              ,BOOK ,,XIV
                   #A
  ,REG>D+ ? K9D ( SUB/.E1 :AT WE H SD M/
2 TAK5 Z SU6ICI5T4 ,ALL PHILOSOPH]S MAKE
! F/ PR9CIPLES 3TR>IES3 Z 9 NATURAL ?+S1
S AL 9 ! CASE ( UN*ANGEA# SUB/.ES4 ,B
S9CE "! _C 2 ANY?+ PRIOR 6! F/ PR9CIPLE
( ALL ?+S1 ! PR9CIPLE _C 2 ! PR9CIPLE &
YET 2 AN ATTRIBUTE ( "S?+ ELSE4 ,6SU7E/
? IS L SAY+ T ! :ITE IS A F/ PR9CIPLE1 N
QUA ANY?+ ELSE B QUA :ITE1 B YET T X IS
PR$ICA# (A SUBJECT1 I4E4 T XS 2+ :ITE
PRESUPPOSES XS 2+ "S?+ ELSE2 ? IS
ABSURD1 = !N T SUBJECT W 2 PRIOR4 ,B ALL
?+S : >E G5]AT$ F _! 3TR>IES 9VOLVE AN
"ULY+ SUBJECT2 A SUBJECT1 !N1 M/ 2
PRES5T 9 ! CASE ( 3TR>IES1 IF ANY":4
,ALL 3TR>IES1 !N1 >E ALW PR$ICA# (A
SUBJECT1 & N"O C EXI/ A"P1 B J Z
APPE>.ES SU7E/ T "! IS NO?+ 3TR>Y
6SUB/.E1 >GU;T 3FIRMS ?4 ,NO 3TR>Y1 !N1
IS ! F/ PR9CIPLE ( ALL ?+S 9 ! FULL
S5SE2 ! F/ PR9CIPLE IS "S?+ DI6]5T4
  ,B ^! ?9K]S MAKE "O (! 3TR>IES MATT]1
"S MAK+ ! UNEQUAL : !Y TAKE 6BE ! ESS;E
( PLURAL;Y-MATT] =! ,"O1 & O!RS MAK+
PLURAL;Y MATT] =! ,"O4 7,! =M] G5]ATE
NUMB]S \ (! DYAD (! UNEQUAL1 I4E4 (! GRT
& SMALL1 &! O!R ?9K] WE H REF]R$
6G5]ATES !M \ ( PLURAL;Y1 :ILE AC 6BO? X
IS G5]AT$ 0! ESS;E (! ,"O47 ,= EV5 !
PHILOSOPH] :O SAYS ! UNEQUAL &! ,"O >E !
ELE;TS1 &! UNEQUAL IS A DYAD -POS$ (!
GRT & SMALL1 TR1TS ! UNEQUAL1 OR ! GRT &
! SMALL1 Z 2+ "O1 & DOES N DRAW ! 4T9C;N
T !Y >E "O 9 DEF9I;N1 B N 9 NUMB]4 ,B !Y
D N DESCRIBE "RLY EV5 ! PR9CIPLES : !Y
CALL ELE;TS1 = "S "N ! GRT &! SMALL )!
,"O & TR1T ^! ?REE Z ELE;TS ( NUMB]S1
TWO 2+ MATT]1 "O ! =M2 :ILE O!RS "N ! _M
& FEW1 2C ! GRT &! SMALL >E M
APPROPRIATE 9 _! NATURE 6MAGNITUDE ?AN
6NUMB]2 & O!RS "N R ! UNIV]SAL "* -MON
6^!-,8T : EXCE$S & T : IS EXCE$$0'4 ,N"O
( ^! V>IETIES ( OP9ION MAKES ANY DI6];E
6SP1K (1 9 VIEW ( "S (! 3SEQU;ES2 !Y
A6ECT ONLY ! AB/RACT OBJEC;NS1 : ^!
?9K]S TAKE C>E 6AVOID 2C ! DEMON/R,NS !Y
!MVS (F] >E AB/RACT1-) ? EXCEP;N1 T IF !
EXCE$+ &! EXCE$$ >E ! PR9CIPLES1 & N !
GRT &! SMALL1 3SI/5CY REQUIRES T NUMB]
%D -E F ! ELE;TS 2F DOES2 = NUMB] IS M
UNIV]SAL ?AN Z ! EXCE$+ &! EXCE$$ >E M
UNIV]SAL ?AN ! GRT &! SMALL4 ,B Z X IS1
!Y SAY "O ( ^! ?+S B D N SAY ! O!R4
,O!RS OPPOSE ! DI6]5T &! O!R 6! ,"O1 &
O!RS OPPOSE PLURAL;Y 6! ,"O4 ,B IF1 Z !Y
CLAIM1 ?+S 3SI/ ( 3TR>IES1 & 6! ,"O EI
"! IS NO?+ 3TR>Y1 OR IF "! IS 6BE ANY?+
X IS PLURAL;Y1 &! UNEQUAL IS 3TR>Y 6!
EQUAL1 &! DI6]5T 6! SAME1 &! O!R 6! ?+
XF1 ^? :O OPPOSE ! ,"O 6PLURAL;Y H MO/
CLAIM 6PLAUSIBIL;Y1 B EV5 _! VIEW IS
9ADEQUATE1 =! ,"O WD ON _! VIEW 2 A FEW2
= PLURAL;Y IS OPPOS$ 6FEW;S1 &! _M 6!
FEW4
  ,8,! "O0' EVID5TLY M1NS A M1SURE4 ,& 9
E CASE "! IS "S "ULY+ ?+ )A 4T9CT NATURE
( XS [N1 E4G4 9 ! SCALE A QU>T]-T"O1 9
SPATIAL MAGNITUDE A F+] OR A FOOT OR
"S?+ (! SORT1 9 RHY?MS A B1T OR A
SYLLA#2 & SIMIL>LY 9 GRAV;Y X IS A
DEF9ITE WEI<T2 & 9 ! SAME WAY 9 ALL
CASES1 9 QUALITIES A QUAL;Y1 9
QUANTITIES A QUANT;Y 7&! M1SURE IS
9DIVISI#1 9 ! =M] CASE 9 K9D1 & 9 !
LATT] 6! S5SE72 : IMPLIES T ! "O IS N 9
XF ! SUB/.E ( ANY?+4 ,& ? IS R1SONA#2 =
,8! "O0' M1NS ! M1SURE ( "S PLURAL;Y1 &
,8NUMB]0' M1NS A M1SUR$ PLURAL;Y &A
PLURAL;Y ( M1SURES4 7,?US X IS NATURAL T
"O IS N A NUMB]2 =! M1SURE IS N M1SURES1
B BO? ! M1SURE &! "O >E />T+-PO9TS47 ,!
M1SURE M/ ALW 2 "S ID5TICAL ?+ PR$ICA# (
ALL ! ?+S X M1SURES1 E4G4 IF ! ?+S >E
HORSES1 ! M1SURE IS ,8HORSE0'1 & IF !Y
>E M51 ,8MAN0'4 ,IF !Y >E A MAN1 A
HORSE1 &A GOD1 ! M1SURE IS P]H ,8LIV+
2+0'1 &! NUMB] ( !M W 2 A NUMB] ( LIV+
2+S4 ,IF ! ?+S >E ,8MAN0' & ,8PALE0' &
,8WALK+0'1 ^! W SC>CELY H A NUMB]1 2C
ALL 2L;G 6A SUBJECT : IS "O &! SAME 9
NUMB]1 YET ! NUMB] ( ^! W 2 A NUMB] (
,8K9DS0' OR ( "S S* T]M4
  ,^? :O TR1T ! UNEQUAL Z "O ?+1 &! DYAD
Z AN 9DEF9ITE -P.D ( GRT & SMALL1 SAY
:AT IS V F> F 2+ PROBA# OR POSSI#4 ,=
7A7 ^! >E MODIFIC,NS & A3ID5TS1 R ?AN
SUB/RATA1 ( NUMB]S & MAGNITUDES-! _M &
FEW ( NUMB]1 &! GRT & SMALL ( MAGNITUDE-
L EV5 & ODD1 SMOO? & R\<1 /RAI<T &
CURV$4 ,AG1 7B7 A"P F ? MISTAKE1 ! GRT &
! SMALL1 & S ON1 M/ 2 RELATIVE 6"S?+2 B
:AT IS RELATIVE IS L1/ ( ALL ?+S A K9D (
5T;Y OR SUB/.E1 & IS PO/]IOR 6QUAL;Y &
QUANT;Y2 &! RELATIVE IS AN A3ID5T (
QUANT;Y1 Z 0 SD1 N XS MATT]1 S9CE "S?+ )
A 4T9CT NATURE ( XS [N M/ S]VE Z MATT]
BO? 6! RELATIVE 9 G5]AL & 6XS "PS &
K9DS4 ,= "! IS NO?+ EI GRT OR SMALL1 _M
OR FEW1 OR1 9 G5]AL1 RELATIVE 6"S?+
ELSE1 : )\T HAV+ A NATURE ( XS [N IS _M
OR FEW1 GRT OR SMALL1 OR RELATIVE 6"S?+
ELSE4 ,A SIGN T ! RELATIVE IS L1/ ( ALL
A SUB/.E &A R1L ?+ IS ! FACT T X AL"O
HAS NO PROP] G5],N OR DE/RUC;N OR
MOVE;T1 Z 9 RESPECT ( QUANT;Y "! IS
9CR1SE & DIM9U;N1 9 RESPECT ( QUAL;Y
ALT],N1 9 RESPECT ( PLACE LOCOMO;N1 9
RESPECT ( SUB/.E SIMPLE G5],N &
DE/RUC;N4 ,9 RESPECT ( REL,N "! IS NO
PROP] *ANGE2 =1 )\T *ANG+1 A ?+ W 2 N[
GRT] & N[ LESS OR EQUAL1 IF T ) : X IS
-P>$ HAS *ANG$ 9 QUANT;Y4 ,& 7C7 ! MATT]
( EA* ?+1 & "!=E ( SUB/.E1 M/ 2 T : IS
POT5TI,Y (! NATURE 9 "Q2 B ! RELATIVE IS
NEI POT5TI,Y NOR ACTU,Y SUB/.E4 ,X IS
/RANGE1 !N1 OR R IMPOSSI#1 6MAKE N-
SUB/.E AN ELE;T IN1 & PRIOR TO1 SUB/.E2
= ALL ! CATEGORIES >E PO/]IOR 6SUB/.E4
,AG1 7D7 ELE;TS >E N PR$ICAT$ (! ?+S ( :
!Y >E ELE;TS1 B _M & FEW >E PR$ICAT$ BO?
A"P & TGR ( NUMB]1 & L;G & %ORT (! L9E1
& BO? BROAD & N>R[ APPLY 6! PLANE4 ,IF
"! IS A PLURAL;Y1 !N1 ( : ! "O T]M1 VIZ4
FEW1 IS ALW PR$ICAT$1 E4G4 #B 7: _C 2
_M1 = IF X 7 _M1 #A WD 2 FEW71 "! M/ 2
AL "O : IS ABSOLUTELY _M1 E4G4 #AJ IS _M
7IF "! IS NO NUMB] : IS GRT] ?AN #AJ71
OR #AJ1JJJ4 ,H[ !N1 9 VIEW ( ?1 C NUMB]
3SI/ ( FEW & _M8 ,EI BO? "\ 6BE PR$ICAT$
( X1 OR NEI2 B 9 FACT ONLY ! "O OR ! O!R
IS PR$ICAT$4
                   #B
  ,WE M/ 9QUIRE G5],Y1 :E!R ET]NAL ?+S C
3SI/ ( ELE;TS4 ,IF !Y D1 !Y W H MATT]2 =
"EY?+ T 3SI/S ( ELE;TS IS -POSITE4
,S9CE1 !N1 EV5 IF A ?+ EXI/S = "E1 \ ( T
( : X 3SI/S X WD NECESS>ILY AL1 IF X _H
-E 962+1 H -E 962+1 & S9CE "EY?+ -ES 6BE
:AT X -ES 6BE \ ( T : IS X POT5TI,Y 7= X
CD N H -E 6BE \ ( T : _H N ? CAPAC;Y1
NOR CD X 3SI/ ( S* ELE;TS71 & S9CE !
POT5TIAL C 2 EI ACTUAL OR N1-? 2+ S1
H["E "ELA/+ NUMB] OR ANY?+ ELSE T HAS
MATT] IS1 X M/ 2 CAPA# ( N EXI/+1 J Z T
: IS ANY NUMB] ( YE>S OLD IS Z CAPA# ( N
EXI/+ Z T : IS A "D OLD2 IF ? IS CAPA# (
N EXI/+1 S IS T : HAS LA/$ =A "T S L;G T
X HAS NO LIMIT4 ,!Y _C1 !N1 2 ET]NAL1
S9CE T : IS CAPA# ( N EXI/+ IS N ET]NAL1
Z WE _H O3A.N 6%[ 9 ANO!R 3TEXT4 ,IF T :
WE >E N[ SAY+ IS TRUE UNIV]S,Y-T NO
SUB/.E IS ET]NAL UN.S X IS ACTUAL;Y-& IF
! ELE;TS >E MATT] T "ULIES SUB/.E1 NO
ET]NAL SUB/.E C H ELE;TS PRES5T 9 X1 ( :
X 3SI/S4
  ,"! >E "S :O DESCRIBE ! ELE;T : ACTS )
! ,"O Z AN 9DEF9ITE DYAD1 & OBJECT TO
,8! UNEQUAL0'1 R1SONABLY 5\<1 2C (! 5SU+
DI6ICULTIES2 B !Y H GOT RID ONLY ( ^?
OBJEC;NS : 9EVITABLY >ISE F ! TR1T;T (!
UNEQUAL1 I4E4 ! RELATIVE1 Z AN ELE;T2 ^?
: >ISE A"P F ? OP9ION M/ 3FRONT EV5 ^!
?9K]S1 :E!R X IS ID1L NUMB]1 OR
MA!MATICAL1 T !Y 3/RUCT \ ( ^? ELE;TS4
  ,"! >E _M CAUSES : L$ !M (F 96^!
EXPLAN,NS1 & ESPECI,Y ! FACT T !Y FRAM$
! DI6ICULTY 9 AN OBSOLETE =M4 ,= !Y ?"\
T ALL ?+S T >E WD 2 "O 7VIZ4 ,2+ XF71 IF
"O DID N JO9 ISSUE )& REFUTE ! SAY+ (
,P>M5IDES3
  ,8,= N"E W ? HE PROV$1 T ?+S T >E N
>E40'
  ,!Y ?"\ X NEC 6PROVE T T : IS N IS2 =
ONLY ?US-( T : IS & "S?+ ELSE-CD ! ?+S T
>E 2 -POS$1 IF !Y >E _M4
  ,B1 F/1 IF ,82+0' HAS _M S5SES 7= X
M1NS "S"TS SUB/.E1 "S"TS T X IS (A C]TA9
QUAL;Y1 "S"TS T X IS (A C]TA9 QUANT;Y1 &
AT O!R "TS ! O!R CATEGORIES71 :AT SORT (
,8"O0'1 !N1 >E ALL ! ?+S T >E1 IF NON-2+
IS 6BE SUPPOS$ N 6BE8 ,IS X ! SUB/.ES T
>E "O1 OR ! A6EC;NS & SIMIL>LY ! O!R
CATEGORIES Z WELL1 OR ALL TGR-S T !
,8?0' &! ,8S*0' &! ,8S M*0' &! O!R
CATEGORIES T 9DICATE EA* "S "O CLASS (
2+ W ALL 2 "O8 ,B X IS /RANGE1 OR R
IMPOSSI#1 T ! -+ 96PLAY (A S+LE ?+ %D
BR+ X AB T "P ( T : IS IS A ,8?0'1 "P A
,8S*0'1 "P A ,8S M*0'1 "P A ,8"H0'4
  ,SECONDLY1 ( :AT SORT ( NON-2+ & 2+ D
! ?+S T >E 3SI/8 ,= ,8NONBE+0' AL HAS _M
S5SES1 S9CE ,82+0' HAS2 & ,8N 2+ A MAN0'
M1NS N 2+ A C]TA9 SUB/.E1 ,8N 2+
/RAI<T0' N 2+ (A C]TA9 QUAL;Y1 ,8N 2+
?REE CUBITS L;G0' N 2+ (A C]TA9 QUANT;Y4
,:AT SORT ( 2+ & NON-2+1 !N1 0_! UNION
PLURALIZE ! ?+S T >E8 ,? ?9K] M1NS 0!
NON-2+ ! UNION ( : ) 2+ PLURALIZES ! ?+S
T >E1 ! FALSE &! "* ( FALS;Y4 ,? IS AL
:Y X US$ 6BE SD T WE M/ ASSUME "S?+ T IS
FALSE1 Z GEOMET]S ASSUME ! L9E : IS N A
FOOT L;G 6BE A FOOT L;G4 ,B ? _C 2 S4 ,=
NEI D GEOMET]S ASSUME ANY?+ FALSE 7=!
ENUNCI,N IS EXTRANE\S 6! 9F];E71 NOR IS
X NON-2+ 9 ? S5SE T ! ?+S T >E >E G5]AT$
F OR RESOLV$ 9TO4 ,B S9CE ,8NON-2+0'
TAK5 9 XS V>I\S CASES HAS Z _M S5SES Z
"! >E CATEGORIES1 & 2SS ? ! FALSE IS SD
N 6BE1 & S IS ! POT5TIAL1 X IS F ? T
G5],N PROCE$S1 MAN F T : IS N MAN B
POT5TI,Y MAN1 & :ITE F T : IS N :ITE B
POT5TI,Y :ITE1 & ? :E!R X IS "S "O ?+ T
IS G5]AT$ OR _M4
  ,! "Q EVID5TLY IS1 H[ 2+1 9 ! S5SE (
,8! SUB/.ES0'1 IS _M2 =! ?+S T >E G5]AT$
>E NUMB]S & L9ES & BODIES4 ,N[ X IS
/RANGE 69QUIRE H[ 2+ 9 ! S5SE (! ,8:AT0'
IS _M1 & N H[ EI QUALITIES OR QUANTITIES
>E _M4 ,= SURELY ! 9DEF9ITE DYAD OR ,8!
GRT &! SMALL0' IS N A R1SON :Y "! %D 2
TWO K9DS ( :ITE OR _M COL\RS OR FLAV\RS
OR %APES2 = !N ^! AL WD 2 NUMB]S &
UNITS4 ,B IF !Y _H ATTACK$ ^! O!R
CATEGORIES1 !Y WD H SE5 ! CAUSE (!
PLURAL;Y 9 SUB/.ES AL2 =! SAME ?+ OR
"S?+ ANALOG\S IS ! CAUSE4 ,? AB]R,N IS !
R1SON AL :Y 9 SEEK+ ! OPPOSITE ( 2+ &!
"O1 F : ) 2+ &! "O ! ?+S T >E PROCE$1 !Y
POSIT$ ! RELATIVE T]M 7I4E4 ! UNEQUAL71
: IS NEI ! 3TR>Y NOR ! 3TRADICTORY ( ^!1
& IS "O K9D ( 2+ Z ,8:AT0' & QUAL;Y AL
>E4
  ,!Y %D H ASK$ ? "Q AL1 H[ RELATIVE
T]MS >E _M & N "O4 ,B Z X IS1 !Y 9QUIRE
H[ "! >E _M UNITS 2SS ! F/ #A1 B D N G
ON 69QUIRE H[ "! >E _M UNEQUALS 2SS !
UNEQUAL4 ,YET !Y USE !M & SP1K ( GRT &
SMALL1 _M & FEW 7F : PROCE$ NUMB]S71 L;G
& %ORT 7F : PROCE$S ! L9E71 BROAD & N>R[
7F : PROCE$S ! PLANE71 DEEP & %ALL[ 7F :
PROCE$ SOLIDS72 & !Y SP1K ( YET M K9DS (
RELATIVE T]M4 ,:AT IS ! R1SON1 !N1 :Y "!
IS A PLURAL;Y ( ^!8
  ,X IS NEC1 !N1 Z WE SAY1 6PRESUPPOSE =
EA* ?+ T : IS X POT5TI,Y2 &! HOLD] ( ^!
VIEWS FUR!R DCLD :AT T IS : IS POT5TI,Y
A ,8?0' &A SUB/.E B IS N 9 XF 2+-VIZ4 T
X IS ! RELATIVE 7Z IF HE _H SD ,8!
QUALITATIVE0'71 : IS NEI POT5TI,Y ! "O
OR 2+1 NOR ! NEG,N (! "O NOR ( 2+1 B "O
AM;G 2+S4 ,& X 0 M* M NEC1 Z WE SD1 IF
HE 0 9QUIR+ H[ 2+S >E _M1 N 69QUIRE AB
^? 9 ! SAME CATEGORY-H[ "! >E _M SUB/.ES
OR _M QUALITIES-B H[ 2+S Z A :OLE >E _M2
= "S >E SUB/.ES1 "S MODIFIC,NS1 "S
REL,NS4 ,9 ! CATEGORIES O!R ?AN SUB/.E
"! IS YET ANO!R PRO#M 9VOLV$ 9 ! EXI/;E
( PLURAL;Y4 ,S9CE !Y >E N SEP>A# F
SUB/.ES1 QUALITIES & QUANTITIES >E _M J
2C _! SUB/RATUM 2COMES & IS _M2 YET "!
"\ 6BE A MATT] = EA* CATEGORY2 ONLY X _C
2 SEP>A# F SUB/.ES4 ,B 9 ! CASE (
,8?ISES0'1 X IS POSSI# 6EXPLA9 H[ !
,8?0' IS _M ?+S1 UN.S A ?+ IS 6BE TR1T$
Z BO? A ,8?0' &A G5]AL "*4 ,! DI6ICULTY
>IS+ F ! FACTS AB SUB/.ES IS R ?1 H[ "!
>E ACTU,Y _M SUB/.ES & N "O4
  ,B FUR!R1 IF ! ,8?0' &! QUANTITATIVE
>E N ! SAME1 WE >E N TOLD H[ & :Y ! ?+S
T >E >E _M1 B H[ QUANTITIES >E _M4 ,=
ALL ,8NUMB]0' M1NS A QUANT;Y1 & S DOES !
,8UNIT0'1 UN.S X M1NS A M1SURE OR !
QUANTITATIVELY 9DIVISI#4 ,IF1 !N1 !
QUANTITATIVE &! ,8:AT0' >E DI6]5T1 WE >E
N TOLD :;E OR H[ ! ,8:AT0' IS _M2 B IF
ANY "O SAYS !Y >E ! SAME1 HE HAS 6FACE
_M 9CONSI/5CIES4
  ,"O MI<T FIX "O'S ATT5;N AL ON ! "Q1
REG>D+ ! NUMB]S1 :AT JU/IFIES ! 2LIEF T
!Y EXI/4 ,6! 2LIEV] 9 ,ID1S !Y PROVIDE
"S SORT ( CAUSE = EXI/+ ?+S1 S9CE EA*
NUMB] IS AN ,IDEA1 &! ,IDEA IS 6O!R ?+S
"SH[ OR O!R ! CAUSE ( _! 2+2 = LET ?
SUPPOSI;N 2 GRANT$ !M4 ,B Z = HM :O DOES
N HOLD ? VIEW 2C HE SEES ! 9H]5T
OBJEC;NS 6! ,ID1S 7S T X IS N = ? R1SON
T HE POSITS NUMB]S71 B :O POSITS
MA!MATICAL NUMB]1 :Y M/ WE 2LIEVE 8
/ATE;T T S* NUMB] EXI/S1 &( :AT USE IS
S* NUMB] 6O!R ?+S8 ,NEI DOES HE :O SAYS
X EXI/S MA9TA9 T X IS ! CAUSE ( ANY?+
7HE R SAYS X IS A ?+ EXI/+ 0XF71 NOR IS
X OBS]V$ 6BE ! CAUSE ( ANY?+2 =! !OREMS
( >I?METICIANS W ALL 2 F.D TRUE EV5 (
S5SI# ?+S1 Z 0 SD 2F4
                   #C
  ,Z = ^?1 !N1 :O SUPPOSE ! ,ID1S 6EXI/
& 6BE NUMB]S1 0_! ASSUMP;N 9 VIRTUE (!
ME?OD ( SETT+ \ EA* T]M A"P F XS 9/.ES-
(! UN;Y ( EA* G5]AL T]M !Y TRY AT L1/
6EXPLA9 "SH[ :Y NUMB] M/ EXI/4 ,S9CE _!
R1SONS1 H["E1 >E NEI 3CLUSIVE NOR 9 !MVS
POSSI#1 "O M/ N1 = ^! R1SONS AT L1/1
ASS]T ! EXI/;E ( NUMB]4 ,AG1 !
,PY?AGOR1NS1 2C !Y SAW _M ATTRIBUTES (
NUMB]S 2L;G+ TE S5SI# BODIES1 SUPPOS$
R1L ?+S 6BE NUMB]S-N SEP>A# NUMB]S1
H["E1 B NUMB]S ( : R1L ?+S 3SI/4 ,B :Y8
,2C ! ATTRIBUTES ( NUMB]S >E PRES5T 9 A
MUSICAL SCALE & 9 ! H1V5S & 9 _M O!R
?+S4 ,^?1 H["E1 :O SAY T MA!MATICAL
NUMB] AL"O EXI/S _C AC 6_! HYPO!SES SAY
ANY?+ ( ? SORT1 B X US$ 6BE URG$ T ^!
S5SI# ?+S CD N 2 ! SUBJECT (! SCI;ES4 ,B
WE MA9TA9 T !Y >E1 Z WE SD 2F4 ,& X IS
EVID5T T ! OBJECTS ( MA!MATICS D N EXI/
A"P2 = IF !Y EXI/$ A"P _! ATTRIBUTES WD
N H BE5 PRES5T 9 BODIES4 ,N[ !
,PY?AGOR1NS 9 ? PO9T >E OP5 6NO OBJEC;N2
B 9 T !Y 3/RUCT NATURAL BODIES \ (
NUMB]S1 ?+S T H LI<T;S & WEI<T \ ( ?+S T
H N WEI<T OR LI<T;S1 !Y SEEM 6SP1K (
ANO!R H1V5 & O!R BODIES1 N (! S5SI#4 ,B
^? :O MAKE NUMB] SEP>A# ASSUME T X BO?
EXI/S & IS SEP>A# 2C ! AXIOMS WD N 2
TRUE ( S5SI# ?+S1 :ILE ! /ATE;TS (
MA!MATICS >E TRUE & ,8GREET ! S\L0'2 &
SIMIL>LY )! SPATIAL MAGNITUDES (
MA!MATICS4 ,X IS EVID5T1 !N1 BO? T !
RIVAL !ORY W SAY ! 3TR>Y ( ?1 & T !
DI6ICULTY WE RAIS$ J N[1 :Y IF NUMB]S >E
9 NO WAY PRES5T 9 S5SI# ?+S _!
ATTRIBUTES >E PRES5T 9 S5SI# ?+S1 HAS
6BE SOLV$ 0^? :O HOLD ^! VIEWS4
  ,"! >E "S :O1 2C ! PO9T IS ! LIMIT &
EXTREME (! L9E1 ! L9E (! PLANE1 &! PLANE
(! SOLID1 ?9K "! M/ 2 R1L ?+S ( ? SORT4
,WE M/ "!=E EXAM9E ? >GU;T TOO1 & SEE
:E!R X IS N REM>KABLY W1K4 ,= 7I7
EXTREMES >E N SUB/.ES1 B R ALL ^! ?+S >E
LIMITS4 ,= EV5 WALK+1 & MOVE;T 9 G5]AL1
HAS A LIMIT1 S T ON _! !ORY ? W 2 A
,8?0' &A SUB/.E4 ,B T IS ABSURD4 ,N B
:AT 7;II7 EV5 IF !Y >E SUB/.ES1 !Y W ALL
2 ! SUB/.ES (! S5SI# ?+S 9 ? _W2 = X IS
6^! T ! >GU;T APPLI$4 ,:Y !N %D !Y 2
CAPA# ( EXI/+ A"P8
  ,AG1 IF WE >E N TOO EASILY SATISFI$1
WE MAY1 REG>D+ ALL NUMB] &! OBJECTS (
MA!MATICS1 PRESS ? DI6ICULTY1 T !Y
3TRIBUTE NO?+ 6"O ANO!R1 ! PRIOR 6!
PO/]IOR2 = IF NUMB] DID N EXI/1 N"O !
LESS SPATIAL MAGNITUDES WD EXI/ = ^? :O
MA9TA9 ! EXI/;E (! OBJECTS ( MA!MATICS
ONLY1 & IF SPATIAL MAGNITUDES DID N
EXI/1 S\L & S5SI# BODIES WD EXI/4 ,B !
OBS]V$ FACTS %[ T NATURE IS N A S]IES (
EPISODES1 L A BAD TRAG$Y4 ,Z =! 2LIEV]S
9 ! ,ID1S1 ? DI6ICULTY MISSES !M2 = !Y
3/RUCT SPATIAL MAGNITUDES \ ( MATT] &
NUMB]1 L9ES \ (! NUMB] PLANES D\BT.S \ (
SOLIDS \ ( OR !Y USE O!R NUMB]S1 : MAKES
NO DI6];E4 ,B W ^! MAGNITUDES 2 ,ID1S1
OR :AT IS _! MANN] ( EXI/;E1 & :AT D !Y
3TRIBUTE 6?+S8 ,^! 3TRIBUTE NO?+1 Z !
OBJECTS ( MA!MATICS 3TRIBUTE NO?+4 ,B N
EV5 IS ANY !OREM TRUE ( !M1 UN.S WE WANT
6*ANGE ! OBJECTS ( MA!MATICS & 9V5T
DOCTR9ES ( \R [N4 ,B X IS N H>D 6ASSUME
ANY R&OM HYPO!SES & SP9 \ A L;G /R+ (
3CLU.NS4 ,^! ?9K]S1 !N1 >E WR;G 9 ? WAY1
9 WANT+ 6UNITE ! OBJECTS ( MA!MATICS )!
,ID1S4 ,& ^? :O F/ POSIT$ TWO K9DS (
NUMB]1 T (! ,=MS & T : IS MA!MATICAL1
NEI H SD NOR C SAY H[ MA!MATICAL NUMB]
IS 6EXI/ &( :AT X IS 63SI/4 ,= !Y PLACE
X 2T ID1L & S5SI# NUMB]4 ,IF 7I7 X 3SI/S
(! GRT & SMALL1 X W 2 ! SAME Z ! O!R-
ID1L-NUMB] 7HE MAKES SPATIAL MAGNITUDES
\ ( "S O!R SMALL & GRT74 ,& IF 7;II7 HE
"NS "S O!R ELE;T1 HE W 2 MAK+ 8 ELE;TS R
_M4 ,& IF ! PR9CIPLE ( EA* (! TWO K9DS (
NUMB] IS A #A1 UN;Y W 2 "S?+ -MON 6^!1 &
WE M/ 9QUIRE H[ ! "O IS ^! _M ?+S1 :ILE
AT ! SAME "T NUMB]1 AC 6HM1 _C 2 G5]AT$
EXCEPT F "O & AN 9DEF9ITE DYAD4
  ,ALL ? IS ABSURD1 & 3FLICTS BO? ) XF &
)! PROBABILITIES1 & WE SEEM 6SEE 9 X
,SIMONIDES ,8L;G RIGM>OLE0' =! L;G
RIGM>OLE -ES 96PLAY1 L ^? ( SLAVES1 :5
M5 H NO?+ S.D 6SAY4 ,&! V ELE;TS-! GRT &
! SMALL-SEEM 6CRY \ AG/ ! VIOL;E T IS
D"O 6!M2 = !Y _C 9 ANY WAY G5]ATE NUMB]S
O!R ?AN ^? GOT F #A 0D\BL+4
  ,X IS /RANGE AL 6ATTRIBUTE G5],N 6?+S
T >E ET]NAL1 OR R ? IS "O (! ?+S T >E
IMPOSSI#4 ,"! NE$ 2 NO D\BT :E!R !
,PY?AGOR1NS ATTRIBUTE G5],N 6!M OR N2 =
!Y SAY PLA9LY T :5 ! "O _H BE5 3/RUCT$1
:E!R \ ( PLANES OR ( SURFACE OR ( SE$ OR
( ELE;TS : !Y _C EXPRESS1 IMMLY ! NE>E/
"P (! UNLIMIT$ 2GAN 6BE 3/RA9$ & LIMIT$
0! LIMIT4 ,B S9CE !Y >E 3/RUCT+ A _W &
WI% 6SP1K ! LANGUAGE ( NATURAL SCI;E1 X
IS FAIR 6MAKE "S EXAM9,N ( _! PHYSICAL
!ORICS1 B 6LET !M (F F ! PRES5T 9QUIRY2
= WE >E 9VE/IGAT+ ! PR9CIPLES AT "W 9
UN*ANGEA# ?+S1 S T X IS NUMB]S ( ? K9D
^: G5ESIS WE M/ /UDY4
                   #D
  ,^! ?9K]S SAY "! IS NO G5],N (! ODD
NUMB]1 : EVID5TLY IMPLIES T "! IS G5],N
(! EV52 & "S PRES5T ! EV5 Z PRODUC$ F/ F
UNEQUALS-! GRT &! SMALL-:5 ^! >E
EQUALIZ$4 ,! 9EQUAL;Y1 !N1 M/ 2L;G 6!M
2F !Y >E EQUALIZ$4 ,IF !Y _H ALW BE5
EQUALIZ$1 !Y WD N H BE5 UNEQUAL 2F2 = "!
IS NO?+ 2F T : IS ALW4 ,"!=E EVID5TLY !Y
>E N GIV+ _! A3.T (! G5],N ( NUMB]S
M]ELY 6ASSI/ 3TEMPL,N ( _! NATURE4
  ,A DI6ICULTY1 &A REPROA* 6ANY "O :O
F9DS X NO DI6ICULTY1 >E 3TA9$ 9 ! "Q H[
! ELE;TS &! PR9CIPLES >E RELAT$ 6! GD &!
B1UTI;L2 ! DI6ICULTY IS ?1 :E!R ANY (!
ELE;TS IS S* A ?+ Z WE M1N 0! GD XF &!
BE/1 OR ? IS N S1 B ^! >E LAT] 9 ORIG9
?AN ! ELE;TS4 ,! !OLOGIANS SEEM 6AGREE )
"S ?9K]S (! PRES5T "D1 :O ANSW] ! "Q 9 !
NEGATIVE1 & SAY T BO? ! GD &! B1UTI;L
APPE> 9 ! NATURE ( ?+S ONLY :5 T NATURE
HAS MADE "S PROGRESS4 7,? !Y D 6AVOID A
R1L OBJEC;N : 3FRONTS ^? :O SAY1 Z "S D1
T ! "O IS A F/ PR9CIPLE4 ,! OBJEC;N
>ISES N F _! ASCRIB+ GD;S 6! F/ PR9CIPLE
Z AN ATTRIBUTE1 B F _! MAK+ ! "O A
PR9CIPLE-&A PR9CIPLE 9 ! S5SE ( AN
ELE;T-& G5]AT+ NUMB] F ! "O47 ,! OLD
POETS AGREE ) ? 9ASM* Z !Y SAY T N ^? :O
>E F/ 9 "T1 E4G4 ,NI<T & ,H1V5 OR ,*AOS
OR ,OC1N1 REIGN & RULE1 B ,ZEUS4 ,^!
POETS1 H["E1 >E L$ 6SP1K ?US ONLY 2C !Y
?9K (! RUL]S (! _W Z *ANG+2 = ^? ( !M :O
-B9E ! TWO "*S 9 T !Y D N USE MY?ICAL
LANGUAGE "?\T1 E4G4 ,PH]ECYDES & "S
O!RS1 MAKE ! ORIG9AL G5]AT+ AG5T ! ,BE/1
& S D ! ,MAGI1 & "S (! LAT] SAGES AL1
E4G4 BO? ,EMP$OCLES & ,ANAXAGORAS1 ( :OM
"O MADE LOVE AN ELE;T1 &! O!R MADE R1SON
A PR9CIPLE4 ,( ^? :O MA9TA9 ! EXI/;E (!
UN*ANGEA# SUB/.ES "S SAY ! ,"O XF IS !
GD XF2 B !Y ?"\ XS SUB/.E LAY MA9LY 9 XS
UN;Y4
  ,?1 !N1 IS ! PRO#M1-: (! TWO WAYS (
SP1K+ IS "R4 ,X WD 2 /RANGE IF 6T : IS
PRIM>Y & ET]NAL & MO/ SELF-SU6ICI5T ? V
QUAL;Y--SELF-SU6ICI5CY & SELF-MA9T5.E--
2L;GS PRIM>ILY 9 "S O!R WAY ?AN Z A GD4
,B 9DE$ X C 2 = NO O!R R1SON 9DE/RUCTI#
OR SELF-SU6ICI5T ?AN 2C XS NATURE IS GD4
,"!=E 6SAY T ! F/ PR9CIPLE IS GD IS
PROBABLY CORRECT2 B T ? PR9CIPLE %D 2 !
,"O OR1 IF N T1 AT L1/ AN ELE;T1 & AN
ELE;T ( NUMB]S1 IS IMPOSSI#4 ,P[];L
OBJEC;NS >ISE1 6AVOID : "S H GIV5 UP !
!ORY 7VIZ4 ^? :O AGREE T ! ,"O IS A F/
PR9CIPLE & ELE;T1 B ONLY ( MA!MATICAL
NUMB]74 ,= ON ? VIEW ALL ! UNITS 2COME
ID5TICAL ) SPECIES ( GD1 & "! IS A GRT
PROFU.N ( GDS4 ,AG1 IF ! ,=MS >E NUMB]S1
ALL ! ,=MS >E ID5TICAL ) SPECIES ( GD4
,B LET A MAN ASSUME ,ID1S ( ANY?+ HE
PL1SES4 ,IF ^! >E ,ID1S ONLY ( GDS1 !
,ID1S W N 2 SUB/.ES2 B IF ! ,ID1S >E AL
,ID1S ( SUB/.ES1 ALL ANIMALS & PLANTS &
ALL 9DIVIDUALS T %>E 9 ,ID1S W 2 GD4
  ,^! ABSURDITIES FOLL[1 & X AL FOLL[S T
! 3TR>Y ELE;T1 :E!R X IS PLURAL;Y OR !
UNEQUAL1 I4E4 ! GRT & SMALL1 IS ! BAD-
XF4 7,H;E "O ?9K] AVOID$ ATTA*+ ! GD 6!
,"O1 2C X WD NECESS>ILY FOLL[1 S9CE
G5],N IS F 3TR>IES1 T BAD;S IS !
FUNDA;TAL NATURE ( PLURAL;Y2 :ILE O!RS
SAY 9EQUAL;Y IS ! NATURE (! BAD47 ,X
FOLL[S1 !N1 T ALL ?+S P>TAKE (! BAD
EXCEPT "O--! ,"O XF1 & T NUMB]S P>TAKE (
X 9 A M UNDILUT$ =M ?AN SPATIAL
MAGNITUDES1 & T ! BAD IS ! SPACE 9 : !
GD IS R1LIZ$1 & T X P>TAKES 9 & DESIRES
T : T5DS 6DE/ROY X2 = 3TR>Y T5DS 6DE/ROY
3TR>Y4 ,& IF1 Z WE 7 SAY+1 ! MATT] IS T
: IS POT5TI,Y EA* ?+1 E4G4 T ( ACTUAL
FIRE IS T : IS POT5TI,Y FIRE1 ! BAD W 2
J ! POT5TI,Y GD4
  ,ALL ^! OBJEC;NS1 !N1 FOLL[1 "PLY 2C
!Y MAKE E PR9CIPLE AN ELE;T1 "PLY 2C !Y
MAKE 3TR>IES PR9CIPLES1 "PLY 2C !Y MAKE
! ,"O A PR9CIPLE1 "PLY 2C !Y TR1T !
NUMB]S Z ! F/ SUB/.ES1 & Z CAPA# ( EXI/+
A"P1 & Z ,=MS4
                   #E
  ,IF1 !N1 X IS EQU,Y IMPOSSI# N 6PUT !
GD AM;G ! F/ PR9CIPLES & 6PUT X AM;G !M
9 ? WAY1 EVID5TLY ! PR9CIPLES >E N 2+
CORRECTLY DESCRIB$1 NOR >E ! F/ SUB/.ES4
,NOR DOES ANY "O 3CV ! MATT] CORRECTLY
IF HE -P>ES ! PR9CIPLES (! UNIV]SE 6T (
ANIMALS & PLANTS1 ON ! GR.D T ! M -PLETE
ALW -ES F ! 9DEF9ITE & 9COMPLETE-: IS
:AT L1DS ? ?9K] 6SAY T ? IS AL TRUE (!
F/ PR9CIPLES ( R1L;Y1 S T ! ,"O XF IS N
EV5 AN EXI/+ ?+4 ,? IS 9CORRECT1 = EV5 9
? _W ( ANIMALS & PLANTS ! PR9CIPLES F :
^! -E >E -PLETE2 = X IS A MAN T PRODUCES
A MAN1 &! SE$ IS N F/4
  ,X IS \ ( PLACE1 AL1 6G5]ATE PLACE
SIMULTANE\SLY )! MA!MATICAL SOLIDS 7=
PLACE IS PECULI> 6! 9DIVIDUAL ?+S1 & H;E
!Y >E SEP>ATE 9 PLACE2 B MA!MATICAL
OBJECTS >E NO":71 & 6SAY T !Y M/ 2 "S":1
B N SAY :AT K9D ( ?+ _! PLACE IS4
  ,^? :O SAY T EXI/+ ?+S -E F ELE;TS & T
! F/ ( EXI/+ ?+S >E ! NUMB]S1 %D H F/
4T+UI%$ ! S5SES 9 : "O ?+ -ES F ANO!R1 &
!N SD 9 : S5SE NUMB] -ES F XS F/
PR9CIPLES4
  ,09T]MIXTURE8 ,B 7#A7 N "EY?+ IS CAPA#
( 9T]MIXTURE1 & 7#B7 T : IS PRODUC$ 0X
IS DI6]5T F XS ELE;TS1 & ON ? VIEW ! "O
W N REMA9 SEP>ATE OR A 4T9CT 5T;Y2 B !Y
WANT X 6BE S4
  ,0JUXTAPOSI;N1 L A SYLLA#8 ,B !N 7#A7
! ELE;TS M/ H POSI;N2 & 7#B7 HE :O ?9KS
( NUMB] W 2 A# 6?9K (! UN;Y &! PLURAL;Y
A"P2 NUMB] !N W 2 ?-A UNIT & PLURAL;Y1
OR ! "O &! UNEQUAL4
  ,AG1 -+ F C]TA9 ?+S M1NS 9 "O S5SE T
^! >E / 6BE F.D 9 ! PRODUCT1 & 9 ANO!R T
!Y >E N2 : S5SE DOES NUMB] -E F ^!
ELE;TS8 ,ONLY ?+S T >E G5]AT$ C -E F
ELE;TS : >E PRES5T 9 !M4 ,DOES NUMB] -E1
!N1 F XS ELE;TS Z F SE$8 ,B NO?+ C 2
EXCRET$ F T : IS 9DIVISI#4 ,DOES X -E F
XS 3TR>Y1 XS 3TR>Y N P]SI/+8 ,B ALL ?+S
T -E 9 ? WAY -E AL F "S?+ ELSE : DOES
P]SI/4 ,S9CE1 !N1 "O ?9K] PLACES ! #A Z
3TR>Y 6PLURAL;Y1 & ANO!R PLACES X Z
3TR>Y 6! UNEQUAL1 TR1T+ ! #A Z EQUAL1
NUMB] M/ 2 2+ TR1T$ Z -+ F 3TR>IES4 ,"!
IS1 !N1 "S?+ ELSE T P]SI/S1 F : & F "O
3TR>Y ! -P.D IS OR HAS -E 6BE4 ,AG1 :Y 9
! _W D ! O!R ?+S T -E F 3TR>IES1 OR T H
3TR>IES1 P]I% 7EV5 :5 ALL (! 3TR>Y IS
US$ 6PRODUCE !M71 :ILE NUMB] DOES N8
,NO?+ IS SD AB ?4 ,YET :E!R PRES5T OR N
PRES5T 9 ! -P.D ! 3TR>Y DE/ROYS X1 E4G4
,8/RIFE0' DE/ROYS ! ,8MIXTURE0' 7YET X
%D N2 = X IS N 6T T IS 3TR>Y74
  ,ONCE M1 X HAS N BE5 DET]M9$ AT ALL 9
: WAY NUMB]S >E ! CAUSES ( SUB/.ES &(
2+-:E!R 7#A7 Z B.D>IES 7Z PO9TS >E (
SPATIAL MAGNITUDES74 ,? IS H[ ,EURYTUS
DECID$ :AT 0 ! NUMB] ( :AT 7E4G4 "O (
MAN & ANO!R ( HORSE71 VIZ4 0IMITAT+ !
FIGURES ( LIV+ ?+S ) PEB#S1 Z "S P BR+
NUMB]S 96! =MS ( TRIANGLE & SQU>E4 ,OR
7#B7 IS X 2C H>MONY IS A RATIO ( NUMB]S1
& S IS MAN & "EY?+ ELSE8 ,B H[ >E !
ATTRIBUTES-:ITE & SWEET & HOT-NUMB]S8
,EVID5TLY X IS N ! NUMB]S T >E ! ESS;E
OR ! CAUSES (! =M2 =! RATIO IS ! ESS;E1
:ILE ! NUMB] ! CAUSES (! =M2 =! RATIO IS
! ESS;E1 :ILE ! NUMB] IS ! MATT]4 ,E4G4
! ESS;E ( FLE% OR B"O IS NUMB] ONLY 9 ?
WAY1 ,8?REE "PS ( FIRE & TWO ( E>?0'4
,&A NUMB]1 :AT"E NUMB] X IS1 IS ALW A
NUMB] ( C]TA9 ?+S1 EI ( "PS ( FIRE OR
E>? OR ( UNITS2 B ! ESS;E IS T "! IS S
M* ( "O ?+ 6S M* ( ANO!R 9 ! MIXTURE2 &
? IS NO L;G] A NUMB] B A RATIO ( MIXTURE
( NUMB]S1 :E!R ^! >E CORPOR1L OR ( ANY
O!R K9D4
  ,NUMB]1 !N1 :E!R X 2 NUMB] 9 G5]AL OR
! NUMB] : 3SI/S ( AB/RACT UNITS1 IS NEI
! CAUSE Z AG5T1 NOR ! MATT]1 NOR ! RATIO
& =M ( ?+S4 ,NOR1 ( C\RSE1 IS X ! F9AL
CAUSE4
                   #F
  ,"O MI<T AL RAISE ! "Q :AT ! GD IS T
?+S GET F NUMB]S 2C _! -POSI;N IS
EXPRESSI# 0A NUMB]1 EI 0"O : IS EASILY
CALCULA# OR 0AN ODD NUMB]4 ,= 9 FACT
H"OY-WAT] IS NO M :OLE"S IF X IS MIX$ 9
! PROPOR;N ( ?REE "TS ?REE1 B X WD D M
GD IF X 7 9 NO "PICUL> RATIO B WELL
DILUT$ ?AN IF X 7 NUM]IC,Y EXPRESSI# B
/R;G4 ,AG1 ! RATIOS ( MIXTURES >E
EXPRESS$ 0! A4+ ( NUMB]S1 N 0M]E NUMB]S2
E4G4 X IS ,8?REE "PS 6TWO0'1 N ,8?REE
"TS TWO0'4 ,= 9 ANY MULTIPLIC,N ! G5US (
! ?+S MULTIPLI$ M/ 2 ! SAME2 "!=E !
PRODUCT #A;,X#B;,X#C M/ 2 M1SURA# 0#A1 &
#D;,X#E;,X#F 0#D & "!=E ALL PRODUCTS 96:
! SAME FACTOR 5T]S M/ 2 M1SURA# 0T
FACTOR4 ,! NUMB] ( FIRE1 !N1 _C 2
#B;,X#E;,X#C;,X#F & AT ! SAME "T T (
WAT] #B;,X#C4
  ,IF ALL ?+S M/ %>E 9 NUMB]1 X M/ FOLL[
T _M ?+S >E ! SAME1 &! SAME NUMB] M/
2L;G 6"O ?+ & 6ANO!R4 ,IS NUMB] ! CAUSE1
!N1 & DOES ! ?+ EXI/ 2C ( XS NUMB]1 OR
IS ? N C]TA98 ,E4G4 ! MO;NS (! SUN H A
NUMB]1 & AG ^? (! MOON1-YES1 &! LIFE &
PRIME ( EA* ANIMAL4 ,:Y1 !N1 %D N "S (
^! NUMB]S 2 SQU>ES1 "S CUBES1 & "S
EQUAL1 O!RS D\#8 ,"! IS NO R1SON :Y !Y
%D N1 & 9DE$ !Y M/ MOVE )9 ^! LIMITS1
S9CE ALL ?+S 7 ASSUM$ 6%>E 9 NUMB]4 ,& X
0 ASSUM$ T ?+S T DI6]$ MI<T FALL "U !
SAME NUMB]4 ,"!=E IF ! SAME NUMB] _H
2L;G$ 6C]TA9 ?+S1 ^! WD H BE5 ! SAME Z
"O ANO!R1 S9CE !Y WD H _H ! SAME =M (
NUMB]2 E4G4 SUN & MOON WD H BE5 ! SAME4
,B :Y NE$ ^! NUMB]S 2 CAUSES8 ,"! >E
SEV5 V[ELS1 ! SCALE 3SI/S ( SEV5 /R+S1 !
,PLEIADES >E SEV51 AT SEV5 ANIMALS LOSE
_! TEE? 7AT L1/ "S D1 ?\< "S D N71 &!
*AMPIONS :O F"\ AG/ ,!BES 7 SEV54 ,IS X
!N 2C ! NUMB] IS ! K9D ( NUMB] X IS1 T !
*AMPIONS 7 SEV5 OR ! ,PLEIAD 3SI/S (
SEV5 />S8 ,SURELY ! *AMPIONS 7 SEV5 2C
"! 7 SEV5 GATES OR = "S O!R R1SON1 &!
,PLEIAD WE C.T Z SEV51 Z WE C.T ! ,BE> Z
TWELVE1 :ILE O!R PEOPLES C.T M />S 9
BO?4 ,NAY !Y EV5 SAY T ;,X1 ,PS & ;,Z >E
3CORDS & T 2C "! >E ?REE 3CORDS1 ! D\#
3SONANTS AL >E ?REE4 ,!Y Q NEGLECT !
FACT T "! MI<T 2 A ?\S& S* LRS2 = "O
SYMBOL MI<T 2 ASSIGN$ 6,,GP4 ,B IF !Y
SAY T EA* ( ^! ?REE IS EQUAL 6TWO (! O!R
LRS1 & NO O!R IS S1 & IF ! CAUSE IS T "!
>E ?REE "PS (! M\? & "O LR IS 9 EA*
APPLI$ 6SIGMA1 X IS = ? R1SON T "! >E
ONLY ?REE1 N 2C ! 3CORDS >E ?REE2 S9CE Z
A MATT] ( FACT ! 3CORDS >E M ?AN ?REE1 B
( D\# 3SONANTS "! _C 2 M4
  ,^! P >E L ! OLD-FA%ION$ ,HOM]IC
S*OL>S1 :O SEE SMALL RESEMBL.ES B
NEGLECT GRT "OS4 ,"S SAY T "! >E _M S*
CASES1 E4G4 T ! MI4LE /R+S >E REPRES5T$
0N9E & EI<T1 & T ! EPIC V]SE HAS SEV5TE5
SYLLA#S1 : IS EQUAL 9 NUMB] 6! TWO /R+S1
& T ! SCAN.N IS1 9 ! "R HALF (! L9E N9E
SYLLA#S1 & 9 ! LEFT EI<T4 ,& !Y SAY T !
4T.E 9 ! LRS F ALPHA 6OMEGA IS EQUAL 6T
F ! L[E/ NOTE (! FLUTE 6! HI<E/1 & T !
NUMB] ( ? NOTE IS EQUAL 6T (! :OLE *OIR
( H1V54 ,X MAY 2 SUSPECT$ T NO "O CD F9D
DI6ICULTY EI 9 /AT+ S* ANALOGIES OR 9
F9D+ !M 9 ET]NAL ?+S1 S9CE !Y C 2 F.D
EV5 9 P]I%A# ?+S4
  ,B ! LAUD$ "*I/ICS ( NUMB]S1 &!
3TR>IES ( ^!1 & G5],Y ! MA!MATICAL
REL,NS1 Z "S DESCRIBE !M1 MAK+ !M CAUSES
( NATURE1 SEEM1 :5 WE 9SPECT !M 9 ? WAY1
6VANI%2 = N"O ( !M IS A CAUSE 9 ANY (!
S5SES T H BE5 4T+UI%$ 9 REF];E 6! F/
PR9CIPLES4 ,9 A S5SE1 H["E1 !Y MAKE X
PLA9 T GD;S 2L;GS 6NUMB]S1 & T ! ODD1 !
/RAI<T1 ! SQU>E1 ! POT5CIES ( C]TA9
NUMB]S1 >E 9 ! COLUMN (! B1UTI;L4 ,=!
S1SONS &A "PICUL> K9D ( NUMB] G TGR2 &!
O!R AGREE;TS T !Y COLLECT F ! !OREMS (
MA!MATICS ALL H ? M1N+4 ,H;E !Y >E L
CO9CID;ES4 ,= !Y >E A3ID5TS1 B ! ?+S T
AGREE >E ALL APPROPRIATE 6"O ANO!R1 & "O
0ANALOGY4 ,= 9 EA* CATEGORY ( 2+ AN
ANALOG\S T]M IS F.D-Z ! /RAI<T IS 9
L5G?1 S IS ! LEVEL 9 SURFACE1 P]H ! ODD
9 NUMB]1 &! :ITE 9 COL\R4
  ,AG1 X IS N ! ID1L NUMB]S T >E !
CAUSES ( MUSICAL PH5OM5A &! L 7= EQUAL
ID1L NUMB]S DI6] F "O ANO!R 9 =M2 = EV5
! UNITS D72 S T WE NE$ N ASSUME ,ID1S =
? R1SON AT L1/4
  ,^!1 !N1 >E ! RESULTS (! !ORY1 & YET M
MI<T 2 BR"\ TGR4 ,! FACT T \R OPPONNTS H
M* TR\# )! G5],N ( NUMB]S & C 9 NO WAY
MAKE A SY/EM ( !M1 SEEMS 69DICATE T !
OBJECTS ( MA!MATICS >E N SEP>A# F S5SI#
?+S1 Z "S SAY1 & T !Y >E N ! F/
PR9CIPLES4

