This experiment employed an individual differences approach to test the hypothesis that learning modern programming languages resembles second "natural" language learning in adulthood. Behavioral and neural (resting-state EEG) indices of language aptitude were used along with numeracy and fluid cognitive measures (e.g., fluid reasoning, working memory, inhibitory control) as predictors. Rate of learning, programming accuracy, and post-test declarative knowledge were used as outcome measures in 36 individuals who participated in ten 45-minute Python training sessions. The resulting models explained 50-72% of the variance in learning outcomes, with language aptitude measures explaining significant variance in each outcome even when the other factors competed for variance. Across outcome variables, fluid reasoning and working-memory capacity explained 34% of the variance, followed by language aptitude (17%), resting-state EEG power in beta and low-gamma bands (10%), and numeracy (2%). These results provide a novel framework for understanding programming aptitude, suggesting that the importance of numeracy may be overestimated in modern programming education environments. Computer programming has moved from being a niche skill to one that is increasingly central for functioning in modern society. Despite this shift, remarkably little research has investigated the cognitive basis of what it takes to learn programming languages. The implications of such knowledge are wide reaching, both in terms of cultural barriers to pursuing computer sciences 1 and for educational practices 2. Central to both are commonly held ideas about what it takes to be a "good" programmer, many of which have not been empirically instantiated. In fact, remarkably little research has investigated the cognitive bases of "programming aptitude" 3-5 , and, to the best of our knowledge, no research to date has investigated its neural correlates. Critically, the existing research provides inconsistent evidence about the relevance of mathematical skills for learning to program 6-8. Despite this, programming classes in college environments regularly require advanced mathematical courses as prerequisites. This gap between what we know about learning to program and the environments in which programming is taught was described by Jenkins, who argued that "If computing educators are ever to truly develop a learning environment where all the students learn to program quickly and well, it is vital that an understanding of the difficulties and complexities faced by the students is developed. At the moment, the way in which programming is taught and learned is fundamentally broken" 2. Unfortunately, little progress has been made since this call to action 15 years ago. Across the same time period, the nature of programming languages has also changed, reducing the likelihood that the original research on learning to program in Pascal 5 or COBOL 3 , for instance, will generalize to contemporary programming languages. The research described herein is motivated by a...

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Background Scalp-recorded event-related potentials (ERPs) are poorly suited for certain types of source analysis. For example, it is often difficult to precisely assess whether two ERP waveforms were produced by similar neural sources, especially when the waveforms share the same polarity and a similar scalp topography and temporal dynamics. We report here an alternative method to establishing independence of neural sources grounded in the principle of superposition, which stipulates that electrical fields summate where they intersect in time and space. We assessed the independence of two frequently reported positive waves in the ERP literature, the P300 (elicited by unexpected stimuli) and P600 (elicited by syntactic anomalies). Subjects read sentences that contained a word that was either non-anomalous, unexpected in one feature (capitalized, different font, different font color, or ungrammatical), or unexpected in two features (capitalized and different font style, capitalized and different font color, or capitalized and ungrammatical). Thus, in the double anomaly condition, the similarity between a shared feature (i.e., capitalization) and a second feature was systematically manipulated across conditions from larger degree (i.e., font style) to lesser degree (i.e., ungrammatical) of feature similarity. Results We quantified the degree of source independence for the features of interest by applying a novel Additivity Index, which compares ERPs elicited by the doubly anomalous words to composite waveforms formed by mathematically summing the ERP response to singly anomalous words. The degree of source independence is reflected by the degree of summation, with Additivity scores ranging from 0 (completely non-independent) to 1 (completely independent). The computed Additivity Index values varied with feature similarity in the predicted direction: similar features demonstrated lower Additivity Index values, or lower degrees of independence. On the other hand, dissimilar features manifested robust additivity, resulting in larger AI values. Conclusion We quantified the degree to which the P600 and P300 effects are neurally distinct across stimulus features with varying degrees of similarity by computing a continuous measure of independence via the Additivity Index. These findings indicate that the Additivity Index provides a valid and general method for quantifying the neural independence of scalp-recorded brain potentials.