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How do humans understand numbers?
Humans have 86 billion neurons. Yet it is still hard for humans to grasp the concept of numbers. Without exposure to well structured curriculum, most humans would struggle to add two numbers of three digits. It very much seems that symbolic reasoning of numbers is naturally alien to humans, and that humans primarily understand numbers spatially. How is the link between spatial numbers and symbolic numbers established?
- famouswaffles 4y agoI think part of the issue arises from the fact that the result of the arithmetic of numbers is nearly completely divorced from any semantic information contained in the preceeding numbers. It's a big reason LLMs struggle with arithmetic (although gpt-4 is competent at it now). Take the sentence, "John is smiling and is therefore ----". It's not hard to grasp that the missing word is probably happy. Why ? Well all the information you need to make that calculation is embedded in previous context. It's pretty easy. Now take the problem 54859 + 494785 = ? Unlike the above, 54859 and 494785 don't actually tell you anything at all about how to perform addition. The arithmetic of addition (any arithmetic pretty much) is completely divorced from the problem statement. also. it's not like your brain evolutionarily ever had a need to intuit numbers spatially divorced.
- ofalkaed 4y agoI think most people are rather practical when it comes to numbers and adding two three digit numbers is generally not very practical. A cup of rice is simple and direct compared to 7800 grains of rice. How much water does it take to cook 7800 grains of rice? We use 2:1 water to rice with our cup of rice, do we use 2:1 with our grains? What is 15600 rice grains of water? Should we do the conversion through weight or volume? Things get complex fast and with little reward so most just grab a measuring cup and dump two of them filled with water in the pot, one of rice and have their curry. These simple methods of dealing with numbers scale well and avoids math, need more rice than just use a bigger scoop, still 2:1 does not matter if that scoop is an 8 ounce measuring cup or a 5 gallon pail. The numbers themselves are a needless abstraction most of the time and the digits we are born with are all most really need.