uss　this　very　obscure　point；　which　raises　the　whole　question　of　the　supernatural　and　all　the　problems　of　the　hereafter。　The　only　important　thing　to　observe　is　that　at　one　time　it　is　man　who　transmits　his　terror；　his　perception　or　his　idea　of　the　invisible　to　the　animal　and　at　another　the　animal　which　transmits　its　sensations　to　man。　We　have　here；　therefore；　intercommunications　which　spring　from　a　deeper　common　source　than　any　that　we　know　and　which；　to　issue　from　it　or　go　back　to　it；　pass　through　other　channels　than　those　of　our　customary　senses。　Now　all　this　belongs　to　that　unexplained　sensibility；　to　that　secret　treasure；　to　that　as　yet　undetermined　psychic　power　which；　for　lack　of　a　better　term；　we　call　subconsciousness　or　subliminal　consciousness。　Moreover；　it　is　not　surprising　that　in　the　animals；　these　subliminal　faculties　not　only　exist；　but　are　perhaps　keener　and　more　active　than　in　ourselves；　because　it　is　our　conscious　and　abnormally　individualized　life　that　atrophies　them　by　relegating　them　to　a　state　of　idleness　wherein　they　have　fewer　and　fewer　opportunities　of　being　exercised；　whereas　in　our　brothers　who　are　less　detached　from　the　universe；　consciousnessif　we　can　give　that　name　to　a　very　uncertain　and　confused　notion　of　the　egois　reduced　to　a　few　elementary　actions。　They　are　much　less　separated　than　ourselves　from　the　whole　of　the　circumambient　life　and　they　still　possess　a　number　of　those　more　general　and　indeterminate　senses　whereof　we　have　been　deprived　by　the　gradual　encroachment　of　a　narrow　and　intolerant　special　faculty；　our　intelligence。　Among　these　senses　which　up　to　the　present　we　have　described　as　instincts；　for　wantand　it　is　becoming　a　pressing　wantof　a　more　suitable　and　definite　word；　need　I　mention　the　sense　of　direction；　migration；　foreknowledge　of　the　weather；　of　earthquakes　and　avalanches　and　many　others　which　we　doubtless　do　not　even　suspect？　Does　all　this　not　belong　to　a　subconsciousness　which　differs　from　ours　only　in　being　so　much　richer？
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  I　am　fully　aware　that　this　explanation　by　means　of　the　subliminal　consciousness　will　not　explain　very　much　and　will　at　most　invoke　the　aid　of　the　unknown　to　illuminate　the　incomprehensible。　But　to　explain　a　phenomenon；　a　Dr。　J。　de　Modzelwski　very　truly　says；　〃is　to　put　forward　a　theory　which　is　more　familiar　and　more　easily　comprehensible　to　us　than　the　phenomenon　at　issue。〃　This　is　really　what　we　are　constantly　and　almost　exclusively　doing　in　physics；　chemistry；　biology　and　in　every　branch　of　science　without　exception。　To　explain　a　phenomenon　is　not　necessarily　to　make　it　as　clear　and　lucid　as　that　two　and　two　are　four；　and；　even　so；　the　fact　that　two　and　two　are　four　is　not；　when　we　go　to　the　bottom　of　things；　as　clear　and　lucid　as　it　seems。　What　in　this　case；　as　in　most　others；　we　wrongfully　call　explaining　is　simply　confronting　the　unexpected　mystery　which　these　horses　offer　us　with　a　few　phenomena　which　are　themselves　unknown；　but　which　have　been　perceived　longer　and　more　frequently。　And　this　same　mystery；　thus　explained；　will　serve　one　day　to　explain　others。　It　is　in　this　way　that　science　goes　to　work。　We　must　not　blame　it：　it　does　what　it　can；　and　it　does　not　appear　that　there　are　other　ways。
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  If　we　assent　to　this　explanation　by　means　of　the　subliminal　consciousness；　which　is　a　sort　of　mysterious　participation　in　all　that　happens　in　this　world　and　the　others；　many　obstacles　disappear　and　we　enter　into　a　new　region　in　which　we　draw　strangely　nearer　to　the　animals　and　really　become　their　brothers　by　closer　links；　perhaps　the　only　essential　links　in　life。　They　take　part　from　that　moment　in　the　great　human　problems；　in　the　extraordinary　actions　of　our　unknown　guest；　and；　if；　since　we　have　been　observing　the　indwelling　force　more　attentively；　nothing　any　longer　surprises　us　of　that　which　it　realizes　in　us；　no　more　should　anything　surprise　us　of　that　which　it　realizes　in　them。　We　are　on　the　same　plane　with　them；　in　some　as　yet　undetermined　element；　when　it　is　no　longer　the　intelligence　that　reigns　alone；　but　another　spiritual　power；　which　pays　no　heed　to　the　brain；　which　passes　by　other　roads　and　which　might　rather　be　the　psychic　substance　of　the　universe　itself；　no　longer　set　in　grooves；　isolated　and　specialized　by　man；　but　diffused；　multiform　and　perhaps；　if　we　could　trace　it；　equal　in　everything　that　exists。
  There　is；　henceforth；　no　reason　why　the　horses　should　not　participate　in　most　of　the　mediumistic；　phenomena　which　we　find　existing　between　man　and　man；　and　their　mystery　ceases　to　be　distinct　from　those　of　human　metaphysics。　If　their　subliminal　is　akin　to　ours；　we　can　begin　by　extending　to　its　utmost　limits　the　telepathic　theory；　which　has；　so　to　speak；　no　limits；　for；　in　the　matter　of　telepathy；　as　Myers　has　said；　all　that　we　are　permitted　to　declare　is　that　〃life　has　the　power　of　manifesting　itself　to　life。〃　We　may　ask　ourselves；　therefore；　if　the　problem　which　I　set　to　the　horse；　without　knowing　the　terms　of　it；　is　not　communicated　to　my　subliminal；　which　is　ignorant　of　it；　by　that　of　the　horse；　who　has　read　it。　It　is　practically　certain　that　this　is　possible　between　human　subliminals。　Is　it　I　who　see　the　solution　and　transmit　it　to　the　horse；　who　only　repeats　it　to　me？　But；　suppose　that　it　is　a　problem　which　I　myself　am　incapable　of　solving？　Whence　does　the　solution　come；　then？　I　do　not　know　if　the　experiment　has　been　attempted；　under　the　same　conditions；　with　a　human　medium。　For　that　matter；　if　it　succeeded；　it　would　be　very　much　the　same　as　the　no　less　subliminal　phenomenon　of　the　arithmetical　prodigies；　or　lightning　calculators；　with　which；　in　this　rather　superhuman　atmosphere；　we　are　almost　forced　to　compare　the　riddle　of　the　mathematical　horses。　Of　all　the　interpretations；　it　is　the　one　which；　for　the　moment；　appears　to　me　the　least　eccentric　and　the　most　natural。
  We　have　seen　that　the　gift　of　handling　colossal　figures　is　almost　foreign　to　the　intelligence　proper；　one　can；　even　declare　that；　in　certain　cases；　it　is　evidently　and　completely　independent　of　such　intelligence。　In　these　cases；　the　gift　is　manifested　prior　to　any　education　and　from　the　earliest　years　of　childhood。　If　we　refer　to　the　list　of　arithmetical　prodigies　given　by　Dr。　Scripure；＇1＇　we　see　that　the　faculty　made　its　appearance　in　Ampere　at　the　age　of　three；　in　Colburn　at　six；　in　Gauss　at　three；　in　Mangiamele　at　ten；　in　Safford　at　six；　in　Whateley　at　three；　and　so　on。　Generally；　it　lasts　for　only　a　few　years；　becoming　rapidly　enfeebled　with　age　and　usually　vanishing　suddenly　at　the　moment　when　its　possessor　begins　to　go　to　school。
  ＇1＇　American　Journal　of　Psychology；　1　April　1891。
  When　you　ask　those　children　and　even　most　of　the　lightning　calculators　who　have　come　to　man's　estate　how　they　go　to　work　to　solve　the　huge　and　complicated　problems　set　them；　they　reply　that　they　know　nothing　about　it。　Bidder；　for　instance；　declares　that　it　is　impossible　for　him　to　say　how　he　can　instinctively　tell　the　logarithm　of　a　number　consisting　of　seven　or　eight　figures。　It　is　the　same　with　Safford；　who；　at　the　age　of　ten；　used　to　do　in　his　head；　without　ever　making　a　mistake；　multiplication…sums　the　result　of　which　ran　into　thirty…six　figures。　The　solution　presents　itself　authoritatively　and　spontaneously；　it　is　a　vision；　an　impression；　an　inspiration；　an　intuition　coming　one　knows　not　whence；　suddenly　and　indubitably。　As　a　role；　they　do　not　even　try　to　calculate。　Contrary　to　the　general　belief；　they　have　no　peculiar　methods；　or；　if　method　there　be；　it　is　more　a　practical　way　of　subdividing　the　intuition。　One　would　think　that　the　solution　springs　suddenly　from　the　very　enunciation　of　the　problem；　in　the　same　way　as　a　veridical　hallucination。　It　appears　to　rise；　infallible　and　ready…done；　from　a　sort　of　eternal　and　cosmic　reservoir　wherein　the　answers　to　every　question　lie　dormant。　It　must；　therefore；　be　admitted　that　we　have　here　a　phenomenon　that　occurs　above　or　below　the　brain；　by　the　side　of　the　consciousness　and　the　mind；　outside　all　the　intellectual　methods　and　habits；　and　it　is　precisely　for　phenomena　of　this　kind　that　Myers　invented　the　word　〃subliminal。〃＇1＇
  ＇1＇　I　have　no　need　to　recall　the　derivation　of　the　term　subliminal：　beneath　（sub）　the　threshold　（limen）　of　consciousness。　Let　us　add；　as　M。　de　Vesme　very　rightly　remarks；　that　the　subliminal　is　not　exactly　what　classical　psychology　calls　the　subconsciousness；　which　latter　records　only　notions　that　are　normally　perceived　and　possesses　only　normal　faculties；　that　is　to　say；　faculties　recognized　to…day　by　orthodox　science。
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  Does　not　all　this　bring　us　a　little　nearer　to　our　calculating　horses？　From　the　moment　that　it　is　demonstrated　that　the　solution　of　a　mathematical　problem　no　longer　depends　exclusively　on　the　brain；　but　on　another　faculty；　another　spiritual　power　whose　presence　under　various　forms　has　been　ascertained　beyond　a　doubt　in　certain　animals；　it　ceases　to　be　wholly　rash　or　extravagant　to　suggest　that　perhaps；　in　the　horse；　the　same　phenomenon　is　reproduced　and　developed　in　the　same　unknown；　wherein　moreover　the　mysteries　of　numbers　and　those　of　subconsciousness　mingle　in　a　like　darkness。　I　am　well　aware　that　an　explanation　laden　to　such　an　extent　with　mysteries　explains　but　very　little　more　tha