可做指數(shù)函數(shù)引入視頻十的冪課件

Letusgoonajourneyintheuniverse,jumpingthedistancesinPowersof10.讓我們開(kāi)始宇宙發(fā)現(xiàn)之旅，借由10的N次方，跨越由近到遠(yuǎn)，由遠(yuǎn)到近的距離，開(kāi)始對(duì)宇宙宏觀和微觀的旅程Westartatatdistanceof1meter,thenwewillincreasebythepowerof10eachtime.Wewillproceedtothelimitsofourimagination,inthedirectionofthemacrocosm.我們先從1米的距離開(kāi)始，然后每次按10的開(kāi)方，由小到大看宏觀世界，直到我們?nèi)祟?lèi)思維可以想象的盡頭Then,wewillsetoutagainreturningtothestartingpoint.Then,fromtherewewillbeginavoyagetowardstheinfinitelysmallmicrocosm.然后，我們?cè)倩氐狡瘘c(diǎn)，這次，按10的負(fù)開(kāi)方，由大到小看微觀世界Observethelawsoftheuniverseandreflectonyourhumancondition...從中我們觀察宇宙的規(guī)律，反觀我們?nèi)说臓顩rLetusgoonajourneyinthe1Bonvoyage!旅途愉快！Bonvoyage!2Thisiswhatweseeunderoureyes:someleaves...我們視線所及的是一些樹(shù)葉…1001metre1米Thisiswhatweseeunderour3Thevoyagestarts:onemovesawayfromtheprettyleavesandoneseesthetrees...發(fā)現(xiàn)之旅開(kāi)始：視線挪到10米遠(yuǎn)的地方，看到的不再是漂亮的葉片，而是樹(shù)…101

10metres10米Thevoyagestarts:onemovesa4Atthisdistance,oneseesthetrees,thebuildings...在這個(gè)距離，視線看到的是樹(shù)林，還有建筑物…102100metres100米

Atthisdistance,oneseesthe5Nowwechangetokilometers!Fromhereonecanjumpinaparachute!現(xiàn)在視線距離是1公里，這么高的地方都可以跳傘了！1031km1000米Nowwechangetokilometers!6Hereweseeacity.Butonecannotdistinguishthedistrictswell...此刻，我們看到了城市。但是不能清楚地分辨城市里的不同地區(qū)…10410km10公里Hereweseeacity.Butoneca7ThisdistancemakesitpossibletoincludeallthestateofFlorida!100公里的距離，可以將整個(gè)Florida州盡收眼底！105100km100公里Thisdistancemakesitpossibl8Asseenbysatellite!從衛(wèi)星上觀察到的!1061.000km

1000公里Asseenbysatellite!1069Theblueplanet...Oneseesthecontinents,theclouds,thesea...藍(lán)色的星球…看到大陸，看到云和?！?0710.000km1萬(wàn)公里Theblueplanet...Oneseesth10Lostinspace...消失在宇宙中…108100.000km10萬(wàn)公里L(fēng)ostinspace...10811OnecanseetheorbitofthemoonaroundtheEarth...看到月亮圍繞地球運(yùn)轉(zhuǎn)的軌道…1091millionkm100萬(wàn)公里Onecanseetheorbitofthem12PartoftheorbitoftheEarthinblue...一片藍(lán)色中地球的部分運(yùn)轉(zhuǎn)軌道…101010Millionkm1000萬(wàn)公里PartoftheorbitoftheEarth131011100millionkm1億公里Orbitsof:Venus,EarthandMars.金星、地球和火星的運(yùn)轉(zhuǎn)軌道…1011Orbitsof:Venus,Earthan14Orbitsof:Mercury,Venus,Earth,MarsandJupiter.水星，金星，地球，火星和木星的運(yùn)轉(zhuǎn)軌道。1012

1billionkm10億公里

Orbitsof:Mercury,Venus,Ear15Atthisdistance,weseeallthesolarsystem…此刻看到整個(gè)太陽(yáng)系…101310billionkm100億公里Atthisdistance,weseeallt161014

100billionkm1000億公里Oursolarsystemstarts"todisappear"inspace...此刻太陽(yáng)系開(kāi)始從我們視線中漸遠(yuǎn)，消失在宇宙中…1014Oursolarsystemstarts"17Oursunisonlyonestaramongsomanyothers...我們的太陽(yáng)系在這么多星系中此刻看上去象顆星星…10151trillionkm1萬(wàn)億公里Oursunisonlyonestaramong18Wechangetolight-years:howtinyoursunis!1光年的距離:此刻看到我們的太陽(yáng)系是多么的渺?。?0161light-year1光年Wechangetolight-years:how19Hereoneseesonlyinfinitesky...此刻我們看到的是無(wú)限的星空…101710light-years10光年Hereoneseesonlyinfinitesk20NothingotherthanthenebulasoftheMilkyWay...看到的全是銀河中的云翳，別無(wú)他物…1018100light-years100光年Nothingotherthanthenebulas2110191,000light-years1000光年Atthisdistanceweseedeepspace...此刻看到的是深遠(yuǎn)的宇宙…1019Atthisdistanceweseede22Wecontinueour"voyage"intheMilkyWay...繼續(xù)我們?cè)阢y河中的旅程…102010,000light-years1萬(wàn)光年Wecontinueour"voyage"inth23WearriveatthebordersoftheMilkyWay.我們現(xiàn)在到達(dá)了銀河的邊界。1021100,000light-years10萬(wàn)光年Wearriveatthebordersofth24Ourgalaxyandothers...我們的銀河系，和其它的星系…10221Millionlight-years100萬(wàn)光年Ourgalaxyandothers...102225Vastness,infinity...thegalaxiesarecomprisedonlyofsmallthingsand,betweenthem,“empty”spaces.Everywherethesamelawgovernsallthebodiesoftheuniverse.廣袤，無(wú)限…星系都是由更小的星系組成，彼此之間是空無(wú)一物的空間。這個(gè)規(guī)律適用于宇宙中的任何物體。Weareveryfarawayindeed...butletusreturnquicklytoourMotherEarth.我們?cè)诼贸讨写丝套叩煤苓h(yuǎn)很遠(yuǎn)…現(xiàn)在，讓我們回到地球。1023-10millionlight-years

1000萬(wàn)光年Vastness,infinity...thegal26102210222710211021281020102029101910193010181018311017101732101610163310151015341014101435101310133610121012371011101138101010103910910940108WecanseetheEarth!!!我們看到了地球!!!108WecanseetheEarth!!!41107Ourhumanraceisconcentratedonthissmallblueplanet...人類(lèi)都集中生活在這個(gè)看起來(lái)小小的藍(lán)色星球上…107Ourhumanraceisconcentra42106Thelawsofnatureareidenticalintwodirections…goingouttothemacrocosm,andcomingintowardsthemicrocosm自然規(guī)律在正反兩個(gè)方向上都是相似的…無(wú)論是宏觀向外擴(kuò)張，還是微觀向內(nèi)縮小106Thelawsofnatureareiden43105YousawtheEarthlostinspace...我們看到地球消失在宇宙中…105YousawtheEarthlostins44104Existentialquestionsemerge:whoarewe,fromwheredocome,wherearewegoing...???存在的問(wèn)題開(kāi)始冒出來(lái)：我們是誰(shuí)，來(lái)自哪里，去向哪里…???104Existentialquestionsemerg45103Whatisthemeaningoftheuniverse?宇宙存在的意義是什么？103Whatisthemeaningofthe46102Whatavoyage!多么奇妙的旅程！102Whatavoyage!47101Now,let’sproceedtowardssmallerandsmallerdimensionsofspace

現(xiàn)在，讓我們從起點(diǎn)上開(kāi)始相反方向的旅程，開(kāi)始微觀世界的旅程101Now,let’sproceedtowards48Ourpointofdeparture...Remember?還記得嗎？我們的旅程是從這里開(kāi)始的…100Ourpointofdeparture...10049Itisanoakleaf.這是片橡樹(shù)葉子。10-110Centimetres10厘米Itisanoakleaf.10-150Onecanobservethedetailsoftheveinsoftheleaf.可以觀察到葉脈的清晰紋路。10-21Centimetre1厘米Onecanobservethedetailsof51CellularStructures...細(xì)胞組成的結(jié)構(gòu)…10-31Millimetre1毫米CellularStructures...10-352Thecellsarevisible...細(xì)胞開(kāi)始可見(jiàn)…10-4100microns100微米Thecellsarevisible...10-453Let’smovetowardstheinteriorofthecell...開(kāi)始進(jìn)入細(xì)胞的內(nèi)部…10-510microns10微米Let’smovetowardstheinterio54Thenucleusofanindividualcell…單個(gè)細(xì)胞的核…10-61micron1微米Thenucleusofanindividualc55Onthissmallerscale,onecanseethechromosomes...現(xiàn)在可以看到染色體…10-71,000Angstroms1000埃Onthissmallerscale,onecan56Inthismicroscopicuniverse,onecanseethechainsofDNA...在顯微鏡下，看到的DNA鏈…10-8100Angstroms100埃Inthismicroscopicuniverse,57Fascinating!如此讓人著迷，不可置信!10-910Angstroms10埃Fascinating!10-958"Clouds"ofelectronsinacarbonatom,withlotsofemptyspace.碳原子內(nèi)的電子云，中間是許多的空間。Everythinginourworldismadeinthisway.Notetheresemblancebetweenmacroandmicrocosm!世界的事物都是如此構(gòu)成的?？纯次⒂^和宏觀世界的相似之處。10-101Angstrom1埃"Clouds"ofelectronsinacar59Inthisinfinitelysmallworld,onecannotetheelectronsinthefieldoftheatom...Thisislikethenumerousbodiesinthesky!在這個(gè)無(wú)限縮小的世界中，我們看到原子中的眾多電子…就象星空中的無(wú)數(shù)星體！10-1110picometres10皮米Inthisinfinitelysmallworld60Animmenseemptinessbetweenthenucleusandtheorbitsoftheelectrons...在原子核與電子的軌道之間，是無(wú)限的空間…10-121Picometre1皮米Animmenseemptinessbetweent61Thismeasurementscaleappliestothesizeofthenucleusofanatom.現(xiàn)在看到的是原子中的原子核。10-13100Femtometre100飛米Thismeasurementscaleapplies62Wehaveasinglecarbonatom!看到一個(gè)單個(gè)的碳原子！10-1410Femtometres10飛米Wehaveasinglecarbonatom!63Weareintherealmofscientificimagination:facetofacewithaproton!現(xiàn)在進(jìn)到科學(xué)發(fā)現(xiàn)的深處：原子核中的質(zhì)子！10-151Femtometre1飛米Weareintherealmofscienti64Let’sexaminetheparticlescalledquarks…看看我們眼前的這個(gè)小顆粒，稱(chēng)為夸克…

Andherewemuststop:Wehavearrivedatthelimitsofscientificknowledge!我們得到此打住了：已經(jīng)來(lái)到了科學(xué)目前已知的極限！10-16100Attometres100阿米Let’sexaminetheparticlesca65Andnow?Doyoualwaysfindthatyouarethenaveloftheworld?Theperfectresultofcreation?現(xiàn)在，想想？你是否總是發(fā)現(xiàn)自己是世界的中心？完美創(chuàng)造的結(jié)晶？Whatexistsbeyondthelimits?Arethereanylimits?Ourvoyageintheinfinitelysmalldimensionstoppedwith100attometresandwiththequarkbecausewedonotknowanymore.Intheory,wecouldhavecontinued...Aninfinitejourneyineitherdirection(macrocosmormicrocosm)!已知的極限之外是什么呢？是否存在極限？我們對(duì)微觀世界的探索到100attometer，夸克上打住了，因?yàn)槲覀兡壳耙阎木偷酱?。理論上，我們本可以繼續(xù)…無(wú)論是微觀還是宏觀方向！Ourimaginationiswithoutlimits...我們的想象是沒(méi)有極限的…Question:arewealoneintheuniverse?問(wèn)題：我們?cè)谟钪嬷惺欠窆陋?dú)存在？Andnow?Doyoualwaysfindth66Letusgoonajourneyintheuniverse,jumpingthedistancesinPowersof10.讓我們開(kāi)始宇宙發(fā)現(xiàn)之旅，借由10的N次方，跨越由近到遠(yuǎn)，由遠(yuǎn)到近的距離，開(kāi)始對(duì)宇宙宏觀和微觀的旅程Westartatatdistanceof1meter,thenwewillincreasebythepowerof10eachtime.Wewillproceedtothelimitsofourimagination,inthedirectionofthemacrocosm.我們先從1米的距離開(kāi)始，然后每次按10的開(kāi)方，由小到大看宏觀世界，直到我們?nèi)祟?lèi)思維可以想象的盡頭Then,wewillsetoutagainreturningtothestartingpoint.Then,fromtherewewillbeginavoyagetowardstheinfinitelysmallmicrocosm.然后，我們?cè)倩氐狡瘘c(diǎn)，這次，按10的負(fù)開(kāi)方，由大到小看微觀世界Observethelawsoftheuniverseandreflectonyourhumancondition...從中我們觀察宇宙的規(guī)律，反觀我們?nèi)说臓顩rLetusgoonajourneyinthe67Bonvoyage!旅途愉快！Bonvoyage!68Thisiswhatweseeunderoureyes:someleaves...我們視線所及的是一些樹(shù)葉…1001metre1米Thisiswhatweseeunderour69Thevoyagestarts:onemovesawayfromtheprettyleavesandoneseesthetrees...發(fā)現(xiàn)之旅開(kāi)始：視線挪到10米遠(yuǎn)的地方，看到的不再是漂亮的葉片，而是樹(shù)…101

10metres10米Thevoyagestarts:onemovesa70Atthisdistance,oneseesthetrees,thebuildings...在這個(gè)距離，視線看到的是樹(shù)林，還有建筑物…102100metres100米

Atthisdistance,oneseesthe71Nowwechangetokilometers!Fromhereonecanjumpinaparachute!現(xiàn)在視線距離是1公里，這么高的地方都可以跳傘了！1031km1000米Nowwechangetokilometers!72Hereweseeacity.Butonecannotdistinguishthedistrictswell...此刻，我們看到了城市。但是不能清楚地分辨城市里的不同地區(qū)…10410km10公里Hereweseeacity.Butoneca73ThisdistancemakesitpossibletoincludeallthestateofFlorida!100公里的距離，可以將整個(gè)Florida州盡收眼底！105100km100公里Thisdistancemakesitpossibl74Asseenbysatellite!從衛(wèi)星上觀察到的!1061.000km

1000公里Asseenbysatellite!10675Theblueplanet...Oneseesthecontinents,theclouds,thesea...藍(lán)色的星球…看到大陸，看到云和?！?0710.000km1萬(wàn)公里Theblueplanet...Oneseesth76Lostinspace...消失在宇宙中…108100.000km10萬(wàn)公里L(fēng)ostinspace...10877OnecanseetheorbitofthemoonaroundtheEarth...看到月亮圍繞地球運(yùn)轉(zhuǎn)的軌道…1091millionkm100萬(wàn)公里Onecanseetheorbitofthem78PartoftheorbitoftheEarthinblue...一片藍(lán)色中地球的部分運(yùn)轉(zhuǎn)軌道…101010Millionkm1000萬(wàn)公里PartoftheorbitoftheEarth791011100millionkm1億公里Orbitsof:Venus,EarthandMars.金星、地球和火星的運(yùn)轉(zhuǎn)軌道…1011Orbitsof:Venus,Earthan80Orbitsof:Mercury,Venus,Earth,MarsandJupiter.水星，金星，地球，火星和木星的運(yùn)轉(zhuǎn)軌道。1012

1billionkm10億公里

Orbitsof:Mercury,Venus,Ear81Atthisdistance,weseeallthesolarsystem…此刻看到整個(gè)太陽(yáng)系…101310billionkm100億公里Atthisdistance,weseeallt821014

100billionkm1000億公里Oursolarsystemstarts"todisappear"inspace...此刻太陽(yáng)系開(kāi)始從我們視線中漸遠(yuǎn)，消失在宇宙中…1014Oursolarsystemstarts"83Oursunisonlyonestaramongsomanyothers...我們的太陽(yáng)系在這么多星系中此刻看上去象顆星星…10151trillionkm1萬(wàn)億公里Oursunisonlyonestaramong84Wechangetolight-years:howtinyoursunis!1光年的距離:此刻看到我們的太陽(yáng)系是多么的渺小！10161light-year1光年Wechangetolight-years:how85Hereoneseesonlyinfinitesky...此刻我們看到的是無(wú)限的星空…101710light-years10光年Hereoneseesonlyinfinitesk86NothingotherthanthenebulasoftheMilkyWay...看到的全是銀河中的云翳，別無(wú)他物…1018100light-years100光年Nothingotherthanthenebulas8710191,000light-years1000光年Atthisdistanceweseedeepspace...此刻看到的是深遠(yuǎn)的宇宙…1019Atthisdistanceweseede88Wecontinueour"voyage"intheMilkyWay...繼續(xù)我們?cè)阢y河中的旅程…102010,000light-years1萬(wàn)光年Wecontinueour"voyage"inth89WearriveatthebordersoftheMilkyWay.我們現(xiàn)在到達(dá)了銀河的邊界。1021100,000light-years10萬(wàn)光年Wearriveatthebordersofth90Ourgalaxyandothers...我們的銀河系，和其它的星系…10221Millionlight-years100萬(wàn)光年Ourgalaxyandothers...102291Vastness,infinity...thegalaxiesarecomprisedonlyofsmallthingsand,betweenthem,“empty”spaces.Everywherethesamelawgovernsallthebodiesoftheuniverse.廣袤，無(wú)限…星系都是由更小的星系組成，彼此之間是空無(wú)一物的空間。這個(gè)規(guī)律適用于宇宙中的任何物體。Weareveryfarawayindeed...butletusreturnquicklytoourMotherEarth.我們?cè)诼贸讨写丝套叩煤苓h(yuǎn)很遠(yuǎn)…現(xiàn)在，讓我們回到地球。1023-10millionlight-years

1000萬(wàn)光年Vastness,infinity...thegal921022102293102110219410201020951019101996101810189710171017981016101699101510151001014101410110131013102101210121031011101110410101010105109109106108WecanseetheEarth!!!我們看到了地球!!!108WecanseetheEarth!!!107107Ourhumanraceisconcentratedonthissmallblueplanet...人類(lèi)都集中生活在這個(gè)看起來(lái)小小的藍(lán)色星球上…107Ourhumanraceisconcentra108106Thelawsofnatureareidenticalintwodirections…goingouttothemacrocosm,andcomingintowardsthemicrocosm自然規(guī)律在正反兩個(gè)方向上都是相似的…無(wú)論是宏觀向外擴(kuò)張，還是微觀向內(nèi)縮小106Thelawsofnatureareiden109105YousawtheEarthlostinspace...我們看到地球消失在宇宙中…105YousawtheEarthlostins110104Existentialquestionsemerge:whoarewe,fromwheredocome,wherearewegoing...???存在的問(wèn)題開(kāi)始冒出來(lái)：我們是誰(shuí)，來(lái)自哪里，去向哪里…???104Existentialquestionsemerg111103Whatisthemeaningoftheuniverse?宇宙存在的意義是什么？103Whatisthemeaningofthe112102Whatavoyage!多么奇妙的旅程！102Whatavoyage!113101Now,let’sproceedtowardssmallerandsmallerdimensionsofspace

現(xiàn)在，讓我們從起點(diǎn)上開(kāi)始相反方向的旅程，開(kāi)始微觀世界的旅程101Now,let’sproceedtowards114Ourpointofdeparture...Remember?還記得嗎？我們的旅程是從這里開(kāi)始的…100Ourpointofdeparture...100115Itisanoakleaf.這是片橡樹(shù)葉子。10-110Centimetres10厘米Itisanoakleaf.10-1116Onecanobservethedetailsoftheveinsoftheleaf.可以觀察到葉脈的清晰紋路。10-21Centimetre1厘米Onecanobservethedetailsof117CellularStructures...細(xì)胞組成的結(jié)構(gòu)…10-31Millimetre1毫米CellularStructures...10-3118Thecellsarevisible...細(xì)胞開(kāi)始可見(jiàn)…10-4100microns100微米Thecellsarevisible...10-4119Let’smovetowardstheinteriorofthecell...開(kāi)始進(jìn)入細(xì)胞的內(nèi)部…10-510microns10微米Let’smovetowardstheinterio120Thenucleusofanindividualcell…單個(gè)細(xì)胞的核…10-61micron1微米Thenucleusofanindividualc121Onthissmallerscale,onecanseethechromosomes...現(xiàn)在可以看到染色體…10-71,000Angstroms1000埃Onthissmallerscale,onecan122Inthismicroscopicuniverse,onecanseethechainsofDNA...在顯微鏡下，看到的DNA鏈…10-8100Angstroms100埃Inthismicroscopicuniverse,123Fascinating!如此讓人著迷，不可置信!10-910Angstroms10埃Fascinating!10-9124"Clouds"ofelectronsinacarbonatom,withlotsofemptyspace.碳原子內(nèi)的電子云，中間是許多的空間。Everythinginourworldismadeinthisway.Notetheresemblancebetweenmacroandmicrocosm!世界的事物都是如此構(gòu)成的?？纯次⒂^和宏觀世界的相似之處。10-101Angstrom1埃"Clouds"ofelectronsinacar125Inthisinfinitelysmallworld,onecannotetheelect