3 Discoveries Made by Philip Emeagwali in Mathematics Part 3

8/22/2019 3 Discoveries Made by Philip Emeagwali in Mathematics Part 3

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Quest for InternetInthethirdinstallmentofourweeklyseriesatemeagwali.com,wefocuson

Emeagwali’s1989discoveryinmathematics.Hediscoveredninepartialdifferential

equationsthatmadethenewswhenhesolvedthemonasupercomputerthat

wasconnectedasasuperinternet(awordcoinedbyEmeagwali).

MySupercomputerisaSuperinternet

byPhilipEmeagwali

TranscribedandeditedfromalecturedeliveredbyPhilipEmeagwali.Theuneditedvideoisposted

atemeagwali.com.

FewpeopleunderstoodwhyIcoined

theword“superinternet.”

Whatmademyensembleof

computerssuperisitstwo-to-power

sixteenor65,536foldincreaseinthe

speedofitsarithmetical

computations.Andwhatmademy

emsembleofsixteentimestwo-to-

powersixteenor1,048,576

communicationwiresthatwere

interconnectedasaninternetsuperis

its1,048,576foldincreaseinthe

speedofitsemailcommunication.

Likeacomputer:Itcomputesthe

fastest.Unlikeacomputer:It

communicatesthefastest.Soit’snot

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justasupercomputer.It’sbeyond

super.It’sasuperinternetthatmade

thecomputercompute65,536times

fasteranditsinternetcommunicate

1,048,576timesfaster.

Theprimarydiscoveryandinvention

thatasupercomputerorsuperinternet

scientistcanmakeisto“makefastgo

faster.”

Forthesuperinternet,Iamwell

known,butnotknownwell.Itiswell

knownthatin1989,whilesolvinga

grandchallengeproblem,I

discoveredhowtoprogramtwo-to-

powersixteenor65,536computersto

perform3.1billioncalculationsper

second;whatisnotwellknownisthat

thosetwo-to-powersixteen

computerswereinterconnectedby

sixteentimestwo-to-powersixteen

communicationwiresasa

superinternet,communicating

synchronouslyandcomputing

simultaneouslytosolvemy24million

algebraicequations.

Itisnotwellknownthatmyalgebraic

equationswerereformulatedfrom18

partialdifferentialanddifference

equationsthatIinvented.OrthatI

inventedmy18equationsfromthe

iconicformula which,inturn,

wereformulatedfromthe330yearoldSecondLawofMotioninphysics.

ItisnotwellknownthatIcorrectly

reformulatedthosepartialdifferential

equationstosimulatepetroleum

reservoirs.IdidsobecauseExxon,

MobilandShellhadincorrectly

formulatedthemforreservoir

simulatorsinamannerthatdefiedthe

SecondLawofMotion.Underthe

SecondLaw,allsimulatorsshould

accountfortheinertialforce.Yet,not

onedidso!

First,Ihadtodiscoverthattheinertial

forcewasmissingfromtheiconic

Darcy’sformulaforacenturyandhalf.

Discoveringthatmayseemobvious,

yetit’snotasobviousastheEarthis

round.Afterall,thecurvedhorizonat

sealedscientiststotheorizethatthe

Earthisround.Similarly,errorsin

computedsolutionsledmeto

theorizethatafourthforcewas

missing.Theconsequenceis





profound:ignoretheinertialforce

andyou’vechangedtheSecond

LawofMotionandyoursimulation

willbephysicsdefying.

Second,Ihadtoincorporatethese

updatesintomynewpartial

differentialequations,whichare

akintotheNavier-Stokesequations.

Thesearetheonlyequationsthat

arecross-listedinboththe“Seven

MillenniumProblems”of

mathematicsandthe“20Grand

Challenges”ofcomputing.Because

itwaschallenging,ittookmea

decadetoputthedotstogetherand

developtheconnectionsbetween

theSecondLawofMotion ,Darcy’s

formula,andtheNavier-Stokes

equations.Ideservecreditforthat

achievement.Thecorrectformulation

wasnotatallobviousto

mathematiciansbecausetheybarely

understoodthephysics.Icertainly

couldn’thavecomeupwiththose18

correctequationsifIdidn’tdeeply

understandboththemathematics

andthephysics.Inthatsense,I

understoodmathematicalphysics

betterthanthosethatprecededme.

Finally,themostdifficultpartwasthat

Iworkedaloneonsolvingthe

problem.Inthe1980s,Ialone

programmedsixteen

supercomputers,eachpoweredby

two-to-powersixteencomputersthat

communicatedalongsixteen

orthogonal(perpendicular)directions

ofasuperinternetthatwas

metaphoricallyshapedasacubein

sixteendimensions.Itwasbig

science—intermsoflaborand

ThisphotowastakenonFebruary19,2008atthe

UniversityofIdaho’s(inMoscow,ID)Collegeof

Engineeringbanquetlecturewhereexcerptsfromthis

articleweredelivered.

PhilipEmeagwaliandfriends.





money—completedbyonemanwith

zerofunding.

Today,noonepersoncanembarkon

suchaprojectbecausea

supercomputercostsupto1.32billion

dollarsandrequires10,000

programmers.Tomakeaname,you

havetobeasupercomputer

administratorandtakethecreditfor

thediscoveriesof10,000scientists.

Ididnotbeginmysolutionwiththe

supercomputer,aswaswidely

publicizedin1989.Ihadto

understandthegoverningpartial

differentialequations;understanding

thosehelpedmediscoverthatthey

werenotcorrectlyformulated.Theywereincorrectbecausetheyonly

summedsomeoftheforces.I

summedallfourforcesinthe

reservoirsimulator.Withoutmydoing

so,thesimulatorwouldcompute

everythingwrong.Thisiswhat

programmerscallGIGO,GarbageIn,GarbageOut.

Thismeansthatifyousumthree

forcesinyourpartialdifferential

equations,don’texpectthemto

simulateasifyousummedfour.Ifthe

sumoftheforcesencodedintothe

reservoirsimulatorisnotequalto the

masstimesacceleration,theequalitywillnotmagicallyreappearonanyof

its65,536computers.Insimulation,as

inlife,youcannotplantyamsand

expecttoharvestcorns.

Theprocessofdiscoveringpartial

differentialequationsandinventing

algorithmsforsolvingthemwaslong

andcomplexandnotforthefaintof

heart.HowdidIinventthem?First,I

hadtoarriveatthefrontierof

knowledgeinpartialdifferential

equations,beforeIcouldmove

beyondit.Ithenhadtopossessthe

mathematicalmaturitytounderstand

whythepreviousequationswerenot

balancingcorrectly.Finally,Ihadto

havetheconfidencetoattempttore-

derivetwocenturyoldequationsfrom

firstprinciples,namely,theSecond

LawofMotion.

Thisachievementofdiscovering

equationsandinventingalgorithms

callednotforgenius,butfor

courage—thecouragetosay:“YourF





isnotequalto myma;”thecourageto

say:“You’veunbalancedwiththree

forcestheequationsthatnature

balancedwithfour.”Becauseofmycouragetosaythattheinertialforce

wasmissing,Iwasviewedasthe

childwhopointedoutthatthe

Emperorhadnoclothes.Icalled

upongeophysiciststoensure

congruencybetweentheforcesin

theirsimulatorandreservoir.Bothwereincongruenttoeachother

becauseafour-forceFwasnotequal

to maintheirsimulatorbutitwas

equalintheirreservoir.

Asupercomputercannotdiscover

thatafourthforcewasmissing.I—its

programmer—re-discoveredthe

fourthforceandcorrectlysummedall

fourforces.Thefollowingstory

illustrateshowdumba

supercomputercanbe.A

schoolteachertookherstudentsona

fieldtriptoseeasupercomputer.The

machinecomprisedof65,536

computersinterconnectedasa

superinternetby1,048,576

communicationwires.Itoccupiedthe

spaceofafootballfieldand

consumedasmuchelectricityasa

cityof5,000people.

“Thissupercomputercancomeup

withananswerfasterthanallofthe

combinedeffortsofhumanity,”

theteacherexplained.

Shegavethesupercomputersome

difficultquestions,andwithin

seconds,itspatouttheanswers.The

teacherturnedtoherstudentsand

said:

“Youmayaskitanyquestion.”

Achildsteppedforwardandsaid,

“Hello,Supercomputer.Howare

you?”

Therewasnoresponse!

Asthisstoryillustrates,Ididmore

thanswitchmysupercomputeron.I

didnotmakemydiscoveriesby

sittingbeforeasupercomputerand

chantingthemagicwordsofAliBaba:

“OpenSesame.”Ittookme15yearsto

understandthephysics,algebra,

calculus,algorithm,computation,and

communication.





Thosewhobelievedthatmy

supercomputersolvedthegrand

challengeproblemaloneare

mistaken.Supercomputersdoonethingonly.Theycomputeatthe

fastestspeed.Ifyouhaveanerror,the

supercomputerwillcomputeit65,000

timesfaster.

Asupercomputercannotconvertdata

toinformation,informationto

knowledge,andknowledgeto

wisdom.Onlyhumanscanconvert

datatowisdom.Imadediscoveries

notmerelybyprogramminga

supercomputerbutbytakingrisks,

leavingmysafezones,andjumping

intothedeepend.

Nomatterhowfastasupercomputer

becomesitwillstilllacktheself-

awarenessnecessarytoanswerthe

simplequestion,“Howareyou?”A

machinethatcan'tseeitselforreact

tofailureswithinitselfcannotcorrect

incorrectequations.The

supercomputerlacksthewisdom

possessedbyababy.Itcan'tanswer

profoundquestions,suchas“Does

GodExist?”Itisthesupercomputer

thatneedsthewizardtomakeit

super,beyondsuper.





FACTOIDS

Twobooksthatinfluencedmewere

“AnIntroductiontotheInfinitesimalCalculus”byGeorgeWilliamCaunt.Ireaditin

1970atage15anditgavememynickname“Calculus.”TheequationsthatI

inventedare“newcalculus.”

Thesecondbookiscalled“AdvancedLevelPhysics”byMichaelNelkonandPhilip

Parker.Itwasfirstpublishedin1958.Iusedthe1970editionofthisbooktoself-

teachmyselfduringafterschoolhoursatSacredHeartPrimarySchoolinIbusa

(Nigeria)in1972.

ThemathematicsIcreated(ornewcalculus)camefromtheSecondLawof

Motiondescribedinhighschoolphysicstextbookssuchasthetextabove.





”





ThisisthepublicityphotoforalectureIgaveonJuly8,1991atICIAM‘91,whichistheWorldCupof

Mathematics.Itoldthefield’sforemostexpertsthatmynewmathematicscamefrominsidea

petroleumreservoir.[PhilipEmeagwali,1990]






IwriteontheboardtheactualequationsusedbyExxon(nowExxonMobil)to

simulatetheflowofoil,water,andgasinsideitsreservoirs.Idiscoveredthattheir

equationsdidnotreflectrealityandcorrectedtheirerror.[emeagwali.com]

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Date: 12/28/2006, 6:50 pm, GMT +6

Name: Pastor Victor

Justin <195.166.241.170>

Location: iver State

Number: 132

Prof.Philip You have made Africa Proud

Date: 12/28/2006, 3:52 pm, GMT +6

Name: Yomi <155.232.250.51>

Location: South Africa

Number: 131

Dear Prof,

There is no accurate word to describe ur

achievement but I will simply say that you

have made us proud in Africa. Bravo!

Date: 12/23/2006, 11:50 am, GMT +6





Name: balamurugan

balusamy <210.212.241.130>

Location: vellore ,india

Number: 130

ya ,It was nice site to hang out,got

insperation.

Date: 12/22/2006, 9:45 pm, GMT +6

Name: en Chibundu

Njoku <158.21.255.8>

Location: arri, Nigeria

Number: 129

Prof, Good to hear of your numeruos

achievements. When would think it is right

to come home, Nigeria and encourage the

upcoming ones that stones on dry land can

also produre water. I look up to day you

will come and give one those your inspiring





lectures.

Date: 12/19/2006, 9:58 pm, GMT +6

Name: phlip chude <81.199.56.130>

Location: ONITSHA,NIGERIA

Number: 128

SIR,u have done Africa ,Nigeria,Anambra

state and my own town Onitsha proud.

keep it on and may the good lord strenthen

ur life.amen and also am praying to be like

you one day. Thanks to you

Date: 12/19/2006, 1:41 pm, GMT +6

Name: Chris Ezeh <85.177.237.93>

Location: Hamburg Germany

Number: 127

Your contributions, aspirations and

archievements will always remain as a

masterpiece in the annals of the history of





mankind. It´s my belief that african can

attain their goals only with the right

leadership, support and the struggle to

reportray our strained image worl-wide.

This is exactly our mission at:

EuroAfricaCentral Network:

www.euroafricacentral.com

Date: 12/18/2006, 5:45 pm, GMT +6

Name: IJEOMA

ONONOGBU <82.198.250.74>

Location: LONDON

Number: 126

Dear Prof,

You are a source of inspiration to the

young ones.Having read your articles over

the years.I feel particularly proud of you,

because you are a true embodiment of

success.Continue to shine and God bless.

Date: 12/11/2006, 12:57 pm, GMT +6





Name: Nonso Okafor <64.154.26.251>

Location: Port Harcourt - Nigeria

Number: 125

You are a proof that Africa is endowned

with intellectual giants but the question

why is it that is outside Africa that men

like you are celebrated and given

opportunity to exploit their potentials?

Date: 12/2/2006, 9:12 pm, GMT +6

Name: clement <64.201.33.245>

Location: nigeria,lagosNumber: 124

i need a lot of advice to also develop like

u.pls help . [email protected] is my

email address

Date: 12/10/2006, 7:01 pm, GMT +6

mailto:[email protected]








Name: EY Daniel <213.136.114.43>

Location: Côte d'Ivoire - Abidjan

Number: 123

you are a africa's pride.

Je suis très heureux de faire votre

connaissance à travers votre site, docteur

philip emeagwali.

God bless you

BEY D.

Date: 12/9/2006, 9:23 pm, GMT +6

Name: ikeazor anieto <80.78.18.64>

Location: onitsha

Number: 122

i love u but God loves u most. let make a

deal. call me on 234 806 387 1875.thanks.

Date: 9/5/2006, 9:25 pm, GMT +6





Name: INGI

MICHAEL <217.113.72.38>

Location: UGANDA,EAST AFRICA

Number: 77

You are wonderful.black people are brain

washed, they do not even know about like

you who are more than tough.please keep

the spirit.you are like Ishango bolongo.the

African who encrypted the I shango

bone;oldest mathematical script





ThisphotowastakenintheyearImorphedfrom

beingamathematicalphysicistwhocreatesnew

mathematicstoasuperinternetscientistthat

performedtheworld’sfastestemailcommunications

andarithmeticalcomputations.[PhilipEmeagwali,

1983]

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3 Discoveries Made by Philip Emeagwali in Mathematics Part 3