﻿326 
  SOUTH 
  AMERICAN 
  INDIANS 
  [B. 
  A. 
  E. 
  Bull. 
  143 
  

  

  ilar 
  to 
  our 
  own. 
  The 
  group 
  of 
  knots 
  farthest 
  away 
  from 
  the 
  main 
  cord 
  

   were 
  units, 
  the 
  next 
  group 
  tens, 
  the 
  next 
  hundreds, 
  etc. 
  (Locke, 
  1923). 
  

   Nordenskiold 
  added 
  that 
  he 
  had 
  seen 
  only 
  one 
  quipu 
  with 
  a 
  knot 
  in 
  

   the 
  10,000 
  place, 
  and 
  stated 
  that 
  there 
  was 
  no 
  sign 
  for 
  zero 
  in 
  the 
  

   quipus 
  (Nordenskiold, 
  1925 
  b, 
  pp. 
  7-8, 
  36). 
  Zero, 
  however, 
  means 
  

   simply 
  that 
  no 
  number 
  is 
  to 
  be 
  read 
  in 
  the 
  place 
  where 
  it 
  occurs, 
  but 
  

   the 
  place 
  is 
  to 
  be 
  counted. 
  String 
  No. 
  14 
  on 
  Nordenskiold's 
  quipu 
  

   No. 
  6 
  (pi. 
  3) 
  and 
  other 
  examples 
  show 
  quite 
  clearly 
  that 
  zero 
  was 
  indi- 
  

   cated 
  by 
  the 
  absence 
  of 
  a 
  knot 
  in 
  the 
  desired 
  place, 
  and 
  as 
  long 
  as 
  only 
  

   one 
  number 
  was 
  knotted 
  on 
  a 
  string, 
  and 
  the 
  number 
  of 
  places 
  was 
  

   known, 
  no 
  possible 
  confusion 
  could 
  result. 
  The 
  quipu 
  had 
  to 
  be 
  ac- 
  

   companied 
  by 
  an 
  oral 
  comment 
  anyway, 
  so 
  that 
  if 
  it 
  were 
  not 
  clear 
  

   from 
  the 
  way 
  the 
  knots 
  were 
  spaced 
  on 
  the 
  various 
  strings 
  how 
  many 
  

   places 
  were 
  intended, 
  this 
  information 
  could 
  be 
  included 
  in 
  the 
  instruc- 
  

   tions. 
  There 
  is 
  no 
  doubt 
  from 
  Nordenskiold's 
  examples 
  that 
  the 
  con- 
  

   cept 
  of 
  an 
  empty 
  place 
  in 
  the 
  number, 
  which 
  is 
  what 
  our 
  zero 
  stands 
  

   for, 
  was 
  certainly 
  understood 
  by 
  the 
  makers 
  of 
  the 
  Coast 
  quipus. 
  

  

  The 
  quipu 
  is 
  still 
  generally 
  used 
  among 
  Andean 
  shepherds 
  for 
  count- 
  

   ing. 
  As 
  several 
  different 
  ways 
  of 
  tying 
  it 
  are 
  known, 
  it 
  would 
  not 
  be 
  

   surprising 
  to 
  find 
  ancient 
  quipus 
  which 
  were 
  tied 
  differently. 
  A 
  quipu 
  

   represented 
  a 
  series 
  of 
  numbers 
  which 
  could, 
  perhaps, 
  be 
  read 
  by 
  any 
  

   trained 
  Inca 
  accountant, 
  but, 
  in 
  order 
  that 
  anyone 
  but 
  the 
  original 
  

   maker 
  might 
  understand 
  what 
  the 
  numbers 
  referred 
  to, 
  the 
  quipu 
  had 
  

   to 
  be 
  explained. 
  

  

  The 
  quipu 
  is 
  excellently 
  adapted 
  for 
  recording 
  numbers, 
  but 
  would 
  

   be 
  an 
  exceedingly 
  clumsy 
  instrument 
  with 
  which 
  to 
  calculate. 
  The 
  

   chroniclers 
  make 
  it 
  quite 
  clear 
  that 
  calculation 
  was 
  done 
  with 
  piles 
  of 
  

   pebbles 
  or 
  grains, 
  or 
  by 
  means 
  of 
  an 
  abacus 
  consisting 
  of 
  a 
  tray 
  with 
  

   rows 
  of 
  compartments 
  in 
  which 
  counters 
  could 
  be 
  moved. 
  The 
  

   results 
  of 
  the 
  calculation 
  could 
  then 
  be 
  recorded 
  on 
  the 
  quipu 
  (Wassen, 
  

   1940). 
  

  

  In 
  addition 
  to 
  recording 
  numbers, 
  the 
  quipu 
  was 
  used 
  as 
  a 
  memory 
  

   aid 
  in 
  reciting 
  genealogies, 
  liturgical 
  material, 
  and 
  narrative 
  verse, 
  so 
  

   that 
  some 
  chroniclers 
  (e. 
  g., 
  Valera 
  and 
  Morua) 
  speak 
  of 
  Inca 
  history 
  

   as 
  based 
  on 
  the 
  quipus 
  in 
  such 
  a 
  way 
  that 
  they 
  might 
  appear 
  to 
  have 
  

   been 
  a 
  form 
  of 
  writing, 
  which 
  they 
  certainly 
  were 
  not. 
  

  

  The 
  Inca 
  had 
  a 
  special 
  class 
  of 
  professional 
  quipu 
  interpreters 
  

   (khipo-kamayoq), 
  whose 
  duty 
  it 
  was 
  to 
  memorize 
  the 
  statistical, 
  his- 
  

   torical, 
  and 
  liturgical 
  material 
  accumulated 
  by 
  the 
  government 
  and 
  

   to 
  be 
  prepared 
  at 
  all 
  times 
  to 
  repeat 
  it 
  for 
  the 
  benefit 
  of 
  officials 
  who 
  

   desired 
  to 
  refer 
  to 
  it. 
  37 
  

  

  At 
  least 
  in 
  some 
  districts, 
  painted 
  sticks 
  were 
  probably 
  used 
  as 
  aids 
  

  

  37 
  The 
  most 
  important 
  descriptions 
  of 
  Inca 
  quipus 
  in 
  the 
  chroniclers 
  are 
  the 
  following: 
  Cieza, 
  1880, 
  bk. 
  2, 
  

   ch 
  . 
  12; 
  Molina 
  of 
  Cuzco, 
  1913, 
  pp. 
  125-126; 
  Acosta, 
  1940, 
  bk. 
  6, 
  chs. 
  8, 
  14, 
  19; 
  Garcilaso, 
  1723, 
  pt. 
  1, 
  bk. 
  6, 
  chs. 
  7- 
  

   9; 
  Calancha, 
  1638, 
  bk. 
  1, 
  ch. 
  14; 
  Cobo, 
  1890-95, 
  bk. 
  12, 
  ch. 
  37; 
  Fray 
  Antonio, 
  1920, 
  pp. 
  6-7; 
  Morua, 
  1922-25, 
  bk. 
  

   3, 
  chs. 
  14, 
  25; 
  Poma. 
  1936. 
  pp. 
  335, 
  358, 
  360, 
  800. 
  

  

  