As promised, I made my decision today, regarding whether to take two courses starting in Feb, or just the one.
Well, I chose two; both the courses Astrophysics (S382) and The Relativistic Universe (S383).
They both start on the 2nd of Feb and each have different challenges, in their own right. Having self studied the 'Book 0', prep material that the O.U provides as a brush up on the prerequisite knowledge for both of these courses; I have already noted some teeny-tiny elements of these courses, that will probably drive me insane, by October.
I suspect that they wouldn't bother most people; but combine my recent drilling in pure-mathematical rigour, my dyslexia and a general bit of miserable old git; these little issues are surely going to send me 'round the bend'.
I guess that the issue for me, is the rather unclear and nonsensical way that astrophysicists and cosmologists appear to throw around mathematical and unit notations with wild abandonment, not dissimilar to the experience that I had this afternoon, pouring my Alphabetti Spaghetti onto two pieces of burnt toast.
For example, in mathematics, we could use the letter r for the radius of a circle. But if you are a 'telescope-anorak', (as my wife has now taken to calling me! hmm), then you will have created your own symbols, just for the hell of it.
Hey, why not let d be the radius of an imaginary sphere when working out how bright a star appears in space? Or, better still, lets use the symbol R on the same page, to describe the radius of that star.
This is a heady world where F is flux, not force; m is magnitude, not mass and i is an angle of inclination; which has nothing to do with complex numbers, I can assure you.
I think it's going to take some 'parrot-fashion' wrote learning, for me to grasp all of these different uses of the same symbols, within the same texts.
So, if you ever hear on the news, of a crazy man being committed to an institution after being found walking around Birmingham town centre shouting, 'Come back Group Theory, all is forgiven!'
Then please, think of me ;-)
Mm not sure that is a legitimate complaint. Usually the symbols are well defined in the text and derive from the context. Certainly not one that justifies the criticism that Physicists and Astrophysicists are sloppy with their use of mathematics.
ReplyDeleteWhat has the complex i to do with an angle, i seems a perfectly good symbol to use for an angle of inclination. Why use theta or phi what have they got to do with inclination or whatever they are just arbitrary labels. It's only convention that has made them the usual default symbols to use for angles.
As for dimensional analysis it is one of the most rigorous ways of making sure that your equations are consistent with each other. It really is something you must try and understand if you want to progress further with physics or astrophysics. Yes the different units may be confusing but would you really want to measure large scale distances in metres for example.
I think you will find that when you get to the beauty of Einstein's Field equations and how their solutions can explain black holes and give rise to the Fundamental equations governing the expansion of the universe then you might realise how powerful the combination of maths and physics can be in explaining the world around us. Of course be prepared for the fact that at Level 3 there just isnt the time to derive everything. I spent two tedious weeks last summer calculating the components of the Riemann Tensor for the Robertson Walker metric an exercise I don't particlularly want to have to repeat.
As for pure maths well if you want to cope with say 4 different definitions of continuity within 20 pages as was done in M338 you are welcome. Or endless chains of definitions followed by yet more endless chains of definitions with no idea of where it's all leading.
Ok thats a caricature, but no more than your accusations of handwaving or sloppiness in the use of mathematics by physicists or astrophysicist.
Anyway you've made your decision so good luck with it.
Best wishes Chris
I'm afraid you won't change my view on this. And I don't for one minute think that sloppiness has anything to do with it. I think it all probably stems from the fact that Astronomy is as old as the hills and the overlap of symbols is a natural product of pockets of astronomy being discovered or explored through such a long time period. Regardless the true reasons, I am not sure that my complaint about an over complication of an already challenging subject, is not a legitimate one to make. As for multiple explanations of the same concept such as continuity, that is quite different. That repetition is about enrichment of concepts.
ReplyDeleteBut, as the post says, these are the minor niggles of a grumpy old git, so please take them with the pinch of condiment that they deserve.
Best regards Dan
Having had a quick look at the book you referred to I admit that some of the coordinate systems may be confusing and also you will not really have had much chance to discover the conceptual and logical structure of physics. The way it is presented would seem to be a mixture of simple algebraic manipulation and caclulating things in obscure units. That is more to do with astronomy than physics itself. Certainly from that book you would not in my opinion get a balanced view of how physics works.
ReplyDeleteAs I've remarked before one of the best books to get an overview of the underlying conceptual structure of physics is Longair's book concepts of theoretical physics.
http://www.amazon.co.uk/dp/052152878X/ref=asc_df_052152878X11326181?smid=A3P5ROKL5A1OLE&tag=googlecouk06-21&linkCode=asn&creative=22206&creativeASIN=052152878X
Which would be good preparation for any one undertaking your journey and who has a certain mathematical ability which would be achieved by doing the equivalent of MST209 and to whioh you seemed to be making some progress.
If I had my way I would base the second level physics course on Longair's book rather than the current version which at least going from the exam papers seems a bit thin on the ground in establishing the mathematical basis of the subject.
Perhaps you are letting the way the OU presents the physics cloud your judgement as to what mathematical physics or theoretical physics is really about.
Anyway good luck I might enrol on quantum mechanics this term
so that I can do the project on quantum entanglement next October alongside Logic and Number theory
Best wishes Chris
Cheers Chris. It would be great to see you on the number theory mod next October. I imagine we will have many lively and enriching debates on that subject. It might give us an opportunity to do some collaborative number work such as that which Duncan is currently exploring and that you touched on with your Cambridge computer project(which I must admit I don't yet have the skill for)
ReplyDeleteDan