Glad you shed some light on this, on how numbers are not just an intellectual invention but an intuition/sense so foundational that it is seen in the development of various animals (including ourselves). Thought the part about how we perceive changes in size, speed, and proximity similarly was a particularly interesting point
Another cool addition to this would be some of the earliest computers or theoretical machines from the first half of the 20th century. I remember taking a class about algorithms once where the professor showed us some basic machines, similar to the finite state machine but more primitive, that would often use counting to accomplish certain tasks differently than we might do so with symbolic algebra. While these were limited in what types of things they could do, it was neat to see the concept, especially when taking into consideration how things like those eventually evolved into the Turing machine and physical tape computers that formed the basis of modern computing.
Glad you shed some light on this, on how numbers are not just an intellectual invention but an intuition/sense so foundational that it is seen in the development of various animals (including ourselves). Thought the part about how we perceive changes in size, speed, and proximity similarly was a particularly interesting point
Another cool addition to this would be some of the earliest computers or theoretical machines from the first half of the 20th century. I remember taking a class about algorithms once where the professor showed us some basic machines, similar to the finite state machine but more primitive, that would often use counting to accomplish certain tasks differently than we might do so with symbolic algebra. While these were limited in what types of things they could do, it was neat to see the concept, especially when taking into consideration how things like those eventually evolved into the Turing machine and physical tape computers that formed the basis of modern computing.
Thank you, Mark. Maybe you can point me to these theoretical machines. I’m interested!
The machines I was referring to are DFAs and NFAs a.k.a. (non)deterministic finite automata. Sent you some more info about it.