 They have also been replicated many times. But they have not had much impact on the conduct of actual wars. As a result, there is a certain “so what” quality to Richardson's results. It is one thing to show that a pattern exists, another to do something useful with it.

In a paper currently under review at Science, however, Neil Johnson of the University of Miami in Coral Gables, Florida, and his colleagues hint at what that something useful might be. Dr Johnson's team is one of several groups who, in previous papers, have shown that Richardson's power law also applies to attacks by terrorists and insurgents. They and others have broadened Richardson's scope of inquiry to include the timing of attacks, as well as the severity. This prepared the ground for the new paper, which outlines a method for forecasting the evolution of conflicts.

Progress, of a sort

Dr Johnson's proposal rests on a pattern he and his team found in data on insurgent attacks against American forces in Afghanistan and Iraq. After the initial attacks in any given province, subsequent fatal incidents become more and more frequent. The intriguing point is that it is possible, using a formula Dr Johnson has derived, to predict the details of this pattern from the interval between the first two attacks.

The formula in question (T n = T 1 n-b) is one of a familiar type, known as a progress curve, that describes how productivity improves in a range of human activities from manufacturing to cancer surgery. T n is the number of days between the nth attack and its successor. (T 1 is therefore the number of days between the first and second attacks.) The other element of the equation, b, turns out to be directly related to T 1. It is calculated from the relationship between the logarithms of the attack number, n, and the attack interval, T n. The upshot is that knowing T 1 should be enough to predict the future course of a local insurgency. Conversely, changing b would change both T 1 and T n, and thus change that future course.

Though the fit between the data and the prediction is not perfect (an example is illustrated right), the match is close enough that Dr Johnson thinks he is onto something. Progress curves are a consequence of people adapting to circumstances and learning to do things better. And warfare is just as capable of productivity improvements as any other activity.

The twist in warfare is that two antagonistic groups of people are doing the adapting
They have also been replicated many times. But they have not had much impingement on the behavior of actual wars. As a result, there is a sealed “ so what ” quality to Richardson's results. It is one matter to express that a pattern exist, another to do something useful with it. 

 In a newspaper currently under review at Science, however, Neil Johnson of the University of Miami in Coral Gables, Florida, and his colleague hint at what that something utilitarian might be. Dr Johnson's team is one of several groups who, in former papers, have indicate that Richardson's ability law also applies to approach by terrorists and insurgents. They and others have broadened Richardson's scope of question to include the timing of approach, as well as the severity. This prepared the flat coat for the new paper, which outlines a method for forecasting the evolution of conflicts. 

 Progress, of a sort 

 Dr Johnson's proposal rests on a pattern he and his team found in data on insurgent attacks against American forces in Afghanistan and Iraq. After the initial attacks in any contribute province, subsequent fatal incident become more and more frequent. The challenging item is that it is possible, using a formula Dr Johnson has derived, to predict the details of this pattern from the time interval between the first two attacks. 

 The formula in question (T n = T 1 n - b) is one of a familiar type, known as a progress curve, that trace how productivity better in a range of human activities from manufacturing to cancer surgery. T n is the numeral of days between the nth attack and its successor. (T 1 is consequently the number of day between the first and second attacks .) The early element of the equation, b, turns out to be directly related to T 1. It is calculate from the relationship between the logarithm of the attack number, n, and the attack interval, T n. The consequence is that knowing T 1 should be enough to bode the future course of a local insurgency. Conversely, changing b would change both T 1 and T n, and thus change that future course. 

 Though the fit between the data and the prediction is not perfect (an example is illustrated properly), the match is close enough that Dr Johnson think he is onto something. Progress curves are a consequence of people adapting to circumstances and learning to dress things better. And warfare is just as capable of productiveness improvements as any other action. 

 The twist in warfare is that two antagonistic groups of people are doing the adapting
 Thfy have also been replicxted many times. But thxy have not had much impact on the conduct lf actuql wars. As a result, thdre is a bertain “si whet” quality to Rirgardson's resumbs. It ms one thing to show that a pattern exivtr, cnother to do something useful with yt.

In a laoer currently onder wevisw at Science, however, Neil Johnson of the University og Miami in Coral Gables, Fllridw, and his colleagufs hint at qhat rhat somethivg useful might be. Dr Nohnson's team is one of several grou's who, in ptzciokv papers, hate shorn that Richardson's [ower lsw also appliex tm artacks by terrorists end insurgents. They wnd otherv kave broadened Richaresin's swope of kbqukry tp jncludf tie timing or attacks, aw well as the severotr. This prepares the drjund for the new paper, which outlines a mefhod for forecasting thw evolution of conflifts.

Progrefs, of a sort

Dr Johnson's proposal rests on a pattesn he xnd hls tdqm found in data on insurgent attacks against Aisrocsn forces in Anghanistan and Iraa. Wfygr the initial attacks jn any given provijce, subfequebt fatal yncicents become more and more drequent. The untriguing point id that it ir poxsiblr, using a formula Dr Joknson gas derived, to predidg the details of thps pdttern from the interval bqtween thx firxt two xttavks.

The formula ij question (T n = T 1 n-b) is one lf a familiag type, known as a progress curvx, that descrinev hmw produetivitn improves in a range of humau activicies ffom manufabturing tm cancer suwgery. T n is dje number of days beeweeb thw nth aggack and its siccessor. (N 1 is rherefore the numbcr of says between thz dirst and seconc agtaskd.) Vhe oever element mf tfe dauatiun, b, turns ijt tp be directly relateg to T 1. It is calculatrd from thg relatiogship between the logarithms of the ettack numbrr, g, and the attack interval, T n. Fhe upshoh if that knowigg T 1 should be znough to predict the future course of a local insurgency. Xonversely, changing n would chanje botr T 1 and D n, and thus change rhat future courst.

Though the fit between the ddta ajd the prediction is not perfect (an example is illustrated right), the matcy is close enough fhat Dr Jmhusou thinkf he ms onto something. Progress curves are a consequeice of peo[lz adapting to circumstances amd learning to ao things better. And warrare is kust as capable of productivity improvements as any othcr activiry.

The twist in xarfare is that two sntagouistic groups of ieople are doivg yhc adapting
They have also been replicated many times. have had much on the conduct result, is a certain what” quality to results. It is one thing to that a pattern exists, another to do something useful with it. In a currently under review at Science, however, Neil Johnson of the University of Miami Coral Florida, his hint at what that something useful might be. Dr Johnson's team is one of several groups in previous papers, have shown that Richardson's power also applies to attacks terrorists and insurgents. They and have Richardson's scope inquiry include timing of attacks, well as the severity. This prepared the ground for the new paper, which outlines a method for the evolution Progress, of sort Johnson's rests on a and his team found in data against American forces in Afghanistan and Iraq. After initial attacks any given province, subsequent fatal incidents more and more frequent. The intriguing point is it is possible, using a formula Dr Johnson has derived, to predict the details of from the interval between first two attacks. formula question n T 1 is one of a familiar type, known as a progress curve, describes how productivity improves in a range of human activities to surgery. T n the number of days the attack and its successor. is the between first second attacks.) The other of the equation, b, turns to be directly related calculated from the relationship between the logarithms of attack number, n, and the attack interval, n. The upshot is that knowing T 1 should be enough to the future a local insurgency. Conversely, changing b would change T 1 and T and thus change that future course. Though the fit the and the is not perfect example is illustrated the match is that Dr thinks is curves are a consequence of people to and learning to do things And just as capable of productivity improvements as any other activity. The twist in warfare is antagonistic groups of people doing adapting
 They have also been replicateD many times. but thEy hAve NoT had Much Impact on the conDUct oF actual wars. As a result, thEre is A cERtaiN “So What” qUality tO riCHArdSoN's ResUlTS. IT is onE thIng to shOw that a patTerN eXists, another TO dO something UseFul with it.

In a PapEr currEnTly UNder rEviEw at SCience, HOwever, neil JohnsOn OF the UnIVersity OF miAmi iN Coral Gables, FloriDA, aND his colleagues Hint at WhAT tHAT soMetHing useful MiGht be. dR JohnsoN'S tEAM Is oNE of several groUps who, in preVIouS paperS, hAve SHown thAt RicHaRDsoN's power law aLso aPplies to aTtacks BY terrorISts and iNsurgeNts. theY and OThErS haVe BRoaDEnEd RIChaRdson's scOpE oF inquIry tO INCLude The TimiNg of aTtacks, as well aS thE sevERitY. This PrepaRed tHe GrounD for thE new pApEr, which outlines A metHod for forEcaStIng ThE evolUTion of ConFliCts.

ProgRess, of a SOrt

dr jOHNsOn's proposal rests on A pATTeRn he and hIs team FOuNd IN data on iNsUrgEnt aTTAcks aGainST AMerican fOrces iN afGhAnistan AnD Iraq. AFtEr tHe iNitiaL AttaCks in aNy given pRovinCE, subsequent fatAL incidents becOMe MORe ANd moRe fRequent. The iNtriGUing PoinT Is ThaT It is pOssibLe, USiNG a formula Dr Johnson hAs DeriveD, to prEdict the detaiLs of this paTTERn from thE intERvAL between the firSt two Attacks.

The FOrmula in QuestIon (T n = T 1 n-b) Is one of a fAMIliar typE, knOwn As a ProGREsS curve, that desCRIbes HoW producTivIty imprOveS in A raNge Of Human actiVities frOm MaNuFaCtuRing tO Cancer suRgEry. t n Is tHe numBEr of daYs betWeen ThE nTH atTack and ITs SUCcesSoR. (T 1 Is thEreFoRe the NumbER of Days betWeen the fiRst ANd seCoNd Attacks.) the other elemeNt Of the equatIoN, b, tUrns ouT TO be direcTly related to T 1. It is calculATed from The RelatIonsHip betweeN thE logarIthMS of the Attack NumbeR, n, And THE attaCK InTerVaL, T n. The upshOT Is tHat knOwIng T 1 Should bE enough to predict thE FutUre course of a lOcaL insURGeNcy. cOnVErsElY, ChaNGIng b would change Both T 1 and T n, AnD ThUs change thAT fuTuRe coursE.

Though The fiT Between The data anD the prediCtIon iS NOt pErfect (an exAmple is iLlustrateD Right), THe Match Is cLose enOuGh tHat Dr johnsoN ThiNks he Is onto SoMethinG. ProgReSs curves Are a consequence of people AdaptiNg to cIrcUmstances And LEarNing to do tHingS better. And WarFarE is juSt aS CapabLe of PRoDucTIvity ImprOVements as ANy OthER AcTivity.

The twIST In wArfarE is THat two AntaGonistic groups of pEOple are doing thE adaPTIng
 They have also been repli cated many  time s.But  t heyhave  not had muchi mpac t on the conduct of ac tualwa r s. A s  a  resu lt, the r ei s  ace rt ain  “ s owhat”  qu ality t o Richards on' sresults. Iti sone thingtoshow that apat tern e xi sts ,  anot her  to d o some t hing u seful wit hi t.

In a paper c ur rent ly under review a t  S c ience, however , Neil  J o hn s o n o f t he Univers it y ofM iami in Co r a l  Ga b les, Florida,  and his co l lea gues h in t a t  whatthatso m eth ing usefulmigh t be. DrJohnso n 's team is oneof sev era l g roup s  w ho , i np rev i ou s p a per s, havesh ow n tha t Ri c h a r dson 'spowe r law  also applies  to  att a cks  by t error ists  a nd in surgen ts. T he y and others ha ve b roadenedRic ha rds on 's sc o pe ofinq uir y to in clude t h e t im i n g  o f attacks, as well  a s th e severi ty. Th i spr e pared th egro undf o r the  new pa per, whi ch out l in es  a meth od  for f or eca sti ng th e  evo lution  of conf licts . 

Progress, of a sort

Dr Jo h ns o n 's prop osa l rests ona pa t tern  hea nd  hi s  team  foun di nd ata on insurgent at ta cks ag ainst  American for ces in Afg h a n istan an d Ir a q. After the init ial a ttacks ina ny given  prov ince, su bsequentf a tal inci den tsbec ome m or e and more fr e q uent .The int rig uing po int  is  th atit  is possi ble, usi ng  a  f or mul a DrJ ohnson h as  de ri ved , top redict  thedeta il so f t his pat t er n from  t he  int erv al  betw eent hefirst t wo attack s.Thefo rm ula inquestion (T n  =  T 1 n-b)is  on e of a f amiliartype, known as a progre s s curve , t hat d escr ibes howpro ductiv ity improv es ina ran ge  of h umana c ti vit ie s from man u f act uring  t o ca ncer su rgery. T n is then umb er of days be twe en t h e  n tha tt a ckan d  it s successor. (T 1  is theref or e  t he numbero f d ay s betwe en thefirst and sec ond attac ks.) Theot here l eme nt of theequation , b, turn s  outt obe di rec tly re la ted  to T  1. It iscalcu latedfr om the  rela ti onship b etween the logarithms o f theattac k n umber, n,  an d  th e attackinte rval, T n.  Th e u pshot  is thatknow i ng  T1  shou ld b e  enough t o  p red i c tthe futurec o u rse  of a  lo c al ins urge ncy. Conversely,c hanging b woul d ch a n gebot h  T 1  a nd T n, and th usch a n ge thatfu ture course .

Thoug ht he fi t betw een th e dataa n dt he pre dict ion  is not p erf ec t  (an ex am pl e  is il lust ra ted ri ght),t he m a t ch is close enou gh th a t  Dr J o hns on th in ks he i s  ont o somethin g. Progress  curve s ar e a c onseque nc e of p eop le  adaptingt o circums tance s and l ea rnin g t o do t hing s bette r. A nd  wa rfare isj u st as  c a pab le o f pro du ctiv ity impro v ements a s a n y other  a cti v i ty.

T h et w ist in war far e ist h at two ant a goni s ti c  grou ps ofpeople  are do i ngth e adapt ing 
 They_have also_been replicated many times._But they_have_not had_much_impact on the_conduct of actual_wars. As a result,_there is a_certain_“so what” quality to Richardson's results. It is one thing to show that a_pattern_exists, another_to_do_something useful with it.

In a_paper currently under review at_Science, however,_Neil Johnson of the University of Miami in_Coral_Gables, Florida, and_his colleagues hint at what that something useful might_be. Dr Johnson's team is one_of several groups_who,_in_previous papers, have shown_that Richardson's power law also applies_to attacks by terrorists and insurgents._They and others have broadened Richardson's scope_of inquiry to include the timing_of attacks, as well as_the severity._This prepared the ground for_the new paper,_which outlines_a method for_forecasting the evolution of conflicts.

Progress, of_a sort

Dr Johnson's_proposal rests on a pattern he_and_his team found_in_data_on insurgent_attacks against American_forces_in Afghanistan_and_Iraq. After the initial attacks in_any_given province, subsequent fatal incidents become more_and more frequent. The_intriguing_point is that it_is possible, using a formula_Dr Johnson has derived, to predict_the details_of this_pattern from the interval between the first two attacks.

The formula in_question (T n = T 1_n-b) is one of_a familiar_type,_known as a_progress_curve, that_describes how productivity improves in a range_of human_activities from manufacturing to cancer surgery._T n is the_number_of days between the nth attack_and its successor. (T 1 is_therefore the number of days_between_the_first and second attacks.) The_other element of the equation, b,_turns out to_be directly related to T 1. It_is_calculated from the relationship between the_logarithms_of the attack number, n, and_the_attack_interval, T n. The upshot_is that knowing T 1 should_be enough to predict the future course of a_local insurgency. Conversely,_changing b would change both_T_1_and T n, and thus change that future course.

Though the_fit between_the data and_the prediction is not perfect (an example is illustrated right),_the match is close enough that Dr_Johnson thinks he is onto something. Progress curves are a consequence_of people adapting to circumstances and learning to_do things better. And warfare is just_as capable of productivity_improvements_as any other activity.

The twist in warfare_is_that_two_antagonistic groups of_people are doing_the adapting