- #1
Ittiandro
- 54
- 3
I am 72 and my background is in the humanities (I read classic authors in Latin and Greek, which I learned in high school in Italy, I love history and I have a more recent M.A. in Philosophy from a Canadian University).
Over the last few years, though, I developed a strong (and totally unexpected !) interest not so much in physics as in two of its most…esoteric branches, namely Relativity, in both its divisions, and the Quantum theory, an interest due in part, I guess, to my natural intellectual curiosity and also to their metaphysical underpinnings and the philosophical questions they raise...
The problem is that my mathematical skills are inversely proportional to my relative proficiency in the humanities, which means almost null. Although I did maths in college, my relationship with this discipline has always been one of aversion and in the end this has compromised my mathematical literacy and the possibility of any further exploration in the sciences field.
Mindful of my troubled relationship with maths, I thought at first, somewhat naïvely, that I could sail through the Special and General Relativity without maths, i.e. conceptually. I found this reasoning vindicated, at least in part, as far as Special Relativity is concerned, because the relativistic properties of space and time ( time dilation, space contraction, etc) , can be grasped, in spite of their apparent counter intuitiveness, with as little maths as some elementary algebra and the Pythagoras theorem.
I think this is because time and space (at least the Euclidean space!) are entities which are after all apprehended by our senses in our common experience and we know what we are referring to when we speak of them, although imperfectly, because we are never exposed to velocities even remotely approaching c.
When it comes to General Relativity, however, the counter intuitiveness of concepts like curved space ( and its interaction with matter) is compounded by the fact that we can’t even represent, for example, curved space in our mind and we have therefore to resort to maths to give it some kind of reality.
If it were not for the fact that the postulates of both the General and Special Relativity have been experimentally verified over the last 100 years and have been successfully incorporated into many branches of technology because of their highly predictive power, one would be tempted to think ( as many, not necessarily uneducated, people do) that using maths to give an apodictic foundation to the “reality” of curved space and the like is as futile as trying to prove the existence of centaurs with some mathematical lucubration.
This is not, of course, my view and I have therefore come to the conclusion that if I want to satisfy my intellectual curiosity in regard to Relativity and the like, I have to take the bull by the horns and learn maths.
This brings me to my question.
Can somebody lay out for me a tentative self-taught curriculum of the maths required to bring me up to the General Relativity level,( if this can be achieved, as I hope, within the rather limited and, alas, so rapidly shrinking time of my earthly existence )?.
The C.O.W. ( Calculus on the Web) course provides, in my opinion, an excellent template suitable to my purpose. I took the pre-calculus and the 1st calculus level a couple of years ago just to test myself and to my surprise I was able to go through all the exercises, even though no keys are provided ( the correct solution is required to go to the next step, though.). If something similar were available through the Internet in the field of Relativity, I’d like to hear.
Perhaps I should stress that my starting perspective is that maths, far from being a reality in itself, is but a language, whose goal is to explain an underlying reality, in this case the reality of the physical world, by conveying, through the shorthand of its symbols, concepts and logical links which cannot be otherwise conveyed by the verbal constructs of our common languages.
The curriculum I am searching for should be therefore streamlined to what is strictly necessary to understand the basic concepts of the General Relativity Theory, ( which would be already quite enough of a hurdle!) without side-stepping into the more speculative and perhaps more unnecessary aspects of pure mathematics, in which, from what I read, even some physicists like to indulge…
Any suggestions about reading material, and other learning tools will be appreciated.
Thanks for your helpIttiandro
Over the last few years, though, I developed a strong (and totally unexpected !) interest not so much in physics as in two of its most…esoteric branches, namely Relativity, in both its divisions, and the Quantum theory, an interest due in part, I guess, to my natural intellectual curiosity and also to their metaphysical underpinnings and the philosophical questions they raise...
The problem is that my mathematical skills are inversely proportional to my relative proficiency in the humanities, which means almost null. Although I did maths in college, my relationship with this discipline has always been one of aversion and in the end this has compromised my mathematical literacy and the possibility of any further exploration in the sciences field.
Mindful of my troubled relationship with maths, I thought at first, somewhat naïvely, that I could sail through the Special and General Relativity without maths, i.e. conceptually. I found this reasoning vindicated, at least in part, as far as Special Relativity is concerned, because the relativistic properties of space and time ( time dilation, space contraction, etc) , can be grasped, in spite of their apparent counter intuitiveness, with as little maths as some elementary algebra and the Pythagoras theorem.
I think this is because time and space (at least the Euclidean space!) are entities which are after all apprehended by our senses in our common experience and we know what we are referring to when we speak of them, although imperfectly, because we are never exposed to velocities even remotely approaching c.
When it comes to General Relativity, however, the counter intuitiveness of concepts like curved space ( and its interaction with matter) is compounded by the fact that we can’t even represent, for example, curved space in our mind and we have therefore to resort to maths to give it some kind of reality.
If it were not for the fact that the postulates of both the General and Special Relativity have been experimentally verified over the last 100 years and have been successfully incorporated into many branches of technology because of their highly predictive power, one would be tempted to think ( as many, not necessarily uneducated, people do) that using maths to give an apodictic foundation to the “reality” of curved space and the like is as futile as trying to prove the existence of centaurs with some mathematical lucubration.
This is not, of course, my view and I have therefore come to the conclusion that if I want to satisfy my intellectual curiosity in regard to Relativity and the like, I have to take the bull by the horns and learn maths.
This brings me to my question.
Can somebody lay out for me a tentative self-taught curriculum of the maths required to bring me up to the General Relativity level,( if this can be achieved, as I hope, within the rather limited and, alas, so rapidly shrinking time of my earthly existence )?.
The C.O.W. ( Calculus on the Web) course provides, in my opinion, an excellent template suitable to my purpose. I took the pre-calculus and the 1st calculus level a couple of years ago just to test myself and to my surprise I was able to go through all the exercises, even though no keys are provided ( the correct solution is required to go to the next step, though.). If something similar were available through the Internet in the field of Relativity, I’d like to hear.
Perhaps I should stress that my starting perspective is that maths, far from being a reality in itself, is but a language, whose goal is to explain an underlying reality, in this case the reality of the physical world, by conveying, through the shorthand of its symbols, concepts and logical links which cannot be otherwise conveyed by the verbal constructs of our common languages.
The curriculum I am searching for should be therefore streamlined to what is strictly necessary to understand the basic concepts of the General Relativity Theory, ( which would be already quite enough of a hurdle!) without side-stepping into the more speculative and perhaps more unnecessary aspects of pure mathematics, in which, from what I read, even some physicists like to indulge…
Any suggestions about reading material, and other learning tools will be appreciated.
Thanks for your helpIttiandro