1 < 2 and 2 < 3: Non-Linguistic Appreciations of Numerical Order

Abstract

Ordinal understanding is involved in understanding social hierarchies, series of actions, and everyday events. Moreover, an appreciation of numerical order is critical to understanding number at a highly abstract, conceptual level. In this paper, we review findings concerning the development and expression of ordinal numerical knowledge in preverbal human infants in light of literature about the same cognitive abilities in non-human animals. We attempt to reconcile seemingly contradictory evidence, provide new directions for prospective research, and evaluate the shared basis of ordinal knowledge among non-verbal organisms. Our review of the research leads us to conclude that both infants and non-human animals are adapted to respond to monotonic progressions in numerical order, consonant with mathematical definitions of numerical order. Further, we suggest that patterns in the way that infants and non-human animals process numerical order can be accounted for by changes across development, the conditions under which representations are generated, or both.

Representation of different exact numbers of prey by a spider-eating predator

“…Our experiments are not designed to determine whether Portia literally counts the number of prey in a scene according to all of the criteria pertaining to 'true counting' [37] and we are not proposing that spiders understand numbers as abstract entities [38,39], but we are interested in whether Portia does something more precise than representing countable things as a value of a continuous variable (see [40,41]). Our hypothesis is that Portia relies on representations that correspond to specific cardinal numbers (see [42]). …”

Numerical Sequence Recognition: Is Familiarity or Ordinality the Primary Factor in Performance?

“…Numerical representations consist of two interrelated aspects: a representation of quantity or cardinality (Dehaene, 1997) and a representation of relative order or ordinality (Anderson & Cordes, 2013;Jacob & Nieder, 2008;Tzelgov & Ganor-Stern, 2004). Cardinality is a core concept of numerical representation because it reflects "how many" things are in a set, that is, size, number, or quantity.…”

“…Ordinality is therefore an integral aspect of numerical cognition, reflecting relations and relative positions among numerical quantities, such as coming before or after one another. This ability to distinguish relative order information is essential to mathematical learning and, like cardinality, is present in non-human animals and infants even early on in their development (Anderson & Cordes, 2013;Bisazza et al, 2010;Brannon, 2002;Brannon & Cantlon, 2006;Brannon & Terrace, 1998. Therefore, learners need to acquire the basic concepts of cardinality and ordinality and how they interrelate.…”

Sequential recall of meaningful and arbitrary sequences by orangutans and human children: Does content matter?

“…The ability to discriminate between larger and smaller quantities based on either number or size may be adaptive (e.g., when detecting food quantity or the number of aggressive conspecifics in the vicinity; Anderson et al 2007;Bonanni et al 2011;Shettleworth 2010, chap. 10) and is clearly evident in the behavior of many different animal species (Agrillo and Bisazza 2014;Anderson and Cordes 2013;Davis and Pérusse 1988). In captive tests, multiple species (including primates, felids, bears, birds, and fish) can spontaneously discriminate between two arrays with different numbers of food items or social companions (for a review, see Agrillo and Bisazza 2014).…”