On the notion of number in humans and machines Norbert Bátfai1,*, Dávid Papp2, Gergő Bogacsovics1, Máté Szabó1, Viktor Szilárd Simkó1, Márió Bersenszki1, Gergely Szabó1, Lajos Kovács1, Ferencz Kovács1, and Erik Szilveszter Varga1 1Department of Information Technology, University of Debrecen, Hungary 2Department of Psychology, University of Debrecen, Hungary *Corresponding author: Norbert Bátfai,
[email protected] July 1, 2019 Abstract In this paper, we performed two types of software experiments to study the numerosity classification (subitizing) in humans and machines. Ex- periments focus on a particular kind of task is referred to as Semantic MNIST or simply SMNIST where the numerosity of objects placed in an image must be determined. The experiments called SMNIST for Humans are intended to measure the capacity of the Object File System in humans. In this type of experiment the measurement result is in well agreement with the value known from the cognitive psychology literature. The ex- periments called SMNIST for Machines serve similar purposes but they investigate existing, well known (but originally developed for other pur- pose) and under development deep learning computer programs. These measurement results can be interpreted similar to the results from SM- NIST for Humans. The main thesis of this paper can be formulated as follows: in machines the image classification artificial neural networks can learn to distinguish numerosities with better accuracy when these nu- merosities are smaller than the capacity of OFS in humans. Finally, we outline a conceptual framework to investigate the notion of number in humans and machines. arXiv:1906.12213v1 [cs.CV] 27 Jun 2019 Keywords: numerosity classification, object file system, machine learning, MNIST, esport.