Is Mathematics reliable for understanding 'reality'?
I have a curious basic question that is stuck in mind for long. How far is Mathematics representative of reality, the physical world? It seems silly and not worth the time of someone who is far advanced in scientific knowledge. But as I read a bit, I seem to get stronger on the grounds for my doubt, but I am not there from where I can posit the question in a ‘mathematical’ fashion. But, I feel that if the question is capable of producing uncertainty, all theories that work backwards or forwards on mathematical equations could come under cloud. The lofty heights of knowledge of a distant past and a remote corner may be just fantasizing.
I am aware I look stupid. The vast progress in science has been on the back of Maths, with mind-boggling achievements like exploring outer space and sending satellites that are remote controlled with precision based on Maths.
My mind seeks conviction that Maths is a true measure of reality out there. My mind does not seek similar confirmation about the reality itself.
Some quotations
David Hume:
“Mathematical propositions must pay a price for yielding absolute truth about anything which exists, about any matters of fact. Mathematics is only empty, abstract, formal truth, which tells you nothing about existence. No proposition which states a relation between ideas (the propositions of arithmetic, geometry, algebra or logic) can establish any truth about existence. Thus there is a trade off. Statements about formal relations of ideas, like 2+2=4, give us knowledge which has certainty, but on the other hand it is merely formal truth, empty, abstract, it gives no information about existence. Statements about matters of fact, on the other hand, give us information about facts, about existence, but they provide no certainty, not even a basis for probability.”
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” Albert Einstein
Russell: "Not only is mathematics independent of us and our thoughts, but in another sense we and the whole universe of existing things are independent of mathematics."
" .. pure mathematics can never pronounce upon questions of actual existence : the world of reason, in a sense, controls the world of fact, but it is not at any point creative of fact,and in the application of its results to the world in time and space, its certainty and precision are lost among approximations and working hypotheses."
“.. mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”
“A book should have either intelligibility or correctness; to combine the two is impossible, but to lack both is to be unworthy of such a place as Euclid has occupied in education.”
Proof of induction is basic to Maths. That is assumptive.
For long we believed in Euclid and even today, we work with it in school and even in engineering, etc. But, it is not realistic (vide Russell above).
I have a curious basic question that is stuck in mind for long. How far is Mathematics representative of reality, the physical world? It seems silly and not worth the time of someone who is far advanced in scientific knowledge. But as I read a bit, I seem to get stronger on the grounds for my doubt, but I am not there from where I can posit the question in a ‘mathematical’ fashion. But, I feel that if the question is capable of producing uncertainty, all theories that work backwards or forwards on mathematical equations could come under cloud. The lofty heights of knowledge of a distant past and a remote corner may be just fantasizing.
I am aware I look stupid. The vast progress in science has been on the back of Maths, with mind-boggling achievements like exploring outer space and sending satellites that are remote controlled with precision based on Maths.
My mind seeks conviction that Maths is a true measure of reality out there. My mind does not seek similar confirmation about the reality itself.
Some quotations
David Hume:
“Mathematical propositions must pay a price for yielding absolute truth about anything which exists, about any matters of fact. Mathematics is only empty, abstract, formal truth, which tells you nothing about existence. No proposition which states a relation between ideas (the propositions of arithmetic, geometry, algebra or logic) can establish any truth about existence. Thus there is a trade off. Statements about formal relations of ideas, like 2+2=4, give us knowledge which has certainty, but on the other hand it is merely formal truth, empty, abstract, it gives no information about existence. Statements about matters of fact, on the other hand, give us information about facts, about existence, but they provide no certainty, not even a basis for probability.”
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” Albert Einstein
Russell: "Not only is mathematics independent of us and our thoughts, but in another sense we and the whole universe of existing things are independent of mathematics."
" .. pure mathematics can never pronounce upon questions of actual existence : the world of reason, in a sense, controls the world of fact, but it is not at any point creative of fact,and in the application of its results to the world in time and space, its certainty and precision are lost among approximations and working hypotheses."
“.. mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”
“A book should have either intelligibility or correctness; to combine the two is impossible, but to lack both is to be unworthy of such a place as Euclid has occupied in education.”
Proof of induction is basic to Maths. That is assumptive.
For long we believed in Euclid and even today, we work with it in school and even in engineering, etc. But, it is not realistic (vide Russell above).
No comments:
Post a Comment