- #1
drummerguy198
- 12
- 0
Question on the universal "correctness" of mathematics
I began thinking of this question long ago, but only now, that I am reading A History of Mathematics, 2nd edition, have I decided to ask for the perspectives and thoughts of others. I am slightly reluctant to ask this question, for it may seem a bit silly, and may even seem unanswerable. Really, it most likely is, but that is not the point.
Math is, as most mathematicians, scientists, and engineers would agree, a large volume of theorems, laws, and ideas conjured up by countless people over thousands of years. Many mathematicians have devised theories that, to this day, have yet to be proven incorrect. This entire system of laws and theories is, and pardon the redundancy, an ebb and flow of ideas, a way of thinking of things. Taking the quantification of the world around us and manipulating those numbers. Many ways (once again pardon the redundancy) of manipulating those numbers are still used extensively today.
So, finally, to my question. Look at everything we know of mathematics. Everything is either an extension or a correction of a basic axiom. Is it possible that somewhere else in this vast universe of ours, someone else has created an entirely knew math, complete with axioms completely alien to us? Take Euclid's common notions, his postulates, and many of the other things we take for granted as common logic. Is it possible that this basic logic we take for granted could be wrong somewhere else in another galaxy for example? (I have excluded from this question anything mathematical relating to the physical properties of that part of the universe. However, I may have been wrong in doing so. I am not sure if the physical behavior of a being's environment could affect its method of logical thought.)
I ask that when answering, you explain why as well. Hopefully some of you who are much farther along in your studies can thing teach me a few things.
I began thinking of this question long ago, but only now, that I am reading A History of Mathematics, 2nd edition, have I decided to ask for the perspectives and thoughts of others. I am slightly reluctant to ask this question, for it may seem a bit silly, and may even seem unanswerable. Really, it most likely is, but that is not the point.
Math is, as most mathematicians, scientists, and engineers would agree, a large volume of theorems, laws, and ideas conjured up by countless people over thousands of years. Many mathematicians have devised theories that, to this day, have yet to be proven incorrect. This entire system of laws and theories is, and pardon the redundancy, an ebb and flow of ideas, a way of thinking of things. Taking the quantification of the world around us and manipulating those numbers. Many ways (once again pardon the redundancy) of manipulating those numbers are still used extensively today.
So, finally, to my question. Look at everything we know of mathematics. Everything is either an extension or a correction of a basic axiom. Is it possible that somewhere else in this vast universe of ours, someone else has created an entirely knew math, complete with axioms completely alien to us? Take Euclid's common notions, his postulates, and many of the other things we take for granted as common logic. Is it possible that this basic logic we take for granted could be wrong somewhere else in another galaxy for example? (I have excluded from this question anything mathematical relating to the physical properties of that part of the universe. However, I may have been wrong in doing so. I am not sure if the physical behavior of a being's environment could affect its method of logical thought.)
I ask that when answering, you explain why as well. Hopefully some of you who are much farther along in your studies can thing teach me a few things.