The Law of Small Numbers Hope your 2024 is off to a good start! I plan to continue to build on my prior themes to illustrate from different angles what we know about human cognition to counter the naive, hubristic views of human omniscience offered from a self-erected pedestal. "Who can't do math?" was my recent post tackling the puzzling stances about the mathematical inability of Large Language Models (LLMs)--see link below. This article in Quanta popped up soon after that discussing some interesting research on how our minds juggle numbers. It give us a glimpse of how our minds work and the long evolutionary road taken to reach our current levels of cognition. This from the article is very important to keep in mind, often forgotten in the extant blithe views: “There’s not many things in cognition where people have been able to pinpoint very plausible biological foundations.” "Its findings suggest that the brain uses a combination of two mechanisms to judge how many objects it sees. One estimates quantities. The second sharpens the accuracy of those estimates — but only for small numbers." The article rightly states: "Although the new study does not end the debate, the findings start to untangle the biological basis for how the brain judges quantities, which could inform bigger questions about memory, attention and even mathematics." Let's question views of AI that cannot be tethered firmly to plausible models of cognition--drawn from neuroscience and the social sciences--to combat both hype and skepticism. It's perfectly fine to offer a theory or an opinion making it clear that facts are few and it's a view.
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4moStanislas Dehaene has been writing about how humans perceive numbers for a long time. Last week I read https://www.unicog.org/publications/Dehaene%20TICS%202022%20final%20proofs.pdf which is about the discrete symbolic number sense only. The attached figure and quote are for a well-known block tapping psychology task. There appears to be a neuron-level limit of encoding 4 symbols per reasoning step. "Crucially, MEG signals contained direct information about the postulated numerical and also allowed the ordinal position of items within a subsequence to be decoded. For instance, when tracing the four successive corners of a square, MEG signals contained numerical codes for the numbers one to four, suggesting that participants encoded the sequence using the mental equivalent of a ‘for i = 1:4’ loop"