye on the ball. Thee trate fe not weakness; they are, onthe ovieury, of the highest importance {pve jus fading a aystem of thought hick i reas the complex ‘hemuceua of te phwial word, Laat ei edacng mature tow eience. ‘Te job ot industry, however, abt the advancement of astral eciese, but Le cevslopmert, production and scle of marketable gos, The physics, the chemist, and especially the engisecr, with cei inlereet in acts, things and svoney ar obviasly better adapted to contrite diecty to these ends. To the extent Wat the mathemaicin takes on project Fesponsility, he i fored to comprorie; he most specilveinsesd of feocalize; he ros ad with enezete deta instead of ehfrart principles Soue mnthenackstns ceanct do thow Unings ct all come by Aligesce and setsemtaint con dn chet very wel To (he exten, however, that they foccoed along she lines they are funeioning ao: ae ealematiians ut as engineer, Ae rinthernickus thee place Frosty is not to apply the inte attention hv qacisl deca by ise goud product Conversa service, and efieiantproceses ure levied; their fonction fo ve counssl wn aubance to those who do supply thse things, tn iyi their everyday viet in the light of sclauic thong 2nd Conversely fo translate the abstract language of sien ito terms mote Stal for concrete espslaton 7 In bse words the matberalsian in industry, Wo the extent to"which bb furlin was a mtaemetician,(s comslant, ota project men (Quasotioes Neerar for Sze as om Tusa Metheaticon ‘he sucesfalincustrnl muhematiar nat ant rly be competent saa malnenaticen; be mut sks have th other qualities which constant requires “it, though his major interes wil necessnvily be abstract he must have ficient interest ln practcal sre o provide stil or use work and {us teconce bim to the cmmpeomises und approximations which are nace sary eves inthe theureicltretment of prea problems, This ueully ‘pean Heat the typeof mathematisiaa who coulé not do «god englesing job fhe toro his hand to twill not gt on ess well nan alse! career, Seonil, he mins be gregarious end eympethetie, Tf ue shuts hinsel of fom Wis astcites, mc of bis thinking wil have no avin on Uilr needs ad that which does will exert Jess infuence thn it might. Ee oes not tanslate his toughls into their lange, they will mise the ‘Sgutcance f much of bis work and he wil lavett amit clientele, Tied, he must be cooperative aa easels A man canooe be at ance consultant and compotcar #2 is asacates. Selsaeing ails to gain ‘cedit for his contributions to the Indasiry wil inewtably alienate ie lientele, There are tu reasons for thie: Ty the Get pce a mathemati ‘can's appraisal af mathensical work, even if mle from x tached point ff view, heavily weighted on the sie nf fx fundameatalecentieeg- iicauce where ity intra value should be judged on very dsrest grounds and can Dest be apple Ly the engreer In the send pace, the engineer in change of poject can ye credit without ebarrsenent for help received; itis to Liscrdi to ive buat were ip wast be had Tye same story told by snotber sad partially by the consllane bins, Ins ao entirely diferent tvor. "Foorth, he mast bo versie, Jobe ckange, and even the sane job say give ree to questions mich coquize very diferent ccathemetial "if, be must be a man of qutstaxding ably. No one wants the advice of medicrity. Amung instil saathematiclan ene mo place for the average man inponoon sd Superson Pechipa the greatest hazard i hing reathonaticions for iodusty arses ftom the fact tat the employment lier is not often a jade of Toathemateal abifly. Parulosically, however, his mister are not ‘evaly msde in judging seathensatealapttade, since peneral shale ring 5 em unusually tsteorthy index of natheateal ability. But ‘because ofa feeling of iacsncatsnco bred hy hit lack of ra ‘bematio Tore spe he mantle of ebacity ovesatherchasacrevieic ith regu tu whic he should erust his own judgment. If, for example, the applicant five an incobereat account ofthe prob: on whieh he has heen working, the interviewer exten the ground of is on leek of mathematical Uualsog, an excuse which wuld be quite adequete if tae cgcunstaaces dovaned that he meet she applicant on the apabcant'sgrouné. What bo ae ets SYSTEM PECM ICAL soITRFAL overlooks is thst the applicant fas fled to meee hin on sown ground; fas flel, hn othee word, to diay the essential ability to trate is ‘hones ino the laoguage of hi heaeer Or portaps a personality defect Ie encusd on de ground tha “alae, be ie working by himself a tt ave vo ree: posh," wheses infact tke mal value of cesultant Tomes notin bathe doe a is des, bt io how zauc of gets throm to his aescstes The applicant who fe boastful ve posing ex quralais ‘ould aoe be hiv ow the general theory #hal “all matbematcins are uees” ‘High senda i all guck anaes, ara interest in. practical hinge asinel, ares important eg technic metheratice) ably, ‘hese ste fei specie ioat, ane the ren ffl thera sre 0b be fou la every rashet place. ‘They ae however, ce requirements plc in the aatare “he ob and mo god a come Kom fling to recogiae them. ‘Meet the right wan & bleed, Ee fe not iienlt person to supers iT 1s fnetion ns a consulate seat of the salle hepe enya mind. “The brout objectives ust be to avoid beeies which woud tend deter Lis scocintes from seeking bis tevios alto wate zat his work is oly Sppraised anv aly compenssted. The three barriers mos Bly to arise between him and his asociates ave jealyy sed tape tad urwealiy Sealousy is eoavoidale i che wan Rimgelf is eleedking; uae ech s.ftan sited toobe ie nevi, Bue the mai not aways to ble. ‘Ritecerous and ompeeative wsrait willbe spoil yan atmaspaere to Highly changed ith prazes rents or by @ sary poley Which bases fevinine upon the dha value of the last year work. Actally the “pogsee™ which igalicaat Lo management wil be far move accurately anptasce by his colleagues than by alm, hence bie reports havo ile ‘elueexcope as Cy give bit an opportanity tv sewn axe citi his frm sctivitis. IE top tach empiis iy placed upoa them, even this Sele wil be hs aad they wil be wrsen a Ube spit of making a ease for Tiel, which exady the apt most certain to breed jelous. Sim- larly, ary policy based om dally eeturns is esentilly unjust fr the roney value o" varius bits of thenresea ork be almost no coreation ‘with ce acentVeacumer wih chey require. This docs not mean tat @ ‘rothertici’s pay ehold in Us ong von, be independent of the dollar Valu of his services Te meen only thi whether e gets aris his yes, {nd bow big tal be, shout propany be bare on the sine aracer and Stisinction hiv cieatele, and ot vpn the eommercal importance ofthe sustons they sr Fito ia i at Yen, Red tnpe is easly evoided by avoiding IL Nu eagneer, whatever his rank inthe orgznizetion, ought over need perian ta eau a mathe mmatichn inthe company's empiey, and the mathetatcan fn tm nught rtd specie work order or expente allowance before giving Ws vir. Tithis respect he shouldbe on the same basis as the frelance investigators wy are tse fad in roet Inge reesch liberstore, ad who ane senerally Kren ste engineers, Unavallabilty is a more serous mutter. It % well rengoitd that 4 linkscrial research the angen jo ning tends to take poeeeence ver the fporant one Tale to themselves, fuacamersal studies yive ‘may to Cie dezled develoomert “wien oeght 9 go int prodeetion ext moat” Matheratialstuie ane no more siesptale thon other uvimeatal search to auch faterrinns, I the flee pon the cacer of tae mathenatican may be more fa reaching, fora 00a aes ign An unget vot af spel earcter he souablity oe conaltant ceases hat le temporary inane. hfe wale tothe Sadusey egeater 454 project man then as 9 coneltent this aotd uot be a cause for nel Thu. ten yal mathem tick in x poor engines, an epee ‘mathemati Inloa repre engines, ennrsmate for both employer and employee ‘The Mothomatst Rezerch Deartnont ofthe ti Tete Lberseries nthe Rall Teepe Kaluatovies mer sce hve been geonped together a8 a eecaate ofganation writ. They have nn mare specie fenetin than eo be lp to thle ass dae ne ats the Labor tora, No ciacer isliged teal shen ably pase of his works fo perccalar jobs come to them by resson of prerogative; converly there is no sore of hep which an engineer or physi iy’ ack It them if he so desires. No routine nod be eosplied wit ia advance fn et a scare dir service, ul no reports exited aftemad chou Willer rere ace frequently prpned wen needed for sien reser The expense of the group is estabuted Irealy over the activo o ts Laborstaie, unt change: casper juis.Rvery elo! simcse to msntn 2 spit of sevice among the manera Iie group, ard thong neon Silty fr eoginering projecte cecsioaallydecenis upon thet Hs repitded ab an vadesanblenecstity to be avusted wlraver pn’ ble liquidated a the etliest wppersuniy Tho group hes Fancioned soceesully fort number af year. The mem bers are respected by ther engineering associates, and like their jobs Infomation roganding their activities reaches managameat alm eatiely ue ELE SYSTRW PecuNICAL JOURIAL Brough sportanecis achmlsgennss made by the exgiaees ther ast. "These eoptesons of appresataa sre ners, bul vatber erratic ia cat hey eancentste attention fiat on ope mua, then on anther, asthe genios snl trang of the india! Taper to clic withthe imporian. job of ‘he moments "This hae not aGasted the ror of che group adversely, Faby becauee a erie nor sade to avoid etic sary revisions it Sich ke man who sat the sna ate iit beets at Ue expense tether wio are doing equaly good bt les consplcuous we, From tie suniwine of the men, dhe prisipsl advanteges of being exncine! together head of aiatited droog the cngiaosing depart tents dp the stimulus of eratee th men of Uke itersts, From the Smijne af managersent, the eantages are wider avaiaity, grater $eviility in matching ta tele of the rsa withthe reqsrerants of the jou, ands moze uniform spprsial of ably beoure oF supers isn by ‘an of alaguate mathematic’ ground. So fara hnowny mathematicae have ot been organize ino separate adminisuative grote. is oiler industries. In most laboratories thee ‘bumbers have bee nut too small fo make seh an arengementfosble, fe they have bean tented aR engineers cistioutedehrongiont. the Sarions general departnents, I; eed, however, shat there are fer insite in whic this axrargerent ld be inceduced with proit at thie tne, ane Las te suicont merit te jst ite adoption wheneser posse. Tae atiemotisin 3 th Set! Labortory What bas een side eles pisorty to cosine ia large indas- lees. "Toe quelenion for -uceaa in tesa indasry aro mo sen, tough the lative emphasis tobe pln wpm them is somewhere: Dotter of perwmily (regions, vnlTahnes, ete) are nat quite wo inportant, bese ey ee let to some extent y the irendly eo erence tftheemall group. Oh theater iw sing ines things us well as eas ad the ality Zo Cansate fom we Tangusge of enacrete experience to chat of sbot-actLloupht ans coaverly, take az evan gresterimprace dhe Dr IL BL. Evj, aimsela worker ina sual labortory 8 "Ty ode toe of opi vl, the atecatiia es Leap as ch svi touten” Toa telconly ope organ, amply Se Phe Und cence nance Set ray teelee, ca Le oUzina ea bythe leet copes teen Lae re oan. 1 alr oration, empving Mferintenes nly coe seats nif mat alto ay 93eher {pun could beef the toc or sha oxime IL he too. tetial nn, no secs ns bungee es ef ing fo ell wp hs soos td ge ls fee aly pnts cn the yoend_ Ta fet veo Me be bighly ‘le experi. estan he ssid a fet noes “tg dow Sheet’ “Secondhand istrmssea ie lage oer cual “Fhe moll nt war ch on nny Toho tbe eee rman eo tun wl spell pale. Appel ened meter, i frefenty bod Vigo, eta be very mut ore setae seis palpate inne our predic Due ta bs tesiing i eae tng he shoul be baer able ose hah se often det an doer ie anda esa plelens veld Marier Beploysd ‘The number of mathemascians employe ig eomminfxtons ectsial rmanofuetering, pevoloun sad aber tinted st about 100, The number employed in other places is no doubt somevast less but it i= probably nat ap insguicant part af the whol since mathematician are found tere and chese is tome very small Idtsres, For emi, the rash Developmone Company with a toil engizeting force of only 17, as found icsdesible to supplemens this group witha man bins! pecially sta comltans fa mathematics TL peehape not tn wc of tho mans to estimate tbe total umber at 180, nol incladingneinces ad etateticins, “This mamber can be checked ia another say. The menberchi lst of the Auercan Muthencicl Society Iste 207 mn with instal ade roses, OF Hew, 102 ave in name end insurance fmt and ace p= Sombly statstnus, The remaining 100 mares ae those of indus fmployees with mathematical sstorstestroag enough to Welong to em ‘gesinatnn devoted enlavely to the pronoton of snes! research, Some of thee are not matnersticase hy the deulon adoyeed in this per. On the oer han, tere are a 158 names for whieh only street Acdueses are given, some of whom are now to be induetiat matheeae clans, -Beancing tse urcersintoragrine ore anothtz, sud eweniering shat meny industrial cena ican find litle prof ia elongiy to a stocaton dewolo? primarily eo pure mathematics, the estimate given hove dots aot copeae unressnahle Bacare Denoat ‘The ayaa of ftsee demind seven more specaltive tha che stim on af Preznt penne. ‘Two statements, omever st) waves 1} Tas demand for matvemstsine wil never be cezspasnble tr ‘hat fs pbyicts, chemists ot eipiaers. (2) Hr wil cortinly increase beyend the number at preset employed, The fiat statement is jusiEed by vhe Sact that physicist, chemite, ae BELL SYSTEM FACIENICA TOURHAL and other experimental workers deal direly wth tbe matress an ator reoures which its he busine uf Sndusey to expleit, whereas Iatheretiirs tuck these things rly Ita sceoncaey “The cen sateteat would pertape be grated ea the general gsound that thvnuout the waole of tut, rscrch is becoming mare complex Gnd theoretical, sn Renee the valut of eotmliants in genesl, and of Fratberasca consulta opuetiular, must incre, Ts not noes, Irovever, t>raly solely on such general considerations. Dist evidence frst in certain industiey, ntably seis where many of the major fetuch prelens are generally recogazed to be moe resi accesible to ‘emetical ston experirenl sty, andincestin others, sub ex outeia Chemisty where ane aay sonny asume that modern rolcular ‘hysce will ur bein eo play om portant pare in detoraining speeds of fetction, There ie also the genealalersess of excites tn the dolar five of taooretia!frmenovl ia planing expenwve expvineats, and The gradually changing alate somard mithematice Ut stems fom t fe Dee W. X. Dutwell Chairman 0! tie rusty Development Compiy, “upped ted toward «peer sw of ads indy which area siuansine ith the eee toward te acceeanne or nth snd doves depetmers a necrary adjnes 0 sera sk eon Isa brsming mote #50 mece gael renga! tha mbes po uly a accent ol fora egies hy Ses and eum mae Zep pueucg af tong eo aay hoeeioal mcd nd en oat liane tet prblass but tt fe ain perfor 2 poe fection {the recorting aclu fe those gneiss lc ay the foe for ihe advaoe of cciense “nose ‘eeu irs ongialion ars oor, te we 3 9 conc i oll lnportnt and eave satuasly heving etree whee Loe mathematica ‘perso hs tig serving na ere of salbemateal and phys Uc emetic nlucicy the dn of eouinentl wove a sorelines ‘Uinnating the aeed rie 1 therefore the euate of 160 mathematics in indus realty not be too wide af the mack to forecast several res chat lier cade or Ee hence Seace of Supply Tol on these estimates, & demand for new penne of the order of 10-2 gear may be priced, Tals camber soem sll; but if we Teilerate that meinerity has no plce nthe cnculsing eld, aod that ‘Seopa sth.