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the Piraha's numerical cognition and performance
with numbers higher than three (according to
Bar-David et al., 2009).
It is believed that, in contrast with the Arabic
decimal system used today almost everywhere,
the Mayans counted with fingers and toes and
thus they used the Maya vigesimal system based
on groups of twenty units (Maya Mathematical
System, 2012). One may wonder whether the
covering of toes with shoes might influence the
developing of counting systems by limiting pos-
sibility to use this counting tool to ten. The Maya
discovered a notion of zero, and thus the 20 units
meant [0-19] with a significant zero, while in the
decimal system we apply [0-9] as a placeholder.
Each number, from zero to 19, had its name. They
only used three symbols: an ovular shell for a zero,
a dot, and a dash, alone or combined, and wrote
them vertically or horizontally.
Ancient Egyptians performed division as mul-
tiplication in reverse: they repeatedly doubled the
divisor to obtain the dividend. Actually, we often
avoid using exact verbal number words when we
say, some, less, a few, several, many, numerous,
or a couple. A rosary designed as a string of
beads for keeping count in practicing devotion,
a calculating tool abacus, the secular strings of
worry beads komboloi used in Greece and other
countries, and Hindu prayer beads can be seen
as examples of numerical cognition processed
without verbalizing.
On the other hand, there is evidence for pre-
cise numerical representation in the absence of
language, indicating that language is not neces-
sary to represent small exact numbers or large
approximate numbers, and one does not have to
know language to understand number. Research-
ers explored the counting systems in native tribes
of South America, and indigenous Australian
Aborigines looking for languages that encode the
linguistic as well as numerical information. The
quipu, a system of knotted cords, is a numerical
recording system that was used in the Inca Empire
in the Andean region in the 15th and 16th centuries.
Gary Urton, a specialist in Andean archaeology,
posed that this combination of fiber types, dye
colors, and intricate knotting contains a seven-
bit binary code capable of conveying more than
1,500 separate units of information. According
to Marcia and Robert Ascher (1980, 1997), most
information on quipus is numeric, and these num-
bers can be read. Each cluster of knots is a digit,
and there are three main types of knots: simple
overhand knots; “long knots”, consisting of an
overhand knot with one or more additional turns;
and figure-of-eight knots. Butterworth, Reeve,
Reynolds, & Lloyd (2008) questioned claims that
thoughts about numbers are impossible without
the words to express them, that children cannot
have the concept of exact numbers until they know
the words for them, and adults in cultures whose
languages lack a counting vocabulary similarly
cannot possess these concepts. They have shown
that children who are monolingual speakers of two
Australian languages with very restricted number
vocabularies possess the same numerical concepts
as a comparable group of English-speaking indig-
enous Australian children.
Dunn, Greenhill, Levinson, & Gray (2011) pose
that cultural evolution, rather than innate param-
eters or universal tendencies, is the primary factor
that determines linguistic structure and diversity,
with the current state shaping and constraining
future states. Data collected by Gelman and But-
terworth (2005) imply that numerical concepts
have an ontogenetic origin (resulting from the
development of an individual organism) and a
neural basis that are independent of language.
They question theories about the necessity of using
language to develop numerical concepts, both in
the case of the child developmental psychology
and the counting systems in Amazonian cultures
that have very restricted number vocabularies,
with the lack of language for exact large numbers.
Preverbal humans and animals can represent
number through analog magnitudes - nonverbal
approximate representation of number values
(Dehaine, 1999). Adult people, when told to tap
