- 69975 the
- 39175 be
- 36432 of
- 28872 and
- 26800 a
- 26190 to
- 21338 in
- 20033 he
- 12458 have
- 11247 it
- 10790 that
- 9495 for
- 8555 they
- 8516 I
- 7289 with
- 7254 as
- 6976 not
- 6742 on
- 6164 she
- 5377 at
- 5307 by
- 5146 this
- 4931 we
- 4695 you
- 4389 do
- 4383 but
- 4371 from
- 4204 or
- 3560 which
- 3480 one
- 3062 would
- 3002 all
- 2903 will
- 2851 there
- 2793 say
- 2678 who
- 2378 make
- 2333 when
- 2218 can
- 2203 more
- 2199 if
- 2149 no
- 2132 man
- 2099 out
- 2035 other
- 1986 so
- 1965 what
- 1940 time
- 1895 up
- 1849 go
- 1816 about
- 1794 than
- 1790 into
- 1782 could
- 1773 state
- 1751 only
- 1698 new
- 1673 year
- 1618 some
- 1586 take
- 1577 come
- 1575 these
- 1531 know
- 1520 see
- 1512 use
- 1488 get
- 1430 like
- 1377 then
- 1361 first
- 1348 any
- 1315 work
- 1314 now
- 1307 may
- 1303 such
- 1270 give
- 1239 over
- 1225 think
- 1203 most
- 1179 even
- 1086 find
- 1077 day
- 1070 also
- 1070 after
- 1036 way
- 1030 many
- 1022 must
- 1021 look
- 1018 before
- 1018 great
- 1017 back
- 987 through
- 957 long
- 949 where
- 937 much
- 915 should
- 906 well
- 905 people
- 903 down
- 895 own
- 889 just
- 883 because
- 879 good
- 878 each
- 864 those
- 853 feel
- 853 seem
- 849 how
- 847 high
- 835 too
- 835 place
- 833 little
- 832 world
- 797 very
- 792 still
- 789 nation
- 784 hand
- 780 old
- 774 life
- 771 tell
- 768 write
- 768 become
- 761 here
- 755 show
- 745 house
- 731 both
- 730 between
- 723 need
- 719 mean
- 711 call
- 710 develop
- 707 under
- 705 last
- 704 right
- 703 move
- 702 thing
- 700 general
- 697 school
- 697 never
- 690 same
- 690 another
- 681 begin
- 680 while
- 678 number
- 672 part
- 668 turn
- 664 real
- 662 leave
- 660 might
- 654 want
- 645 point
- 639 form
- 639 off
- 638 child
- 634 few
- 632 small
- 629 since
- 627 against
- 614 ask
- 611 late
- 611 home
- 605 interest
- 605 large
- 601 person
- 600 end
- 596 open
- 590 public
- 589 follow
- 588 during
- 584 present
- 583 without
- 580 again
- 577 hold
- 568 govern
- 567 around
- 565 possible
- 564 head
- 563 consider
- 560 word
- 560 program
- 560 problem
- 552 however
- 552 lead
- 548 system
- 546 set
- 539 order
- 539 eye
- 538 plan
- 534 run
- 534 keep
- 534 face
- 534 fact
- 534 group
- 533 play
- 531 stand
- 529 increase
- 529 early
- 528 course
- 527 change
- 523 help
- 522 line
- 521 city
- 513 put
- 511 close
- 506 case
- 504 force
- 501 meet
- 501 once
- 501 water
- 498 upon
- 496 war
- 496 build
- 496 hear
- 496 light
- 495 unite
- 493 live
- 492 every
- 491 country
- 490 bring
- 490 center
- 489 let
- 488 side
- 487 try
- 486 provide
- 484 continue
- 482 name
- 481 certain
- 480 power
- 479 pay
- 473 result
- 473 question
- 471 study
- 468 woman
- 464 member
- 463 until
- 461 far
- 460 night
- 458 always
- 458 service
- 458 away
- 457 report
- 454 something
- 453 company
- 452 week
- 451 church
- 451 toward
- 451 start
- 449 social
- 445 room
- 443 figure
- 441 nature
- 440 though
- 438 young
- 437 less
- 434 enough
- 433 almost
- 432 read
- 426 include
- 424 president
- 423 nothing
- 419 yet
- 418 better
- 417 big
- 413 boy
- 412 cost
- 412 business
- 411 value
- 409 second
- 407 why
- 406 clear
- 405 expect
- 405 family
- 401 complete
- 401 act
- 401 sense
- 400 mind
- 399 experience
- 396 art
- 395 next
- 395 near
- 394 direct
- 393 car
- 393 law
- 387 industry
- 386 important
- 381 girl
- 379 god
- 378 several
- 377 matter
- 376 usual
- 373 rather
- 371 per
- 369 often
- 369 kind
- 369 among
- 368 white
- 365 reason
- 365 action
- 364 return
- 364 foot
- 360 care
- 360 simple
- 359 within
- 358 love
- 358 human
- 355 along
- 353 appear
- 353 doctor
- 353 believe
- 352 speak
- 351 active
- 351 student
- 350 month
- 349 drive
- 348 concern
- 348 best
- 348 door
- 346 hope
- 345 example
- 345 inform
- 344 body
- 344 ever
- 343 least
- 343 probable
- 343 understand
- 342 reach
- 340 effect
- 339 different
- 337 idea
- 337 whole
- 335 control
- 333 condition
- 333 field
- 333 pass
- 333 fall
- 332 note
- 332 special
- 332 talk
- 331 particular
- 330 today
- 329 measure
- 328 walk
- 328 teach
- 327 low
- 327 hour
- 326 type
- 326 carry
- 324 rate
- 324 remain
- 324 full
- 323 street
- 323 easy
- 323 although
- 321 record
- 321 sit
- 320 determine
- 315 level
- 313 local
- 312 sure
- 312 receive
- 311 thus
- 309 moment
- 308 spirit
- 308 train
- 308 college
- 307 religion
- 307 perhaps
- 306 music
- 306 grow
- 305 free
- 304 cause
- 302 serve
- 302 age
- 302 book
- 302 board
- 302 recent
- 301 sound
- 301 office
- 300 cut
- 299 step
- 297 class
- 297 true
- 297 history
- 296 position
- 296 above
- 295 strong
- 294 friend
- 293 necessary
- 292 add
- 292 court
- 291 deal
- 290 tax
- 289 support
- 286 party
- 286 whether
- 285 either
- 285 land
- 285 material
- 285 happen
- 285 education
- 284 death
- 284 agree
- 283 arm
- 282 mother
- 282 across
- 281 quite
- 281 anything
- 281 town
- 281 past
- 281 view
- 281 society
- 280 manage
- 280 answer
- 280 break
- 279 organize
- 277 half
- 276 fire
- 276 lose
- 275 money
- 275 stop
- 275 actual
- 274 already
- 274 effort
- 273 wait
- 273 department
- 273 able
- 272 political
- 271 learn
- 271 voice
- 269 air
- 269 together
- 269 shall
- 269 cover
- 269 common
- 268 subject
- 266 draw
- 265 short
- 265 wife
- 265 treat
- 263 limit
- 262 road
- 262 letter
- 260 color
- 260 behind
- 258 produce
- 258 send
- 258 term
- 257 total
- 256 university
- 254 rise
- 254 century
- 253 success
- 253 minute
- 251 remember
- 250 purpose
- 250 test
- 248 fight
- 247 watch
- 247 situation
- 246 south
- 246 ago
- 245 difference
- 245 stage
- 244 father
- 243 table
- 242 rest
- 242 bear
- 240 entire
- 240 market
- 240 prepare
- 240 explain
- 239 offer
- 239 plant
- 238 charge
- 238 ground
- 238 west
- 237 picture
- 237 hard
- 234 front
- 233 lie
- 232 modern
- 231 dark
- 230 surface
- 230 rule
- 230 regard
- 229 dance
- 229 peace
- 227 observe
- 227 future
- 227 wall
- 225 farm
- 225 claim
- 225 firm
- 223 operation
- 223 further
- 223 pressure
- 222 property
- 222 morning
- 222 amount
- 221 top
- 221 outside
- 221 piece
- 221 sometimes
- 220 beauty
- 220 trade
- 220 fear
- 220 demand
- 220 wonder
- 219 list
- 219 accept
- 218 judge
- 218 paint
- 217 mile
- 217 soon
- 215 responsible
- 214 allow
- 214 secretary
- 214 heart
- 213 union
- 213 slow
- 213 island
- 213 enter
- 213 drink
- 212 story
- 211 experiment
- 211 stay
- 210 paper
- 210 space
- 210 apply
- 209 decide
- 208 share
- 207 desire
- 207 spend
- 207 sign
- 206 therefore
- 206 various
- 206 visit
- 205 supply
- 205 officer
- 205 doubt
- 204 private
- 204 immediate collins merriam-webster
- 204 wish
- 204 contain
- 204 feed
- 204 raise
- 204 describe
- 203 ready
- 203 horse
- 202 son
- 202 exist
- 202 north
- 201 suggest
- 200 station
- 200 effective
- 199 food
- 199 deep
- 198 wide
- 197 alone
- 196 character
- 195 english
- 196 happy
- 196 critic collins merriam-webster
- 195 unit
- 195 product
- 195 respect
- 195 drop
- 195 nor
- 195 fill
- 194 cold
- 193 represent collins merriam-webster
- 193 sudden
- 192 basic
- 192 kill
- 191 fine
- 191 trouble
- 191 mark
- 191 single
- 190 press
- 189 heavy
- 189 attempt
- 189 origin collins merriam-webster
- 189 standard
- 188 everything
- 188 committee
- 188 moral
- 187 black
- 186 red
- 186 bad
- 186 earth
- 185 accord
- 185 else
- 185 mere
- 184 die
- 184 remark
- 184 basis
- 184 except
- 183 equal
- 183 east
- 183 event
- 183 employ
- 183 defense
- 183 smile
- 183 river
- 183 improve
- 182 game
- 181 detail
- 181 account
- 181 cent
- 181 sort
- 180 reduce
- 180 club
- 180 buy
- 180 attention
- 180 ship
- 179 decision
- 178 wear
- 178 inside
- 178 win
- 178 suppose
- 178 ride
- 177 operate
- 177 realize
- 177 sale
- 177 choose
- 177 park
- 177 square
- 176 vote
- 176 price
- 176 district
- 175 dead
- 175 foreign
- 175 window
- 175 beyond
- 174 direction
- 174 strike
- 174 instead
- 173 trial
- 173 practice
- 173 catch
- 172 opportunity
- 172 likely
- 170 recognize
- 170 permit
- 170 serious
- 170 attack
- 170 floor
- 168 association
- 168 spring
- 167 lot
- 167 stock
- 167 lack
- 167 hair
- 167 science
- 166 relation
- 166 profession
- 166 pattern
- 165 quick
- 164 medical
- 165 influence
- 165 occasion
- 165 machine
- 164 compare
- 163 husband
- 163 blue
- 163 international
- 162 fair
- 162 especially
- 162 indeed
- 162 imagine
- 162 surprise
- 162 average
- 161 official
- 161 temperature
- 161 difficult
- 160 sing
- 160 hit
- 160 tree
- 160 race
- 160 police
- 160 touch
- 159 relative
- 159 throw
- 159 quality
- 159 former
- 158 pull
- 157 chance
- 157 prove
- 157 argue
- 157 settle
- 156 growth
- 156 date
- 156 heat
- 155 save
- 155 performance
- 155 count
- 155 production
- 154 listen
- 152 main
- 154 pick
- 154 size
- 152 cool
- 152 army
- 152 patient
- 151 combine
- 151 summer
- 151 hall
- 151 slight
- 151 command
- 151 enjoy
- 151 length
- 150 proper
- 150 express
- 150 health
- 150 chief
- 149 evening
- 149 store
- 149 language
- 148 degree
- 148 lay
- 147 current
- 147 gun
- 147 dog
- 147 hotel
- 147 strange
- 147 separate
- 146 boat
- 146 fail
- 146 clean
- 146 dress
- 146 anyone
- 146 gain
- 146 pain
- 145 object
- 145 knowledge
- 145 depend
- 145 relate
- 145 below
- 144 dollar
- 144 advance
- 144 shape
- 144 arrange
- 144 population
- 144 yes
- 144 sell
- 144 mention
- 144 dry
- 144 check
- 144 poet
- 143 sleep
- 143 join
- 143 hot
- 143 bed
- 143 electric
- 143 dream
- 142 due
- 142 season
- 142 manner
- 142 fit
- 142 left
- 141 progress
- 141 neither
- 141 strength
- 140 notice
- 140 finish
- 140 opinion
- 140 bill
- 140 western
- 140 truth
- 138 wrong
- 138 travel
- 138 suit
- 137 bank
- 137 exact
- 137 honor
- 137 brother
- 136 quiet
- 136 marry
- 136 corner
- 135 handle
- 135 danger
- 135 hospital
- 135 pool
- 135 promise
- 135 blood
- 135 shoot
- 135 scene
- 134 literature
- 134 arrive
- 134 film
- 133 base
- 133 freedom
- 133 bar
- 133 maybe
- 133 hang
- 133 suffer
- 133 manufacture
- 132 frequent
- 132 rock
- 132 loss
- 131 burn
- 131 sun
- 131 audience
- 130 essential
- 130 glass
- 130 prevent
- 130 poem
- 130 poor
- 130 inch
- 129 song
- 129 skill
- 129 post
- 129 popular
- 129 radio
- 129 animal
- 128 conscious
- 128 worth
- 128 eat
- 128 election
- 128 faith
- 128 wave
- 128 murder
- 128 model
- 128 forget
- 127 extend
- 127 edge
- 127 distance
- 127 memory
- 127 recommend
- 126 division
- 126 staff
- 126 leg
- 126 discussion
- 126 address
- 126 fly
- 125 dependent
- 125 ball
- 125 shake
- 125 frame
- 125 extreme
- 124 engineer
- 124 thick
- 124 comfort
- 124 latter
- 124 camp
- 124 oil
- 124 discover
- 124 examine
- 123 difficulty
- 123 tooth
- 123 middle
- 123 choice
- 123 refer
- 123 enemy
- 123 practical
- 122 marriage
- 122 bridge
- 122 declare
- 122 lady
- 122 cross
- 122 daily
- 122 afternoon
- 121 attend
- 121 director
- 121 balance
- 121 wash
- 121 capital
- 120 speed
- 120 block
- 120 citizen
- 119 mouth
- 119 hill
- 118 green
- 118 please
- 118 motor
- 118 agency
- 118 encourage
- 118 governor
- 117 worry
- 117 affair
- 117 shoulder
- 117 bright
- 116 mass
- 116 sample
- 116 pretty
- 116 repeat
- 115 roll
- 115 push
- 115 trip
- 115 council
- 115 clothe
- 115 parent
- 115 forward
- 114 sharp
- 114 straight
- 113 gas
- 113 weight
- 113 discuss
- 113 fix
- 113 load
- 112 master
- 112 whatever
- 112 round
- 112 rapid
- 112 laugh
- 111 finger
- 111 spot
- 110 propose
- 110 shop
- 110 broad
- 110 replace
- 110 reply
- 110 extent
- 109 lock
- 109 employee
- 109 ahead
- 109 sight
- 109 spread
- 109 wind
- 109 approve
- 109 destroy
- 108 none
- 108 pound
- 108 fame
- 108 importance
- 107 reflect
- 107 advantage
- 107 match
- 107 regular
- 107 wage
- 107 refuse
- 107 existence
- 106 hardly
- 106 perform
- 106 title
- 105 tend
- 105 exercise
- 105 thin
- 105 coat
- 105 bit
- 105 mountain
- 105 youth
- 104 behavior
- 104 newspaper
- 104 secret
- 104 ability
- 104 sea
- 104 soft
- 104 justice
- 104 reasonable
- 104 circle
- 104 solid
- 104 page
- 103 weapon
- 103 fast
- 103 representative
- 103 search
- 103 pure
- 103 escape
- 102 crowd
- 102 stick
- 101 telephone
- 101 avoid
- 101 garden
- 101 favor
- 101 news
- 101 unless
- 100 dinner
- 100 someone
- 100 signal
- 100 yard
- 100 ideal
- 100 warm
- 100 miss
- 100 shelter
- 100 soldier
- 99 article
- 99 cry
- 99 captain
- 99 familiar
- 99 seat
- 99 guest
- 98 weak
- 98 excite
- 98 king
- 98 everyone
- 98 wine
- 97 hole
- 97 duty
- 97 beat
- 97 perfect
- 97 bottom
- 97 compose
- 97 battle
- 97 expense
- 97 cattle
- 96 flow
- 95 kitchen
- 95 dust
- 95 bottle
- 94 admit
- 94 tear
- 94 tire
- 94 expression
- 93 exception
- 93 application
- 93 belong
- 93 rich
- 93 failure
- 93 struggle
- 93 instrument
- 93 variety
- 93 narrow
- 92 theater
- 92 collection
- 92 rain
- 92 review
- 92 preserve
- 92 leadership
- 91 clay
- 91 daughter
- 91 fellow
- 91 swing
- 91 thank
- 90 library
- 90 fat
- 90 reserve
- 89 tour
- 89 nice
- 89 warn
- 89 ring
- 89 bitter
- 89 chair
- 89 yesterday
- 89 scientific
- 88 flower
- 88 wheel
- 88 solution
- 88 aim
- 88 gather
- 88 invite
- 88 moreover
- 88 fresh
- 88 forest
- 87 winter
- 87 box
- 87 belief
- 87 ordinary
- 87 impossible
- 87 print
- 87 gray
- 87 taste
- 87 lip
- 87 speech
- 87 reference
- 86 stain
- 86 connection
- 86 otherwise
- 86 stretch
- 86 knife
- 86 village
- 86 blow
- 85 mistake
- 85 sweet
- 85 shout
- 85 divide
- 85 guard
- 85 worse
- 85 exchange
- 85 rare
- 84 commercial
- 84 request
- 84 appoint
- 84 agent
- 83 dependence
- 83 bird
- 83 wild
- 83 motion
- 83 guess
- 83 neighbor
- 82 seed
- 82 fashion
- 82 loan
- 82 correct
- 81 plain
- 81 mail
- 81 retire
- 81 opposite
- 81 prefer
- 81 safe
- 81 evil
- 81 double
- 81 wood
- 80 empty
- 80 baby
- 80 advise
- 80 content
- 80 sport
- 80 lift
- 80 literary
- 80 curious
- 80 tie
- 80 flat
- 80 message
- 80 neck
- 79 hate
- 79 dirt
- 79 delight
- 79 trust
- 79 nobody
- 79 valley
- 79 tool
- 78 presence
- 78 cook
- 78 railroad
- 78 minister
- 78 coffee
- 78 brush
- 78 beside
- 78 collect
- 77 guide
- 77 luck
- 77 profit
- 77 lord
- 77 everybody
- 77 prison
- 77 cloud
- 77 slave
- 77 chairman
- 76 soil
- 76 distinguish
- 76 introduce
- 76 urge
- 76 blind
- 75 arise
- 75 upper
- 75 curve
- 75 membership
- 75 key
- 75 entertain
- 75 soul
- 75 neighborhood
- 74 friendly
- 74 pair
- 74 stone
- 74 lean
- 74 protect
- 74 advertise
- 74 mystery
- 73 welcome
- 73 knee
- 73 jump
- 73 snake
- 73 stream
- 73 avenue
- 73 brown
- 73 disease
- 73 hat
- 73 excellent
- 72 formal
- 72 snow
- 72 sheet
- 72 somehow
- 72 unity
- 72 sky
- 72 rough
- 72 smooth
- 72 weather
- 72 steady
- 72 threaten
- 72 depth
- 71 oppose
- 71 deliver
- 71 ancient
- 71 pray
- 71 adopt
- 71 birth
- 71 appearance
- 71 universe
- 71 busy
- 71 hurry
- 71 coast
- 71 forth
- 70 smell
- 70 furnish
- 70 female
- 70 hide
- 70 wire
- 70 proposal
- 70 ought
- 70 victory
- 69 quarter
- 69 engine
- 69 customer
- 69 waste
- 69 fool
- 69 intend
- 69 intention
- 69 desk
- 69 politics
- 69 passage
- 69 lawyer
- 68 root
- 68 climb
- 68 metal
- 68 gradual
- 68 hunt
- 68 protection
- 68 satisfy
- 68 roof
- 68 branch
- 68 pleasure
- 68 witness
- 68 loose
- 67 nose
- 67 mine
- 67 band
- 67 aside
- 67 risk
- 67 tomorrow
- 67 remind
- 67 ear
- 67 fish
- 67 shore
- 66 operator
- 66 civilize
- 66 being
- 66 silent
- 66 screen
- 66 bind
- 66 earn
- 66 pack
- 66 colony
- 66 besides
- 66 slip
- 66 cousin
- 66 scale
- 66 relief
- 66 explore
- 66 stem
- 65 brain
- 65 musician
- 65 defend
- 65 bend
- 65 somebody
- 65 shadow
- 64 mix
- 64 smoke
- 64 description
- 64 fruit
- 64 guilt
- 64 yield
- 64 sensitive
- 64 salt
- 64 pale
- 64 sweep
- 64 completion
- 64 throat
- 64 agriculture
- 64 admire
- 63 gentle
- 63 dozen
- 63 particle
- 63 pleasant
- 63 bay
- 63 cup
- 63 competition
- 63 moon
- 63 terrible
- 63 strip
- 63 mechanic
- 63 shock
- 63 conversation
- 63 angle
- 62 tall
- 62 plenty
- 62 star
- 62 yellow
- 62 sick
- 62 thorough
- 62 absolute
- 62 succeed
- 61 surround
- 61 proud
- 61 dear
- 61 card
- 61 lake
- 61 breath
- 61 afraid
- 61 silence
- 61 onto
- 60 shoe
- 60 somewhere
- 60 chain
- 60 slide
- 60 copy
- 60 machinery
- 60 wake
- 60 severe
- 60 pocket
- 60 bone
- 59 honest
- 59 freeze
- 59 dictionary
- 59 calm
- 59 swim
- 59 ice
- 59 male
- 59 skin
- 59 crack
- 59 rush
- 59 wet
- 58 meat
- 58 commerce
- 58 joint
- 58 gift
- 58 host
- 58 suspect
- 58 path
- 58 uncle
- 58 afford
- 58 instant
- 58 satisfactory
- 58 height
- 58 track
- 58 confidence
- 58 grass
- 57 suggestion
- 57 favorite
- 57 breakfast
- 57 apart
- 57 chest
- 57 entrance
- 57 march
- 57 sink
- 57 northern
- 57 iron
- 57 alive
- 57 ill
- 57 bag
- 57 disturb
- 57 native
- 57 bedroom
- 57 violent
- 57 beneath
- 57 pause
- 57 tough
- 56 substance
- 56 threat
- 56 charm
- 56 absence
- 56 factory
- 56 spite
- 56 meal
- 56 universal
- 56 accident
- 56 highway
- 56 sentence
- 56 liberty
- 55 wise
- 55 noise
- 55 discovery
- 55 tube
- 55 flash
- 55 twist
- 55 fence
- 55 childhood
- 55 joy
- 55 sister
- 54 sad
- 54 efficiency
- 54 disappear
- 54 defeat
- 54 extensive
- 54 rent
- 54 comparison
- 54 possess
- 54 grace
- 54 flesh
- 54 liquid
- 54 scientist
- 54 ease
- 53 heaven
- 53 milk
- 53 sympathy
- 53 rank
- 53 restaurant
- 53 frequency
- 53 angry
- 53 shade
- 53 accuse
- 53 necessity
- 53 knock
- 53 loud
- 53 permanent
- 53 row
- 53 lovely
- 53 confuse
- 52 gold
- 52 frighten
- 52 solve
- 52 grave
- 52 salary
- 52 photograph
- 52 advice
- 52 abroad
- 51 wound
- 51 virtue
- 51 dare
- 51 queen
- 51 extra
- 51 attract
- 50 numerous
- 50 pink
- 50 gate
- 50 expensive
- 50 shut
- 50 chicken
- 50 forgive
- 50 holy
- 50 wooden
- 49 prompt
- 49 crime
- 49 sorry
- 49 republic
- 49 anger
- 49 visitor
- 49 pile
- 49 violence
- 49 steel
- 49 wing
- 49 stair
- 49 partner
- 49 delay
- 49 gentleman
- 48 pour
- 48 confusion
- 48 damage
- 48 kick
- 48 safety
- 48 burst
- 48 network
- 48 resistance
- 48 screw
- 48 pride
- 48 till
- 47 hire
- 47 verb
- 47 preach
- 47 clerk
- 47 everywhere
- 47 anyway
- 47 fan
- 47 connect
- 47 egg
- 47 efficient
- 47 grain
- 46 calculate
- 46 drag
- 46 opposition
- 46 worship
- 46 arrest
- 46 discipline
- 46 string
- 46 harbor
- 46 camera
- 46 mechanism
- 46 cow
- 46 grand
- 46 funny
- 46 insurance
- 46 reduction
- 46 strict
- 46 lesson
- 46 tight
- 45 sand
- 45 plate
- 45 qualify
- 45 elsewhere
- 45 mad
- 45 interference
- 45 pupil
- 45 fold
- 45 royal
- 45 valuable
- 45 whisper
- 45 anybody
- 45 hurt
- 45 excess
- 44 quantity
- 44 fun
- 44 mud
- 44 extension
- 44 recognition
- 44 kiss
- 44 crop
- 44 sail
- 44 attractive
- 44 habit
- 44 relieve
- 44 wisdom
- 44 persuade
- 43 certainty
- 43 cloth
- 43 eager
- 43 deserve
- 43 sympathetic
- 43 cure
- 43 trap
- 43 puzzle
- 43 powder
- 43 raw
- 43 mankind
- 43 glad
- 43 blame
- 43 whenever
- 43 anxiety
- 42 bus
- 42 tremble
- 42 sacred
- 42 fortunate
- 42 glory
- 42 golden
- 42 neat
- 42 weekend
- 42 treasury
- 42 overcome
- 42 cat
- 42 sacrifice
- 42 complain
- 42 elect
- 41 roar
- 41 sake
- 41 temple
- 41 self
- 41 compete
- 41 nurse
- 41 stuff
- 41 stomach
- 41 peculiar
- 41 repair
- 41 storm
- 41 ton
- 41 desert
- 41 allowance
- 41 servant
- 41 hunger
- 41 conscience
- 41 bread
- 41 crash
- 40 tip
- 40 strengthen
- 40 proof
- 40 generous
- 40 sir
- 40 tonight
- 40 whip
- 40 tongue
- 40 mill
- 40 merchant
- 40 coal
- 40 ruin
- 40 introduction
- 40 courage
- 40 actor
- 40 belt
- 39 stir
- 39 package
- 39 punish
- 39 reflection
- 39 breathe
- 39 anywhere
- 39 amuse
- 39 dull
- 39 fate
- 39 net
- 39 fellowship
- 39 fault
- 39 furniture
- 39 beam
- 39 pencil
- 39 border
- 39 disappoint
- 38 flame
- 38 joke
- 38 bless
- 38 corn
- 38 shell
- 38 tempt
- 38 supper
- 38 destruction
- 38 dive
- 38 anxious
- 38 shine
- 38 cheap
- 38 dish
- 38 distant
- 38 greet
- 37 flood
- 37 excuse
- 37 insect
- 37 ocean
- 37 ceremony
- 37 decrease
- 37 prize
- 37 harm
- 37 insure
- 37 verse
- 37 pot
- 37 sincere
- 36 cotton
- 36 leaf
- 36 rub
- 36 medicine
- 36 stroke
- 36 bite
- 36 lung
- 36 lonely
- 36 admission
- 36 stupid
- 36 scratch
- 36 composition
- 36 broadcast
- 36 drum
- 36 resist
- 36 neglect
- 35 absent
- 35 passenger
- 35 adventure
- 35 beg
- 35 pipe
- 35 beard
- 35 bold
- 35 meanwhile
- 35 devil
- 35 cheer
- 35 nut
- 35 split
- 35 melt
- 35 swear
- 35 sugar
- 35 bury
- 35 wipe
- 35 faint
- 35 creature
- 35 tail
- 35 wealth
- 34 earnest
- 34 translate
- 34 suspicion
- 34 noble
- 34 inquiry
- 34 journey
- 34 hesitate
- 34 extraordinary
- 34 borrow
- 34 owe
- 34 funeral
- 34 ambition
- 34 mixture
- 34 slope
- 34 criminal
- 34 seldom
- 34 map
- 34 spin
- 34 praise
- 34 spare
- 33 plow
- 33 telegraph
- 33 barrel
- 33 straighten
- 33 scarce
- 33 lunch
- 33 slavery
- 33 creep
- 33 sweat
- 33 gay
- 33 stiff
- 33 brave
- 33 seize
- 33 convenient
- 33 horizon
- 33 moderate
- 33 complicate
- 33 dig
- 33 curse
- 33 weigh
- 33 priest
- 33 excessive
- 33 quarrel
- 32 widow
- 32 modest
- 32 dine
- 32 politician
- 32 custom
- 32 educate
- 32 salesman
- 32 nail
- 32 tap
- 32 eastern
- 32 possession
- 32 satisfaction
- 32 behave
- 32 mercy
- 31 scatter
- 31 objection
- 31 silver
- 31 tent
- 31 saddle
- 31 wrap
- 31 nest
- 31 grind
- 31 spell
- 31 plaster
- 31 arch
- 31 swell
- 31 friendship
- 31 bath
- 30 bundle
- 30 grateful
- 30 crown
- 30 boundary
- 30 nowhere
- 30 asleep
- 30 clock
- 30 boil
- 30 altogether
- 30 lend
- 30 holiday
- 30 precious
- 30 wander
- 30 ugly
- 30 reputation
- 30 ticket
- 30 pretend
- 30 dismiss
- 30 delicate
- 29 despair
- 29 awake
- 29 tea
- 29 FALSE
- 29 fortune
- 29 cap
- 29 thread
- 29 haste
- 29 bare
- 29 shirt
- 29 bargain
- 28 leather
- 28 rail
- 28 butter
- 28 dot
- 28 inquire
- 28 warmth
- 28 decisive
- 28 vessel
- 28 pity
- 28 steam
- 28 pin
- 28 bound
- 28 companion
- 28 toe
- 28 reward
- 28 forbid
- 28 wherever
- 28 tower
- 27 bathe
- 27 lodge
- 27 swallow
- 27 multiply
- 27 bow
- 27 kingdom
- 27 garage
- 27 permission
- 27 pump
- 27 prevention
- 27 urgent
- 27 aunt
- 27 zero
- 27 idle
- 27 fever
- 27 christmas
- 27 regret
- 26 jaw
- 26 soap
- 26 pronounce
- 26 empire
- 26 bowl
- 26 outline
- 26 organ
- 26 imitation
- 26 caution
- 26 mineral
- 26 disagree
- 26 blade
- 26 trick
- 26 treasure
- 26 immense
- 25 convenience
- 25 disapprove
- 25 destructive
- 25 fork
- 25 noon
- 25 ownership
- 25 tune
- 25 polish
- 25 poison
- 25 shame
- 25 loyalty
- 25 cottage
- 25 astonish
- 25 shave
- 25 feather
- 25 sauce
- 25 lid
- 25 debt
- 25 fade
- 25 confess
- 25 classification
- 24 descend
- 24 cape
- 24 mild
- 24 clever
- 24 envelope
- 24 invention
- 24 sheep
- 24 splendid
- 24 stamp
- 24 float
- 24 brick
- 24 rice
- 24 businessman
- 24 backward
- 24 qualification
- 24 artificial
- 24 attraction
- 24 lamp
- 24 curl
- 23 shower
- 23 elder
- 23 bunch
- 23 bell
- 23 steer
- 23 flavor
- 23 spit
- 23 rob
- 23 cream
- 23 interrupt
- 23 pen
- 23 weave
- 23 orange
- 23 rescue
- 23 crush
- 23 humble
- 23 fancy
- 23 decay
- 23 polite
- 23 tribe
- 22 bleed
- 22 coin
- 22 fond
- 22 autumn
- 22 classify
- 22 omit
- 22 loyal
- 22 needle
- 22 lessen
- 22 complaint
- 22 pad
- 22 steep
- 22 skirt
- 22 curtain
- 22 calculation
- 22 laughter
- 22 solemn
- 22 grease
- 22 interfere
- 22 explode
- 22 fasten
- 21 flag
- 21 resign
- 21 postpone
- 21 patience
- 21 boast
- 21 rope
- 21 envy
- 21 airplane
- 21 rid
- 21 shield
- 21 veil
- 21 kneel
- 21 tray
- 21 explosive
- 21 brass
- 21 taxi
- 21 wax
- 21 duck
- 21 button
- 21 invent
- 20 remedy
- 20 bush
- 20 thunder
- 20 weaken
- 20 poverty
- 20 scrape
- 20 arrow
- 20 tender
- 20 cruel
- 20 soften
- 20 mouse
- 20 hay
- 20 anyhow
- 20 alike
- 20 circular
- 20 juice
- 20 shelf
- 20 bake
- 20 hatred
- 20 cautious
- 19 basket
- 19 wreck
- 19 width
- 19 confident
- 19 log
- 19 heap
- 19 suck
- 19 ladder
- 19 gap
- 19 obey
- 19 hut
- 19 axe
- 19 translation
- 19 collar
- 19 delivery
- 19 reproduce
- 19 confession
- 19 pan
- 19 prejudice
- 19 voyage
- 19 tobacco
- 18 simplicity
- 18 paste
- 18 cake
- 18 elephant
- 18 ribbon
- 18 harvest
- 18 ashamed
- 18 cave
- 18 customary
- 18 thief
- 18 damp
- 18 sew
- 18 rust
- 18 separation
- 18 waiter
- 18 pet
- 18 straw
- 18 upset
- 18 towel
- 18 refresh
- 17 essence
- 17 fur
- 17 ambitious
- 17 defendant
- 17 daylight
- 17 dip
- 17 suspicious
- 17 imaginary
- 17 ash
- 17 carriage
- 17 educator
- 17 saw
- 17 stove
- 17 rubber
- 17 rug
- 17 misery
- 17 awkward
- 17 rival
- 16 roast
- 16 deed
- 16 preference
- 16 explosion
- 16 theatrical
- 16 cultivate
- 16 collector
- 16 miserable
- 16 wrist
- 16 rabbit
- 16 accustom
- 16 tide
- 16 insult
- 16 thumb
- 16 lump
- 16 annoy
- 16 toy
- 16 heal
- 16 shallow
- 16 repetition
- 16 soup
- 15 whistle
- 15 scenery
- 15 apple
- 15 offense
- 15 cork
- 15 ripe
- 15 temper
- 15 sore
- 15 pinch
- 15 diamond
- 15 razor
- 15 imaginative
- 15 hook
- 15 copper
- 15 landlord
- 14 influential
- 14 rot
- 14 hollow
- 14 enclose
- 14 harden
- 14 wicked
- 14 stiffen
- 14 silk
- 14 upright
- 14 selfish
- 14 stripe
- 14 pig
- 14 inward
- 14 excellence
- 14 rake
- 14 purple
- 14 hasten
- 14 shorten
- 14 applause
- 14 ache
- 14 apology
- 14 knot
- 14 nephew
- 14 cushion
- 14 drown
- 14 nursery
- 14 pint
- 14 fierce
- 13 imitate
- 13 aloud
- 13 gaiety
- 13 robbery
- 13 tighten
- 13 perfection
- 13 scorn
- 13 whoever
- 13 trunk
- 13 wool
- 13 sailor
- 13 competitor
- 13 moonlight
- 13 deer
- 13 bean
- 13 everyday
- 13 drawer
- 13 disregard
- 12 nowadays
- 12 patriotic
- 12 tin
- 12 penny
- 12 cage
- 12 pardon
- 12 lately
- 12 offend
- 12 coarse
- 12 spoil
- 12 horizontal
- 12 sting
- 12 ditch
- 12 librarian
- 12 meantime
- 12 cough
- 12 deaf
- 12 sword
- 12 messenger
- 12 vain
- 12 castle
- 12 elastic
- 12 comb
- 12 rod
- 11 widen
- 11 sorrow
- 11 inventor
- 11 cliff
- 11 umbrella
- 11 interruption
- 11 merry
- 11 gallon
- 11 conquest
- 11 headache
- 11 tailor
- 11 bucket
- 11 scent
- 11 signature
- 11 cart
- 11 darken
- 11 sometime
- 11 applaud
- 11 underneath
- 11 hello
- 11 pretense
- 11 descent
- 11 conquer
- 11 framework
- 11 confidential
- 11 adoption
- 11 disgust
- 11 waist
- 11 momentary
- 11 receipt
- 10 pearl
- 10 ray
- 10 lazy
- 10 limb
- 10 grammatical
- 10 beast
- 10 monkey
- 10 jewel
- 10 persuasion
- 10 obedience
- 10 sock
- 10 vowel
- 10 hammer
- 10 inn
- 10 chimney
- 10 dissatisfaction
- 10 annoyance
- 10 ornament
- 10 honesty
- 10 outward
- 10 sharpen
- 10 handkerchief
- 9 greed
- 9 heavenly
- 9 thirst
- 9 niece
- 9 spill
- 9 loaf
- 9 wheat
- 9 worm
- 9 secrecy
- 9 rude
- 9 heighten
- 9 flatten
- 9 loosen
- 9 cheese
- 9 rivalry
- 9 royalty
- 9 discontent
- 9 complication
- 9 fright
- 9 indoor
- 9 flour
- 9 actress
- 8 congratulation
- 8 ounce
- 8 fry
- 8 everlasting
- 8 goat
- 8 ink
- 8 disappearance
- 8 reproduction
- 8 thicken
- 8 avoidance
- 8 spoon
- 8 strap
- 8 deceive
- 7 lengthen
- 7 revenge
- 7 correction
- 7 descendant
- 7 hesitation
- 7 spade
- 7 basin
- 7 weed
- 7 omission
- 7 old-fashioned
- 7 bicycle
- 7 breadth
- 7 photography
- 7 coward
- 7 mat
- 7 rejoice
- 7 cheat
- 7 congratulate
- 7 discomfort
- 7 enclosure
- 7 attentive
- 7 paw
- 6 overflow
- 6 dissatisfy
- 6 multiplication
- 6 whichever
- 6 tidy
- 6 bribe
- 6 mend
- 6 stocking
- 6 feast
- 6 nuisance
- 6 thorn
- 6 tame
- 5 inclusive
- 5 homemade
- 5 handwriting
- 5 chalk
- 5 sour
- 5 slippery
- 5 procession
- 5 ripen
- 5 jealous
- 5 jealousy
- 5 liar
- 5 homecoming
- 5 barber
- 5 whiten
- 5 berry
- 5 lighten
- 5 pigeon
- 5 hinder
- 4 bravery
- 4 baggage
- 4 noun
- 4 amongst
- 4 grammar
- 4 cultivation
- 4 companionship
- 4 rubbish
- 4 modesty
- 4 woolen
- 4 deepen
- 4 pastry
- 4 cupboard
- 4 quart
- 4 canal
- 4 notebook
- 4 deceit
- 3 parcel
- 3 brighten
- 3 moderation
- 3 punctual
- 3 hurrah
- 3 lipstick
- 3 uppermost
- 3 fatten
- 3 conqueror
- 2 hindrance
- 2 cowardice
- 2 obedient
- 2 saucer
- 2 madden
- 2 scold
- 2 weekday
- 2 rotten
- 2 disrespect
- 1 widower
- 1 deafen
- 1 donkey
- 1 businesslike
- 1 motherhood
- 1 sadden
- 1 handshake
- 1 calculator
- 1 headdress
- 1 scissors
- 1 translator
- 1 possessor
- 1 shilling
- 1 redden
- 1 motherly
- 0 whose
- 0 cultivator
- 0 whom
- 0 homework
- 0 electrician
- 0 oar
- 0 bribery
- 0 sweeten
- 0 sow
- 0 pronunciation
- 0 beak
- 0 plural
A Toast to your health（告别心理亚健康的良方）
Instead of waiting for stress or illness to come and then reacting to it, set goals and structure life in ways that are mostly likely to forge a healthy foundation. The following nine steps to greater happiness and better mental health are presented as guideline to encourage you to take a more active role in your own life and to create a more positive psychological environment for yourself and others. Think of the steps as year-round resolutions.
与其等压力或疾病自己找上门时再去应付，不如设定目标来健康地组织你的生活。下面9步可以带来更多的快乐和更好的精神健康，可以作为一种指导，鼓励你更加积极地生活，并为你自己和他人创建一个更加积极的心理环境。下面的步骤可以在一年内实施。
- Never say bad things about yourself. Look for sources of your unhappiness in elements that can be modified by future actions. Give yourself and others only constructive criticism —— what can be done differently next time to get what you want?
永远不要说关于你的不好的事情。寻找那些你将来采取行动可以加以改变的不快乐的根源。只给你自己和他人建设性的批评－下次应该采取什么不同的做法来得到你想要的东西？
- Compare your reactions, thoughts and feelings with those of friends, co-workers, family members and others so that you can gauge the appropriateness and relevance of your response against a suitable social norm.
将你的反应、想法和感受同你的朋友、同事、家庭成员以及其他人进行比较，从而使你可以估计出自己行为的适宜性以及你的反应和适宜的社会规范的关系。
- Have several close friends with whom you can share feelings, joys and worries. Work at developing, maintaining and expanding your social support networks.
结交一些密友，你可以同他们分享感受、快乐和忧虑。致力于发展、保持和拓展你的社会支持网络。
- Developing a sense of balanced time perspective in which you can flexibly focus on the demands of the task, the situation, and your needs; be future oriented when there is work to be done, present oriented when the goal is archieved and pleasure is at hand, and past orented to keey you in touch with your roots.
发展一种平衡时间的观点，从而可以灵活地对待你的工作、环境的要求和自身需求。有工作在手时请面向未来，目标达到、有快乐在握时请珍惜现在，和你的老友联系时请珍惜过去。
- Always take full credit for your sucesses and happiness(and share positive feelings with other people). Keep an inventory of all the qualities that make you special and unique —— those qualities you can offer others. For example, a shy person can provide a talkative person with the gift of attentive listening. Know your sources of personal strength and available coping resources.
永远对你的成功和快乐充满信心（并且和他人分享你的积极感受）。清楚地了解你独特的、与众不同的品质－那些你可以提供给他人的品质。例如，一个害羞的人可以给一个善谈者提供专注的倾听。了解你的个人优势和可以有效进行应对的资源。
- When you feel you are losing control over your emotions, distance youself from the situation by physically leaving it, role-playing the position of another person in the situation or conflict, projecting your imagination into the future to gain perspective on what seems an overwhelming problem now, or talking to a a sympathetic listener. Allow youself to feel and express your emotions.
当你感觉你就要对自己的情绪失去控制时，请用离开的办法避开使你不快的环境，或者站在另一个人的立场考虑一下，或者设想未来，使你看到问题得以克服的前景，或者向一个同情者加以倾诉。请允许你自己感受和表达自己的情绪。
- Remember that failure and disappointment are sometimes blessing in disguise. They may tell you that your goals are not right for you or may save you from bigger letdowns later on. Learn from every failure. Acknowledge setbacks by saying, ‘I made a mistake’, and move on. Every accident, misfortune or violation of your expectations is potentially a wonderful oppportunity in disguise.
记住失败和失望有时是伪装下的祝福。它们可以告诉你目标可能并不适合你，或者救你于未来更大的失败之前。吃一堑，长一智。遭受挫折后说一句“我犯了个错误”，再继续前进。你所经历的每一次事故、不幸和挫折实际上都是一个潜在的美妙机会，只是它们未以真面目示人。
- If you discover you cannot help yourself or another person in distress, seek the counsel of a trained specialist in your student health department or community. In some cases, a problem that appears to be psychological may really be physical and vice versa. Check out your student mental health services before you need them, and use them without concern about being stigmatised.
如果你发现你无法使自己或他人走出忧郁，那就向学校或社区的健康部门受过训练的专业人员寻求建议。在某些情况下，有些看上去的心理问题实际上是生理问题，有些则正好相反。在你需要它们之前就了解一下你的学生心理健康服务内容，而在运用它们时不必有任何被诬蔑的疑虑。
- Cultivate healthy pleasures. Take time out to relax, to meditate, to get a message, to fly a kite and to enjoy hobbies and activities you can do alone and that help you get in touch with and better appreciate yourself.
培养健康的愉悦。花些时间去放松、去反省、去收集信息、去放风筝、去享受你的爱好、去进行一些可以独处的活动，以及那些你可以做到并得到更好的享受的活动。
Psychology and Life, Chapter 13 Emotion, stress and health, by Richard J Gerrig, Philip G Zimbardo, Andrew J Campbell, Steven R Cumming, Fiona J Wilkes
《心理学与生活》第16版
算法与数据结构
Rosetta Code
http://rosettacode.org/wiki/Rosetta_Code
用不同语言来演示各种算法。
Greatest common divisor
欧几里得算法
http://rosettacode.org/wiki/Greatest_common_divisor
Elliptic Curve Digital Signature Algorithm
https://rosettacode.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm
leetcode
practicer
读书摘抄
The Number Mysteries: A Mathematical Odyssey through Everyday Life
du Sautoy, Marcus
One THE CURIOUS INCIDENT OF THE NEVER-ENDING PRIMES
p. 29
The Chinese were probably one of the first cultures to single out the primes as important numbers. They believed that each number had its own gender—even numbers were female, and odd numbers were male. They realized that some odd numbers were rather special. For example, if you have 15 stones, there is a way to arrange them into a nice-looking rectangle, in three rows of five. But if you have 17 stones, you can’t make a neat array: all you can do is line them up in a straight line. For the Chinese, the primes were therefore the really macho numbers. The odd numbers that aren’t prime, though they were male, were somehow rather effeminate. This ancient Chinese perspective homed in on the essential property of being prime, because the number of stones in a pile is prime if there is no way to arrange them into a nice rectangle.
Applied Combinatorics
Prelude
第6页
This book seeks to develop facility at combinatorial reasoning, which is the basis for analyzing a wide range of problems in computer science and discrete applied mathematics.
Preface
第1页
Combinatorial reasoning underlies all analysis of computer systems. It plays similar role in discrete operations research problems and in finite probability.
This book teaches students in the mathematical sciences how to reason and model combinatorially. It seeks to develop proficiency in basic discrete math problem solving in the way that a calculus textbook develops proficiency in basic analysis problems solving.
The three principal aspects of combinatorial reasoning emphasized in this book are: the systematic analysis of different possibilities, the exploration of the logical structure of a problem(e.g.,finding manageable sub pieces or first solving the problem with three objects instead of n), and ingenuity.
Becoming a Better Programmer
chapter 14 Software Development is
第131页
Too much modern software is like my Alphabetti custard: it’s the wrong thing, written the wrong way.
chapter 24 Live to Love to Learn
第221页
The Knowledge Portfolio
Be aware of the risk/reward balance of the items in your portfolio.
Purposefully manage your knowledge portfolio.
Complexity
第233页
What Is Network Thinking?
Network thinking means focusing on relationships between entities rather than the entities themselves.
Prime Numbers
prime number theorem and the prime counting function
第183页
De la Vallée Poussin also showed that Gauss’s estimate Li(x) is a better approximation to π (x) than x/(log x - a) no matter what value is assigned to the constant a (and also that the best value for a is 1).
第243页
And yet—Pythagoras claimed that the universe was made of numbers and Leopold Kronecker (1823–1891) claimed that “God made the integers and all the rest is the work of man.” Who knows? Perhaps the world is even more cunningly constructed out of the prime numbers!
The Riemann Hypothesis by Karl Sabbagh
p. 112-113
Even politics can enter the Riemann arena sometimes, as Alexander Ivic described. “There was a mathematician in the Soviet Union … called Nikolai Gavrilov, who in the early 1960s was a big Communist boss in one of the Ukrainian cities. He was an amateur mathematician, and he got hold of the Riemann Hypothesis and thought he had a proof, and being a man of power he organized for his proof to be published. You should know that at that time the Soviets were competing, especially with the United States, in all fields - the cosmos, high technology, and so on - and they had very fine number theorists and mathematicians in general. Especially one Gelfond and one Yuri Linnik. Now, when these men got hold of a false proof of the Riemann Hypothesis, it is said, Gelfond had a heart attack and Linnik was choking and gasping for breath. He almost died from shock. They were so frustrated because much damage had been done to Soviet mathematics by this false proof of the Riemann Hypothesis appearing.”
当代数学大师-沃尔夫数学奖得主及其建树与见解-第四版
A.塞尔伯格( Selberg, Atle)
第1876页
当有人问他，如果作为非专业人士问你“黎曼假设告诉了我们关于素数的哪些东西？” 他明快地答道：“它告诉我们素数分布得相当好，以最大可能分布得均衡，分布得适宜。当然，我们不能期望一个完全均衡的分布。”
当有人问他，“你是否认为黎曼假设是正确的？” 他答道：“如果在我们的宇宙中还有什么东西是正确的，那必定就是黎曼假设，若找不出正确的理由，那纯粹的美学理由就够了。
谈谈方法
第三部分
第739页
一定要经过长期训练，反复思考，才能熟练地从这个角度去看万事万物。我相信，那些古代哲学家之所以能够摆脱命运的干扰，漠视痛苦和贫困，安乐赛过神仙，其秘密主要就在于此。因为他们不断地考察自然给他们划定的界限，终于大彻大悟，确信除了自己的思想之外，没有一样东西可以由他们做主，确信只要认清这一点就可以心无挂碍，不为外物所动；他们对自己的思想作出了绝对的支配，因此也就有理由认为自己又富又强，逍遥安乐，胜过所有的别人，别人不懂这种哲学，不管得到自然和命运多大优待，还是不能支配一切、事事如愿以偿的。
第734页
我的第三条准则是：永远只求克服自己，不求克服命运，只求改变自己的愿望，不求改变世间的秩序。总之，要始终相信：除了我们自己的思想以外，没有一样事情可以完全由我们做主。
七堂极简物理课
尾声 我们
第578页
我们的爱与真诚与生俱来，我们天生就渴望懂得更多，渴望不断学习。我们对世界的认知在不断增长。在知识的边界，我们的求知欲在燃烧。我们渴望探索空间纹理的细微之处，探索宇宙的起源，时间的本质，黑洞的现象，以及我们思维的运行。
现在，在人类已知事物的最前沿，我们将要航行于未知的海洋，世界的奥秘与美丽熠熠生辉，让我们目眩神迷。
第564页
诚如古罗马哲学家卢克莱修（Titus Lucretius Carus）所言：“我们对生命的胃口是贪得无厌的，我们对生命的渴求是永不满足的。”（《物性论》卷三，第1084行）
终极理论之梦
第一章 序幕
第1页
在我看来，好的科学哲学是对历史和科学发现的迷人解说。但是，我们不应指望靠它来指导今天的科学家如何去工作，或告诉他们将要发现什么。
从异教徒到基督徒
第五章 澄清佛教的迷雾
二、 罪与业
第1777页
如果宗教是意味着超脱凡世的，我反对它。如果宗教是意味着我们必须从这个现世、知觉的生活中走出，且有多快就多快地“逃避”它，像一只老鼠放弃快要下沉的船一样，我是和它对立的。我认为一个人必须有中国人的共有意识，勇敢地接受现世的生活，且像禅宗的信徒一样和它和平共处。而我强烈地觉得宗教（任何宗教）一天固执于一个来世，趋向于否定现世，且从上帝所赐给我们的这般丰富且有知觉的生命中逃避，我们将因此种做法而妨碍宗教（任何宗教）与近代青年的意识接触。我们将是上帝真正不知感恩的儿女，甚至不值得禅宗的信徒称我们为堂兄弟。
第六章 理性在宗教
二、现在的姿态
第1850页
在所谓宗教信仰与意见的繁茂丛林中，一切谬见，弗朗西斯·培根的“四个假象”，都被介绍了：一切偏见（种族的假象），例如上帝必然是一种人性的存在，一个神与人同性的上帝的观念；一切与个人的或国家的成见相符的信仰（洞穴的假象），例如做一个基督徒和做一个白人，事实上有同样意义的流行习惯；一切言辞的虚构及混乱（市场的假象）；一切以人造的哲学系统为根据的不合理的教条（舞台的假象），例如加尔文的“完全堕落”的教义。
三、可理解的止境
第1934页
柏拉图说得对，我们所能看见及知道的，只是一个影子的世界。我们感官的知觉，只能给我们一个现象世界的图，这是理性所能告诉我们的一切：在现象的背后是本性，是物体本身，而我们永远不能凭我们心的推理来知道绝对的真理。多么可怜！这是对人类缺陷的悲哀的宣判：它是以官觉的知识为根据，自然的东西的存在是知识而已，我们所认为存在的不过是知觉，且可能是一种幻觉，我们的体质注定我们要隔着一张幕来看东西，而且永远不能和绝对真理面对面。尽我们想做的来做，某些东西仍常留在后面，即那些可知世界的剩余区。这是对人类智力的侮辱，悲哀地宣判人的心智已至绝境。对此，人自觉无力反抗。佛曾宣讲它，柏拉图曾说明它，一群献身于对机械与攻击人类知识定律经历世纪之久的哲学家，伤心地承认它，而新近的科学也证实了它。
第1929页
把柏拉图洞穴的比喻放在现代科学中来看，是否适用和正确是超乎我们所能估计的。爱丁丝说：“真正了解到物质科学所谈及的是一个影子世界，是近代最有意义的进步之一。”而杰恩斯追求以太的量子及波长的时候说：“人们已开始觉得这个宇宙看来像一个伟大的思想，多过像一架伟大的机器。”量子的确成为物理学上的困惑。量子让我们首次看到物质与能力渡过不可见的边界的地方，使我们确认对于物质的老概念已不再适用。当我们对物质做进一步的探究，到了把次原子的极小量充以一百万伏特的电，我们简直是失去了它。这是今天舆论的客观趋势。
第1829页
其实人想及上帝时，必须把他抽离一切实在，而不将他想象为一个占据空间的形式，只是一种事物的秩序。上帝不是存在，纯是动力——一个形而上学世界秩序的元素。
现实不似你所见
11. 无穷的终结
第1950页
《数沙者》像是在开玩笑，但意义深远。凭借比启蒙运动早大约一千年的想象力，阿基米德对某种认识做出了反抗，这种认识坚持认为存在一些人类思想本质上无法触及的奥秘。他没有宣称确切地知道宇宙的维度，或者沙子的具体数目。他主张的不是知识的完备性，正好相反，他十分清楚他估算的近似性和暂时性。他谈到宇宙真实的大小有哪些可能，但没有做出明确的选择。重要的不是假设我们通晓一切，而是相反：意识到昨天的无知可能被今天阐明，今天的无知可以被明天照亮。
4. 量子
第1187页
在量子力学描述的世界中，实在只存在于物理系统之间的关联之中。并不是事物进入关联，而是关联是“事物”的基础。量子力学的世界不是物体的世界，它是事件的世界。事物通过基本事件的发生而建立，就像哲学家尼尔森·古德曼（Nelson Goodman）在20世纪50年代写出的美妙语句那样：“物体是一个不变的过程”。
黎曼猜想漫谈
未竟的探索
第183页
在所有高难度的数学猜想中，若以它们跟其他数学命题之间的关系，乃至与物理学那样的自然科学领域之间的关系（这些关系在很大程度上决定了一个数学猜想的重要性）而论，黎曼猜想可以说是无与伦比的。
与费马猜想或哥德巴赫猜想那种连中学生都能看懂题意的数学猜想不同，理解黎曼猜想是有一定“门槛”的，因为仅仅理解其表述就需要有一些复分析方面的知识。
《黎曼猜想漫谈》读后感（代序）
第10页
一旦这些RH解决了，人类就站在一个不知比现在高多少的数学平台上，看到更远得多的风景。— 王元
从存在到演化
第3章 量子力学
第918页
算符的引入从根本上改变了我们对自然的描述，因此把它说成“量子革命”是很恰当的。
一个算符的本征函数用来描述系统的状态，其中该算符所代表的物理量具有确定的值（即本征值）。因此用物理学的术语来说，不可对易性意味着，不可能存在这样的状态，在其中，比如说坐标q和动量p同时具有确定的值。这就是著名的海森伯测不准关系的内容。
第四章 热力学
第61页
总是和耗散结构相连的三个方面：用化学方程所表达的功能；不稳定性所产生的时空结构；以及触发这个不稳定性的涨落。
The Riemann Hypothesis
Prime Time
第13页
Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate. — Leonhard Euler
The Millennium Problems
The Riemann Hypothesis - Bernhard Riemann
第25页
While for many mathematicians “intuitive work” can be hit-or-miss, Riemann’s mathematical intuitions were incredibly acute, and his results generally turned out to be correct.
ZERO The Gauntlet is Thrown
第14页
Perhaps the best way to read this book is to think of the seven problems as the commonplace mathematics of the twenty-fifth century.
心理学与生活
chapter 12 Emotion, Stress, And Health — A toast to your health
第430页
- Never say bad things about yourself.
在成年时期，社会关系和个人的成就占重要地位。
社会亲密感是成年期心理健康的先决条件，重要的不是社会交往的数量，而是质量。亲密感是一种对他人承担性爱、情感及道德承诺的能力。它要求坦率、勇气、伦理感，并且往往要牺牲一些个人偏好。
再生力的本质：良好的适应，依赖于成为一名“关注他人”的人－即成为一名关心他人、富有同情心并拥有良好的社会关系的人士。
编程珠玑(第二版)
第1章 开篇 – 1.7 进阶阅读
第9页
程序员的主要问题不一定是技术上的，更可能是心理上的；因为他试图解决一个错误的问题，所以他不能取得进步。通过打破概念上的障碍，转而解决一个更简单的问题，这样我们最终解决他的问题了。
James L.Adams所著的《Conceptual Blocking》研究了这种跳跃，通常它可以说是一种通向创造性思维的令人愉悦的激励。Adams将概念性障碍定义为“妨碍问题解决者正确认识问题或获得解答的心理屏障”。
第二版的尾声
第167页
Tom Duff：尽可能盗用别人的代码。
库非常伟大，任何时候都尽可能使用它们。
Thinking, Fast and Slow
Part 4. choices — 32 keeping score — Regret
第346页
Regret is one of the counterfactual emotions that are triggered by the availability of alternatives to reality.
素数论
第5章 重要的猜想
第105页
素数首先就是一些谜。
第2章 Riemann zeta函数
第41页
19世纪上半叶，Gauss根据当时已有的素数表，猜测对数积分li(x)给出了素数稀疏分布律的一个极好的近似，从而将Legendre的直觉精确化。
法文版前言
素数表显示了素数的混沌特性，而其表面的无序性最终却与一些，比如说源于物理现象的经典随机模型相吻合。…为什么像素数这样高度确定的序列能够包含着那样的随机性。
确定性的终结
引言 一种新的理性？
第3页
James Clerk Maxwell 就谈到＂一种新型的知识＂会克服决定论的偏见。
问题解决心理学
第三章 问题表征：＂顿悟＂的案例
第63页
Reproductive thinking是问题的structurally blind,其表现是没有真正理解问题后面的结构。
与“众”不同的心理学
第十章 人类认知的死穴
第235页
很多人头脑里不具备概率推理的基本定律，或者即使有也不够用。
第一章 充满活力的心理学
第19页
公众更倾向于用哲学的思辩、神学的预言或是民间的常识来解释世界。
博大精深的素数
第四章 素数是如何分布的？
第162页
许多数学家都认为素数分布问题具有极大的美学动力。
机遇与混沌
11. 混沌：一个新的范式
第65页
物理学家杨振宁（C. N. Yang）邀请我去做了一个报告。之后，他取笑了我的”有争议的湍流思想” ⏤ 在当时这是一个恰如其分的评价。
学会提问
第1章 提出正确问题的益处
第5页
如果一个读者始终依赖于海绵式思维，那么他将始终相信其最后接收到的信息。不管对个人还是社会，成为别人思想的傀儡都是一件可怕的事。
海绵式思维强调知识的获得，而淘金式思维强调与知识积极的互动。
认知心理学
第11章 问题解决与创造性
第312页
专家不仅仅拥有丰富的知识，而且知识的组织性更好，这样才使得他们能更有效地利用他们的知识。而且，专家的图式不仅包括更多某个问题领域的陈述性知识，而且与该领域相关的程序性策略也比新手更多。
薄伽梵歌论
附：薄伽梵歌 1957年海外初版序言
第465页
然舍是则无以立，不得已必落于言筌，则曰至真，即至善而尽美，曰太极，即全智而遍能；在印度教辄曰超上大梵，曰彼一，人格化而为薄伽梵，薄伽梵者，称谓之至尊，佛乘固尝以此尊称如来者也。欧西文字，辄译曰：天主，上帝，皆是也。
旁观者
第3章 怀恩师
第70页
不要从别人的错误中学习，看看别人是怎么做对的。
数学的语言
序曲 何谓数学
第3页
数学是研究模式的科学（science of patterns）。
我们内心的冲突
序言
第2页
神经症是由文化因素引起的。
神经症产生于人际关系的紊乱失调。
第1页
精神失调者…而是饱受内心冲突折磨的人。
第十章 人格衰竭
第111页
表明冲突存在的三种大的紊乱失调：其一是遇事都犹豫不决。精力被分散的第二个典型症状是一种普遍性的办事无效率，即一个人由于内心有冲突不能发挥最好的能力造成的。第三个典型的紊乱症状是普遍性怠惰，主动性和行动能力瘫痪，奋斗的方向不明确，对自我的严重疏离。
乔布斯产品圣经
179 发明比思想更能改变世界
第191页
那时我开始认为，也许爱迪生给世界带来的改变，比马克思和印度高僧尼姆•卡洛里•巴巴加起来的还要多。
项目百态
模式 33 扑克之夜
第80页
互相熟悉可以使彼此互相信任，也可以使彼此更有耐心。
除了在一起玩耍，我们从来没有在其他事情上面感觉到如此地有活力，如此放开地表现自己，以及如此地专注痴迷。—Charles E.Schaefer
混沌
第4章 生命的盛衰
第73页
__在世界上压倒一切的是非线性__。
如果有更多的人明白简单的非线性系统并不必然具有简单的动力学性质，那我们大家的日子都会好过得多。
数学的故事
第237页
Sophus Lie的新颖想法：Galois理论在微分方程上应该有一个相应的理论。
第352页
Jack Wisdom和Jacques Laskar：1、发现太阳系的动力学特性是混沌的。2、这俩位天文学家还证明了：月球潮汐能使地球保持稳定，否则的话，就会导致混沌运动，而致使天气迅速变化，从暖期一下子变到冰川时代，又从冰川时代迅速变回暖期。因此，混沌理论证明，如果没有月球，地球将会是一个非常不宜居的地方。
完美的证明
第110页
Everyone is a bastard, everyone is bad, with the possible exception of Jesus Christ. Einstein is bad too, because he did not leave America after the nuclear bomb was detonated over his objections.In the end, through the general interconnectedness of events, a person becomes, in some way or another, to a greater or lesser extent, party to everything that happens in the world, and if he can exert any influence whatsoever on any event, then he becomes responsible for it.
Alexandrov：
每个人都是混账、坏蛋，只有耶稣基督除外。爱因斯坦也是个坏蛋，因为在原子弹被引爆之后，他并没有离开美国，尽管他曾极力反对使用原子弹。
最终，通过事物之间的普遍联系，一个人会以这样或那样的方式，在深浅不等的程度上与世界上发生的所有事物都扯上干系。如果一个人可以对任何一个事件施加任何影响，那么他就要为此承担责任。
第二章 如何培养数学家
第17页
佩雷尔曼的母亲名叫Lubov，是犹太人，20世纪60年代的数学专业研究生，当了名数学老师。
The Music of the Primes
chapter one : who wants to be a millionaire?
第1页
Somebody allegedly asked Hilbert, ‘If you were to be received like Barbarossa, after five hundred years, what would you do?’ His reply:’I would ask, “Has someone proved the Riemann Hypothesis?”’
第10页
The dependence of so many results on Riemann’s challenge is why mathematicians refer to it as a hypothesis rather than a conjecture.
the atoms of arithmetic
第55页
As we shall see, Riemann’s Hypothesis can be interpreted as an example of a general philosophy among mathematicians that, given a choice between an ugly world and an aesthetic one, Nature always choose the latter.
Riemann’s Imaginary Mathematical Looking-Glass
第66页
His contemporaries were to see nothing of him while he waded through Cauchy’s output. Several weeks later Riemann resurfaced, declaring that ‘this is a new mathematics’. What had captured Cauchy and Riemann’s imagination was the emerging power of imaginary numbers.
chapter five The Mathematical RelayRace: Realising Riemann’s Revolution
第102页
Euclid in Alexandria. Euler in St. Petersburg. The Göttingen trio — Gauss, Dirichlet, Riemann. The problem of prime numbers had been passed on like a baton from one generation to another. The new perspectives of each generation provided impetus for a fresh surge along the track. Each wave of mathematicians left its characteristic mark on the primes, a reflection of their era’s particular cultural outlook on the mathematical world.
第106页
As Hilbert wrote in 1897, he wanted to implement ‘Riemann’s principle according to which proofs should be impelled by thought alone and not by computation’.
第128页
But Gauss had made a second conjecture: that his guess would always overestimate the number of primes…
But in 1912 Littlewood proved that as you counted higher you would eventually come to regions of numbers where Gauss’s guess switch from overestimating to underestimating the number of primes.
Littlewood also showed that Riemann’s refinement might look more accurate as we count through the first million numbers, but in the farther reaches of universe of numbers Gauss’s guess would sometimes give the better prediction.
Indeed, to this day no one has actually counted far enough to arrive at a region of numbers where Gauss’s guess underestimates the primes. It is only through Littlewood’s theoretical analysis and the power of mathematical proof that we can be sure that somewhere along the line Gauss’s original prediction is false.
第131页
From now on, proof was everything. Nothing could be trusted without conclusive evidence.
chapter six Ramanujan, the Mathematical Mystic
第136页
Mathematics seems to bring out the cranks.
chapter seven Mathematical Exodus: From Göttingen to Princeton
第159页
Selberg spoke about his view on the Riemann Hypothesis. Although he had made a major contribution on the way to a proof. he stressed that there was still very little to support its truth. ‘I think the reason that we were tempted to believe the Riemann Hypothesis then was essentially that it is the most beautiful and simple distribution that we can have. You have this symmetry down the line. It would lead also to the most natural distribution of primes. You think that at least something should be right in this universe.’
第160页
Some misinterpreted his comments, thinking that Selberg was casting doubt on the validity of the Riemann Hypothesis. Yet he was not as pessimistic as Littlewood who believed the lack of evidence meant the Hypothesis was false. ‘I have always been a strong believer in the Riemann Hypothesis. I would never bet against it. But at that stage I maintained that we didn’t really have any results either numerical or theoretical that pointed very strongly to its truth. What the results pointed to was that it was mostly true.’
第165页
Hardy once dismissively declared, ‘Probability is not a notion of pure mathematics but of philosophy or physics.’
第167页
Erdös liked this probabilistic interpretation of the Riemann Hypothesis.
chapter eight Machines of the Mind
第184页
Hilbert responded with a view shared by many mathematicians: ‘It is a completely misunderstanding of our science to construct differences according to peoples and races and the reasons for which this has been done are very shabby ones. Mathematics knows no races…for mathematics, the whole cultural world is a single country.’
第197页
Julia Robinson: ‘We can conceive of a chemistry that is different from ours, or a biology, but we cannot conceive a different mathematics of numbers. What is proved about numbers will be a fact in any universe.’
第202页
Cohen has been one of the few mathematicians to admit that he was actively working on this notoriously difficult problem. So far, though, it has held firm against his attack.
Chapter Nine The Computer Age: From the Mind to the Desktop
第222页
The Mertens Conjecture is very closely related to the Riemann Hypothesis, and its disproof showed mathematicians that if the Riemann Hypothesis were true, it was only just true.
chapter 10 - Cracking Numbers and Codes
第224页
If Gauss were alive today, he would be a hacker. — Peter Sarnak
Chapter 11 - From Orderly Zeros to Quantum Chaos
第257页
Gödel himself had voiced such concerns in relation to the Riemann Hypothesis: perhaps the axioms that formed the foundation of the mathematical edifice were not broad enough to carry the required proof, in which case you might continue building upwards and never find a connection to the Hypothesis.
第261页
As Littlewood had advised Montgomery during his time in Cambridge, ‘Don’t be afraid to work on hard problems because you might solve something interesting along the way.’
Atle Selberg had become something of a latter-day Gauss.
第263页
Chowla, who dragged Montgomery over and introduce to Dyson, is the only person ever to have bullied Selberg into writing a joint paper.
Chapter 12 - The Missing Piece of the Jigsaw
第291页
One epic in particular was to become a close companion throughout André Weil’s life: the Bhagavad-Gita, the song of God from the Mahabharata.
Chapter 12 - The Missing Piece of the Jigsaw
第311页
Many of the mathematicians who have contributed to our understanding of the primes have been rewarded with long lives. Having proved the prime number theorem in 1896, Jacques Hadamard and Charles de la Vallée-Poussin both lived into their nineties. People had begun to believe that their having proved the Prime Number Theorem had made them immortal. The belief in a connection between longevity and the primes has been further fulled by Atle Selberg and Paul Erdös, whose alternative elementary proof the Prime Number Theorem in the 1940s saw both of them live into their eighties. Mathematicians joke about a new conjecture: anyone who prove the Riemann Hypothesis will indeed become immortal.
Dr.Riemann’s Zeros
Proofs and refutations
There was a mathematician in the Soviet Union … called Nikolai Gavrilov, who in the early 1960s was a big Communist boss in one of the Ukrainian cities. He was an ameteur mathematician, and he got hold of the Riemann Hypothesis and thought he had a proof, and being a man of power he organized for his proof to be published. The fortunate thing is that the proof did get published. You should know that at that time the Soviets were competing, especially with the United States, in all fields - the cosmos, high technology, and so on - and they had fine number theorists and mathematicians in general. Especially one Gelfond and one Yuri Linnik. Now, when these men got hold of a false proof of the Riemann Hypothesis, it is said, Gelfond had a heart attack and Linnik was choking and gasping for breath. He almost died from shock. They were so frustrated because much damage had been done to Soviet mathematics by this false proof of the Riemann Hypothesis appearing.
How to Write Email in English
The email address you use
As a general rule, firstname.lastname@emailprovider.com is a good format for your email address.
To/from field
From
It should simply be your first and last names, appropriately capitalised and spelt correctly, with no extra bits like hearts or exclamation marks.
To
your recipient’s email address
CC
“CC” field stands for “Carbon Copy”, and it means that they will see the email but will also see that it’s not directly addressed to them. Don’t use it unless there is a real need for this person to see the communication.
BCC
If you’re emailing several people, it’s bad form to include all their email addresses in the “To” field. In this instance, you should put your own email address in the “To” field and put those of your recipients into the “BCC” field. This stands for “Blind Carbon Copy”, and it means they’ll all see the email but won’t see who else you’ve sent it to.
Subject line
Write something descriptive in the subject line that summarises what the email is about. Don’t make it too long.
Salutation
However, go by how they address you; if their emails to you start “Dear”, you reply with “Dear”; if they start “Hi”, you can reply with “Hi”. An alternative email greeting that lies somewhere between formal and informal is “Good morning” or “Good afternoon”. This is perhaps a little friendlier and more personal than “Dear”, so if your style is not naturally very formal then this is an acceptable form of email greeting.
Signing off an email
These common conventions include:
- Best wishes,
- Kind regards,
- Best regards,
- All the best,
- Thanks,
- Thanks in advance,
- Many thanks,
- Sincerely,
- Yours truly,
- Thanks again,
- Appreciatively,
- Respectfully,
With all of these, make sure you have a comma at the end of the line, as in the examples above.
无线网络的未来
无线网络变得越来越普遍，大如蜂窝移动通信网络，小如无线局域网。大卫•奇斯纳尔试图效仿阿瑟•克拉克，对无线网络技术的发展前景进行预测。
新千年的元旦——一个历史性的日子。世界各地的电信公司将同时取消长途资费，所有的电话都将作为本地通话计费。这听起来异想天开，但这可是大约十年前阿瑟•克拉克[1]曾经作出的预测。
事与愿违，现实总是不及愿望美好。电信运营商依旧按你拨打的被叫号码的程控交换距离来计费。然而，情况并非完全与阿瑟爵士的预言相反。这几年来我打国际长途电话付出的几乎只是宽带连接成本。但与公用电话交换网不同的是，IP电话的两端是连接在互联网上的设备。其实不管是固定电话还是IP电话，通话两端的物理链路经过的中继线缆一般都差不多。
全IP网络
英国的有线电话骨干网（由英国电信经营）和下一代无线电话网络都有一个共同点：他们本质上都是IP网络并把电话作为IP电话(VoIP)处理。我现在的手机支持UMTS [2]（通用移动通讯系统），每当我使用它就会自动分配一个10/8的子网IP地址。这意味着它位于网络地址转换(NAT) 背后，因此就不能再接受入站连接。
10/8子网是最大的可分配私有网络。作为8位CIDR [3]前缀，它容许224（等于16,777,216，将近1700万）个不同的IP地址。与连接到移动电话网络的庞大设备数量相比，这根本不算多，这也是为什么移动运营商很可能率先部署IPv6的原因。采用IPv6，一家公司（甚至个人）都能轻易获得64位网络前缀，意味着前64位可用来标识网络，后64位可用来标识设备。对此可以这么理解，这家公司拥有足够的地址空间使每个有效的IPv4地址都能扩张为互联网那么大的网络，或换言之每个人都可以在他（或她）的网络上接入30亿个IP独立的设备。更重要的是，它容许全世界每台设备都具有各自唯一的IP地址，路由表记录稀少，如此路由的代价大为降低。
IPv6带来与移动电话密切相关的另一个优点就是移动IPv6，其中设备可以改变其在网络中的位置而继续保持路由，其已有的连接不会被中断。在信号塔之间移动位置通常在协议栈的底层就已经做了处理，但这种新的构架允许手机在两个彼此独立的网络之间移动同时保持连接，只要两端都采用IPv6连接。
全IP网络强调提供接入和提供服务之间的区别——一个正在被移动运营商搞模糊的分别。每当你打电话，你就在使用他们的网络，当你在使用他们的路由系统的时候，同时也在使用移动运营商与其他电话网络之间的协议。
电话号码与联系人的对应关系已经不像过去那么重要。过去我打电话的过程很麻烦：首先，我会先在一个纸质的通讯录或本地缓存中寻找对方的电话号码——要么是个电话簿或是我的大脑记忆，然后拨这个号码（后来变成了按键）。相比之下，现在我只是从通讯录中选择这个人的名字，然后就按下拨号键。最近一项研究称人们的记忆力越来越糟，因为他们连朋友的电话号码都记不住了。对我而言，不仅仅是我不再记住我朋友的电话号码——我根本就没在意那个号码是什么。很多时候，一个朋友通过电子邮件或蓝牙把电子名片发送给我，而我从来都不会去看号码那一栏。打电话（而不是联系某人）的概念看来已经依稀有些过时了。
连接的移动性
802.11标准家族不太知名的一个标准是802.11r。这个标准着眼于在无线接入点之间进行快速切换。802.11接入点在户内通常只限于几个房间那么大的范围，户外则大约一百米左右。一个走动中的人几分钟之内就可能需要在六个左右的接入点之间跳转。802.11r标准针对这个需要提供了相应的机制。如果你坐在一个与两个无线接入点距离大致相等的位置上，你或许觉察到你的网络连接不时地停顿片刻，因为你的网络堆栈在接入点之间进行切换。802.11r标准改善了停顿时间，把切换时间降低到1秒以内。这样的改进使802.11对手机用户切实可行。在安装了.11r支持的无线接入区域，你可以边走边打电话，而不会察觉你的电话在接入点之间的跳转——就像现在当你的手机在信号塔之间跳转时你根本没注意到一样。（好吧，理论上你不会注意到；实际上，你可能会察觉到）
如果所有的接入点都在一个网段上，这种切换行之有效。然而，想象你走在一条布满了接入点的街道上，这些接入点都开放并且配置在一个网络上。你从其中一头往另一头走，你打的电话被第一家的网络连接路由。当你在这条街上继续走动时，你的电话被无缝地在接入点之间切换，直到你到达另外那头。在这点上，你的电话的数据包被一打接入点中继转发给被你呼叫的那方，这不是很有效率。理想的情况下，在这点之前你就会开始用新接入点上行数据。不幸的是，每个接入点都有不同的可路由的子网地址，这样如果你切换成新的接入点来上行数据，你就会突然切换IP地址，而这将中断你的连接。
这就是移动IPv6的用武之地。IPv4也有一个针对移动的变种，依赖于三角路由——简单来说，老的网络连接充当数据包的中继，每当你移动数据包就暗中增加。对IPv6，IPSec允许安全地更新路由表。目前，切换时间大约1秒，这对VoIP电话来说还不够快，但这个切换时间有望得到改善。
对移动IPv6来说，网络间的边界变得平滑。如果你坐在一个提供免费wifi的咖啡厅，你也许就想使用咖啡厅的网络，而不是使用需要花钱的移动运营商的网络。如果你边打电话边走进咖啡厅，你当然想自动切换到咖啡厅的免费wifi网络，而不是继续使用移动运营商那资源稀缺而费用昂贵的蜂窝网络。
提供接入
移动运营商很善于根据不同数据类型来收取不同的费用。他们的整个业务模式都基于此方案。如果每条文本信息你付10美分，算下来大约折合750美元/MB。许多人愿意为短信支付这些钱，但这样的话加载InformIT首页的费用就超过500美元，而我怀疑大多数人会愿意为浏览网页花那么多钱。
你可以在你的手机上运行一个即时通讯软件，即便是XMPP这样臃肿的协议算下来其成本也只是短信费用的一部分。不幸的是，你不能用它与手机上没有装IM客户端的用户沟通，这降低了它的可用性。你不只在为IM的带宽而付费，而且也需要为网络服务付费。
电话按与别的数据不同的方式计费。这样设计更合理。然而，由于电话的要求与浏览网页和电子邮件很不一样。GSM和相关的协议用于语音通话的传输速度大约为12Kb/秒。以这个速度，你打一个小时电话也只用了大约5MB的数据流量——这在现代网络中不值一提。
然而对语音通话来说带宽并非一切。如果延迟超过200毫秒左右，你很可能就会感觉到通话质量不好。更重要的是抖动，比起延迟都还要重要。如果延迟时间稍有增加，通话的双方就会产生说与听之间的脱节。如果延迟减缓，你只有以丢包的方式才能赶上，因为你不能以高于实时的速度回放音频而没有察觉。（你可以加快点速度，但很有限）。你可以通过在每个接收端进行缓冲来补偿抖动带来的损失，但这种方法增加了延迟，而这是你极力避免的事。
所以网络接入中你在为三件事买单：带宽、延迟和抖动。对于带宽来说，你想提高就得多掏钱；对延迟和抖动，你想降低就得多花钱。即时只是提供IP连接，移动网络仍旧能通过提供不同的QoS服务质量来收取不同档次的费用。如果你想打个电话，你或许会选择具有低延迟和低抖动而费用较高的连接，你更愿意在信号质量方面而不是带宽上花钱。
软件无线电: 工程师的梦想，监管者的梦魇
随着GNU Radio之类开源项目的出现，近几年来一个有趣的发展是软件无线电。当然，无线电系统不能完全是软件的，但其需要的硬件相对简单——差不多就是一架天线和一个数模转换/模数转换器。
过去，无线电设备的执法较容易。你检查硬件是否工作在限定频率和功率范围内；如果是，你就可以核准其批量生产。
对软件无线电来说，功率和频率都由软件控制。这对监管机构来说构成问题，尤其是与开源驱动一起使用的时候，因为这意味着终端用户能轻易地把合法设备换成不合法设备。（当然，总有人可能会通过增加放大器和天线做到这一点，但是如果你只需要下载固件的补丁，事情就变得更加容易了）
尽管令监管者不爽，软件无线电的确给通信带来一些有趣的变化。当你能够把同样一台硬件用于接收HDTV和WiFi两种信号时（同时，只要你有一个足够快的处理器），就带来了很多可能性。纯软件无线电是令人难以置信的处理器密集型应用，因此对移动设备意义不大（手机专用芯片计算能力不强），但它提供了一些启示。动态配置的信号处理单元能够集成到相同的包中，这样你现在就能得到能够运行许多不同无线协议的低功耗芯片。
未来几年里设备有可能会支持WiFi, WiMAX, HSPDA, GSM和其他流行的低功耗协议，以及在它们之间进行快速切换的能力。
尽管这种变化就其自身而言并非完全有用，当与移动IPv6相结合后就变得激动人心——给你的设备一种在各种各样的协议之间跳转的能力，可以针对你的需要选择最省钱的那种协议。
什么是频谱?
可悲的是，无线电频谱是一种稀缺资源。频率越低传输距离越远，但数据传输率越低。频率高则传输距离不远。这就是为什么WiFi比移动通信快得多的原因之一。另一个是信道竞争。信号传输距离越远，你需要的接入点越少（有利的一面），而同时有更多的人在共享这个信号（不利的一面）
一些较新的发展可能会缓解频谱稀缺面临的压力，尽管它们（总是）非常占用处理器计算能力。如果你在建筑物密集的地区或丘陵地区观看模拟电视，你或许会注意到重影。这是由于一个信号从发射机直接到达，而另一个信号从山上反弹过来，延迟到达。
在建筑物密集的地区，信号会被建筑物、树木反弹，某些频率甚至能被人反弹。对于大多数现有的协议，你必须计算反弹的均值以尝试找到你真正想要的那个信号。有了更精确的设备，你有另外更好的选择。你能用不同路径的信息来确定一个特定的端点。几个设备可以在同一地区以相同频率同时发射，提供了更多可用的频谱。
虽然并非完全相关，但这种缓兵之计表明一定宽度的频谱并不意味着等量的数字带宽。技术进步允许你在同等大小的信号空间中传输更多的信号。但就目前而言，这一事实并没有改变这样的现状，即频谱相对地还是稀缺。
目前我们有两种截然相反的供互联网接入的频谱分配方式：蜂窝网络和未管制的（WiFi及其邻接频谱区间）。前者被集中统一控制，网络覆盖面广。后者不受监管，任何人都能使用，但覆盖的范围有限。
我在前面提及的一些技术使这些界线有点模糊。有线电视公司可以部署一个很高效的城域网，给所有客户提供WiFi接入，使客户能通过Mesh多路径路由和移动IPv6的组合在二者之间按需跳转。
在美国，最近作出的一项决定允许一些以前用于电视的频谱（频道与频道之间那些所谓的“空白频谱”）也可以用于数据网络。这对城域网来说是个不错的频率范围，为其实现方式提供了另一种选择。
这里可用的频率范围甚至比用于蜂窝移动通信的频率还要低，因此信号传输距离更远（毫不奇怪，只要你想想移动通信基站比电视发射塔要密集得多）。这使它对提供覆盖面广的服务很有吸引力。由于FCC（联邦通讯委员会）决定将这一范围的频谱免授权开放使用，任何人都可以开展这种覆盖业务。一个城市可以拥有许多提供快速、覆盖范围小的接入方式的热点地区，同时还有一个更大的基站以较低的接入速率覆盖整个地区作为候选。当你走在两个热点之间时，你的手机转为使用空白频谱系统，而不影响你的覆盖范围（尽管你的可用带宽可能会减少）。
未来有望看到你的手持设备能透明地在由不同服务提供商控制的和不同服务质量的网络之间自由切换。提供统一的接入服务、不同级别的最低连接质量和其他多种选择将给创新型公司带来在诸多领域建立新的商业模式的机遇。
[1] 科幻小说作家，提出卫星通信地外中继的概念，作出的很多预测也大多应验
[2] 全球使用率最高的3G移动通信标准，采用WCDMA
[3] 无类别域间路由
2010，译言网
原文：The Future of Wireless Networking - InformIT
Google搜索引擎的工作原理
搜索引擎之于Google，就像Windows之于微软，搜索引擎是互联网巨头Goolge的王牌，而今搜索对互联网来说太重要了，互联网搜索甚至已经提升到了搜索文化的高度，在海量信息的因特网上，搜索引擎是网民的罗盘，而Google做出了Internet上最好的指南针。
PPCblog.com呈现给我们一幅由Jess Bachman（在WallStats.com工作）精心描绘的示意图，这张流程图展示了每天拥有3亿次点击量的Google搜索按钮背后搜索引擎在那不到1秒的响应时间内所进行的处理。
这是我刚付印的最新示意图，这张流程图演示了在你点击Google搜索按钮后，在Google返回查询结果前那一眨眼的功夫里，Google是如何处理你的搜索请求的？这可是搜索巨人Google年赢利额高达200亿美元的杀手级应用，也是Internet首屈一指的商业和技术神话，大家肯定都想知道Google这棵摇钱树背后的秘密。
Google官方对其搜索技术的叙述
我们搜索技术的后端软件会在服务器侧触发一系列执行时间不到1秒的并行计算，Google问世前的传统搜索引擎的搜索结果严重依赖于关键词在页面上出现的频度，我们使用了200多个指标信号（其中包括我们拥有专利的PageRank页面等级加权算法）用来检查万维网的链接结构（佩奇和布林最初的想法是把万维网的链接结构用图论的有向无环图来建模）并决定网页的重要程度，我们假定一个网页的重要程度取决于别的页面对它的引用，就像学术论文中的引用指数一样，重要的论文总是会被很多其他论文引用。然后我们再根据搜索条件进行超文本匹配分析（对bot抓取的页面内容进行关键词倒排索引检索）确定跟搜索请求最相关的网页。综合最重要的网页和跟搜索请求最相关的网页两个方面，我们就能按重要程度和用户搜索请求相关程度把查询结果排序后呈现给我们的用户。
数据中心：Google用来索引世界的塔
Google的数据中心高度机密，我们能了解到的不多：
1． 在美国本土有19个以上的数据中心，其余17个数据中心分布在美国以外的世界各地。
2． 每个数据中心有50万平方英尺那么大，建造一个数据中心要花费约6亿美元。
3． Google数据中心是世界上最高效的设施之一，而且也非常环保，几乎没有碳排放。
4． 数据中心使用50到100兆瓦的电力，由于需要冷却，通常建在便于用水的地方。
5． Google服务器安置在一个一组容得下1160台服务器的有房子那么大的标准集装箱容器中。
处理流程
1．你写博客、或在Twitter上推微博、更新站点等诸如此类往Web上添加内容的操作
2．Google bots程序（一种作为搜索引擎构件的智能代理程序）抓取你网页的title和description、keyword等内容
（1）Google爬虫沿着链接路径周游万维网，如果没有超文本路径到你的站点，你的站点将不会被索引
（2）如果你在robots.txt中设置不许索引，Google爬虫程序将不会抓取你的网页
（3）如果链接到你站点的超文本链接上有nofollow标签，Google爬虫将不会从这些链接路径周游到你的站点。
（4）Google也能通过blog软件或xml站点地图找到你的网站
（5）从PageRank越高的网站链接到你的网站的链接越多，你的网站的PageRank就越高。
（6）Google爬虫将周游所有未标注为nofollow的链接
3．一旦被Google爬虫访问到，网页几秒内就被索引了
（1）网页内容被存储在一个倒排索引中
① 网页标题和链接数据被保存在一个索引中，用于广度优先搜索
② 网页内容保存在另一个索引中，以用于检索频率不高的长尾、个性化、深度优先搜索
（2）当你用Google搜索时，你并没有在检索时时更新的万维网，而是在检索Google的缓存，Google定期更新其索引库，在Twitter实时搜索等的竞争下，Google的索引库更新周期趋短。
4．Google基于链接评估域名和网页的总体PageRank值。
5．检查网页以防止作弊行为
(1) Google的搜索质量和反垃圾信息审查和优化算法
(2) 1万多远程测试用户评价搜索结果的质量
(3) Google征请用户对有PageRank讹诈嫌疑的垃圾信息进行举报
(4) Google接到 (美国)数字千年版权法案的通知，要求Google从搜索结果中剔除涉嫌盗版的内容
6．在对页面做了损害分析后，现在每个页面都有很多用于辅助用户搜索的数据片（比如检索关键词）反向引用着它
7．用户发出搜索请求
（1）Google搜索质量工程师Patrick Riley：在大多数Google搜索中，你的搜索处于许多并行的控制过程或Google实验室的创新项目组过程中，可以说每一个查询请求都会参与一些Google的创意实验。
8．Google会用同义词匹配与你的搜索关键词语义相近的查询结果
9．生成初步的查询结果
（1）Google当然能返回成千上万数量无限的查询结果，但一般只显示不到1000条的查询结果，出于“少则得，多则惑”的考虑。
（2）对查询结果做本地化处理，本土站点在查询结果中优先出现
10．对查询结果集按权威性和PageRank进行排序，重复的查询结果被剔除。
(1) Google根据关键词、广告类型、用户所处位置找出相关的被竞价拍卖的关键词广告
(2) 关键词广告必须遵守当地法律条文
① 广告业主的非法广告将被取缔
② 如果关键词的搜索流量过低或关键词广告点击量偏低，则会被自动禁用
③ 出于商业策略，像亚马逊这样的客户会给予优惠折扣。
(3) 关键词相关广告按收益潜力（对关键词进行竞价拍卖后的广告质量不断进行评估）排序
(4) 对广告业主来说广告内容一般都是固定的，但有时使用动态关键词使关键词广告与搜索关键词相关度更高
① 一些广告本身允许增加易变的附属信息，比如网站链接、电话号码、产品链接、地址等
(5) 当广告拥有了相当高的点击率，则会显示在搜索结果列表的上方，以使其更显眼。
(6) 其余的广告依序显示在相应的位置
11．对查询结果进行过滤处理
(1) 对通常的查询（比如在Google首页上发出的搜索请求），Google会把相关的专题性垂直搜索结果（比如新闻、购物、视频、书籍、地图等）也加到返回的查询结果中
(2) 个性化方面：用户访问过的网站在查询结果列表中会更靠上
(3) 大量使用锚点的网站有可能被从查询结果中删除
(4) 搜索结果集的聚簇性：如果网页被其他高PageRank的网站引用，则网页的重要性会大大提高。
(5) 趋势分析：对搜索流量爆增或有大量新闻的搜索关键词，Google会在新的查询结果中增加额外的PageRank权值。（Google有反映关键词搜索流量的Google趋势专题页面）
(6) 同一个域名下的多个网页如果具有相同的PageRank会被归为一组。
- 最终返回给浏览器端的用户一个人性化的、布局良好的、查询结果和广告泾渭分明的有机查询结果页面。
所有这些步骤在总共不到1秒的响应时间内完成，每天3亿次的点击量给Google带来了超过200亿美元的年收入。
2010，译言网
YAML
YAML: YAML Ain’t Markup Language
http://yaml.org
YAML 语言教程
http://www.ruanyifeng.com/blog/2016/07/yaml.html
YAML 是专门用来写配置文件的语言，非常简洁和强大，远比 JSON 格式方便。
YAML SYNTAX
https://learn.getgrav.org/advanced/yaml
Learn X in Y minutes
Where X=yaml
https://learnxinyminutes.com/docs/yaml/
arXiv papers
DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization
Amir Ali Ahmadi, Anirudha Majumdar
https://arxiv.org/abs/1706.02586
In recent years, optimization theory has been greatly impacted by the advent of sum of squares (SOS) optimization. The reliance of this technique on large-scale semidefinite programs however, has limited the scale of problems to which it can be applied. In this paper, we introduce DSOS and SDSOS optimization as more tractable alternatives to sum of squares optimization that rely instead on linear and second order cone programs respectively. These are optimization problems over certain subsets of sum of squares polynomials (or equivalently subsets of positive semidefinite matrices), which can be of interest in general applications of semidefinite programming where scalability is a limitation. We show that some basic theorems from SOS optimization which rely on results from real algebraic geometry are still valid for DSOS and SDSOS optimization. Furthermore, we show with numerical experiments from diverse application areas—polynomial optimization, statistics and machine learning, derivative pricing, and control theory—that with reasonable tradeoffs in accuracy, we can handle problems at scales that are currently far beyond the reach of sum of squares approaches. Finally, we provide a review of recent techniques that bridge the gap between our DSOS/SDSOS approach and the SOS approach at the expense of additional running time. The appendix of the paper introduces an accompanying MATLAB package for DSOS and SDSOS optimization.
https://www.solidot.org/story?sid=56606
A Practical \( O(R\log\log n+n) \) time Algorithm for Computing the Longest Common Subsequence
Daxin Zhu, Lei Wang, Yingjie Wu and Xiaodong Wang
https://arxiv.org/abs/1508.05553
In this paper, we revisit the much studied LCS problem for two given sequences. Based on the algorithm of Iliopoulos and Rahman for solving the LCS problem, we have suggested 3 new improved algorithms. We first reformulate the problem in a very succinct form. The problem LCS is abstracted to an abstract data type DS on an ordered positive integer set with a special operation Update(S,x). For the two input sequences X and Y of equal length n, the first improved algorithm uses a van Emde Boas tree for DS and its time and space complexities are \( O(R\log\log n+n) \) and O(R), where R is the number of matched pairs of the two input sequences. The second algorithm uses a balanced binary search tree for DS and its time and space complexities are \( O(R\log L+n) \) and O(R), where L is the length of the longest common subsequence of X and Y. The third algorithm uses an ordered vector for DS and its time and space complexities are O(nL) and O(R).