, two contradictory theories may, provided they are not mixed up, and that they do not seek the substance of things, may be both useful instruments of research, and perhaps reading Maxwell's Treatise would be less suggestive if it had not opened to us so many new divergent paths. (Poincaré 1890, IX)11 According to Poincaré, this appearance of fragmentation conceals the fundamental idea of the Treatise. It corresponds to a profound change in the concept of mechanistic reduction of phenomena: Maxwell does not give a mechanical explanation of electricity and magnetism; he merely demonstrates that this explanation is possible. (...) If a phenomenon includes a complete mechanical explanation, it will include an infinity of others which will also give a good account of all the peculiarities revealed by experience. (Poincaré 1890, VII, XIV) This theorem, stated in Maxwell's Treatise (Maxwell 1873, II, §831), is demonstrated in detail by Poincaré, using the Lagrangian formalism. The generalized coordinates correspond to observable/measurable parameters. These can be related to an unobservable molecular coordinate system. There are an infinity of such systems which, by transformation of variables, allow us to obtain the same Hamilton function, T + U. This theorem justifies the attitude of those who find the "complete explanations" (typical of the ideal of the Laplacian program) unnecessary, especially the speculations on the ultimate structure of the ether. But the opposite attitude remains valid: Among all these possible explanations, how can we make a choice for which the help of experience is lacking? Perhaps a day will come when physicists will lose interest in these questions, inaccessible to positive methods, and abandon them to the metaphysicians. This day has not come; man does not resign himself so easily to ignore eternally the substance of things. (Poincaré 1890, XV) Then Poincaré remarks how ontological preoccupations about the nature of the substance or the inner mechanism are alien to the spirit of Maxwell's fundamental idea: The same spirit is found throughout the work. What is essential, that is, what must remain common to all theories, is brought to light; anything that would fit a particular theory is almost always ignored. The reader thus finds himself in the presence of an form almost empty of matter which he is at first tempted to take for a fleeting and elusive shadow. But the efforts to which he is thus condemned 11 On the interpretation of Maxwell by Poincaré see Darrigol (1993, 216-7, 220-223). Jo
, two contradictory theories may, provided they are not mixed up, and that they do not search the means of things, may be both useful instruments of inquiry, and perhaps reading Maxwell's Treatise would be less suggestive if it had not unfold to us so many new divergent way. (Poincaré 1890, IX)11 According to Poincaré, this appearance of fragmentation conceals the cardinal idea of the Treatise. It corresponds to a profound change in the concept of mechanistic decrease of phenomena: Maxwell does not give a mechanical explanation of electricity and magnetism; he merely attest that this explanation is possible. (...) If a phenomenon includes a accomplished mechanical explanation, it will include an infinity of others which will also impart a good account of all the peculiarities revealed by experience. (Poincaré 1890, VII, XIV) This theorem, state in Maxwell's Treatise (Maxwell 1873, II, § 831), is demonstrated in detail by Poincaré, using the Lagrangian formalism. The generalized coordinates correspond to discernible / measurable parameters. These can be related to an unobservable molecular coordinate system. There are an infinity of such systems which, by transformation of variable star, allow us to obtain the same Hamilton function, T + U. This theorem justifies the attitude of those who find the " complete explanations " (typical of the ideal of the Laplacian plan) unnecessary, especially the speculations on the ultimate social organization of the quintessence. But the opposite attitude remains valid: Among all these possible explanation, how can we make a choice for which the help of experience is lacking? possibly a day will come when physicists will lose interest in these questions, inaccessible to positive methods, and abandon them to the metaphysicians. This day has not come; man does not release himself so well to dismiss eternally the substance of things. (Poincaré 1890, XV) Then Poincaré remarks how ontological preoccupancy about the nature of the substance or the inner mechanism are alien to the spirit of Maxwell's cardinal idea: The like spirit is found throughout the work. What is essential, that is, what must remain coarse to all theories, is brought to luminosity; anything that would fit a especial theory is about always ignored. The proofreader thus finds himself in the bearing of an form almost empty of matter which he is at first tempted to take for a fleeting and elusive shadow. But the efforts to which he is thus condemned 11 On the interpretation of Maxwell by Poincaré understand Darrigol (1993, 216 - 7, 220 - 223). Jo
, twl contradictory theories may, provided tkwy are not mjxed up, xnd that they do not seek thx suvstanxe of things, may be bogh useful instrumwnts if researci, and pevkaps dcadiny Naxwell's Treatlse would ba less suggesthvd nf it had not opened to us so many nqw divetgfnt paths. (Poinsaré 1890, YX)11 Adbovding to Poincaré, this appearance of frajmentation concrals the fundamental idea lf tje Treatise. It corgesponds to a pwifound changd in the concept of medhanistic reduction of phenomenx: Maxcell does nit gigg a mechanicel expjanation of ckectriwity anc magnetism; he mecely demonstrates that thms explanation is pofsible. (...) Ix c phenomenon includes a compnete mecfqnizal eeplznatioj, iv will inclhde an infibity of others whicn rpkl also give a gooq wccount of all the peculiarities revealtd by experience. (Poincaré 1890, VIU, XIV) This theorem, stwted in Mwxwell's Treatise (Maxwell 1873, II, §831), is demonstrated in getaim by Pjkbcwré, using the Lagrangian formalism. The generalyaec boordinates correfpond to obxegvsfle/measurable paramzfeds. These can be repated tj an ynobservafle kolecular coordinate system. There are au ibfinity of such sydtems which, by jransfprmation of variables, aulow us to obtaln the sajd Hamilton functkon, T + U. This theorem justifies the attivude pf thosd whp find the "complfte ew[lanations" (typical of tke idaal of the Laplacian program) unnecessary, xxpecially thg s[ecllations jn thc ultimate strusture of the ejher. But che opoosite attptude remeins valid: Aiong all thesa possible ex'lanationf, hoq cab we mayd a choice for which thv kelp of ezperience is lackikg? Pethzps a day will eune when physicixts wijl lpsq interest in there diestiuns, inacceswkble to positive methods, and abandon them to tne metaphywicians. Ehis day has mot come; man does jot rxsign iimselg sj easily to ignore eternally tge substajce of things. (Pjincqré 1890, XV) Then 'oincaré remarks how ontological preoccupetions about the naturg of the substance or uhe inner mecianism are aliet to the spirit of Mqxwell's fundamentsl idea: The same spirjt is xound throughout the work. What is essential, that is, what must remain common to all tiejries, is brkughy to niyht; anythyng vhet would fit a pagticular theory is almost always ignored. Tke reader thus finds himself on the presence of an form almost empty of mattrr which he is at first tempted to take for a fleeting snd elusuve sgadow. But vhe efforts to which he is thus condembed 11 On the interoreyabion of Madwelk yy Poincaré see Darrigol (1993, 216-7, 220-223). Jo
, two contradictory theories may, provided they mixed and that do not seek be useful instruments of and perhaps reading Treatise would be less suggestive if had not opened to us so many new divergent paths. (Poincaré 1890, IX)11 to Poincaré, this appearance of fragmentation conceals the fundamental idea of the Treatise. corresponds a change the concept of mechanistic reduction of phenomena: Maxwell does not give a mechanical explanation of electricity magnetism; he merely demonstrates that this explanation is (...) If a phenomenon a complete mechanical explanation, it include infinity of which also a good account all the peculiarities revealed by experience. (Poincaré 1890, VII, XIV) This theorem, stated in Maxwell's Treatise (Maxwell II, §831), in detail Poincaré, the formalism. The generalized to observable/measurable parameters. These can be unobservable molecular coordinate system. There are an infinity such systems by transformation of variables, allow us obtain the same Hamilton function, T + U. theorem justifies the attitude of those who find the "complete explanations" (typical of the ideal Laplacian program) unnecessary, especially speculations on the structure the But opposite attitude valid: Among all these possible explanations, how can we make a for which the help of experience is lacking? Perhaps a come physicists will lose in these questions, inaccessible positive and abandon them to This has does resign so easily to ignore the substance of things. (Poincaré XV) Then Poincaré remarks nature of the substance or the inner mechanism alien to the spirit of Maxwell's fundamental The same spirit is found throughout the work. What is essential, that what must to all theories, is brought to light; anything would fit a particular is almost always ignored. The reader thus finds himself the of an almost empty of which he is first tempted to a fleeting elusive But which he is thus condemned 11 the of Maxwell by Poincaré see (1993, Jo
, two contradictory theories mAy, provided They aRe nOt mIxEd up, And tHat they do not seEK the Substance of things, may be Both uSeFUl inSTrUmentS of reseARcH, ANd pErHaPs rEaDInG MaxwEll'S TreatiSe would be lEss SuGgestive if it HAd Not opened tO us So many new divErgEnt patHs. (poiNCaré 1890, Ix)11 AcCordiNg to PoINcaré, tHis appearAnCE of fraGMentatiON CoNceaLs the fundamental iDEa OF the Treatise. It CorresPoNDs TO A prOfoUnd change iN tHe conCEpt of meCHaNISTic REduction of pheNomena: MaxweLL doEs not gIvE a mEChanicAl expLaNAtiOn of electriCity And magnetIsm; he mERely demONstrateS that tHis ExpLanaTIoN iS poSsIBle. (...) iF a PheNOmeNon incluDeS a ComplEte mECHANicaL exPlanAtion, It will include An iNfinITy oF otheRs whiCh wiLl Also gIve a goOd accOuNt of all the peculIariTies reveaLed By ExpErIence. (pOincarÉ 1890, VIi, XIv) This thEorem, stATed In mAXWeLl's Treatise (Maxwell 1873, iI, §831), IS DeMonstratEd in deTAiL bY poincaré, UsIng The LAGRangiAn foRMaLism. The gEneralIZeD cOordinaTeS correSpOnd To oBservABle/mEasuraBle paramEters. tHese can be relatED to an unobservABlE MOlECulaR coOrdinate sysTem. THEre aRe an INfIniTY of suCh sysTeMS wHIch, by transformation Of VariabLes, alLow us to obtain The same HamILTOn functiOn, T + U. tHiS Theorem justifiEs the Attitude of THose who fInd thE "completE explanatIONs" (typicaL of The IdeAl oF THe laplacian progRAM) unnEcEssary, eSpeCially tHe sPecUlaTioNs On the ultiMate struCtUrE oF tHe eTher. BUT the oppoSiTe aTtItuDe remAIns valId: AmoNg alL tHeSE poSsible eXPlANAtioNs, HoW can We mAkE a choIce fOR whIch the hElp of expeRieNCe is LaCkIng? PerhAps a day will coMe When physicIsTs wIll losE INterest iN these questions, inaccessIBle to poSitIve meThodS, and abandOn tHem to tHe mETaphysIcians. this dAy Has NOT come; MAN dOes NoT resign himSELf sO easiLy To igNore eteRnally the substance OF thIngs. (Poincaré 1890, Xv) ThEn PoINCaRé rEMaRKs hOw ONtoLOGical preoccupatIons about tHe NAtUre of the suBStaNcE or the iNner mecHanisM Are alieN to the spiRit of MaxwElL's fuNDAmeNtal idea: ThE same spiRit is founD ThrouGHoUt the WorK. What iS eSseNtial, That is, WHat Must rEmain cOmMon to aLl theOrIes, is broUght to light; anything that Would fIt a paRtiCular theoRy iS AlmOst always IgnoRed. The readEr tHus Finds HimSElf in The pREsEncE Of an fOrm aLMost empty OF mAttER WhIch he is at fiRST TemPted tO taKE for a fLeetIng and elusive shadOW. But the efforts To whICH he Is tHUs coNdEmned 11 On the inteRprEtATIon of MaxWeLl by PoincarÉ see DarrIgOL (1993, 216-7, 220-223). Jo
, two contradictory theori es may, pr ovide d t hey  a re n ot m ixed up, and t h at t hey do not seek the su bstan ce of t h in gs, m ay be b o th u sef ul  i nst ru m en ts of  re search,  and perha psre ading Maxwel l 's  Treatisewou ld be less s ugg estive  i f i t  hadnot  open ed tou s so m any new d iv e rgentp aths. ( P o in caré  1890, IX)11 Acco r di n g to Poincaré,  thisap p ea r a nce  of  fragmenta ti on co n ceals t h ef u n dam e ntal idea ofthe Treatis e . I t corr es pon d s to a  prof ou n d c hange in th e co ncept ofmechan i stic re d uctionof phe nom ena : Ma x we ll  do es not gi vea  me chanical  e xp lanat iono f e lect ric ityand m agnetism; hemer elyd emo nstra tes t hatth is ex planat ion i spossible. (...)  Ifa phenome non  i ncl ud es ac omplet e m ech anicalexplana t ion ,i t wi ll include an infi ni t y  o f others  which wi ll also giv ea g ooda c count  ofa ll  the pec uliari t ie sreveale dby exp er ien ce.  (Poi n caré  1890,  VII, XI V) Th i s theorem, sta t ed in Maxwell ' sT r ea t ise(Ma xwell 1873,  II, §831 ), i s  d emo n strat ed in  d e ta i l by Poincaré, usin gthe La grang ian formalism . The gene r a l ized coo rdin a te s  correspond to  obse rvable/mea s urable p arame ters. Th ese can b e relatedtoanuno bse r v ab le molecularc o ordi na te syst em.  Thereare  an  in fin it y of such  systems  w hi ch ,bytrans f ormation  o f v ar iab les,a llow u s toobta in  t h e s ame Ham i lt o n  fun ct io n, T  +U.  This  the o rem  justif ies the a tti t udeof  t hose wh o find the "c om plete expl an ati ons" ( t y pical of  the ideal of the Lapla c ian pro gra m) un nece ssary, es pec iallythe specul ations  on t he  ul t i mates t ru ctu re  of the et h e r.But t he  opp osite a ttitude remains va l id:  Among all th ese  pos s i bl e e x pl a nat io n s,h o w can we make a  choice fo rw hi ch the hel p  of  e xperien ce is l ackin g ? Perha ps a daywill come  w henp h ysi cists will  lose in terest in these qu estio ns,  inacc es sib le to  posit i vemetho ds, an dabando n the mto the m etaphysicians. This day  has n ot co me;  man does  no t  re sign hims elfso easilytoign ore e ter n allythes ub sta n ce of  thi n gs. (Poin c ar é 1 8 9 0,  XV) Then P o i n car é rem ark s  how o ntol ogical preoccupat i ons about thenatu r e  of  th e  sub st ance or the in ner  m e c hanism a re  alien to t he spiri to f Max well's  funda mentali d ea :  The s amespi rit is fo und  t h roughou tth e  work.  Wha tis ess ential ,  tha t is, what must re mainc o mmont o a ll th eo ries, i s  bro ught to li ght; anythi ng tha t wo uld f it a pa rt icular  th eo ry is almo s t alwaysignor ed. The  r eade r t hus fi ndsh i mself  inth e p resence o f an fo rm alm ostempty  o f ma tter whic h  he is a t f i rst tem pt edt o  takef or a  fleetingand  elus i v e shadow.B ut t h ee ffort s to w hich h e is th u s c on demned11O n  the inte rpretatio n  of  M axwe ll by Po in caré  s eeDa rrigol (1993, 2 16-7, 22 0-223).J o 
, two_contradictory theories_may, provided they are_not mixed_up,_and that_they_do not seek_the substance of_things, may be both_useful instruments of_research,_and perhaps reading Maxwell's Treatise would be less suggestive if it had not opened_to_us so_many_new_divergent paths. (Poincaré 1890, IX)11_According to Poincaré, this appearance_of fragmentation_conceals the fundamental idea of the Treatise. It_corresponds_to a profound_change in the concept of mechanistic reduction of phenomena:_Maxwell does not give a mechanical_explanation of electricity_and_magnetism;_he merely demonstrates that_this explanation is possible. (...) If_a phenomenon includes a complete mechanical_explanation, it will include an infinity of_others which will also give a_good account of all the_peculiarities revealed_by experience. (Poincaré 1890, VII,_XIV) This theorem,_stated in_Maxwell's Treatise (Maxwell_1873, II, §831), is demonstrated in_detail by Poincaré,_using the Lagrangian formalism. The generalized_coordinates_correspond to observable/measurable_parameters._These_can be_related to an_unobservable_molecular coordinate_system._There are an infinity of such_systems_which, by transformation of variables, allow us_to obtain the same_Hamilton_function, T + U._This theorem justifies the attitude_of those who find the "complete_explanations" (typical_of the_ideal of the Laplacian program) unnecessary, especially the speculations on the_ultimate structure of the ether. But_the opposite attitude remains_valid: Among_all_these possible explanations,_how_can we_make a choice for which the help_of experience_is lacking? Perhaps a day will_come when physicists will_lose_interest in these questions, inaccessible to_positive methods, and abandon them to_the metaphysicians. This day has_not_come;_man does not resign himself_so easily to ignore eternally the_substance of things._(Poincaré 1890, XV) Then Poincaré remarks how_ontological_preoccupations about the nature of the_substance_or the inner mechanism are alien_to_the_spirit of Maxwell's fundamental idea:_The same spirit is found throughout_the work. What is essential, that is, what must_remain common to_all theories, is brought to_light;_anything_that would fit a particular theory is almost always ignored._The reader_thus finds himself_in the presence of an form almost empty of matter_which he is at first tempted to_take for a fleeting and elusive shadow. But the efforts to_which he is thus condemned 11 On the_interpretation of Maxwell by Poincaré see Darrigol_(1993, 216-7, 220-223). Jo