Where do numbers come from?
From a conversation with ChatGPT. Only my side is shown.
I want to understand the motivations behind creating numbers and a measurement system, how did people come up with these abstractions that we call numbers and why did they do so? what other options did they have and why do we have a system that we have right now?
Is there a book that can explain these concepts? I want to understand math at it’s core
these are more of pop culture books! Imagine if there were aliens who did not know maths, how would they start this process, how and why would they create an abstraction called as one which represents a quantity? how did they establish relationships like 1+1 makes a 2 whereas 2 was just another abstraction What I am trying to achieve here is look at the concept of numbers from various perspectives - motivations, history, application and just abstract thinking. Doing this will help me develop a deeper sense of math. Are there any books like these
I researched these books, this is what I feel:
- human body can only perceive change in states, furthermore these perception are not absolute, for the same change in a quantifiable variable the perception can be different
- one way to solidify these quantizations so there is a general consensus among the masses is to create abstractions, which is a measure of these changes and then can also be logged for analysis, comparison and communication
- there are two problems with it: the quantization process itself can be inaccurate because it is a measure done by humans, however we can increase the degree of accuracy by using ever more advanced and sophisticated instruments; secondly its an infinite process, the abstraction cannot be completed or its open ended since there is no limit to the abstractions
- so we created a solution to understand reality by creating a caricature of it, but there is an infinite resolution to that caricature
- Finally creating abstraction is in the end a process of splitting, by taking a whole and either bundling it up into a new or existing category or splitting it further into a new or existing category, at the end of the day it is more categorization
Math then is the study of defining these abstractions or categories and then using them to study their properties - giving us leverage over vast data of perception - helping us manipulate it for predictions, estimations, analysis etc. Eg - planetary motion data is huge, but statistics gives us a way to navigate it.