, , Temple University New York Times Newsweek. : , .

:

Innumeracy. Mathematical illiteracy and its consequences John Allen Paulos, 1988 : 133, 106 77 , . 3606305, fax 3638173 . : 1991 ISBN: 960-221-020-6 : , -: : :

JOHN ALLEN PAULOS

-

Sheila, Leah Daniel

1. , , 400 Forbes . Von Neumann .. 2. : chuch-a-luck 3. , 9 16 20 24 27 30 34 39 43 48 52 55 59 62 66 70 76 79 83

86 , - UFO, 89 92 , 95 100 104 4. ; , : 5. , : .... Laissez-faire: I II: , : 108 114 119 121 126 129 131 138 146 149 154 157 160 166 168 172 175 182 191

. , , , '. , . . , . * Innumeracy: , ' illiteracy (, ). : ( , ), , , . ( : , ..), , , . ( , .. , ) , . (...)

10

, . , *, . , , ' **. 50% 50% , 100% . , ' , . , , . : , , , . . ' , , - , , * imply infer. , (...) ** continually continuously. , (...)

11

, , , , , , , , UFO, , , , . ( Allan Bloom*), . , , . , . " , . , , , . ' , . * , (...)

12

. - , , , ' . ' , . ' : , , , . , , : ; , . - , . . , . -

13

*. .

* : - at least to those whose fear of mathematics is not so great that (num)(ber) is automatically read as (numb)(er). number num, . numb (, ) () , . , , (...)

1

. , , . . ' * . , . , 1.528,47 . * Maine: , . (...)

16

, , , . , : . G. . Hardy , , . , 1729 , : ', , ! . , .

,

, , , . , , . , , ' . ( ), . ,

17

, - ( ) . , , . , , 45.000 . , 1985 28 - 1,6 . : 68.000 , 75.000 , 20.000 5.300 . , : , , , . , , .

18

, 12.000 . . , . ; ; ; . . . , ' , , . 1.000.000, 1.000.000.000 1.000.000.000.000. Kronlund Phillips , ( ) , . ' , , ) , 6) 99%, ) . -

19

, . , * . ' : 10 1 , 4 10.000 109 . 10" 1 10, 10~4 1 10.000 0,0001 "2 . 4 x 106 4 1.000.000 4.000.000, 5,3 x 8 5,3 100.000.000 530.000.000, 2 "3 2 x 1 / 1.000 0,002, 3,4 -7 3,4 1/10.000.000 0,00000034. ; * , *, . 7,39842 x 10 : . : ' -8* , , . , , (...).

20

2,5 x 5 5 x 11 . : 0,00000001 250.000 500.000.000.000 .

,

Scientific American Douglas Hofstadter Ideal Toy Company, ' . 4 1019 , 4 19 . . . : , 6 - McDonald, 120 . 4 x 1019 , , . , , ' ' . , , , -

21

, . ; Homo sapiens 10 , , . 300 ( ), 150 . . 250 , 4 . , , 5.000 . ( ) ; () 25.000 25 5.000 , (, ' ). Trident . ,

22

, 1.008 . . ' . , 13 14. . . ; ; ; ; . ; . . , ; , , . , 5 3,8 , 19 (19 x 109) . 1.000

23

, 19 x 6 . 19 x 6 267. ' 267 , 1/50 ! To Central Park 3.360 , 3,36 . , ' 6 . - 1.000 . , 2 . : ! , , , , . , , 3.200 , , 8 0,008 . 400.000 . . , , . -

24

[ ] , , : , , , , ; , , . .

400 Forbes

, * , Paul Bunyan** *** . . 17.913 . . , * , , Jonathan Swift . (...) ** , (...) *** , Franqois Rabelais . (...)

25

300 . . ; : ... , ... (, 19). , 3.000 7.000 , 2 ! , , , 960 , , , . . , , , . , ( ) . , . ( . , . , , -

26

, . . , , ' . , 1,80 . 9 , , . 5, 5 3 , - - 5 2 . , . , ' , . 6%, 6%. , . ' , ' . Forbes, 25.000 . 400 (4 x 8, )

27

1/16.000 , , , , 25 , 1/16.000 , . , , .

, , , , . , , ' . , ( ) , . . , ,

28

*. , , , , 3.500 . , . , , . , . , 6 x 6 63 . 106 , 6 3 x 106 . 6 3 6 9 . 4/3 x x , 1,6 ( ) 4/3 1.600.000.000.0003 x 6 3 x 106 x 109. 54 .* , (...)

29

. . . , , 40 . , 40 . "12 . Donald Knuth -13 (1/10 ) . 125. , , 125 . , . , 300.000 , , -13 . 15 , 1042

30

. , 42 ( ), . , . ( ), , . ' ' Rhode Island*. , , - .

. . , . ( , 2.730 . . ( , ), (...)

31

, .) . , , x . , , 5 x 3 = 15 , (, 2, 3, 4, 5) (, 2, 3) : 11, 12, 13, 21, 22, 23, 31, 32, 33, 41, 42, 43, 51, 52, 53. , , 4 x 7 x 3 = 84 , . , 6 x 6 = 36 . 6 5 = 30 . 6 x 6 x 6 = 216. 6 x 5 x 4 = 120. , -

32

. 8 x 6, 8 . ( 0 1 ), , , . ( , 8 .) , 262 4*. , 26 x 25 x 10 x 9 x 8 x 7. , , , 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40.320 . ; 40.320 , ; , ' . ( ) 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5.040 ( ). , , , . 10.080 * 26 , (...)

33

. , , 10.080/40.320 = 1/4. . 2 x II 14 , . Raymond Queneau Cent mille milliards de podmes [ ], . . . , 1014 , . . ' -, , . , .

34

Von Neumann Baskin-Robbins . ' 31 30 29 = 26.970' , . , 26.970 6 4.495 . 6 6 = 3 x 2 x 1 , .. ' , : , , , , . , (31 x 30 x 29)/(3 2 x 1) = 4.495. 40 . , (40 39 38 37 36 35) = 2.763.633.600 . ( ) , 2.763.633.600 720 , : 3.838.380. 720 = 6 x 5 x 4 x 3 x 2 x 1 . , ,

35

. 52 x 51 x 50 x 49 x 48 . , (5 x 4 x 3 x 2 x 1) 2.598.960 . , . , , 48/2.598.960 ( = 1 50.000), , . : (31 x 30 x 29)/(3 2 x 1) - (40 x 39 x 38 x 37 x 36 x 35)/(6 x 5 x 4 x 3 x 2 x 1) (52 x 51 x 50 x 49 x 48) /(5 x 4 x 3 x 2 x 1) . . . . , , , . , 1/2 1/2 = 1/4, --, -, -, --

36

. , (1/2)5 = 1/32, . 18/38 , (18/38)5 ( 0,024-2,4%). , 11/12 , (11/12)12 ( 0,352-35,2%). , , . Pascal Antoine Gombaud, Chevalier de Mre. de Mfcre : . 1 (20% 80% ). 5/6 , (5/6)4 . , 1, ( ) ' ,

37

1-(5/6) 4 = 0,52. , 1-(35/36)24 = 0,49. AIDS . AIDS, , , ( ). ] 499/500. , , (499/500)2, (499/500). (499/500)346 1/2, 50% AIDS ( 50% ). , , ' ( ) 50% . , ,

38

. . . . John von Neumann, , , . . , . -, , -, . , . , 60% 40%, - 0,6 x 0,4 = 0,24 - 0,4 0,6 = 0,24. , , ( ). . . 20% , ; ; -

39

, ; ; , , , ; ; , 20% . , , (0,2)3 x (0,8)7. (0,2)3 (0,8)7. , , . , (10 9 8)/(3 2 1) = 120 ( ), , 120 x (0,2)3 (0,8)7. , , ' , , . , .

- , -

40

. , *. 99% , 98% . 95%, 90%, 80% 75%. , . , . ( ), : 50%. . . , . , ! . ; , 99%, . : * . (...)

41

. , . , /. 1-/ . , , ' [1-/] 3 . , , ' [1-/] 8 . , , , 1[1/]. , ( 4/5 , 2,2 22 ) ( 44 ) 0,99. , , .

2 , , , . . . . , , . .

.

44

. . , ' , . : - , ' , , . - , , . , , ... - 1492 1942. - , . . - Sears Woolworth (1,816 1.816) . - - (INF) 8 1987, . , . , , ..

45

, , . ' ( ). . 366 ( 29 ), 367 , ' . ; 50% ; , ; 183. 365. . ' , , . , . , ( ) 365 x 365 x 365 x 365 x 365. * 3655 , (365 364 363 362 x 361) 365 , 364 . , -

46

(365 364 363 362 361) 3655, . 1 ( 100%, ), . 23 5 1/2, 50% . , Johnny Carson . Johnny Carson , 120 , , 19 . , , , . 50% ^ , 19 . , 253 , 50% 19 . : 19 364/365 , 19 364/365 x 364/365. , 19 (364/365), = 253, 1/2. 253 19 1/2, 50%.

47

, . Martin Gardner, , . , CAT () WARM (), , . , Gardner . -JFMAMJJASOND- JASON () -MVEMJSUND- SUN (). ; ... . , . , . , - , . Koch. -

48

. , .

, , . . 200 1.500 1.500 , 1% 99% ' . , ' , , , . 1.500 ( 1.500 ), , , . . 1.500 , , ,

49

. , ' , . Stanley Milgrim, () - . -, -. Milgrim , . , , a priori . , . , , . ' ; . ' ( + 1), . ' ' ; ( + 2), , . . ,

50

, . , , , , .. , . . , . : . . , . ; , . 63 100 . : , 63% . . , ' ; 63% . ( : ;)

51

, . 21 20, , , . , Dirichlet, . 367 , . . 500.000, , . 2,2 . Wilson Goode 223.569 , . 2.200.000 500.000, : . ( , . ;)

52

, . , puts, calls, Ginnie Maes zero coupons*. , . , , , ; , 19 1987. ( ), . 32.00 . , . 16.000 ' 16.000 . , , 16.000 .

* .

53

8.000 8.000 . , , 8.000 . , ' 8.000 : 4.000 , 4.000 . , 4.000 . , 500 . ' 500 , 500 . , 250.000 . . , . . . , , . , . , . , , , ' , . '

54

. , , ' . . . , ' , . . , , . , , , . , , ( ). ; -

55

, , , . , , . : . . : , , , .., , , . , , . , .

: chuck-a-luck

, . . , 1/4 2, 1/3 6, 1/3 15 1/12

56

54, 12. [12 = (2 1/4) + (6 1/3) + (15 1/3) + (54 1/12)]. , , . 10.000 200.000 , 1.000 50.000 , 50 2.000 , (0 ). . , ' (200.000 x 1/10.000) + (50.000 x 1/1.000) + (2.000 1/50) + (0 9.789/10.000) = 20 + 50 + 40 + 0 = 110 . . . , 80 (1/20)3 ( 20 ), 80 (1/20)3 ' ( ) . . . -

57

, , . , . ; ( ) ( ). 99/100, (99/100)50. (99/ )50. * , [1 - (99/1)50], [1 (99/100)50]. (1 x (99/100)50) + (51 [1 - (99/100)50]) = 21 . , , . , . . , chuck-a-luck . chuck-a-luck .

58

1 6 . , 3 . , 2 , 1 . , , 1 . , , 1 , ' . Joan Rivers: ; ( ' .) , , , 4. , 4 1/6 x 1/6 x 1/6 = 1/216, 216 3 . 4 , , ' . 4 : 44, 4X4 44, 4. 5/6 x 1/6 x 1/6 = 5/216, . 4

* Chicago Tribune CBS. (...).

59

15/216, 2 . 4 . 4 1/6 5/6 5/6 = 25/216, 4 4. 75/216 4 1 . 4 , . (1/ 216 + 15/216 + 75/216) 1 ( 100%) 125/216. , , 125 216 chuck-a-luck, 1 . (3 . 1/216) + (2 . 15/216) + (1 . x 75/216) + ( - 1 . 125/216) = ( - 17/216 .) = - 0,08 ., , , 8 .

- . , ... . ' . .

60

. - - . . : . ' , ; , , ' . , , : 3, 5, 1, 6, 2, 4. , , , , . * , : 4, 6, 1, 7, 3, 5, 2. . ( ), . . . 37% , -

61

' ( ) . , , , (24 = 4 x 3 x 2 x 1). 37% 25% 50%, , : ) (25% = 4) . ) (50% = 4) . , . , 1 , , , 2 .. , 3 2 1 4 , , . . 1234 1243 1324 1342 1423 1432 2134(A) 2143(A) 2314(,) 2341(,) 2413(,) 2431(,) 3124(A) 3142(A) 3214(B) 3241(B) 3412(,) 3421 4123(A) 4132(A) 4213(B) 4231(B) 4312(B) 4321

62

, (37% 25) . , , , ' . ( .) , . 37% 37% . : . . , .

1964 . . , , . . . . -

63

: - 1/10, - 1/4, - 1/10, - 1/3, - 1/10 - 1/1.000. : 1/ 10 1/4 1/10 1/3 1/10 x 1/1.000 = 1/12.000.000, . . . (? 1/12.000.000 . , 2.000.000 , , , , . 1/12.000.000, 8% . . 1/12.000.000, . , 600 . ' , , , 600

64

. , . . . , , . , 3.838.380 , 2 13 17 20 29 36 1 2 3 4 5 6; . . , .. Babe Ruth Lou Gehrig. Babe Ruth Lou Gehrig. Babe Ruth Lou Gehrig. Lou Gehrig Babe Ruth. ; , . Babe Ruth 0,300 Lou Gehrig 0,290, Ruth Gehrig . , Ruth 0,400 Gehrig 0,390, Ruth Gehrig . Gehrig ' , Ruth: 0,357 0,333.

65

. -. , . ' , . , , , , , . Gehrig . . ( ) . , .

66

, , , , , . , ; , ' . . , : 7:00, 7:05, 7:20, 7:25 . , . , , .

-

67

, . , . , , , . , , . , , . , ' . , , 90% , , 45% 55% ! , , 96% 48% 52% . : . , , ( ).

68

519 481 , . 1/2 . ( , , . , 519.) , : 1 . : , , , . , , . , . 519 481, . ( ) , , ( ) . ,

69

. . , , , , . , , . . , 1/2, . . , ' . ,

70

. , . , , , . . . , ' . .

, . , , . ( ) . -

71

( ) . . ( : ) . . , Amos Tversky Daniel Kahneman 50% - , , . , . , , 50%. 20% 25% , 10% . 50% . , , 65% , , 65%, * .

72

. , . [...]* , ' , . . , , , 800 . 1/2 1/2 1/2 = 1/8, 800 . , , . : , , , 1/8 (1/2)3. 3/8, 300 800 . , 300 .* ( ) - Pete Rose .

73

' , ( ) . , , , , Poisson. . , Poisson , , . , , . .

3 Raymond Smullyan . : . * . . -. 1969. , , .* , (...)

76

; !

!

, The Skeptical Inquirer . William Cowper

,

, . , , . : Duvalier *. , , , , .

* Baby Doc: Jean Claude Duvalier, Francois Duvalier, 1957-1971, Papa Doc. (...)

77

, , . , . , ' . . -, , -- . , , , . . , Wilhelm Fliess, , . Fliess 23 28, , , , . : 23 + 28 . , 6 = (23 x 10) + [28x ( - 8)]. , , 28 23. , 23

78

28 - -, . , . . : , , ... ' , , , Karl Popper, . . , , . , , , , . , . ' , , . , ' , . . , . ,

79

UFO* UFO . , UFO. . ( 100 1 ), . , , - .

, , , Uri Geller . [ESP: extrasensory perception] , . .* Unidentified Flying Objects - . (...)

80

, , . ' , , . , . : . - - . , . , , , : . . -

81

, ( J. . Rhine) ( S. G. Soal) . Jeane Dixon ( Jeane Dixon*), , . , **, . . ( , ), , . - - . , , -

' Jean Dixon , . (...) " New Age: , "80, , , , .. (...)

82

. , . ' . Horace Mann , Horace Greeley, Go West, young man ( , ], . , . . . ' , , . , .

83

, . (, , , ..) The Skeptical Inquirer, CSICOP (Committee for the Scientific Investigation of Claims of the Paranormal), , Paul Kurtz .

. , ' , Ford . : , , ' *. ( .) , . , .

* -: (grand-slam home run) (basesloaded triple), (...)

84

10.000. 9.999 10.000. . , , , 9.999/10.000 9.999/10.000. , (9.999/10.000) (9.999/10.000)365. (9.999/10.000)365 0,964 , 96,4% , . 3,6% . 3,6% * . , . . . . . , , ,

85

, , (1 12, "12), ' ; ' . , , (2,5 x 8 x 2,5 x 10) 6,25 x 1016 , -12, 6,25 x 1016 x "12, 60.000. 60.000 . . (1/35) ( , 200.000, 35 , , . - , . [creation science], . , ' . : , , ;

86

. . 1986 52% . , . , , ' . . : ) , , ( ) ) , ' - , & - - ' , . , ;

87

, , . , , . , , . (, Shawn Carlson ) , . ( , ) . 116 , ( ) . : , ' , . John McGervey, Case Western Reserve, 16.000 American Men of Science 6.000 Who's Who in American Politics , . Bernard Silverman 3.000

88

. ; , , ' . , . ( ), , . , , , , .. , . . , . , , , . , . , , , .

89

, Carl Sagan, , , . , : , , , , . , . , , ' , .

, - UFO, , . , , , , The intruders Budd Hopkins Communion Whitley Strieber. . ,

90

. . , , . . 10 (1011) , 1/10 . , , , , , . (108) . , 1/10 . , 10 (107), , , 1/10 ! 6 - . ; , 14 , '

91

300.000 - 10 . , , 14 106 108 . 8 500, , 500 - ! , , . , . , , , . 100 ( ) 12-15 , 10.000 . 2.000 . , -

92

. , , , , , , . . , , UFO - [Unidentified Flying Objects]. , .

: ) , ) ) , . , , , . . ( [placebo effect]), . ' ,

93

. , , , . , , , , ' . , ( ), . ' * , . , . , . ( ' . * .)* : There's a long way from Adonai to I Don't Know, to I Deny - to adapt a line from poet

94

, . , , , ' , ' . , . ; , , , . . Willard Van Orman Quine . , . , , , .Howard Nemerov. Adonai , , (...)

95

, . . , , , , , , , . , , , , Quine, .

, . . , . ; , 110 . 1,90 , 110 .

96

12 1/36. 12 11 1/3. ( 6,6 6,5 5,6 12, 11.) . : , -, - 1/3. , , 1, 100%. , , , , 1/5. ' , , , 19/20 0,95. , , , . , ; , ; 2/3 1/2 . , - , , , , () () . , , , , . , ,

97

, , , , . , , . , . . , ' . ' , - . , - - -. - . ; . . . - , , - , , - , . 2/3. -, - 1/2 ' . -- .

98

[blackjack] , . . 18/38, . : 7 1/6, 7 7. . , ' , . (4/52 x 4/ 52) (4/52 x 3/51), . , , , 12/52 10/22. - () - , ( ) . * , * , (...)

99

. , , \ , . Bayes, Thomas Bayes . , AIDS. 98%, , 98 100 , 98 100. 0,5% - - . . : ; . , . 10.000 . ' ; , 50 ' 10.000 (0,5% 10.000) , , 98% 50 , 49 . 9.950 , 2% , 199 (0,02 x 9.950 = 199). , 248 (199 + 49 = 248) (199) , -

100

49/248, 20% ! ( , , 98%.) 98% AIDS .. Wall Street Journal, , 75% . , . , .

, , . . (ahavah) 13,

101

(ehad). , , 26, Yahweh, . 26 : 26 , : ' ' . * (45) (19) 26.

(gematria) , 10 - 10 1, 20 2, . , Yahweh 10, , , 1, Yahweh 17, (tov). , ' Yahweh 186, (Maqom), . (), , , , , , . ' 284, . , , 801, ,

102

. , , 365, . 666, , . . , , 666 , . : , , 666. , , , 666 . , * Ronald Wilson Reagan . . (, , * Fundamentalists: 20 . ' , . (...)

103

) , , , .. , . , . Georges Ifrah From One to Zero [ ] ( ) 666, . , , . Procter and Gamble - . , , . , . , , . , . , , ( ). , -

104

. , , . ( ) tabula-rasa ( Rorschach*) , , .

, . . , - - . - , - , - . , . , .., , . * , , (...)

105

, . . , . , Van Dumholtz , . ' . ' , . , . 35.000 ; ; ; 1 = 100 . 1/4 = 25 . 1/4 1/2 25 5, 1/2 = 5 ! , . Pat Robertson, , , . ,

106

. : , , , . , , , , . , : . ,

4 ; ' - : , 2,01 , , , 6% 2,01 - 0,12 . , . , , .

108

/ , , . Walt Whitman

; , , , .