Do the Math and Delight

Criticism / Michelle Sizemore

:: Do the Math and Delight ::

Why are we talk­ing math in a jour­nal of poet­ry and prose? This ques­tion cap­tures a test­ed and reli­able divi­sion between the arts/humanities and quan­ti­ta­tive fields both in aca­d­e­mics and the wider cul­ture. While there is cer­tain­ly no con­sen­sus on whether math­e­mat­ics is a sci­ence, it is fre­quent­ly grouped with sci­ences and oth­er fields that rely on it. Wit­ness the STEM vs. STEAM debates in K-12 edu­ca­tion. Advo­cates for STEM (a cur­ricu­lum inte­grat­ing Sci­ence, Tech­nol­o­gy, Engi­neer­ing, and Math­e­mat­ics) argue that study of the arts will dilute the STEM focus. Mean­while, advo­cates for STEAM (a cur­ricu­lum adding the Arts to STEM, an extrav­a­gant “A” wedged into this short acronym augur­ing sen­si­ble career choic­es) argue that the arts enhance the sci­ences. [i] Sim­i­lar debates roil post-sec­ondary edu­ca­tion. And admin­is­tra­tors and fac­ul­ty aren’t the only ones weigh­ing in on the val­ue of lib­er­al edu­ca­tion vs. STEM or pro­fes­sion­al edu­ca­tion. Case in point: the acri­mo­nious Twit­ter feud between STEM majors and Human­i­ties, Social Sci­ence, and Edu­ca­tion majors last Decem­ber. [ii] 

The hedges go up more quick­ly out­side the com­pass of cur­ricu­lum and instruc­tion. Chitchat over the years in every con­ceiv­able set­ting has yield­ed a pat­tern in which acquain­tances, after learn­ing what I do for a liv­ing, either con­fess to being bad at Eng­lish but good at math or declare, in sol­i­dar­i­ty, that writ­ing comes eas­i­ly while num­bers are stumpers. These divi­sions seem overblown. Most peo­ple write every day, com­pos­ing texts, emails, Face­book posts, tweets, snaps. Most peo­ple also go to the store with­out haul­ing in an aba­cus.

This col­lec­tion of exam­ples points to the habit­u­al par­ti­tion­ing of lan­guage and math, even though these two “adver­saries” hold unde­ni­able affini­ties. Poets and math­e­mati­cians alike have long rec­og­nized the reci­procity between the dis­ci­plines. Emi­ly Dick­in­son, for one, lav­ished her poet­ry with math. Approx­i­mate­ly 200 of her poems make ref­er­ence to math­e­mat­i­cal terms and con­cepts, demon­strat­ing com­pat­i­bil­i­ty between math­e­mat­i­cal prin­ci­ples and lyri­cal sen­si­bil­i­ty. As Seo-Young Jen­nie Chu writes, “Not only did [Dick­in­son] have a poet­ic under­stand­ing of math­e­mat­ics, but she had a deeply math­e­mat­i­cal under­stand­ing of her own poet­ic enter­prise.” [iii] Albert Ein­stein used poet­ry as a metaphor to express the beau­ty of math­e­mat­i­cal endeav­or, char­ac­ter­iz­ing “pure math­e­mat­ics” as “the poet­ry of log­i­cal ideas.” [iv]

It is not uncom­mon for math­e­mati­cians to locate a kin­ship between math­e­mat­ics and lit­er­a­ture in their shared aes­thet­ic prop­er­ties. For some, “aes­thet­ics” names clas­sic aes­thet­ic qual­i­ties of art such as beau­ty, ele­gance, sym­me­try, and bal­ance. Masahiko Fuji­wara observes:

It is impos­si­ble to put in words the intrin­sic grace of a the­o­rem… I can only describe it as being akin to a per­fect piece of music in which each note is irre­place­able or to a haiku in which no syl­la­ble can be changed. The beau­ty I speak of is like the exquis­ite ten­sion that holds togeth­er aspects of a work of art; a frag­ile seren­i­ty that cements its per­fec­tion. And so the mag­net­ic force that draws art—and there­fore literature—to math­e­mat­ics is the dig­ni­fied beau­ty of its pure log­ic. [v]

Like so many in his dis­ci­pline, Fuji­wara joins the­o­rems and proofs with works of art such as lit­er­a­ture because of the “grace” and “beau­ty” of their com­po­si­tion. Oth­er math­e­mati­cians empha­size the aes­thet­ic expe­ri­ence of solv­ing a prob­lem, the plea­sure tak­en in arriv­ing at mean­ing, of “com­ing-to-under­stand­ing,” in the words of David W. Hen­der­son and Daina Taim­i­na. [vi] Mul­ti­ple mean­ings of “aes­thet­ics” also cir­cu­late are also in cir­cu­la­tion in art crit­i­cism and lit­er­ary stud­ies, where the com­mon wis­dom is to “encour­age a vari­ety of inves­ti­ga­tions under its aegis” rather than “to pre­scribe a sin­gle def­i­n­i­tion.” [vii] Math­e­mat­i­cal aes­thet­ics can there­fore denote the beau­ty of the work, the sen­su­ous expe­ri­ence of per­form­ing the work, and more. This lat­ter sense, the feel­ings evoked by the doing, is espe­cial­ly com­pelling to me.

Of course math­e­mati­cians and artists don’t have a cor­ner on the aes­thet­ic expe­ri­ence of “com­ing-to-under­stand­ing.” The plea­sure of solv­ing a prob­lem belongs to every read­er of mys­ter­ies and every fan of cryp­tog­ra­phy adven­ture movies. If you’re hav­ing trou­ble plac­ing this genre, think Nation­al Trea­sure. The 2004 film stars Nico­las Cage as Ben­jamin Franklin Gates, a his­to­ri­an-crypt­an­a­lyst who has devot­ed his life to the dis­cov­ery of a rumored nation­al trea­sure hid­den by the U.S. Found­ing Fathers. Gates fol­lows a trail of obscure clues: one etched inside the stem of a meer­schaum pipe con­cealed in a gun­pow­der bar­rel in a sunken ship at the bot­tom of the Arc­tic Ocean, anoth­er writ­ten on the back of the Dec­la­ra­tion of Inde­pen­dence in invis­i­ble ink, and so on. Pre­dictably, each puz­zle and solu­tion leads him clos­er to the trea­sure (buried all along in a secret grot­to sev­er­al sto­ries beneath Boston’s Old North Church). Crit­ics and movie-goers who panned the film cit­ed its overblown and improb­a­ble plot. Because Hol­ly­wood films are usu­al­ly sub­tle. [viii]

But I enjoyed the pre­pos­ter­ous­ness of the trea­sure hunt. I enjoyed watch­ing Gates and his team solve clues requir­ing dex­ter­i­ty with words and num­bers. The code con­cealed on the back of the Dec­la­ra­tion is an Otten­dorf or book cipher, which uses a book or anoth­er writ­ten text to encode and decode a mes­sage record­ed in num­bers. To decode the mes­sage, Gates and crew have to match the Declaration’s “mag­ic num­bers,” as one char­ac­ter calls them, to cor­re­spond­ing words in a key, in this case The Silence Dogood Let­ters. The num­ber clus­ters found on the Dec­la­ra­tion (10–11-8, 10–4-7, 9–2-2, 14–8-2, etc.) refer to the page num­ber of The Silence Dogood Let­ters, the line on the page, and the let­ter in the line, respec­tive­ly. [ix] As a schol­ar of ear­ly Amer­i­ca, I was thrilled to encounter these eigh­teenth-cen­tu­ry texts on the big screen, along with land­marks and arcana from the found­ing era: Inde­pen­dence Hall, the Lib­er­ty Bell, Paul Revere, freema­son­ry, George Washington’s elec­tion cam­paign but­tons. His­tor­i­cal padding? Yes. But any annoy­ance at dri­ve-through his­to­ry was off­set by the sat­is­fac­tion of being in on the eso­ter­ism.

In a film relent­less with its inclu­sion of Amer­i­can Inde­pen­dence ref­er­ences, it’s no sur­prise Ben­jamin Franklin gets fold­ed in. But Franklin is more than a pass­ing men­tion; his pres­ence hangs over the entire film. Franklin is the protagonist’s name­sake, he’s the author of The Silence Dogood Let­ters, he invents the bifo­cals they use to view the 3-D trea­sure map on the Dec­la­ra­tion. A Franklin imper­son­ator makes an appear­ance at the Franklin Muse­um in Philadel­phia, and in a delet­ed scene they must deci­pher Franklin’s “Join or Die” polit­i­cal car­toon to escape death. Per­haps the screen­writ­ers were pay­ing homage to Franklin’s inge­nu­ity in a movie that rev­els in the clev­er­ness and resource­ful­ness of its prob­lem-solv­ing hero. Or per­haps, more direct­ly, they were allud­ing to Franklin’s real-life pre­oc­cu­pa­tion with cryp­tog­ra­phy. He devel­oped numer­i­cal codes for secret mes­sages dur­ing the Rev­o­lu­tion­ary War and for Amer­i­can diplo­mat­ic cor­re­spon­dence after­ward. [x] Re-watch­ing the movie remind­ed me that the poly­math­ic Franklin is a quin­tes­sen­tial exam­ple of some­one who not only delight­ed in puz­zle-mak­ing and prob­lem-solv­ing but also joined num­bers and let­ters in his pur­suits.

Nev­er­the­less, Franklin has a rep­u­ta­tion for being bad at math. Much of this owes to Franklin’s own descrip­tion of his “igno­rance of fig­ures.” [xi] Ear­ly in the Auto­bi­og­ra­phy of Ben­jamin Franklin he recounts how at age nine his father sent him to George Brownell’s school, where he “acquired fair writ­ing pret­ty soon but… failed in… arith­metic and made no progress in it.” [xii] Schol­ars from lit­er­ary stud­ies to com­put­er sci­ence have gen­er­al­ly tak­en him at his word, no doubt due to the endur­ing con­cep­tu­al oppo­si­tion between writ­ing and math. Despite his noto­ri­ety as math-defi­cient, Franklin was actu­al­ly gift­ed. He used pop­u­la­tion sta­tis­tics in his “Obser­va­tions Con­cern­ing the Increase of Mankind, Peo­pling of Coun­tries, Etc.” (1751) and employed geom­e­try in his inven­tion of the glass armon­i­ca (a musi­cal instru­ment con­sist­ing of spin­ning glass discs). The list of Franklin’s math­e­mat­i­cal inves­ti­ga­tions goes on—utility the­o­ry, account­ing, applied math­e­mat­ics, nav­i­ga­tion, day­light sav­ing time. [xiii]

To ful­ly appre­ci­ate these devel­op­ments, we have to look past his part in the nation­al ori­gin sto­ry. He wasn’t only a key play­er in the Unit­ed States’ found­ing, but also a lead­ing sci­en­tist in a transat­lantic com­mu­ni­ty of schol­ars. [xiv] From the late 1740s through the late 1760s, Franklin’s study of elec­tric­i­ty devel­oped with­in a net­work of com­mu­ni­ca­tion with and sup­port from a con­frere of Atlantic sci­en­tists, cul­mi­nat­ing in Exper­i­ments and Obser­va­tions on Elec­tric­i­ty (a series of let­ters to Eng­lish friend and patron Peter Collinson, orig­i­nal­ly pub­lished in 1751 and under­go­ing sub­se­quent edi­tions through 1769). In 1756, Franklin’s research on elec­tric­i­ty and inven­tion of the light­ning rod earned him the dis­tinc­tion of fel­low at the Roy­al Soci­ety of Lon­don, Britain’s fore­most sci­en­tif­ic orga­ni­za­tion. Franklin’s Exper­i­ments and Obser­va­tions on Elec­tric­i­ty was a tow­er­ing achieve­ment of Enlight­en­ment-era science—but it was not, as we might expect of a sci­en­tif­ic work in the Age of Rea­son, strict­ly com­mit­ted to the advance of rea­son. [xv] For one, “mag­i­cal” math puz­zles crop up in the vol­ume.

Occu­py­ing Franklin’s think­ing for near­ly half a cen­tu­ry were numer­i­cal puz­zles known as “mag­ic squares” and “mag­ic cir­cles.” It may be tempt­ing to triv­i­al­ize such pur­suits as many of his biog­ra­phers have—Sudoku for the eigh­teenth cen­tu­ry, Can­dy Crush for the insuf­fer­able meet­ing. We know, for instance, that Franklin doo­dled with these games to “amuse [him­self]” dur­ing the speech­es at the Penn­syl­va­nia Assem­bly. [xvi] He would have gained access to these puz­zles through the transat­lantic cir­cu­la­tion of texts such as Jacques Ozanam’s Recre­ations Math­e­mat­i­cal and Phys­i­cal and John Tipper’s The Ladies’ Diary, or, the Woman’s Almanack. First pub­lished in France in the 1690s and then revised by a vari­ety of edi­tors over the next 150 years, Ozanam’s Recre­ations would remain the most impor­tant ref­er­ence on recre­ation­al math­e­mat­ics for over two cen­turies. Tipper’s The Ladies’ Diary was a pop­u­lar British almanac that ran from 1704 through 1752 and com­bined con­ven­tion­al almanac sub­jects with rid­dles and math­e­mat­i­cal puz­zles. Franklin rou­tine­ly solved these pre­made mag­i­cal squares and cir­cles and also invent­ed his own. [xvii]

Mag­ic squares and mag­ic cir­cles are like crosswords—except with num­bers. You fill in the spaces with num­bers instead of let­ters. The goal with a mag­ic square is to make each line of num­bers across, down, or diag­o­nal­ly total the same val­ue. The solu­tion for this puz­zle is 15. [xvi­ii] Puz­zles like these had pre­oc­cu­pied thinkers for cen­turies before Franklin made his con­tri­bu­tions. His­to­ri­ans trace them to philoso­phers and the­olo­gians in Chi­na as ear­ly as the fourth cen­tu­ry BCE, then to Mesopotamia, and then across most of the known world by the end of the first mil­len­ni­um. These numer­i­cal arrange­ments were believed to pos­sess super­nat­ur­al prop­er­ties and fig­ured mean­ing­ful­ly in Chi­nese, Mid­dle East­ern, and West­ern occultism. They were incor­po­rat­ed into incan­ta­tions and spells, embla­zoned on amulets, tal­is­mans, and plates, and admin­is­tered in div­ina­tion and cos­mo­log­i­cal rep­re­sen­ta­tion.

In ancient Chi­na, for instance, these 3x3 squares, called the Lo Shu, were ren­dered in graph­ic form. 9–5-1, 4–9-2, and so on. Peo­ple regard­ed these matri­ces as super­nat­ur­al because they rep­re­sent­ed the uni­verse in micro­cosm: nine squares con­veyed the Nine Divi­sions of Heav­en, the Nine Con­ti­nents, the Nine Ter­ri­to­ries, the Nine Divi­sions of the Mid­dle King­dom. The Lo Shu, more­over, was a pro­found expres­sion of equi­lib­ri­um. The black dots des­ig­nate even num­bers and cor­re­spond with yin (the pas­sive and neg­a­tive force in the uni­verse) while the white dots des­ig­nate odd num­bers and cor­re­spond with yang (the active and pos­i­tive force in the uni­verse). The eight even and odd num­bers rep­re­sent­ing yin and yang are held in bal­ance around the axi­al cen­ter (the num­ber 5). Thus the Lo Shu square could effec­tive­ly sym­bol­ize the world in bal­anced har­mo­ny around a pow­er­ful cen­tral axis. [xix]

Mag­ic squares embody the aes­thet­ic qual­i­ties of bal­ance and sym­me­try, and beau­ty when one beholds their geo­met­ri­cal pat­terns and forms. Cer­tain­ly Franklin was drawn to both the aes­thet­ic qual­i­ties of mag­ic squares and the aes­thet­ic expe­ri­ence of solv­ing them. But why are such puz­zles tucked in among Franklin’s writ­ings on elec­tric­i­ty?

Before the famous encounter between light­ning, kite, and key in 1752, Franklin began his elec­tri­cal exper­i­ments more mod­est­ly with glass tubes in 1746, offer­ing an ini­tial the­o­ry clas­si­fy­ing elec­tric­i­ty as a flu­id. The tech­ni­cal details of this exper­i­ment aren’t as impor­tant here as the con­cepts of “plus” and “minus.” Accord­ing to this the­o­ry, the glass tube began in a “pos­i­tive” state or a “plus” con­di­tion, and rub­bing the glass removed part of the elec­tric­i­ty from it, leav­ing it “minus” some of its elec­tri­cal flu­id or in a “neg­a­tive” state. Franklin would even­tu­al­ly refine his the­o­ry of elec­tric­i­ty, liken­ing it to a fire rather than a flu­id and adjust­ing some oth­er essen­tial points, but retain­ing the elec­tri­cal vocab­u­lary of plus/minus, positive/negative, and equi­lib­ri­um that he invented—and is still used today. [xx] 

Now we may be get­ting clos­er to an expla­na­tion of why a dis­cus­sion of mag­i­cal squares turns up in a vol­ume on elec­tric­i­ty. On some lev­el, the numerol­o­gy of the square—its demon­stra­tion of absolute equal­i­ty and per­fect balance—resonated with Franklin’s elec­tri­cal con­cep­tion of equi­lib­ri­um and the even and odd num­bers car­ry­ing sym­bol­ic con­no­ta­tions of pos­i­tive and neg­a­tive. While he may not have exact­ly had in mind yin and yang, he did hint at the mys­tery of cos­mic bal­ance in the phys­i­cal world when speak­ing of mag­ic squares and elec­tri­cal phe­nom­e­na, describ­ing both as “mirac­u­lous.” [xxi] “Com­ing-to-under­stand­ing,” for Franklin and con­tem­po­raries who stud­ied elec­tric­i­ty, meant advanc­ing a ratio­nal expla­na­tion of electricity’s behav­ior while main­tain­ing an appre­ci­a­tion of electricity’s mystery—its “won­der­ful” and “amaz­ing” power—and by exten­sion the pow­er of nature. [xxii] 

Thus, in part, the plea­sure Franklin took in elec­tri­cal and math­e­mat­i­cal prob­lem-solv­ing derived from con­tem­pla­tive won­der in the inex­plic­a­ble work­ings of nature. In Exper­i­ments and Obser­va­tions on Elec­tric­i­ty, he describes his inno­va­tions with the 16x16 mag­i­cal square as the “most mag­i­cal­ly mag­i­cal of any mag­ic square ever made by any magi­cian.” [xxi­ii] Franklin’s mar­veling at the de trop “mag­i­cal­ly mag­i­cal” char­ac­ter of his square reveals an impor­tant dis­tinc­tion between the eigh­teenth-cen­tu­ry sci­en­tif­ic world’s under­stand­ing of mag­ic and that of the pre-Sci­en­tif­ic Rev­o­lu­tion. Rather than an attri­bu­tion of super­nat­ur­al prop­er­ties to the square, Franklin’s remark is an asser­tion of admi­ra­tion and delight, “mag­ic” denot­ing “an inex­plic­a­ble and remark­able influ­ence pro­duc­ing sur­pris­ing results” or “an enchant­i­ng or mys­ti­cal qual­i­ty” (OED). [xxiv] His won­der at nature’s mys­ter­ies isn’t rev­er­en­tial but play­ful, a fit­ting tone for pur­suits regard­ed as enter­tain­ment. 

In the cor­re­spon­dence between Franklin and oth­er Roy­al Soci­ety mem­bers, researchers often mod­u­late descrip­tions of their intel­lec­tu­al curios­i­ty by char­ac­ter­iz­ing their activ­i­ties as a pas­time or a diver­sion. Franklin’s let­ters to Collinson repeat­ed­ly offer his recital of elec­tri­cal exper­i­ments and mag­i­cal squares for the pur­pose of Collinson’s “amuse­ment.” [xxv] This empha­sis on learned enter­tain­ment among mem­bers of the Roy­al Soci­ety and oth­er intel­lec­tu­al cir­cles sig­nals the emerg­ing prac­tice of aca­d­e­m­ic socia­bil­i­ty in the lat­ter half of the eigh­teenth cen­tu­ry. [xxvi] After all, Franklin con­veys his find­ings on elec­tric­i­ty in a let­ter exchange with a col­league and friend rather than in a for­mal dis­ser­ta­tion. Far from divid­ing lan­guage and num­bers, then, the sci­en­tif­ic com­mu­ni­ty devel­oped lit­er­ary con­ven­tions and gen­res for the delight in fig­ures.

While edu­cat­ed layper­sons did read sci­ence writ­ing like Exper­i­ments and Obser­va­tions, more often they grat­i­fied their math­e­mat­i­cal curios­i­ty with prob­lems in almanacs and puz­zle and game books. These brain-teasers belong to a larg­er cat­e­go­ry of eigh­teenth-cen­tu­ry enter­tain­ment includ­ing rid­dles and games, which encour­aged new pat­terns of thought and elicit­ed sur­prise, won­der, and delight through prob­lem-solv­ing. [xxvii] It’s intrigu­ing to think about an ear­li­er gen­er­a­tion that open­ly acknowl­edged the plea­sure as well as the prag­mat­ic val­ue of math—that devel­oped a rela­tion­ship to math defined by recre­ation rather than com­pul­sion, by cre­ativ­i­ty, inge­nu­ity, and enjoy­ment rather than tedi­um and pan­ic. I’m not sure we’ve got­ten to the point where large num­bers of peo­ple con­ceive of math as fun, but maybe we’re mak­ing our way there. Most nation­al and local news­pa­pers con­tain “Games and Puz­zles” sec­tions that increas­ing­ly fea­ture much more than the cross­word. The relaunch of the New York Times Mag­a­zine includes math puz­zles and games like KenKen, Sudoku, and SET along­side its famed Sun­day cross­word. Hun­dreds of new apps make math enjoy­able and read­i­ly acces­si­ble for chil­dren and adults look­ing to sharp­en their skills or sim­ply to pass the time. The land of games and puz­zles may be the renewed meet­ing ground for words and num­bers. What pos­si­bil­i­ties lie ahead with greater nim­ble­ness in both lan­guage and math? What cross-pol­li­na­tions might occur from this “bilin­gual­ism”? We must do the words, and do the math.

 


[i] As STEAM’s sup­ple­men­tary appeal for the arts implies, the goal isn’t to inte­grate the arts and sciences—to achieve mutu­al influence—but rather to serve the STEM fields. I’m not inter­est­ed in tak­ing sides in this debate here, rather in point­ing out the fun­da­men­tal sep­a­ra­tion and hier­ar­chy between the arts and sci­ences even in efforts to join them.
[ii] @jaboukie, “i WISH i could just read clif­ford the big red dog and make flower crowns,” Twit­ter (5 Decem­ber 2018, 1:53 p.m.).
[iii] Seo-Young Jen­nie Chu, “Dick­in­son and Math­e­mat­ics,” The Emi­ly Dick­in­son Jour­nal 15.1 (2006), 36.
[iv] Albert Ein­stein, “The Late Emmy Noe­ther: Pro­fes­sor Ein­stein Writes in Appre­ci­a­tion of a Fel­low-Math­e­mati­cian,” The New York Times (4 May 1935), 12. Print.
[v] Masahiko Fuji­wara, “Lit­er­a­ture and Math­e­mat­ics,” Asymp­tote (Jan­u­ary 2011).
[vi] David W. Hen­der­son and Daina Taim­i­na, “Expe­ri­enc­ing Mean­ings in Geom­e­try,” Math­e­mat­ics and the Aes­thet­ic: New Approach­es to an Ancient Infin­i­ty, Ed. Nathalie Sin­clair et al. (Springer, 2007), 83.
[vii] Cindy Wein­stein and Christo­pher Loo­by, “Intro­duc­tion,” Amer­i­can Literature’s Aes­thet­ic Dimen­sions (Colum­bia Univ. Press, 2012), 4.
[viii] See Roger Ebert, “Nation­al Trea­sure,” Roger Ebert.com (18 Novem­ber 2004); Stephen Hold­en, “A Secret Trea­sure Map That Ends in Man­hat­tan,” New York Times (19 Novem­ber 2004); Cari­na Chocano, “Bank­rupt Nation­al Trea­sure,” L.A. Times (19 Novem­ber 2004); “Nation­al Trea­sure (2004),Rot­ten Toma­toes (Accessed 19 May 2018). 
[ix] Simon Singh, The Code Book: The Sci­ence of Secre­cy from Ancient Egypt to Quan­tum Cryp­tog­ra­phy (Anchor, 2000).
[x] Ralph E. Weber, Unit­ed States Diplo­mat­ic Codes and Ciphers, 1775–1938 (Prec­dent Pub­lish­ing Inc., 1979); David Kahn, The Code­break­ers: The Sto­ry of Secret Writ­ing (Scrib­n­er, 1996), 185.
[xi] Ben­jamin Franklin, Auto­bi­og­ra­phy of Ben­jamin Franklin. 1791 ed. (Wal­ter J. Black, Inc., 1941), 24.
[xii] Franklin, Auto­bi­og­ra­phy, 13.
[xiii] Paul C. Pasles, Ben­jamin Franklin’s Num­bers: An Unsung Math­e­mat­i­cal Odyssey (Prince­ton Univ. Press, 2008), 5–11.
[xiv] Bernard Cohen, Ben­jamin Franklin’s Sci­ence (Har­vard Univ. Press, 1990); Park Ben­jamin, A His­to­ry of Elec­tric­i­ty: From Antiq­ui­ty to the Days of Ben­jamin Franklin (John Wiley & Sons, 1898).
[xv] James Del­bour­go, A Most Amaz­ing Scene of Won­ders: Elec­tric­i­ty and Enlight­en­ment in Ear­ly Amer­i­ca (Har­vard Univ. Press, 2006), 8.
[xvi] Franklin, Auto­bi­og­ra­phy, 189.
[xvii] Pasles, 117–137.
[xvi­ii] The object of this “cross-num­ber” puz­zle is to fill in the box­es so that each of the rows across, up and down, and diag­o­nal­ly equal the same sum. The best way to begin is to fig­ure out the total of all 9 box­es, which must be filled in with the num­bers 1–9. 1+2+3+4+5+6+7+8+9=45. Since we know each row must equal the same val­ue, and since there are three equal rows, we can divide by 3 to deter­mine the sum of each row: 15. From there, fill in the num­bers on the grid until each row equals 15 in every direc­tion. I’m indebt­ed to Paul C. Pasles’s Ben­jamin Franklin’s Num­bers for its lucid expla­na­tion of these puz­zles.
[xix] Pasles, 20–27; Schuyler Cam­mann, “The Mag­ic Square of Three in Old Chi­nese Phi­los­o­phy and Reli­gion,” His­to­ry of Reli­gions 1.1 (1961), 37–80.
[xx] Cohen, 14–39.
[xxi] Ben­jamin Franklin, Exper­i­ments and Obser­va­tions in Elec­tric­i­ty, 4th ed. (David Hen­ry, 1769), 14.
[xxii] Franklin, Exper­i­ments, 3, 35, 375, 485; Del­bour­go, 11.
[xxi­ii] Franklin, Exper­i­ments, 353.
[xxiv] “mag­ic, n.” OED Online, (Oxford Uni­ver­si­ty Press, March 2018).
[xxv] Franklin, Exper­i­ments, 177, 237, 354.
[xxvi] Susan Scott Par­rish, Amer­i­can Curios­i­ty: Cul­tures of Nat­ur­al His­to­ry in the colo­nial British Atlantic World (Univ. of North Car­oli­na Press, 2006).
[xxvii] See Jil­lian Hey­dt-Steven­son, “Games, Rid­dles, and Cha­rades,” The Cam­bridge Com­pan­ion to Emma, Ed. Peter Sabor (Cam­bridge Univ. Press, 2015), 150–165; Mary Chad­wick, “‘The Most Dan­ger­ous Tal­ent’: Rid­dles as Fem­i­nine Pas­time,” Women, Pop­u­lar Cul­ture, and the Eigh­teenth Cen­tu­ry, Ed. Tiffany Pot­ter (Univ. of Toron­to Press, 2012), 185–201.

 

Bib­li­og­ra­phy

Ben­jamin, Park. A His­to­ry of Elec­tric­i­ty: From Antiq­ui­ty to the Days of Ben­jamin Franklin. New York: John Wiley & Sons, 1898.

Cam­mann, Schuyler. “The Mag­ic Square of Three in Old Chi­nese Phi­los­o­phy and Reli­gion,” His­to­ry of Reli­gions 1.1 (1961).

Chad­wick, Mary. “‘The Most Dan­ger­ous Tal­ent’: Rid­dles as Fem­i­nine Pas­time,” Women, Pop­u­lar Cul­ture, and the Eigh­teenth Cen­tu­ry, Ed. Tiffany Pot­ter. Toron­to: Univ. of Toron­to Press, 2012.

Cohen, Bernard. Ben­jamin Franklin’s Sci­ence. Cam­bridge: Har­vard Univ. Press, 1990.

Chu, Seo-Young Jen­nie. “Dick­in­son and Math­e­mat­ics,” The Emi­ly Dick­in­son Jour­nal 15.1 (2006), 35–55.

Del­bour­go, James. A Most Amaz­ing Scene of Won­ders: Elec­tric­i­ty and Enlight­en­ment in Ear­ly Amer­i­ca. Cam­bridge: Har­vard Univ. Press, 2006.

Ein­stein, Albert. “The Late Emmy Noe­ther: Pro­fes­sor Ein­stein Writes in Appre­ci­a­tion of a Fel­low-Math­e­mati­cian,” The New York Times (4 May 1935), 12. Print.

Franklin, Ben­jamin. Auto­bi­og­ra­phy of Ben­jamin Franklin. 1791 ed. New York: Wal­ter J. Black, Inc., 1941.

Franklin, Ben­jamin. Exper­i­ments and Obser­va­tions in Elec­tric­i­ty, 4th ed. Lon­don: David Hen­ry, 1769. Google Books. Accessed May 20, 2018. https://books.google.com/books/about/Experiments_And_Observations_On_Electric.html?id=-48_AAAAcAAJ

Fuji­wara, Masahiko. “Lit­er­a­ture and Math­e­mat­ics,” Asymp­tote (Jan­u­ary 2011). Accessed May 20, 2018. https://www.asymptotejournal.com/nonfiction/masahiko-fujiwara-literature-and-mathematics/

Hen­der­son, David W. and Daina Taim­i­na. “Expe­ri­enc­ing Mean­ings in Geom­e­try,” Math­e­mat­ics and the Aes­thet­ic: New Approach­es to an Ancient Infin­i­ty, Ed. Nathalie Sin­clair et al. New York: Springer, 2007.

Hey­dt-Steven­son, Jil­lian. “Games, Rid­dles, and Cha­rades,” The Cam­bridge Com­pan­ion to Emma, Ed. Peter Sabor. Cam­bridge: Cam­bridge Univ. Press, 2015, 150–165.

Kahn, David. The Code­break­ers: The Sto­ry of Secret Writ­ing. New York: Scrib­n­er, 1996.

Par­rish, Susan Scott. Amer­i­can Curios­i­ty: Cul­tures of Nat­ur­al His­to­ry in the colo­nial British Atlantic World. Chapel Hill, Univ. of North Car­oli­na Press, 2006.

Pasles, Paul C. Ben­jamin Franklin’s Num­bers: An Unsung Math­e­mat­i­cal Odyssey. Prince­ton: Prince­ton Univ. Press, 2008.

Singh, Simon. The Code Book: The Sci­ence of Secre­cy from Ancient Egypt to Quan­tum Cryp­tog­ra­phy. New York: Anchor, 2000.

Weber, Ralph E. Unit­ed States Diplo­mat­ic Codes and Ciphers, 1775–1938. Fish­er, IN: Prece­dent Pub­lish­ing Inc., 1979.

Wein­stein, Cindy and Christo­pher Loo­by, “Intro­duc­tion,” Amer­i­can Literature’s Aes­thet­ic Dimen­sions. New York: Colum­bia Univ. Press, 2012.

 

Michelle Size­more is Asso­ciate Pro­fes­sor of Eng­lish at the Uni­ver­si­ty of Ken­tucky. She is the author of Amer­i­can Enchant­ment: Rit­u­als of the Peo­ple in the Post-Rev­o­lu­tion­ary World (Oxford, 2017) and has pub­lished arti­cles and reviews in Lega­cy, Stud­ies in Amer­i­can Fic­tion, Amer­i­can Lit­er­ary His­to­ry, Ear­ly Amer­i­can Lit­er­a­ture, and oth­er venues.