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21.11.15, ˿202111º
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飬һ˵ձйá˵ԵȻã
⻵һ棬һձйĴæձռй
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ΣӵӵĪDemocracy롰͡ӵ
˹Science롰ѧͬʱΪҪӵǵ㲻ò
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ת飺ȻŽ䣬磬ԡɻ
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Ӧת÷ɿ죬ټ򵥲ҮҮ
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˵

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ɻ˼Ӣ߸߿գתƽȵԶģʽ

λϣɻһСʱˣһֱûн̸

˯ˣΣμǻ¼ܼܵ
ܵڳӱ߳ܵ͡ܣôԣ
ܵ˵Ȼ˸ƣվȥ
ңϱԲӵױ̨ǰϸĻױеضԵϱ˵
ͣٴ粻٣򶹽ˣðθᡣϵϱǺ
ȳ԰ɣûŪأ˾ˣȣĲء
ˣػת

ȻеΣǰʵ﷢
ңڸʵ飬ͥģ
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ҵչҵ񣬵ǵܵܲΪߣӣΪǺרҵ
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˳Ȼ˫ǩ֣ǺԼʵ޸ģԤߴ
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ҵίļԼ̸ǶԼͼԼ̸̸ɫ䡣Ŷ
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ʱ㲥ﴫսMH370Ļ
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ȻҲͻȻϣʧȥ򣬻߸ң֪ȥ
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εдգ

оֽϵķ棬ɷķʣЦѽһ
׵ģ߼⡣ϲ߼ˣҿκκ඼ݶģն
Ҫġ̤ʵصӣձЩ޿޲ɵ
ճ;ܶô鼦ôĩ֪㹢ڻ
ԸʹȻӳĲķ衣

ľ߲ƷĹ˸ǡ

ҴسĬ

һ죬ľ뱸ˣοʼдС˵ͷľ
ֻܽصҶǸ¾ɹ۵㣬Ǿǣƽ
Ȥ£Ŀ׷ѻֻͣʣܿ
򣬡ǲʵǡ塯߰桯
ҲЩС˵쿪˼ģջǵͷػصԼ
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߼ͥMݱĽǣŮԽԽ
ƢеԽԽ˳ܣʵ˵ǣڵͬΣŮԽ
Խ͸ˡ

Ƶ⣬ǷҲ͸дˣ


Ȱԭ֮the Beatlesƪ

 Yiren

һû磬ʹ尾Ŀ޷Ȱ
ԭּVideoʱʱػҷʧ
Ȼֲ֣ܹкܿػҼŬ
ǰĶ֣Ҹ̵ȥø
кдҵҼǵԭ֣
빲־߹֮

ȽһȰҡֶ - the Beatles    

ӢֵJohn Lennon, Paul McCartney, George Harrison
Ringo Starr (ԭRichard Starkey) 20ҵDebute磬ٵ
ŲʮֶӵĽɢٵLennon 40ꡢHarrison 58Ӣٵ
ֻʣ½ʮMcCartneyStarrΪһͷβthe Beatles
ԣĸˣֻVideoȻݳʱ
Ÿоthe BeatlesԶഺפĻҵ

Ϊһʮֶӣй˿ֻܶϵ˵
ȥ˽the BeatlesĸThe Beatlesԭĸ
188 [1]󲿷ֶӺLennonMcCartneyһ (
˵Ĵָʲ)Ĺ׾עLennon-McCartney⣬
Harrison25ףStarr2 ϲ¼
the Beatlesĸ78ףÿȥвųʱÿҹ˾˼ʱ
ÿʱҾͻ78׸ѭҵȥ
Ҫthe BeatlesĴԸthe BeatlesԱȡõĳɾͺ
the BeatlesɢԱķչ

һThe BeatlesĴԸ

1.  

The Beatles 裬ѵǵഺɶɣǵļͿȡ
The New York TimesJeannette Catsoulis2015귢ڸñ
һƪ The Beatles Awaken a New Sensation ô1964
the Beatlesݳʱܵ: һthe Beatlesݳ
ϣһҵԸ߳ģʱഺǰڵô֪? ǸԽ
˶֮ǰͻûгֵʱ֪Ϊ I want to hold your 
hand ǰ߾硱 [2]

(1) I want to hold your hand

һLennonMcCartney1963һһݳȼഺ
ɵ衣ȥաʡãҲHarrison
LennonļMcCartneyı˹StarrĻһг
Ϊthe Beatlesȫĵ [3]Rolling Stones 2004/2010
500 ʼΰĸ16 [4]

(2) She loves you 

׸LennonMcCartney1963һһHarrison
鳪һ׺ܲѰĸΪһ˼裬ϻöԴһ
˼ǣҡ⣬׸ѰĵطǸĲдΪ
ϲ˵İΪһмȥһֲһİ飬


You think you lost your love,
Well, I saw her yesterday.
It's you she's thinking of C
And she told me what to say.
She says she loves you ...
You hurt her
She didn't know why
It wasn't your fault
And didn't turn around
Oh yes she loves you
Because with you alone she can only be happy...

˸the BeatlesӢߵĵҲ60
ߵĵ [5]Rolling Stones 2004/2010500 ʼ
ΰĸУ64 [4]

(3) I should have known better

һLennon1964굥McCartneyһݳ衣
ȥǳĻãHarrison߳ļ׸
ϲthe BeatlesһֳVideoУĸ˶件ıţ
Lennonм仹٣McCartneyʱȥбһLennonԱϴ
Ľ࣬HarrisonҲޱȵһһߵļthe 
BeatlesԱһֳݵһVideoȤǣڸVideoĩβ
һԣҵthe Beatlesıݣ־ʱ
򣬷Լһһthe Beatles
ľ硣

(4) And I love her

һMcCartney1964굥һ衣McCartney
ĸӻļĻİöMcCartneyΪ
һ״Լ [6]

(5) When I am sixty-four 

һMcCartney195614ʱ1967깫
ĸ [7]СӵԸܺϲһ𲢱ϡ
McCartneyȥ滺öStarrгĻִһ
˿˺ǣҡҺϲ׸裬Ҳ뵽the BeatlesλԱ
ûл64꣬һ˿ĺ͸̾

(6) Yesterday

McCartney1965굥༪ݳһԴ˸е
裬Ҳthe BeatlesĵһSoloݵĸָ
˶ˣȻУг2200汾Ϊ¼ʷ
ĸ [8]1999BBC radioбͶƱΪ20Ѹ 
[8]Rolling Stones 2004/2010500 ʼΰĸУ
13 [4]McCartneythe Beatle׸
McCartneyεʱ˼ɣڸǰ
 [8]дʱҲˣ˯ʱεµ뷨ϱ


2. HarrisonֶʱĴ

Harrisonֶһ (LennonStarrС3꣬McCartneyС1
)the Beatlesʱڵִ͸質Ż󲿷ʱLennon
McCartneyλڸǣ˵Լֶ  ĸ֡
ֶʱĸ C While my guitar gently 
weeps  Something׸Rolling Stones 2004/2010
500 ʼΰĸ񵥣ֱе136͵278 [4]ͬʱҲ
Rolling Stones 2010the BeatlesʼTop 10 [9]

(1) While my guitar gently weeps

׸Harrison1968굥ģԴй
׾HarrisonĸҵһοⱾ鲢Ķ󣬷
򵽵ĶĻܵȴ෴ [10]:

...I look at the floor and I see it needs sweeping
Still my guitar gently weeps.
I don't know why nobody told you
How to unfold your love
I don't know how someone controlled you
They bought and sold you...
With every mistake we must surely be learning
Still my guitar gently weeps
I don't know how you were diverted
You were perverted too
I don't know how you were inverted.

׸贫粢ûʵĻʧ˵ 
"The love there that's sleeping"ȥޱȵöͬʱִ
һ˿ʧ͸ˣϲthe Beatles֮һ⣬׸Rolling 
Stones 2008100 ʼΰļ7 [11]

(2) Something

һHarrison1969굥裬ʷѧ
Ϊ׸ӳHarrisonִˮƽܹLennonMcCartney [12]
ʱHarrisonPattieLennonYoko, McCartneyLinda
StarrMaureenڶĻСȥ滺Ŷڣ
ʺʱڵŮ׸150ҷthe Beatles 
Yesterday ֮ĵڶױĸBroadcast Music 
Incorporatedг20ͱ෭ĸ17ͬʱIvor 
Novello AwardΪ1969ʺĸ [12]

3. StarrֶʱĴOctopuss Garden

һStarr1968괴һ׸
ƽStarr׸Harrison׸: This cosmic 
song is lovely and so peaceful [13]ᵽ:

I'd like to be
Under the sea
In an octopus' garden
In the shade...
Oh what joy
For every girl and boy
Knowing they're happy
And they're safe...

⣬Ѻƽͻ죬ʱΪΪһ׶ͯ [13]

4. ˸и

The BeatlesڣMcCartneyΪֶӵʵ쵼ߣ󲿷ָ
Ϊֶٽɢ˸Сод
Ե3ף

(1) Hey Jude

һMcCartney1968굥ݳһthe Beatlesļ
ĸԴֶӺڽҪɢļ䣬LennonΪ
Yoko뿪Cynthia 5ĶJulianڴڼ䣬McCartney
Cynthia Julian·ϱд׸裬ԭΪHey Jules
ΪˡHey JudeοJulianڸĸֿѹ [14]
ʵ:

Hey Jude, don't make it bad.
Take a sad song and make it better.
Remember to let her into your heart,
Then you can start to make it better.
Hey Jude, don't be afraid.
You were made to go out and get her.
The minute you let her under your skin,
Then you begin to make it better.
And anytime you feel the pain, hey Jude, refrain,
Don't carry the world upon your shoulders.
For well you know that it's a fool who plays it cool
By making his world a little colder...

˸ȥ滺˸Сöɳֵ
McCartneyִ츳׸Rolling Stones 2004/2010
500 ʼΰĸУΪthe Beatlesߵĵе8 
[4]2012׶ذ˻ῪĻʽϣ70McCartneyȻڸǰ
׸ڼ仹ߵ̨ϻֺ͹ڻڳһ
߳׸裬ֳմﵽ˸߳

(2) The long and winding road

һMcCartney1968굥1970깫һ׺˸
ĸͼֶӳԱߵĽŹϵ˶
ˣᡣһthe BeatlesڵĹֳVideoУMcCartney
ǰϰ׸裬ų뿴ȥеǷϣLennonYokoһ
̡̺飬the Beatlesڵ龰

(3) Let it be 

׸McCartney1968굥1970깫һ˸
ͼͬǰ The long and winding road McCartney
ֶӽܵĽɢǳʧʱ14ʱ
ȥĸסһεʱMary: It will be 
all right, just let it be׸Ϊ Let it be [15]
:

When I find myself in times of trouble, Mother Mary comes to me
Speaking words of wisdom, let it be
And in my hour of darkness she is standing right in front of me
Speaking words of wisdom, let it be
Let it be, let it be, let it be, let it be
Whisper words of wisdom, let it be
And when the broken hearted people living in the world agree
There will be an answer, let it be
For though they may be parted, there is still a chance that they 
will see
There will be an answer, let it be...

׸УMcCartney˶ĸĸࡢHarrison
LennonöгļࡢStarrĻİɴﵽ
׸McCartney뿪ֶǰthe Beatlesһ׵Ҳthe 
BeatlesΪ֪ĸ֮һRolling Stones 2004/2010500 
ʼΰĸУ20 [4]

ϸ⣬ƼһЩΪ֪the Beatlesĸ

໶ Thank you girl (ΪLennonPaul McCartneyһ
׸ڶŮԵԻΪStarrĴǻҲӵ
˼), Hold me tight, Ob-La-Di, Ob-La-Da, Drive my car, 
Birthday

滺ö Golden slumber, Carry that weigh, We can 
work out, Black bird, Two of us, Do you want a secret, 
Wait, Free as birds (ΪֶӽɢLennon1977the 
BeatlesԱپһ¼Ƶ), Here, there and everywhere, Yes it 
is; 

г˵ This boy (Lennon, McCarney, Harrisonͬʱ
ϳг); 

˵ Girl, Dont let me down (׸LennonΪ
Yokoһ˸)

˼ǣҶ˵ Things we said todayAsk my why

Դ˼ Nowhere man (the Beatles һ׷鰮
)    

˻ᳰЦ: ʱ˾Ȼǽүүϵ
ȣүүǱʱû˵ʲôҡ֣Ҳû
˽the BeatlesĸΣΪMozartֵٶ
û˵ϵΪĸҵִ
ͨȥأȶԣthe Beatles־ͽMozartĹŵ
ֵ𣿾ԣͬΪ˸֣Mozartĵ40Ҫ͹
the Beatles Let it be 𣿷ҲѧGary Gutting 
2013귢The New York TimeһƪΪ Mozart vs the Beatles 
¾۵:  ֹֻ֧ͨײȨ
...the Beatlesöɡ٩ĸʡصɡ
ðյ...ǣͬķϸ [16]Ȥǣ
Gutting»һ̿ͨһλʦ̨
Mozart̨дһкһŮȴץز
ơʦպʻصԼĳȻ󲥷
Britney SpearsCDŶݳȥ룬ڵϮᣬ
̵ĴҵҲȥ͵ƵĹŵ֣Ͼÿʱ
ÿ̶ȥɸԵ֡ٴΣRolling Stones 2010500 
ʼΰĸУ60ĸռ39.2%70ռ26.2%80
ռ11%90ռ4.4%2000ռ5.4% [4]Щݳ˵ִ
ͼֵˮ׼Ե½ƣҸΪʱ
ǻۺʹҲ½ˡ

The BeatlesԱĳɾͺ

1. The BeatlesԭԸElvis Presleyʱ
ӢҡַԴthe Beatlesʱ

2. The Beatlesߵ [17]֮⣬
60ӢߵԪľΣ֮Уάְѻʹ̶ÿ
2.8ԪĳŵһΣľthe BeatlesǸֶӵ
ҵѲݳ׬Ǯ [18]ýͳ19641966the 
Beatlesÿ׬650Ԫ [18]the BeatlesɢĽͣ
Ա2013Ϊ7ǧ1Ԫ [19]ÿ׬2.25Ԫ

3. Rolling Stones 2004/2010г500ʼΰĸУ
ѡҾthe Beatles23ףнǰ10010 [4]

4.  The Beatlesʷۣ

(1) Rolling Stones 2004/2005/2011100 λʼΰ
Уthe Beatleλ [20]     

(2) Billboard 2008гɹ100λУthe Beatles
λ [21]

(3) Times ռ20100λӰУthe Beatles 
[22]

5. The BeatlesԱʷۣ

(1) BBC 2002Ӣʷ100 λΰӢУLennon
McChartneyֱе819ǵĿѧֻCharles Darwin 
Isaac NewtonλHarrisonе62James Wattϲ
ԱCharlie Chaplin [23]

(2) Rolling Stones 2015100 λʼΰSongwriter У
McChartneyе2Lennonе 3Harrisonе65 [24]

(3) Rolling Stones 2010100 λʼΰSingerУ
Lennonе 5McChartney19 [25]      

(4) Rolling Stones 2015100λΰļУHarrison
11Lennonе55 [26]Lennonִ͸質ţΪ֪
Ҳһλܳɫļ֣Lennon˵ֶСļ֡

(5) Rolling Stones 2016100λʼΰĹУStarr
е14 [27]StarrȻǸҡֶдõĹ֣
ֶԱҡ֣˳ΪҡֵĽ̸Ϊ
ԼĸоǻȥֵʤһĹ
һ C Ĳȥʹ򣬸ԡ

The BeatlesɢԱķչ

The Beatles ɢλԱԷչԼҵΪƽ
͸ѧ˼Lennon ˿ImagingRolling Stones׸
Ϊ׸LennonΰƷ [28]׸ƽ峺ɣ
ĺҽȿRolling Stones  2004/2010г500ΰĸ
е3 [4]2012׶ذ˻ĻʽϣLennonڸǰ
׸Video

Imagine there's no heaven
It's easy if you try
No hell below us
Above us, only sky
Imagine all the people
Livin' for today
Ah..., ·Lennon Get back (the BeatlesMcCartney
һ) ߡ

McCartneyֶӸսɢһʱһֱˣǴ
 "Maybe I'm Amazed" ʱľôģ

Maybe I'm amazed at what's going on ... 
Maybe I'm a man and maybe you're the only woman who could ever 
help me; 
Baby won't you help me understand ... 
Maybe I'm amazed at the way you pulled me out of time, hung me on 
the line, 
Maybe I'm amazed at the way I really need you."McCartney
LindaԱ齨WingֶӣΪ70ɹֶ֮һ 
[29]⣬McCartneyҲеּ֮һ2020Ʋ
Ϊ8Ӣ [30]2020󱬷ʱصĸǲһֱ
Ϊ One World: Together At Home ĻֻᣬԸл͹
սǰߵҽԱ78McCartneyӦμ˱ݣ壬һ
ߵһݳthe Beatlesʱڴ Lady Madonna

HarrisonֶӽɢչԼҵҲȡ˻Ի͵ĳɾͣ
һĸ My sweet lord Ϊ1970׺1971
Ѯһĵ [31]HarrisonҲǺܸеּңǰƸΪ1
Ӣ [32]

StarrֶӽɢԼҵҲչϣΪ
еĹ֣2020ƲƸΪ3.5Ӣ [33]

Եؽthe Beatlesthe Beatlesȴֹ

Դ׸ֿthe Beatles

202110ŦԼ
(ԭԸֵּĽ)

ο

[1] Wikipedia: List of songs recorded by the Beatles

https://en.wikipedia.org/wiki/List_of_songs_recorded_by_the_Beatles
[2] Jeannette Catsouli, The Beatles Awaken a New Sensation. The 
New York Times, 2015.  
https://www.nytimes.com/2015/08/18/arts/music/the-beatles-awaken-a-new
-sensation.html?referrer=masthead 
[3] Wikipedia: I Want to Hold Your Hand
https://en.wikipedia.org/wiki/I_Want_to_Hold_Your_Hand 
[4] RollingStone: 500 Greatest Songs of All Time

https://www.rollingstone.com/music/music-lists/500-greatest-songs-of-a
ll-time-151127/jackson-browne-running-on-empty-151104/
[5] Wikipedia: She Loves You
https://en.wikipedia.org/wiki/She_Loves_You 
[6] Wikipedia: And I Love Her
https://en.wikipedia.org/wiki/And_I_Love_Her 
[7] Wikipedia: When I am Sixty-Four
https://en.wikipedia.org/wiki/When_I%27m_Sixty-Four 
[8] Wikipedia: Yesterday (Beatles song)
https://en.wikipedia.org/wiki/Yesterday_(Beatles_song) 
[9] RollingStone: The Top Ten Beatles Songs of All Time

https://www.rollingstone.com/culture/culture-lists/the-top-ten-beatles
-songs-of-all-time-10664/
[10] Wikipedia: While My Guitar Gently Weeps  
https://en.wikipedia.org/wiki/While_My_Guitar_Gently_Weeps#Personnel 
[11] Rolling Stones 100 Greatest Guitar Songs Of All Time
https://web.archive.org/web/20080531030023/http://www.rollingstone.com
/news/story/20947527/the_100_greatest_guitar_songs_of_all_time/print
[12] Wikipedia: Something (Beatles song)
https://en.wikipedia.org/wiki/Something_(Beatles_song)#Personnel 
[13] Wikipedia: Octopuss Garden
https://en.wikipedia.org/wiki/Octopus%27s_Garden
[14] Wikipedia: Hey Jude
https://en.wikipedia.org/wiki/Hey_Jude
[15] Wikipedia: Let It Be (Beatles song)
https://en.wikipedia.org/wiki/Let_It_Be_(Beatles_song) 
[16] Gary Gutting: Mozart vs. the Beatles, The New York Times, 
2013
https://opinionator.blogs.nytimes.com/2013/07/14/mozart-vs-the-beatles
/?searchResultPosition=1 
[17] Wikipedia: List of best-selling music artists
https://en.wikipedia.org/wiki/List_of_best-selling_music_artists
[18] Kristin Forbes: Financial deglobalization?: capital flows, 
banks, and the Beatles
https://www.bankofengland.co.uk/-/media/boe/files/speech/2014/financia
l-deglobalization-capital-flows-banks-and-the-beatles.pdf?la=en&hash=6
42B6511169CFC797A661157B03BE5035E780339 
[19] Forbes: How The Beatles Earned $71 Million This Year, Sort Of
https://www.forbes.com/sites/zackomalleygreenburg/2013/10/23/how-the-b
eatles-earned-71-million-this-year-sort-of/?sh=3fc1549011cb
[20] RollingStone: 100 Greatest Artists
https://www.rollingstone.com/music/music-lists/100-greatest-artists-14
7446/ 
[21] The Billboard: Hot 100 All-Time Top Artists
https://web.archive.org/web/20080913150551/https://www.billboard.com/b
bcom/specials/hot100/charts/top100-artists-20.shtml
[22] Times: the Beatles- Irrepressible and irresistible, they were 
 and remain  the world's most astonishing rock-'n'-roll band
https://web.archive.org/web/20080822101414/http://www.time.com/time/ti
me100/artists/profile/beatles.html
[23] Wikipedia: 100 Greatest Britons
https://en.wikipedia.org/wiki/100_Greatest_Britons
[24] RollingStone: 100 Greatest Songwriters of All Time
https://www.rollingstone.com/interactive/lists-100-greatest-songwriters/
[25] 100 Greatest Singers of All Time
https://www.rollingstone.com/music/music-lists/100-greatest-singers-of
-all-time-147019/
[26] RollingStone: 100 Greatest Guitarists
https://www.rollingstone.com/music/music-lists/100-greatest-guitarists
-153675/lindsey-buckingham-39147/ 
[27] RollingStone: 100 Greatest Drummers of All Time
https://www.rollingstone.com/music/music-lists/100-greatest-drummers-o
f-all-time-77933/cozy-powell-30367/ 
[28] Wikipedia: Imagine (John Lennon song)
https://en.wikipedia.org/wiki/Imagine_(John_Lennon_song) 
[29] Wikipedia: Paul McCartney and Wings
https://en.wikipedia.org/wiki/Paul_McCartney_and_Wings
[30] Wikipedia: Paul McCartney
https://en.wikipedia.org/wiki/Paul_McCartney
[31] Wikipedia: My Sweet Lord
https://en.wikipedia.org/wiki/My_Sweet_Lord 
[32] Wikipedia: George Harrison
https://en.wikipedia.org/wiki/George_Harrison
[33] Wikipedia: Ringo Starr
https://en.wikipedia.org/wiki/Ringo_Starr


￦ķ

鱡

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ǰЩӣҵרҵͬȺ֮ҡʦʣϸ
ġָȾɫ嵥DNA˵μĸϸ㵥
𣿡ԺֲʣҲǱͷ߲Ρִ֯ѧᵽĸ
ϸȾɫΪ壬DNAΪı壨46XYǷΪȾɫ
DNAƽеĸ

ͬʻظָȾɫ塱ȷָμĸϸǵ
塱

Ҳͬ顪

֮һ׽Իϸĵ弴ȾɫDNA
ģӦǾϸӡμĸϸѶϸΪ
μѣμĸϸֻ˵һμѣǵϸ
ͬȾɫ壬ʱϸڵDNAǶϸ
Ȼ׽ڵǱ̨ǰDNA֮ҲΪ塣ڴ˻ϣδ
˵ʵΪμĸϸǡϸĵ塱

ôµˣ塱͡塱ǸԲϸ
𣿴⣬˵μĸϸ֮DNAǶϸʵҲ׵
ΪϸDNAһɲ䣬DNA֮ǰ46DNAӣ
֮ͷһǶϸ˵μĸϸDNAǶ
ϸָĸʱڵ

֮ҽԻһȾɫһDNAӡ
ֻһȾɫϸһȾɫָһͬԴȾɫ壬Яſ
ŴͱȫϢȾɫϸƶ塭
˸μĸϸ϶Ƕ壬ƵΪ
ͬȾɫ顣ɳĸϸͬԴȾɫ4Ⱦɫɵķ
һΪĴμĸϸƶʡչ˽μѣĸϸ
һ̥ϸѡ󡯵Ľϸǲһ
ȾɫġԣͲõĸ̥
ҲȻҽڵֱӷ񶨴μĸϸǵ壬ΪƵ


Ȼڲɹìܡ

ȣҽڹڶġǡȾɫϸƶ
塱ȴ˵ͬȾɫ顱֮μĸϸ϶Ƕ塱
֪ͬȾɫ顱ҲڡȾɫ顱ѽΪξųأ
Ǹģ壬Υ߼ѧġͬһɡ 

̶ҽΪ϶Ƕ塱ĴμĸϸƵ
ôӶĸϸĴμĸϸȾɫ
룬ǵʲôѵмȲǡ塱ֲǡ塱ϸ
Υ߼ѧġɡôҪĸ
ʲô

ҽ˵ѡμĸϸƶʡ͸ˡ
ȣ塱ǶԷȾɫ̬ϸôȾɫΪһ̸
Σ仰˼ǰѴμĸϸΪϸ߼
˵ùȥȴûԣΪμĸϸĸϸ
ϸڵϸϸڵÿһȾɫ嶼Ƕ壬
ЩϸǶϸɼ塱ĸҲڴμĸϸ

һ˲١⡣ʦڻǱѧ
ΪĽ̿飬ϸı巽棬߼⡣

Ҫ

Ӻ̶ܴ˵ѧǽ߼˼άϵѧʣԿѧ
߼ѧ߼ѧָʽ߼ĻҪ֮һǡҪȷ
ȻҲҪϸйء塱ۣҲƱȷһЩ⣬


ȷЧǲȨ伮˽ѧͬζ岢ĳ
ġ

ϵȨ伮Ǹְٿȫ飨Encyclopediaĵ
Ӣٿȫ顷̫Ӵ󰺹Ҫͼݲܲġң
ѧ죬ֽͼڶЩ㡣бձϿҼʱ
ʮֱݵͰٿȫ飬ǻϿʱѲĵӢİ
Wikipedia, the free encyclopediaάɰٿơ¼ơӢά
ٿơע⡪ĵġάٿơӢάٿơǸȫ
רҵר׫壬ԵɸڲͬרҲ޶µ֪ʶ
⣬ڹʢձΪ롶Ӣٿȫ顷ϰٿȫ顣

棬Ǿͽȷ뱾ֱصļ
໥Ҫ塢Ⱦɫ塢ѡ



˽⡰塱

кܶġ塱絥壨monoploidhaploid
diploid壨triploidı壨tetraploid౶
polyploidȵȡЩӢԭʻǷĴʣڱ
PloidǰĿǰ׺硰mono-һdi-tri-
tetra-ģpoly-ࣩȵȡȻPloidǴʸ

ӢάٿϵͳΪʸġPloidвͬǰ׺֮
-PloidmonoploiddiploidԶתһ
PloidyĶ౾Ӣʵ䣬Ploidyһʵǡԡ˼弴
ԡ֮Ploidyָ/

ô˵Ploidy is the number of complete sets of chromosomes 
in a cell

ȻPloidyĶ塣УȾɫ塰chromosomesΪʣ
֮⣬һȻǳȺ飬ΪȾɫ顱ȫ䷭
ǡ

ԣһϸȾɫ

ȷ綨ˡĶǡȾɫ
Ĺؼһ Ⱦɫ塱һǡǡ

ԣ壨Իһ壩ǺһȾɫ飨һȾɫ
壩弴Ⱦɫ塭Դơע⣬˵ֻȾɫ
DNA

ǣһϸﺬȾɫɼ
ı壨-Ploid磬壨ӢĴΪmonoploidhaploid1
Ⱦɫ壬¼ף壨diploid2ף壨triploid3
ףı壨tetraploid4ף

ϸĻλϸֳ
˺Ͳ鶯Щϸ·ΪࣺһǡֳϸԵľ
ӺʹԵӣڽӴϸ٣ǡϸ
ƤϸϸѪϸϸֶǸĸ
֯ٲάܡϸ໹ռ˾ˣ
ѧҽϸȾɫ屶Ϊ屶Ĵ˵ĳΪ
ʱָþϸıѧоҵ֤Ƕָ
ڵСϸֳϸ֮ĸ١֯ϸ
Ҳ̥ʱڴܾѿʼֱʱڵĸ١֯ϸǶ
ϸ

˵Ϊ֮˵ϸÿϸں2Ⱦɫ顣ÿ
Ⱦɫ23Ⱦɫ塣У22ΪȾɫ塱һСȾɫ
塱ȾɫĹɻһϸеȾɫ46
Ⱦɫ˵Ա죬ŮʡXΣеһXһ
YΡȾɫıʽѧϳΪȾɫ͡Ϊ˼
ĿַʾΪ46XX46XYǰߴŮԸŮ
ϸߴԸԵϸ

˵ֳϸ۾ӻӣǵ壬ֻһȾɫ顣
Ⱦɫǡ23XӵȾɫǡ23X/YXY֮б
򡱣ʾӿЯ1ͬȾɫ壬XεģY
ġ

ǡ塱ӵ֪ʶ

֮塱ֱ漰ǡȾɫ塣



̽֡Ⱦɫ塱صĸ

ѧѧ-ҽѧƶѧƿγѧģйȾɫĳ
ʶǡDNAϸһЩγɸ壬ɢطֲϸ
ǿɱȾȾ״ġȾɫʡЩȾɫϸ
𲽲ϣγһϸ˿״ġȾɫ˿̶һΪȾ
ɫ塱ϸڣȾɫΪµġXΣáȾɫ
塱衰˿һϸѺڣȾɫѣ̶
ѵϸΪǵȾɫ壬ܿɢΪȾɫʡ
֪ȾɫϸǰͽDNAƣʴƲ⣬ڵȾɫ
壬ʵһȾɫDNAƳ˫ݺγɵʱġ˫塱ô
漰˺üĸȾɫʡȾɫ˿Ⱦɫ塢Ⱦɫ塣

Ӣάٿô˵

ֱȾɫʣchromatinȾɫ˿chromonemaȾɫ
chromosomeȾɫ壨chromatidȴʣѯӢάٿӦߢȡ
֪ʶۺժҪ¡

ȾɫϸDNA͵ʵĸ壬ҪǽDNA
װɸոܵĽṹ˿ѺͼѵǰڣȾɫʱ߶Ũ
ά״ṹȾɫ˿Ⱦɫϸǰڵ״һȾɫ壬
ڸ֮ǰһDNAɵģƣSڣ֮ÿȾɫ嶼
DNAɣ֮DNAƱDNAûȾɫ
ȫͬĸΪȾɫ壬ÿһ˱
ƵȾɫһ롣ϸڣȾɫһͬ˿㽫һԽȾ
ɫ壨sister chromatidһҲΪ塱dyadϸ
ѺڣֳеļѢڣɶԵĽȾɫΪ
Ⱦɫ壬ֱΪȾɫ塣

ӢάٿиشĲ˴˺Ӧ໥ӡ֤Ҳԭе֪
ϡ

ֵעǣӢάٿƵȾɫУԳһ˵Ⱦɫһ
Ĳͬ÷¼£Some use the term chromosome in a 
wider sense, to refer to the individualized portions of chromatin in 
cells, either visible or not under light microscopy. Others use the 
concept in a narrower sense, to refer to the individualized portions 
of chromatin during cell division, visible under light microscopy due 
to high condensation.

λҪ㣬ıǡϵġȾɫ塱ָϸеȾɫ
ʸ壬ڹ⾵¿ɼڷڣ򲻿ɼڷǷڣԽȾ
ɫ壻ϵġȾɫ塱ָϸѹеȾɫʸ壬߶Ƚ
ڹ⾵¿ɼ

Ⱦɫ塱ʵһеж̬ĸڲͬﾳ£
ԷֱȾɫʡȾɫ˿Ⱦɫ塱塱˫壩
͡Ⱦɫ塱ңȾɫ֮DNAһݣɣҲ
˫ݣ˫ɣϸڵĲͬ졣

磬˵˵ϸǶ壬46Ⱦɫ塣˵֪˵
ϸǾڷǷ״ֻ̬һС׼ѡڷѻո
ɷѣô˵ϸ46ȾɫʱġȾɫ塱һʵ
ȻǼȴ˷ڵȾɫҲ˸ոշϸڵȾɫ壬
ڷѼϸġȾɫʡȻʱȾɫ
Ⱦɫ塣

֮һ״DNAӣΪ˼򻯹Ҳϵף
ɢεɢϸʱ̬ѧϳΪȾɫʣǸƳ˫
Ӳһϸ˿״ʱΪȾɫ˿ֻɴ״ϸѵϸ
ںʹڣ΢ֳ״˫ڣԼòXΣڣһ
Ⱦɫ塣XεȾɫ壬˵幹ɣ֮Ϊ
塱ֻҪ˿㻹δѿֻǡһȾɫ塣ʱȾɫ
ƺֻǡȾɫ塱һ˿ѿÿȾɫΪȾɫ
塣Ⱦɫ壬ϸܿɿ˲εġȾɫʡ
ȾɫĶ̬ʷ

ϾȾɫںȻеж̬ȷġ

һDNAӣDNAӼƵһDNAӹͬ뵰
ʹɵһ壬ΪȾɫ塣ֺ̬ӵʲô
Ⱦɫ塣

ͺñȸļңԭһһңǽСҡ
Ȣ˸Ҳ̫̫ŮһҷֱռңǻС
ҡٺˣһһңȻСҡ
ļңŮļҲңһ˵ң壩
ң˵ң壬˫壩Ҳҡԣҡ
Ҳеж̬ģ롰Ⱦɫ塱ͬ

Уǡഫֺٰݣը
˵ֻõըġ޺ıߥ޻ʵۺɣӷ
ΪˣΪ˷йߺ޲Űšһ¹ը
Իըʵϣ۵˫¹ը͹Ķ
һϼ񻹹ըСʱŸڽ
ԣҧ˫ɣС˺ԡ۵˫ɣӭ
˵ǣըء

Ⱦɫ״ըôǵDNAγɵģȾɫ
Ⱦɫʣ˫DNAγɵģȾɫ壬壩Ⱦɫ塣



塱͡Ⱦɫ塱ĸȷ֮ǻصͷ⡪μ
ĸϸ㲻㵥壬ͬʱѡ

ҪӴμĸϸĳĸϸ˵

ĸϸǴĳԭϸ˿Ѷġ

˿ʱȾɫΪǡϸÿһԭDNAɵȾɫ
ʣDNAƶγ˫ɵȾɫ壬˫ȾɫϸѺʱ
˿ѿȾɫ壨༴ɵȾɫ壩ֵ
ӴϸȥڴǿȾɫɷѣϸ
ѡϸȾɫжȾɫ壬ӱϸȾɫҲ
ͬжȾɫ塣ˣ˿ǰȾɫ䣬Ҳ
䡣

˵ϸǶ壬סͬԴȾɫ塱һ֮
γܾʱɾӴģԴȾɫ塱һṩĸԴ
Ⱦɫ塱˵ȾɫֱԴͬΪγΪͬԴȾɫ
塱

ͬԴȾɫӢhomologous chromosomesķ롣Ĵʵ䣬Homologous
ݴԴhomologueǰ׺homo-ʾͬһ֮⣬
homologue˼ǡͬ塢൱ͬͬϵͬԴȡ
ԣһȾɫ԰ܶ״СһȾɫ壬˵һȾ
ɫͺ23̬ҪݳȺ˿λãΪ1š
2š3šȡ۸ԴĸԴͬһȾɫ壬̬ͬģ
һԡԣȾɫ homologous chromosomes
ͬȾɫ塱˼Ⱥ˿λͬеĸ
ȾɫλҲͬôΪλͬΪ
ݻʷϣȾɫԴͬġʶڿѧڽ
homologous chromosomesɺʱɡͬԴȾɫ塱ô˵ϸ
Ⱦɫ壬һ234623ԡͬԴȾɫ塱ÿ2

Թ⣬ͷ˿ѡ

ǰ˿ǰѳϸÿȾɫ帴Ƴһһģһĸ
Ȼѿֱӱϸǣϸ4623ԡͬԴ
Ⱦɫ塱ӱϸҲȫ֮ͬϸǶ壬ӱϸȻ
Ⱦɫûм٣ȾɫȻҲûм١
ϸȾɫ塰Ϊ

Ȼ˳ĸϸȻ˱仯ȾɫΪϵش


ĸϸҲϸDNAƣȾɫӵɱ˫ɡ
ǣĳַӵػƵָ£˫Ⱦɫġ˿ѿ
ʱԭȳ˫ԵġͬԴȾɫ塱ֱŤֱͬӱϸ
μĸϸҲ˵ϸѹУĸϸȾɫ
ѣԵġͬԴȾɫ塱˼ҡǣ·ѳ
μĸϸֱ˳ϸгɶԵġͬԴȾɫ塱еһÿ
ϸͬԴȾɫ壬Ǹֻ23Ⱦɫ幹һȾɫˡɼ
˷ϸһȾɫ塰ΪɴˣμĸϸˡȾɫ
ϸӶ˵塣

ֻμĸϸÿȾɫ嶼Ⱦɫ壬һģһ
DNAЯĻ򿽱Ҳһϸ˵μĸϸ
׻ģ23Ⱦɫ˿㶼δѿʻֻһȾ
ɫ顣ԼΪһȾɫ塱Ҳһ׶塱
µ˵ɡһ׺飬˫DNA˫ȾɫȾɫ塱ȴ
׽˵ɡͬȾɫ塱δֿ޷ף
ҽ˵ɡһȾɫ顱ǿ˵һĻ
顱

Ȼ黹ûꡣҽڷֱ˵ ͬȾɫ塱
һȾɫ顱ܿͻ֣ǾͲһĴμĸϸ
ǴӴμĸϸ׼Ϊϸķˡ

ڴμĸϸȾɫеġ˿ûԼļȶ
Խžһսۡһأμĸϸеģǰ
ϸѼͬ˿ѡвٽDNAƣΪ
ʱ23Ⱦɫڳĸϸ׶ξѾƺõ˫壨壩
ֻ轫˿ڣڷеϸ˼׽˵
ͬȾɫ塱ӦĳơͬȾɫ塱Ҳ
˵ġһȾɫ顱ֻǶһ˲ܿ죬⡰һ
Ⱦɫ顱ϸһΪֱӱϸϸ
spermatidӵǰϸ˿ѽͬ˫ɵ
ȾɫѳݵɵȾɫ壬ֱӱϸȾɫûиı䣬
23Ȼ23ȾɫҲͬûиı䣬һס

˵ֺ23Ⱦɫľϸϸϵĵ壬ôͬ
23ȾɫĴμĸϸҲȻϸϵĵ壡Ϊ
塱ݵֻȾɫDNA˫ɻǵɡ

ֵָǣ/μĸϸϸѣлϳ
֮ɷָͬһ¼е׶ΣԱȾɫ
Ǵ¼ıΪѡmeiosisһ
μĸϸηѣΪѵһ׶Σơ
񡱣meiosis񣩣ӴμĸϸΪϸһϸѣ
Ϊѵڶ׶ΣơѢ򡱣meiosis򣩡



ƺˣȴȻδѧˣѧ
ѧо׶ζѧйر塢Ⱦɫ塢ѵ֪ʶΪʲô
ҽѧԺУӽʦĽ׶Σô飿ǰ
ڱȾɫĸȷ˼Ͻ֮⣬Ϊ롰
һ/μѡ˵йϵ

ѧҽѧΧڲѧƣϸѧѧֳѧ
̥֯ѧȣĽ̿顢ٿȫ鶼мѵľܣڻ
Ĺ顪ʵ䶼ȷļѸ䶨塣磬Ȩġţ
ѧϰʵ䡷УmeiosisĶǣֳΪĿĵһַ׶ν
е͵ϸѣ4ϸÿϸȾɫԭϸ
һ롱a special type of cell division that happens in two stages and 
produces four cells, each with half the number of chromosomes of the 
original cell, for the purpose of sexual reproduction. Oxford advanced 
learner's dictionary. 10th edition. Oxford university press 2020
ձӦõʵ䡶еʵ䡷Ҳţʵ˶塣Ҳ˵
ʵ䶼ȷ綨ĸϸʹμĸϸϸѣ
Ϊһμѡ

Ȼ֪ںԭѧ̿ھѹʱ
Ѣ/򡱳Ϊһ/μѡˡĸϸ
μѡ֮˵ˣӢȻ磬
Ѿʮйʢľ֯ѧ̲ġJunqueiras 
֯ѧڲӷʱҲơthe first/second meiotic divisions
Junqueiras Basic HistologyText and atlas13th edition2013. 
p432.

Ȼһ߼

ĸϸȷϸѲγɾϸαΪӣ
ϸѺһμѡѢ/򡱷ֱֻһ
μѵͬ׶ΣԸ˵ɡһ/׶εļѡȴ
˵ɡһ/μѡΪһ/μѡ˵
ϾμѵİʾҪ4ϸѣáһ/μ
ѡѢ/򡱵˵ȻΥʽ߼ͬһɣ
˸ȷĴ

źǣ̲ϵȷֺдšһ/μѡthe 
first/second meiotic divisions͡μѡafter 
two rounds of meiosisϸĸ

ֲϸ߼˳ѧߵ⡣
ΪһμѱʹȾɫĿ룬4623ôμ
εļ룬23ټ11.5Ⱦɫ岻԰ʽڣȻҲ
ûϸ߱תȥDNAļ롣ˣ˱Ŀͷ
ʦ󡪡徿ָȾɫ廹ָDNAˣҲס
λֵĹ۵㡪μĸϸϸĵ壬ȷ
ࡣ

ڸϸ߼Ͻ£κͿԲ

Ӵˣʵʵ˵Ѣ/򡱣Ҫ˵һ/μ
ѡˣ

һҪϸ

߼ĺҪ


͡סססססססססססססססססססססססססססססס

ӾĹ£ʮߡʮˣ

̡ʡ

ʮߣɭľ


ɭû뵽ڱҵʱһ

ĩƴѧ󣬺ɭҲӸ͢صĽڡȻڸ͢
ʱ䲢ҲѾĲ˹̹дű棺ɭ
ͬȵšĩƵȻͬСֻѧĺɭֱ
ύʿġһ

ɭͻĿгɹڷЧӦĽ
㷺顣ΪⲻҪ鷳ĩƽ麣ɭ¯һѧ
оΪѧλĿ

ѾľֻǷѧʹΪ⡣Ժ
ɭ˵Ȼ⣬ܿġ19237£Ҳֻ21ꡣ

ǰڰִѧʿһоάĽڡ
ȻǺɭίԱĳԱ֮һѾ컨׵ά
ĩƵĵλΪҲѧԽԽĩʽо
ʵɧƫƫ꺣ɭѡάʵȴſΣ
˿û¡άһֱڵȴᣬĩƺĵһÿ

ɭĴСʮ㣬ɵضԴͻȻ
άһɵʵ⡣ɭû׼ſڽ࣬
˵Ȼά漴ʣ𲽽Ѷȣ̽ѧ
֪ʶߡɭƣӦ©ٳԱߵĩŴβ廰һЩ
ͼ棬޷ŤתάһС

ãάϷԵĿʵѵһͨ΢ԭ
𣿡ĺɭѾжףΪ

Уάֺɭ֪ʶǷȱ֡
ĩԵظ˸֡зλֻܱ˼
ƽɭǿĳɼӮòʿѧλ

ӽǱӳ󣬺ɭ뿪Ľڣܵ͢ȥҲ
ࡣĲοɭ֤˳Ѿְλ

ͻȻڰ˹ɽͽǿ־ĺɭҡ
дţߵȻսᡣȻͯӾ
ٶȾۼԶԶ㣬ڴȻѰġ

19243£ڸֵ͢ĺɭüڵһ籾
һε̲ԽԽǿҵɻʱĴ
˺ۣȴ޷۵ã

1924꣬ɭڸ͢ѧ

ԭģѾʮˣԭӡӵĹϳɹ֮
ǰƺѾ;ĩ·ֻЩʧеһ
ʹеĳɹģҲֻܸߵƵʣ޷ߵǿ
ȡأԤҲȫʵ׼ȷԤ۲쵽
ͬʱҲԤһЩڵġࡱߡ

˵ԭģʵشȱݡɭòЩе
ɹϹèײ󣬲ʵ

ڲоĿͷס˼죬һֱûܼڣͻȻ
ſڣ˵ʰڶһԶš

ǿ׳ᰮҰʦͽ;Զ㣬ͽ
˴Լ160źɭ˵󱱲ɽҰ⣬˵
ķӣPrince HamletĹ

͵ſŲõоѾɲԽԽߡ
ѾԱߵĵƤڳｨ¥չЩæռ̫ʱ
侫ֻӳſʱ˼

Ǽѵõûô̸ӡƵؽ
ԵĳɳսɵӰ졣Ժɭһγ
ϵ顣ܵϤЩͳ¹Ȼͬһ
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룬籾ְλ

ص͢ɭڵһμĿеż˹̹

ǰɭĿѧԺ˿գûܼλ
ѧҡһΣѾָİ˹̹͢ѧĺ
ɭһεԵʦڽͷ

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޳ݵĺɭе֪˹̹ĿȻ˼׼
Ϊ˹̹ķ̬ȶ𾪡һԣʹ
ʦ֮ҲżԭԷ硣

＾ĩƵĽŲȥѧյֺɭڲ
Эȡһǰ籾ְ

оҲ뺣ɭƵã֮СBKS⵽
ѧ缸һµķԡ²ѵӿ˼ͬ顣
ȻפģʽΪԭģеṩݣȴ޷
⡢ܵӵĹ˶翵Ĳϵ

һƬ˼Уµͻơָ£Ĭ
ڳһµ;뺣ɭЭ

ƪBKSͿĬԼԹ۵˹ء˴
ͳغ㣬˲ģ͵ľ裺ӵĹԾǨʮǰ
ʵͻƣӷշƵ˶Ƶ޹أ
ֻȡԾǨǰǰ˹̹֮ʡҲ
Ϊһ޹ءģֻܼƵʣ޴Ƶߵǿȡ

ԭڲһϵгӡǵƵ뷢䡢յķ
ͬɴ˼㿵նЧӦзӵ໥áʮ
ֻصķ֮һǰʿ˼·

BKSûһʽֻ۱硣Ϊѧ
ǿĬ񡣰ղĶӦԭڷǳĹ
УΪͬھӹƵΪг
աƵһ¡

ԭʼģеĵӹԲΣֻеһںƵʡĩ
󣬹ԲƵʲٵһѧϺ״Ӧ
νġҶ任Fourier transformĬͺɭ㣬
ϵӵλáʱı仯ɲͬƵɲֵĵӣ
ͼҵͬƵʵǿӦڹߵǿȡ

ǻ˳ɹǳɹȻ޲任ֻǳ
Ĺ޷ӦڵĹǲҪ͵硣

ףɭյţͨոشͻơλ
ƫϽѧƵζѧʽ̸ʦ־Ȼµĵ
ĸеԭݸŵ٩һҲ
˹죬Ҳ޷Ժá

ʦȣɭڸ籾Ľչܲ⡣ûҵ
ɻ鵤ҩֻܴȻ19255·ظ͢

ǲ֪οһ⡣һжںɭ
ˣΪҳһ;

ص͢󣬺ɭصļԻ۹Դ׵ò
Σ۾Ҳò򲣶ڼ٣Լϼ
һֽ˻𳵵¹ˣȻ˱еһС

һ2.6ƽĻĵֻмªӪȼ
ʹáԺɭ˵Ĺͺûлۡ

ںĴ£֢״ˣԴʼѡڵͽ
Ķи£Johann von GoetheľʫƪҲ˼

ţٿʼѧҶ˶λúٶȡֻҪ֪
ĳһʱ̵λúٶȣţٶɾͿͨ׼ȷؼڽ
κʱ̵λúٶȡԭģҲһĳһʱ̻
ضϵĳһλãĳضٶȡ

ȻţϤ岻ͬûӣԭӡ
Ľ̸˶ȻԭӵĴڣΪ޷ʵ֤ԭ
ӵĴҴɣοڲĵӹ

ƪ˹̹Կѧ˼ᡱУΪ
۵˼Դ߼ʵ֤ĲԱȰ˹̹Ϊıʴع
˹̹ͨһϵС顱֤ţپԿռ䡢ʱ֮
ڡٵ޷֣Ӷ۵ܽ
ϣʵ޷۲ǺġЩֻǼ
û塣

СͶѧȤĺɭʦֵ߼ʵ֤İС
ϣͻȻӵĹԼλúٶʵǡʵ޷۲
ԭ˵ʵпԹ۲ֻйףһ
ߵƵʺǿȡ֮⣬һйԭӵֻǡ

ǣʶصߵԭģܴͣӼĵӹ
ߣӦͨ׵ӵ˶ʵĬ
Ѿʶ·Ը״̬ļУӡ
Ҷ任ֽΪͬƵʵĳɷ֣ùױӵλú
ȡǵӵλúٶȷֱѧʽƵʳɷֵĵӡ

ھ߱Եĵ״̬УӵĹ˶ٶӦڷƵ
ʡͬ޷áɭֻǾڹ
ĽӵĹڣӵ˶Ȼͨױ㡣
ڵ״̬УӼȲ񲣶ڹ̶ĹתҲ
֮䡰ԾǨֻǰпܴڵ߱ģʽ˶

ΪҳпܷƵʵϣɭøҶ任
ֵļ򵥶ʽһһкܳıЩ
ͼϻῴд֮ľУѭ֮ı
Ҳıչʾекзֱǳлӣг
֮ľ롢ȷֵȸֵ

ɭıڳеľͬÿһСԭ
һܼ֮ľܼ֮ҲǷƵʡ
бԷǳΪӵܼͬʱҲһ
ͬбеֵǷƵʶǿȣҲǰ˹̹
ǸջĿԡ

Ȼ󣬺ɭ층Ҷ任ĶʽЩбλáٶȵ
﷽ʽԼӦɡʱҪЩб㣬
òһνӡ˵ķ˺һ
ЩͷϵȻ߼ϵǢҲغ㡣

ʱѾ賿㡣޷˯ɴܵĺߣںڰʵ
һ߸ߵġ쵽ϵľʯŵȴճԼոշ
ʲô֪Ѿˣsomething has happened

ʮ󣬺ɭ˵ڻسȥһ˺ʦ
һ״εδܵϵָ
ֻߴϽдķ˺ɭĪġ

ַһ򣬺ɭдĳ塣ȻԲޱ𾴣һʱ
û򲣶͸¶һչڸ籾ĬǼѾ
Ĵ޳޸·Ϊˣɭ
ľͽ˲ȻԼǰӢͼƻõѧʣ
˳ͯӾСۣӢϿذԶ㡣

Ȼ˼ؾͰתѧ־Ĳº
ɭǸбΪб㷨ѧĲܾһ
ʶֱȥμӵ¹ѧʱǶ
ǰѧѧʱġmatrix

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Arthur CayleyΪ丳ϸѧ壬֮Ϊ󲢷չӦĴ
ɭԼĥЩǿһ֮֡ǰ
ֻѧһ޵ķ֧ûйκʵ壬ҲΪ
֪

ڻҵһ𽫺ɭѧ淶
һڻؾᰮѧϽξȻʦܵĹһ
ͼݲòĳѧϵ̣

ؼҺֻԼ(Pascual Jordan̡Լոյõ
ʿѧλȴҲһλͨѧĹšǶһɭ
СϵĴֲ˼ѧʽɭȼٻҲ
һС

19259£ɭԼº󣬲Լ
ǳʵɭѧġ19262£Լͺɭ
ġһٵ춨νġѧ

Ҳͬһʱڣͺɭ̿ʼʹһʣѧ
־һбţѧѧϵĵ

ʮˣѦ̵ķ

˹̹յɫʱ̻һƬʾͺף
ءƬңԶӡ䶯һҹ֮ı˲ɫĵλ
ѧýְһѧȥŷ޽ꡣ

¹¹ǩ֤ʱԱֻһ۰˹̹ǩƬ͸
¡

Ȼȴûֱȥ֡

ɫȫûʶƪеشͻơԼĵ󲻾
ĳĵڶƪġƪͼ˹̹ķۣԭз
Է䣬Ҫܼ䡣

˹̹ĳΪ롢Ͷƪġ߰УԼ
ָ۵֮ɫյ˹̹ϸ˽ţ
˰أóȻȥʦڰ裬Ҫѧһʵ
X߼ȥ˵ʵңΪﲻضδ
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һٶȹʱ˹̹Ѷйزɫ-
˹̹ͳơ۵ƪϵġָʾɫоɭ·ľѧ
ǵͳƷɫŬһ
صӡȺΪ֪ڣпгɹ

Ȼа˹̹Ĵǵͳûѧע⡣
һǰ˹̹յְʿѧѦ̣Erwin
 Schrodingerţһͼͳƴ

Ѧ̵һμ˹̹ʱ1913ꡣ갮˹̹Ѧ̵
άҲɣѧ˹ݽǴλϣ
һε֪ԭģͣѦ̵ʱ26꣬Ѿòʿѧλ꣬Ϊ
һڵ֡

ǴѧҵΪƷԼĿѧζм˼ͥСҵѦ
Сʱĸ׺ʹ̡С̵ĺǻ̵г󡣻ûʶʱͿʼÿ
ռǣڣĸ׻ʵؼ¼

ϵάҲʷƾõѧıҵԶĲ
ѦɼҵάҲɴѧʱһǸ沣
ѧȻǡǡѧǰɱˡ19ѦΪ֮
顣

ڴѧͣΪУ԰˽֪ġǸѦ̡ʱ
沣ǹɭŵFriedrich Hasenohrlѧ
ֻȴѧ곤ʮ꣬ǳɭŵϿʱҲ
䣬ֳݣԴ˽ѧе߼ϵѧ
۲ͻȥҰ⻬ѩܿΪѦĿеż

ڴѧڼͱҵ֮Ѧϲʵ顣1910꣬ڹɭŵ
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ڴѧȡְλʱһսѦ̺͹ɭŵӦ
飬ǰߡѦ̵ڱξĲս
йһμҵսѦΪԵзڻʱֳη
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֮ٵ۹ľĴפûپս¡
󷽵ľѧԺΪղӽѧ

ӰĵʦɭŵûôˡսϸȬּǰ
ߣڳбը40ꡣ

ΪսѦ̵вȴġսפ޾
ϾУֻһڤ˼ѧ⡣սʱµ
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ƯѦʿѧӮýϯλǵΪ˹
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Ӵͽ̸ʼꡣ19252£Ѧڿ˹̹òɫͳ
ʱдеļʽ⡣

˹̹ܿţƢػӦķѲûе
вûзгϸµؽͳ뾭ͳƵ


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ҼӲҷ桢׷档ͬĻ֡ԣöӲ
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ͬһ״̬ǣöӲҵĽֻֿܣ桢һ
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öӲöôûвȻͬӲҡȴ
ûԼݡ˴˲ɷֱͳƽȫͬ

Ѧ̿źඥóϷŸм˹ָ̹̹
Ķɫʱûܿ⣬ֻڰ˹̹ͳвʶ
صĵ߸Դ¡

Ѧ̱Ȱ˹̹С꣬ȲС꣬ȲֻСꡣѿе
⡰һȻ϶Ѿ˴µĻƽѦ
ڳɾȻ޷Ϊ顣

ԼһĩȣѦʵ밮˹̹Ϊ
˰˹̹ݽ֮Ѧ̵ĿнŰ˹̹㼣ۡ
ͳơԼ۵෽档ҲΪˣǼϸо˰
˹̹ͳĵѧ֮һ

ĿзҲ밮˹̹ϰڵǹƥûѧ
ֻߡ

ʮŬУѦ̷൱ģѧ罨
СӮýϯλĳɹһֱеۿשߣ
ûԼĴͻơ밮˹̹ȴʦڵĲڡ

1909꣬˹̹˹ͬʱ߱ӵ˫ԡʱ
ʿ˶ɵĵŲͳƷѹǿɲ֣һ
ǲһӡ

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ڲɫͳƺ󣬰˹̹ƹ㵽
ӹɵӡֹʼʩ尴µͳƷʽз
ȻѹǿҲͬɷ֣ӡ

ǣ˹̹ǹ⣬еʵͬʱ汸Ųӵ
ԡʵѧѰҡ֤һͨһխ
죬ӦܿƵ䡣

Ůһʱ̾˵²⣺Ĳʿ֮תĸ
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һܹڰ˹ֻ̹һ裺Ӷĳ
Ƶӵ

ǵ²ʾ򵥹ϵð˹̹ȻԼͳ
ĺ塣˳޵²⡰ڽҿһ޴ɴһǡ
ͬʱҲѾֵ֧²֤ݡ

ʵѧܹӦ֮ǰѦǵһע⵽˹̹ƪ
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Էһ鲻԰Ρѣٴθ˹̹д
ȡ˹̹˲룬һٻŰѦ²˼롣

Ҳǳڶ԰˹̹ŲɣѦڲͬ˲
ܿ췢һƪģòļƵͳʣ֤ʵ
˹̹еĽۡһʽĹס

˹̹뿪ʿѾ11ˡʿѧרΪõǸϯ
λѾΪڣѦռݡڣ˹̹ѧϰ
ʿѧԺ˴ģչҵѳΪһָѧ
ĵ°ݣϣصѧ밮˹̹һоͳһ۵ۼ
Hermann Weyl

ѧУϵܡѧÿھһιͬ̽½չ
ΪԹ㷺Ѧ̾ߡ192511µףؽ˵²


°ò˼顣𵱳ĩѧϰʱʦ׻׻̻壬
һ̡ûз̶²տڰ׻̸
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ںѦһżɽϴε°
Ӧв̡ǺðɣѾҵһ̡

ǹȥļǴͳʥڡѦʰıʼǡ鼮
еĸɽѩʤضȼ١Ĳӣٻר
̴άҲɸһλ֪

Ѧ밮˹̹һͬ㣺ǵԶӵڶŮ
ѡ

Ѧ̴СӢѧҵ㣬ͺŮԵ֡ѧҵ
˵һ̸ۼ޵ŮѣһСһ𳤴СáǺ
ѣһѪͳŮĸȴֻСҵѦ̸סѦ
ʱҲֻƶѵ̣ǰã߾ʵΪܹҺڣѦ
ƻѧ׵Ĺд򹤣׼Ӱࡣ

׵ѡ񡣱̬ϸԸ⿴ص
ޣֹçײǳ޼յĳ֮Ѧ̴Ӿν̣ռ
ûٳһʵŮԡ

1920꣬32Ѧ23İݣAnnemarie Bertel顣Ҳ
²ͥûнܹԷѧʶԨѦ޳
ݣĸԸޡ

ʱսѾѦΪǰ;뿪µڵ¹ѧתս
ѰְҵĻᡣֱ1921Ӯʿѧϯλǲһʱ
ʱҲѾ׷ʵ飬Ϊһѧҡ

ǵСͥȴһֱڶ֮СѦ̷ྴǳϵ
ȴϲЭһֱûܻУҲÿиӵѦ̷ǳ
ʧǼٽ飬ֶǵǲɡŻ
˶ɡӵˣͬʱѺõάϵŻͼͥ

ʢеάҲɡʿǱȻöĳš
֪ʶӾӢײ㣬ǰʱСȻǵѡ
ҲʧΪǡ

ϮСɵϰߣѦһֱдϸռǣÿһλŮ
ĵͽ֡ԺеŮѶǰٷ֮ٵԸ
İ¡

Ȼƫƫ1925׵ռûܱǸʥڻѩ
ϦŮǳΪѧʷϲ֮ա

ͬҲ޷֪ɽ﾿˼ѩжʱڴ
ȡΨһȷǵɽʱıʼǱѾһոµ
ʽ²ⲨġѦ̷̡

ѦʿõѣҲ˰˵Լķ
ʱȦһλѧϵϷʣѦڡ
ĩڵһɫ鱬һҪķ֡꣬ѦѾ38
ꡣ




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