NOTE: My description of parsing up-arrow notation is incorrect; please see my correction here! https://www.youtube.com/watch?v=xN-MpWNsXw0
Graham’s number is…really really big. But our brains start throwing errors at much smaller quantities.
Numberphile’s fantastic video of Ron Graham explaining Graham’s number - https://www.youtube.com/watch?v=HX8bihEe3nA
Two Systems of Non-Symbolic Numerical Cognition by D. Hyde, a review of research on the two psychological systems for cognitive representation of number - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3228256/
A summary of some landmark studies regarding the cognitive representation of number - https://software.rc.fas.harvard.edu/lds/wp-content/uploads/2010/07/feigenson2004.pdf
A great Wikipedia summary of some of the creatures which have demonstrated some capacity for number sense - https://en.wikipedia.org/wiki/Number_sense_in_animals
A study showing the gradual linearization of the approximate number systems logarithmic error allowance during childhood - https://www.ncbi.nlm.nih.gov/pubmed/12741747
An analysis of possible evolutionary reasons the approximate number system is mapped logarithmically - https://www.ncbi.nlm.nih.gov/pubmed/26755188
The 2014 paper which improved on Graham’s upper limit to his Ramsey theorem question - http://www.sciencedirect.com/science/article/pii/S0195669814000936