darwin and modern science-第168节

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A　complex　mechanical　system　may　be　capable　of　motion　in　several　distinct　modes　or　types；　and　the　motions　corresponding　to　each　such　type　may　be　arranged　as　before　in　families。　　For　the　sake　of　simplicity　I　will　suppose　that　only　two　types　are　possible；　so　that　there　will　only　be　two　families；　and　the　rotational　momentum　is　to　be　constant。　　The　two　types　of　motion　will　have　certain　features　in　common　which　we　denote　in　a　sort　of　shorthand　by　the　letter　A。　　Similarly　the　two　types　may　be　described　as　A　＋　a　and　A　＋　b；　so　that　a　and　b　denote　the　specific　differences　which　discriminate　the　families　from　one　another。　　Now　following　in　imagination　the　family　of　the　type　A　＋　a；　let　us　begin　with　the　case　where　the　specific　difference　a　is　well　marked。　　As　we　cast　our　eyes　along　the　series　forming　the　family；　we　find　the　difference　a　becoming　less　conspicuous。　　It　gradually　dwindles　until　it　disappears；　beyond　this　point　it　either　becomes　reversed；　or　else　the　type　has　ceased　to　be　a　possible　one。　　In　our　shorthand　we　have　started　with　A　＋　a；　and　have　watched　the　characteristic　a　dwindling　to　zero。　　When　it　vanishes　we　have　reached　a　type　which　may　be　specified　as　A；　beyond　this　point　the　type　would　be　A　…　a　or　would　be　impossible。

Following　the　A　＋　b　type　in　the　same　way；　b　is　at　first　well　marked；　it　dwindles　to　zero；　and　finally　may　become　negative。　　Hence　in　shorthand　this　second　family　may　be　described　as　A　＋　b；。。。A；。。。A　…　b。

In　each　family　there　is　one　single　member　which　is　indistinguishable　from　a　member　of　the　other　family；　it　is　called　by　Poincare　a　form　of　bifurcation。　　It　is　this　conception　of　a　form　of　bifurcation　which　forms　the　important　consideration　in　problems　dealing　with　the　forms　of　liquid　or　gaseous　bodies　in　rotation。

But　to　return　to　the　general　question；thus　far　the　stability　of　these　families　has　not　been　considered；　and　it　is　the　stability　which　renders　this　way　of　looking　at　the　matter　so　valuable。　　It　may　be　proved　that　if　before　the　point　of　bifurcation　the　type　A　＋　a　was　stable；　then　A　＋　b　must　have　been　unstable。　　Further　as　a　and　b　each　diminish　A　＋　a　becomes　less　pronouncedly　stable；　and　A　＋　b　less　unstable。　　On　reaching　the　point　of　bifurcation　A　＋　a　has　just　ceased　to　be　stable；　or　what　amounts　to　the　same　thing　is　just　becoming　unstable；　and　the　converse　is　true　of　the　A　＋　b　family。　　After　passing　the　point　of　bifurcation　A　＋　a　has　become　definitely　unstable　and　A　＋　b　has　become　stable。　　Hence　the　point　of　bifurcation　is　also　a　point　of　〃exchange　of　stabilities　between　the　two　types。〃　　（In　order　not　to　complicate　unnecessarily　this　explanation　of　a　general　principle　I　have　not　stated　fully　all　the　cases　that　may　occur。　　Thus：　　firstly；　after　bifurcation　A　＋　a　may　be　an　impossible　type　and　A　＋　a　will　then　stop　at　this　point；　or　secondly；　A　＋　b　may　have　been　an　impossible　type　before　bifurcation；　and　will　only　begin　to　be　a　real　one　after　it；　or　thirdly；　both　A　＋　a　and　A　＋　b　may　be　impossible　after　the　point　of　bifurcation；　in　which　case　they　coalesce　and　disappear。　　This　last　case　shows　that　types　arise　and　disappear　in　pairs；　and　that　on　appearance　or　before　disappearance　one　must　be　stable　and　the　other　unstable。）

In　nature　it　is　of　course　only　the　stable　types　of　motion　which　can　persist　for　more　than　a　short　time。　　Thus　the　task　of　the　physical　evolutionist　is　to　determine　the　forms　of　bifurcation；　at　which　he　must；　as　it　were；　change　carriages　in　the　evolutionary　journey　so　as　always　to　follow　the　stable　route。　　He　must　besides　be　able　to　indicate　some　natural　process　which　shall　correspond　in　effect　to　the　ideal　arrangement　of　the　several　types　of　motion　in　families　with　gradually　changing　specific　differences。　　Although；　as　we　shall　see　hereafter；　it　may　frequently　or　even　generally　be　impossible　to　specify　with　exactness　the　forms　of　bifurcation　in　the　process　of　evolution；　yet　the　conception　is　one　of　fundamental　importance。

The　ideas　involved　in　this　sketch　are　no　doubt　somewhat　recondite；　but　I　hope　to　render　them　clearer　to　the　non…mathematical　reader　by　homologous　considerations　in　other　fields　of　thought　（I　considered　this　subject　in　my　Presidential　address　to　the　British　Association　in　1905；　〃Report　of　the　75th　Meeting　of　the　British　Assoc。〃　（S。　Africa；　1905）；　London；　1906；　page　3。　　Some　reviewers　treated　my　speculations　as　fanciful；　but　as　I　believe　that　this　was　due　generally　to　misapprehension；　and　as　I　hold　that　homologous　considerations　as　to　stability　and　instability　are　really　applicable　to　evolution　of　all　sorts；　I　have　thought　it　well　to　return　to　the　subject　in　the　present　paper。）；　and　I　shall　pass　on　thence　to　illustrations　which　will　teach　us　something　of　the　evolution　of　stellar　systems。

States　or　governments　are　organised　schemes　of　action　amongst　groups　of　men；　and　they　belong　to　various　types　to　which　generic　names；　such　as　autocracy；　aristocracy　or　democracy；　are　somewhat　loosely　applied。　　A　definite　type　of　government　corresponds　to　one　of　our　types　of　motion；　and　while　retaining　its　type　it　undergoes　a　slow　change　as　the　civilisation　and　character　of　the　people　change；　and　as　the　relationship　of　the　nation　to　other　nations　changes。　　In　the　language　used　before；　the　government　belongs　to　a　family；　and　as　time　advances　we　proceed　through　the　successive　members　of　the　family。　　A　government　possesses　a　certain　degree　of　stability　hardly　measurable　in　numbers　howeverto　resist　disintegrating　influences　such　as　may　arise　from　wars；　famines；　and　internal　dissensions。　　This　stability　gradually　rises　to　a　maximum　and　gradually　declines。　　The　degree　of　stability　at　any　epoch　will　depend　on　the　fitness　of　some　leading　feature　of　the　government　to　suit　the　slowly　altering　circumstances；　and　that　feature　corresponds　to　the　characteristic　denoted　by　a　in　the　physical　problem。　　A　time　at　length　arrives　when　the　stability　vanishes；　and　the　slightest　shock　will　overturn　the　government。　　At　this　stage　we　have　reached　the　crisis　of　a　point　of　bifurcation；　and　there　will　then　be　some　circumstance；　apparently　quite　insignificant　and　almost　unnoticed；　which　is　such　as　to　prevent　the　occurrence　of　anarchy。　　This　circumstance　or　condition　is　what　we　typified　as　b。　　Insignificant　although　it　may　seem；　it　has　started　the　government　on　a　new　career　of　stability　by　imparting　to　it　a　new　type。　　It　grows　in　importance；　the　form　of　government　becomes　obviously　different；　and　its　stability　increases。　　Then　in　its　turn　this　newly　acquired　stability　declines；　and　we　pass　on　to　a　new　crisis　or　revolution。　　There　is　thus　a　series　of　〃points　of　bifurcation〃　in　history　at　which　the　continuity　of　political　history　is　maintained　by　means　of　changes　in　the　type　of　government。　　These　ideas　seem；　to　me　at　least；　to　give　a　true　account　of　the　history　of　states；　and　I　contend　that　it　is　no　mere　fanciful　analogy　but　a　true　homology；　when　in　both　realms　of　thought　the　physical　and　the　politicalwe　perceive　the　existence　of　forms　of　bifurcation　and　of　exchanges　of　stability。

Further　than　this；　I　would　ask　whether　the　same　train　of　ideas　does　not　also　apply　to　the　evolution　of　animals？　　A　species　is　well　adapted　to　its　environment　when　the　individual　can　withstand　the　shocks　of　famine　or　the　attacks　and　competition　of　other　animals；　it　then　possesses　a　high　degree　of　stability。　　Most　of　the　casual　variations　of　individuals　are　indifferent；　for　they　do　not　tell　much　either　for　or　against　success　in　life；　they　are　small　oscillations　which　leave　the　type　unchanged。　　As　circumstances　change；　the　stability　of　the　species　may　gradually　dwindle　through　the　insufficiency　of　some　definite　quality；　on　which　in　earlier　times　no　such　insistent　demands　were　made。　　The　individual　animals　will　then　tend　to　fail　in　the　struggle　for　life；　the　numbers　will　dwindle　and　extinction　may　ensue。　　But　it　may　be　that　some　new　variation；　at　first　of　insignificant　importance；　may　just　serve　to　turn　the　scale。　　A　new　type　may　be　formed　in　which　the　variation　in　question　is　preserved　and　augmented；　its　stability　may　increase　and　in　time　a　new　species　may　be　produced。

At　the　risk　of　condemnation　as　a　wanderer　beyond　my　province　into　the　region　of　biological　evolution；　I　would　say　that　this　view　accords　with　what　I　understand　to　be　the　views　of　some　naturalists；　who　recognise　the　existence　of　critical　periods　in　biological　history　at　which　extinction　occurs　or　which　form　the　starting…point　for　the　formation　of　new　species。　　Ought　we　not　then　to　expect　that　long　periods　will　elapse　during　which　a　type　of　animal　will　remain　almost　constant；　followed　by　other　periods；　enormously　long　no　doubt　as　measured　in　the　life　of　man；　of　acute　struggle　for　existence　when　the　type　will　change　more　rapidly？　　This　at　least　is　the　view　suggested　by　the　theory　of　stability　in　the　physical　universe。　　（I　make　no　claim　to　extensive　reading　on　this　subject；　but　refer　the　reader　for　example　to　a　paper　by　Professor　A。A。W。　Hubrecht　on　〃De　Vries's　theory　of　Mutations〃；　〃Popular　Science　Monthly〃；　July　1904；　especially　to　page　213。）

And　now　I　propose　to　apply　these　ideas　of　stability　to　the　theory　of　stellar　evolution；　and　finally　to　illustrate　them　by　certain　recent　observations　of　a　very　remarkable　character。

Stars　and　planets　are　formed　of　materials　whic