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Numbers are an important part of the cultural knowledge in the modern world. Its use is fundamental in the conception and development of modern science. There are different sets of numbers called numerical systems. The most frequently used numerical system is the set of natural numbers that is composed of positive integers. Natural numbers have several forms to express the cardinality; the most frequently used is the base-10 number system, it represents the number using base quantities and powers of ten. For example, the current calendar year could be expressed as 2018 ; it’s notation describes the additive and multiplicative composition of base quantities and powers of ten (i.e., 2*103 + 0*102 + 1*101 + 8*100). Also, we can use the notation 11111100010 (i.e., 1*210 + 1*29 + 1*28 + 1*27 + 1*26 + 1*25 + 0*24 + 0*23 + 0*22 + 1*21 + 0*20) to express the same calendar year in base-2. Base number systems express cardinal values using addition and multiplication (two operations defined in natural numbers). However, even if the base-10 system looks close to the human experience; it is an abstract form that requires an external representation to communicate cardinal values. An example of these external representations are cardinal numbers, for example, the number 2018 is represented in English using the words two thousand eighteen, but in Spanish, the cardinal number dos mil dieciocho is used. Cardinal numbers are a particular case in childhood development because it is the first exposure that children have to the natural numbers. Then the properties of the cardinal numbers could be an essential part of children's number comprehension. But one question arises in this frame: What are the children's capacities that permit the children to understand cardinal numbers? One possibility that is proposed in the field of number cognition is that children’s comprehension of recursion in language triggers the acquisition of natural numbers. For some authors, recursion is an operation that is shared between natural numbers (specifically, cardinal numbers) and language (Barner, 2017; Cheung et al., 2017; Yang, 2016). In this study, we explore the relationship between recursion in language and cardinal numbers. To do so, we study the comprehension of recursive genitives and the production of cardinal numbers in English- speaking and Mandarin-speaking children. The results suggest an association in Mandarin-speaking children, but not in English-speaking children. While these empirical results are inconclusive, I provide a theoretical analysis that gives some insights into how the structure of cardinal numbers could be defined using the concept of recursion.

Numerical cognition has been shown to share many aspects of spatial cognition, both behavioural and neurological. However, it is unclear whether a particular type of spatial cognition, visuospatial mental imagery (VSMI), may play a role in symbolic numerical representation. In this thesis, I first show that mental rotation, a form of VSMI, is related to two measures of basic numerical representation. I then show that number-space synaesthesia (NSS), a rare type of VSMI involving visualised spatial layouts for numbers, does not show an advantage in mental rotation, but shows interference in number line mapping. I next present a study investigating links between NSS and the ability to learn novel numerical symbols. I demonstrate that NSS shows an advantage at learning novel numerals, and that transcranial random noise stimulation, which increases cortical excitability, confers broadly similar advantages that nonetheless differ in subtle ways. I present a study of transcranial alternating current stimulation on the same symbol learning paradigm, which fails to demonstrate effects. Lastly, I present data showing that strength of numerical representation in these newly-learnt symbols is correlated with a measure of mental rotation, and also with visual recognition ability for the symbols after, but not before, training. All together, these findings suggest that VSMI does indeed play a role in numerical cognition, and that it may do so from an early stage of learning symbolic numbers.