Much ado about noth­ing: an­cient In­dian text con­tains ear­li­est zero sym­bol

The Guardian Australia - - World News - Han­nah Devlin Sci­ence cor­re­spon­dent

Nowt, nada, zilch: there is noth­ing new about noth­ing­ness. But the mo­ment that the ab­sence of stuff be­came zero, a num­ber in its own right, is re­garded as one of the great­est break­throughs in the his­tory of math­e­mat­ics.

Now sci­en­tists have traced the ori­gins of this con­cep­tual leap to an an­cient In­dian text, known as the Bakhshali man­u­script – a text which has been housed in the UK since 1902.

Ra­dio­car­bon dat­ing re­veals the frag­men­tary text, which is in­scribed on 70 pieces of birch bark and con­tains hun­dreds of ze­roes, dates to as early as the 3rd or 4th cen­tury – about 500 years older than schol­ars pre­vi­ously be­lieved. This makes it the world’s oldest recorded ori­gin of the zero sym­bol that we use to­day.

Mar­cus du Sau­toy, pro­fes­sor of math­e­mat­ics at the Univer­sity of Ox­ford, said: “To­day we take it for granted that the con­cept of zero is used across the globe and our whole dig­i­tal world is based on noth­ing or some­thing. But there was a mo­ment when there wasn’t this num­ber.”

The Bakhshali man­u­script was found in 1881, buried in a field in a vil­lage called Bakhshali, near Pe­shawar, in what is now a re­gion of Pak­istan. It was dis­cov­ered by a lo­cal farmer and later ac­quired by the Bodleian Li­brary in Ox­ford.

Trans­la­tions of the text, which is writ­ten in a form of San­skrit, sug­gest it was a form of train­ing man­ual for mer­chants trad­ing across the Silk Road, and it in­cludes prac­ti­cal arith­metic ex­er­cises and some­thing ap­proach­ing al­ge­bra. “There’s a lot of ‘If some­one buys this and sells this how much have they got left?’” said Du Sau­toy.

In the frag­ile doc­u­ment, zero does not yet fea­ture as a num­ber in its own right, but as a place­holder in a num­ber sys­tem, just as the “0” in “101” in­di­cates no tens. It fea­tures a prob­lem to which the an­swer is zero, but here the an­swer is left blank.

Sev­eral an­cient cul­tures in­de­pen­dently came up with sim­i­lar place­holder sym­bols. The Baby­lo­ni­ans used a dou­ble wedge for noth­ing as part of cu­nei­form sym­bols dat­ing back 5,000 years, while the Mayans used a shell to de­note ab­sence in their com­plex cal­en­dar sys­tem.

How­ever the dot sym­bol in the Bakhshali script is the one that ul­ti­mately evolved into the hol­low-cen­tred ver­sion of the sym­bol that we use to­day. It also sowed the seed for zero as a num­ber, which is first de­scribed in a text called Brah­mas­phutasid­dhanta, writ­ten by the In­dian as­tronomer and math­e­ma­ti­cian Brah­magupta in 628AD.

“This be­comes the birth of the con­cept of zero in it’s own right and this is a to­tal rev­o­lu­tion that hap­pens out of In­dia,” said Du Sau­toy.

The de­vel­op­ment of zero as a math­e­mat­i­cal con­cept may have been in­spired by the re­gion’s long philo­soph­i­cal tra­di­tion of con­tem­plat­ing the void and may ex­plain why the con­cept took so long to catch on in Europe, which lacked the same cul­tural ref­er­ence points.

“This is com­ing out of a cul­ture that is quite happy to con­ceive of the void, to con­ceive of the in­fi­nite,” said Du Sau­toy. “That is ex­cit­ing to recog­nise, that cul­ture is im­por­tant in mak­ing big math­e­mat­i­cal break­throughs.”

De­spite de­vel­op­ing so­phis­ti­cated maths and ge­om­e­try, the an­cient Greeks had no sym­bol for zero, for in­stance, show­ing that while the con­cept zero may now feel fa­mil­iar, it is not an ob­vi­ous one.

“The Euro­peans, even when it was in­tro­duced to them, were like ‘Why would we need a num­ber for noth­ing?’” said Du Sau­toy. “It’s a very ab­stract leap.”

In the lat­est study, three sam­ples were ex­tracted from the man­u­script and an­a­lysed at the Ox­ford Ra­dio­car­bon Ac­cel­er­a­tor Unit. The re­sults re­vealed that the three sam­ples tested date from three dif­fer­ent cen­turies, one from 224-383 AD, an­other from 680-779 AD and an­other from 885-993 AD, rais­ing fur­ther ques­tions about how the man­u­script came to be pack­aged to­gether as a sin­gle doc­u­ment.

The de­vel­op­ment of zero in math­e­mat­ics un­der­pins an in­cred­i­ble range of fur­ther work, in­clud­ing the no­tion of in­fin­ity, the mod­ern no­tion of the vac­uum in quan­tum physics, and some of the deep­est ques­tions in cos­mol­ogy of how the Uni­verse arose – and how it might dis­ap­pear from ex­is­tence in some unimag­in­able fu­ture sce­nario.

Richard Oven­den, head of the Bodleian Li­brary, said the re­sults high­light a Western bias that has of­ten seen the con­tri­bu­tions of South Asian schol­ars be­ing over­looked. “Th­ese sur­pris­ing re­search re­sults tes­tify to the sub­con­ti­nent’s rich and long­stand­ing sci­en­tific tra­di­tion,” he said.

The man­u­script will be on pub­lic dis­play on 4 Oc­to­ber, as part of a ma­jor ex­hi­bi­tion, Il­lu­mi­nat­ing In­dia: 5000 Years of Sci­ence and In­no­va­tion, at the Sci­ence Mu­seum in Lon­don.

Pho­to­graph: Cour­tesy of Bodleian Li­braries/ Univer­sity of Ox­ford

In this close-up im­age you can see the use of a dot as a place­holder in the bot­tom line. This dot evolved into the use of zero as a num­ber in its own right.

Pho­to­graph: Cour­tesy of Bodleian Li­braries/ Univer­sity of Ox­ford

The ‘front’ page (recto) of fo­lio 16 which dates to 224-383 AD.

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