Uploaded December 2016 | Updated September 2026, 2 weeks ago
NOTE: My description of parsing up-arrow notation is incorrect; please see my correction here! youtube.com/watch?v=xN-MpWNsXw0
Graham's number is...really really big. But our brains start throwing errors at much smaller quantities.
-Links for the Curious-
Numberphile's fantastic video of Ron Graham explaining Graham's number - 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 - 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 - en.wikipedia.org/wiki/Number_sense_in_animals
A study showing the gradual “linearization” of the approximate number system’s logarithmic error allowance during childhood - ncbi.nlm.nih.gov/pubmed/12741747
An analysis of possible evolutionary reasons the approximate number system is mapped logarithmically - ncbi.nlm.nih.gov/pubmed/26755188
The 2014 paper which improved on Graham's upper limit to his Ramsey theorem question - sciencedirect.com/science/article/pii/S0195669814000936
NOTE: My description of parsing up-arrow notation is incorrect; please see my correction here! youtube.com/watch?v=xN-MpWNsXw0
Graham's number is...really really big. But our brains start throwing errors at much smaller quantities.
-Links for the Curious-
Numberphile's fantastic video of Ron Graham explaining Graham's number - 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 - 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 - en.wikipedia.org/wiki/Number_sense_in_animals
A study showing the gradual “linearization” of the approximate number system’s logarithmic error allowance during childhood - ncbi.nlm.nih.gov/pubmed/12741747
An analysis of possible evolutionary reasons the approximate number system is mapped logarithmically - ncbi.nlm.nih.gov/pubmed/26755188
The 2014 paper which improved on Graham's upper limit to his Ramsey theorem question - sciencedirect.com/science/article/pii/S0195669814000936
