Of course the other thing that has been going on in my OU life has been the study of A224 Inside Music. I would say on the whole this is a great course. However I do have my reservations but I'm not sure they could be resolved given the nature of the course.

The course covers a lot of a ground in a very short space of time. In terms of theory you are taken up to about ABRSM grade 6 with a mention of a bit more. It assumes as a pre-requisite that you have a basic ability to read music up to about ABRSM grade three. There is an introduction to basic music theory available on Open learn for those who don't have the basics

http://www.open.edu/openlearn/history-the-arts/culture/music/introduction-music-theory/content-section-0

But there is a lot in this course that is not even mentioned in the ABRSM grade exams, such as the discussion of Sonata form and you are taught the basics of analysis of quite complicated pieces.such as Mozart's piano concerto in C minor and Brahm's third symphony.

The core of the course is a crash course in the composition of songs and it really is a crash course. These days any one with a laptop and access to a music notation software such as Sibelius can compose. One no longer needs access to a piano or the ability to hear music in ones head before it's written down or play a musical instrument, something this course takes advantage of. Unfortunately in my opinion Sibelius is really hard to use fluently and to write pieces of music. You have to search through various menus which I never did get the hang of how to use properly. Yes it can be simplified by use of key-board short cuts, but the keyboard short cuts only take you so far. Unfortunately Sibelius has rapidly become the industry standard, so if you aspire to take composing further as I do then it's a necessary evil just like Microsoft Office.

The course material is very interesting, but the composition material is only accessible on-line I guess the OU feel that they have something unique here and don't want outsiders to access it via second hand copies. Even so I would have thought that for those who want to refer to the material once the course is finished it would have only been fair to give the students a hard copy of the material. Especially if they have paid £2500 for it as those in England have to it seems a bit mean to say the least. Ok you can download pdfs of the material but as the material would be quite bulky if printed out, it's hardly the most convenient. However each online unit tried to cover far too much material in the short space of a week. However that is probably true of most OU courses in general, if one were to diligently do all the suggested exercises it would take about two - three weeks per unit. In my case I only managed to seriously look at the first four composition units out of 6 and I was able to draw on my previous knowledge of music.

In terms of other content the course is an odd mix of pop, classical (Art music) and world (Ethnic music) I guess it's trying to be all things to all people. One minute you will be analysing a song by Oasis, then a keyboard piece by Bach, then some jazz and then some world music. All of this is not treated very systematically and most of it to be quite frank just wont be read or listened to by most students as they will be desparately trying to just complete the assignments which are just relentless. Thus although the set piece was nominally Mozarts piano concerto in C minor I more or less ignored it as it wasn't assessed in the assignments.

Also the assignments seem to go from fairly basic ones to really advanced ones in the short space of time. I realise that by only completing 8 assignments you can't cover everything. However I think a real shortcoming was the serious lack of drill exercises as part of the formal assessment. No where were we asked to harmonise a melody, apart from in our songs. As a consequence I have for example a vague idea of what an Augmented 6th is but I lack confidence in how to introduce into my compositions. The course material really did not help here. In this the course is quite different from the ABRSM grade theory exams which start from the basics and build up step by step. I feel the need to do these to actually learn the theory rather than just retain a vague idea of it.

So overall as an introduction to music this course is really quite good, but I doubt I have really learnt the basics in a way that will stick. It does need to be complemented by a detailed study of the mechanics of music in a way similar to that of the ABRSM exams. If done in conjunction with such rigour then this course nicely complements them but byiteslf it is only part of the whole jigsaw. Perhaps it was trying too much, certainly if one were to compare this course with what happens at the first year of a degree level music course at a conventional university this would be sadly lacking. Where is the systematic introduction to harmony and counterpoint? Where is the systematic historic introduction to classical music and the various classical styles? Absolutely nowhere, the older course A214, whilst not so exciting was more systematic in teaching the basics of music and there were drill exercises (although probably not enough). Also a basic overview of the the three main styles of classical music, Baroque, classical and Romantic was given. A214 was more focused than this course and probably better than A224 for it.

As part of a general humanities degree this course fits quite well and it is good that such a course is available but anyone thinking they have studied music at degree level or even A level or higher by doing this course would be kidding themselves. On the whole I enjoyed this course as it helped get me thinking about music again and the composition part was something new to me. However I will certainly need to do a lot more. I will put myself forward for the Grade 5 ABRSM exam in November then all the way up to grade 8 and hopefully start piano lessons so I can consolidate the material here before embarking on the OCA composition courses which seems the next logical step.

## Thursday, 13 June 2013

### Not my greatest day MST326 exam debrief part 1

Well I had MST326 exam this morning and it was a bit of a disaster quite frankly. Things started to go wrong right from the start when I got bogged down in two 'easy' part 1 questions. Only managed to do about half of each question needed. Might just scrape a pass but thats about it. I'll give a fuller debrief in a couple of days but the OU have asked us not to discuss the exam in any detail for a couple of days so I'll do it after the weekend. I can't remember the questions in any great detail anyway. Just that nothing seemed to come out for me. I think I'm getting a bit too old to do detailed tricky calculation type questions under exam conditions admittedly my revision schedule wasn't that great. I do have serious reservations about whether or not to do the MSc in maths if every year it's going to end up with me struggling to do the TMA's on time and being ill prepared for an exam. Indeed I'm beginning to have doubts about the whole OU experience don't get me wrong the courses are interesting and the material is great it's just that I feel under real pressure to do the TMA's and focus on the exam and so I'm just cherry picking the bits of the course relevant to the TMA and the exam and not really learning the material this applies to all the courses I've done since M208 the last OU course I've really enjoyed and made a reasonable stab at.

In the grand scheme of things I don't have to count this course for anything so will quietly drop it and hope I do better on my other courses which will be

Quantum Mechanics exam in October

Then I've registered for Number theory and logic and also the third philosophy level course AA308 Thought and experience and I intend to do the physics project. It will be good to get back into philosophy again. I will have an effective degree in Maths physics and philosophy the courses being

MST121 and MS221 Introducing Maths and exploring mathematics 60 points

M208 Pure Maths 60 points

A211 Introducing Philosophy 60 points

M358 Quantun Physics 30 points

M381 Number theory and logic 30 points

Quantum Physics project 30 points

AA308 Thought and experience Philosophy of Mind 60 poiints

and my least worse of MS324 Waves diffusion etc or MST326 Fluids. If I get grade 2 in quantum physics, and Philosophy of Mind then I should be in a reasonable position to get a 2/I for my second OU degree which should put me in a reasonable postion to do the MA in European Philosophy at St Davids.

Not that I intend to drop my study of maths I really want to get back to studying my own subjects in my own way without a TMA looming ahead. Matters haven't helped that there has been no effective break since Feb 2012 and I'm feeliing quite fatigued with it all. Certainly I don't want to have to be asked to solve a tricky separation of variables question in a ridiculously short time scale as MST326 expected us to do. This is a pity as that was for me the most interesting bit of the course but I just can't do this sort of thing accurately and under time pressure. When they come out it is one of the most satisfying of all experiences but not under exam conditions.

Amongst maths/physics projects I want to take up in the lull are

1) Finally complete the derivation of the Friedmann equations from the equations of General Relativity and apply it to the current standard model of the universe. Part of this will involve solving the resulting differential equations numerically and so I will look at the Cambridge computing projects

2) Dig a bit deeper into Galois theory a topic I started a couple of years ago the book I have in mind is

http://www.amazon.com/Galois-Theory-Beginners-Mathematical-Matehmatical/dp/0821838172

This starts off with explicit solutions for cubic and quartic equations. There is obviously a lot of interest in Galois theory as a search through the statistics for this blog shows that any posts I have that refer to the topic seem to get a large number of hits.

3) Solve Schrodinger's equation in parabolic coordinates for both the bound state problem and the scattering problem. This will be a tour de force of all the techniques used to solve partial differential equations, the resulting solutions go by the ridiculous name of the confluent hyper-geometric function however what is of interest is that the scattering problem can be solved exactly even if the resulting expressions are a tad obscure to extract meaning from.

Plus the small matter of getting back on track with my quantum mechanics course.

In the grand scheme of things I don't have to count this course for anything so will quietly drop it and hope I do better on my other courses which will be

Quantum Mechanics exam in October

Then I've registered for Number theory and logic and also the third philosophy level course AA308 Thought and experience and I intend to do the physics project. It will be good to get back into philosophy again. I will have an effective degree in Maths physics and philosophy the courses being

MST121 and MS221 Introducing Maths and exploring mathematics 60 points

M208 Pure Maths 60 points

A211 Introducing Philosophy 60 points

M358 Quantun Physics 30 points

M381 Number theory and logic 30 points

Quantum Physics project 30 points

AA308 Thought and experience Philosophy of Mind 60 poiints

and my least worse of MS324 Waves diffusion etc or MST326 Fluids. If I get grade 2 in quantum physics, and Philosophy of Mind then I should be in a reasonable position to get a 2/I for my second OU degree which should put me in a reasonable postion to do the MA in European Philosophy at St Davids.

Not that I intend to drop my study of maths I really want to get back to studying my own subjects in my own way without a TMA looming ahead. Matters haven't helped that there has been no effective break since Feb 2012 and I'm feeliing quite fatigued with it all. Certainly I don't want to have to be asked to solve a tricky separation of variables question in a ridiculously short time scale as MST326 expected us to do. This is a pity as that was for me the most interesting bit of the course but I just can't do this sort of thing accurately and under time pressure. When they come out it is one of the most satisfying of all experiences but not under exam conditions.

Amongst maths/physics projects I want to take up in the lull are

1) Finally complete the derivation of the Friedmann equations from the equations of General Relativity and apply it to the current standard model of the universe. Part of this will involve solving the resulting differential equations numerically and so I will look at the Cambridge computing projects

2) Dig a bit deeper into Galois theory a topic I started a couple of years ago the book I have in mind is

http://www.amazon.com/Galois-Theory-Beginners-Mathematical-Matehmatical/dp/0821838172

This starts off with explicit solutions for cubic and quartic equations. There is obviously a lot of interest in Galois theory as a search through the statistics for this blog shows that any posts I have that refer to the topic seem to get a large number of hits.

3) Solve Schrodinger's equation in parabolic coordinates for both the bound state problem and the scattering problem. This will be a tour de force of all the techniques used to solve partial differential equations, the resulting solutions go by the ridiculous name of the confluent hyper-geometric function however what is of interest is that the scattering problem can be solved exactly even if the resulting expressions are a tad obscure to extract meaning from.

Plus the small matter of getting back on track with my quantum mechanics course.

## Wednesday, 5 June 2013

### Two sides of Hume's Fork Weinstein's Geometric Theory

My attention was drawn to an attempt by an outsider to come up with (yet another) Grand Unified theory.

http://www.guardian.co.uk/science/2013/may/23/eric-weinstein-answer-physics-problems

http://www.guardian.co.uk/science/blog/2013/may/23/roll-over-einstein-meet-weinstein

What is unsual about this is that Mr Weinstein hasn't even published a paper describing his theory not even on ArXiv so that other people can examine it and test it's credibility. It would seem that his friendship with Marcus du Sautoy enabled him to give a highly prestigious lecture. I'm sure the guy has come up with some clever maths but like say the current state of superstrings or the multiverse the fact that the theory can't make any predictions and hasn't even been written down means it's definitely in the not even wrong theory.

It does make one question the credibility of Marcus du Sautoy who seems to be latching onto every possible break through in physics (not that Weinstein's attempt could be seen as a breakthrough) and over egg the pudding to say the least. He claimed in a Horizon programme last year that the alleged violation of the speed of light by neutrino's proved superstring theory and M theory. When in fact the result was shown to be due to a faulty cable. I did not see him eating his boxer shorts as Jim Al Khalili offered to if the result was shown to be correct. Marcus du Sautoy righthly has come in for some intense criticism in the way he has handled this issues some links to which can be seen here

http://blogs.scientificamerican.com/cocktail-party-physics/2013/05/24/dear-guardian-youve-been-played/

Anyway this is not the main point of this post. I want to examine what seems to be a misconception by the likes of Marcus du Sautoy about how physics works. People like him seem to think there is a one-one correspondence betweem mathematical structures and the natural world. However any mathematical construction when applied to the real world can only be an approximation not the real thing.

Hume put the dilemma quite precisely in his Fork. Humans use two types of reasoning deductive and inductive. Deductive reasoning such as mathematics applies to the realm of ideas whereas we use inductive reasoning to apply to matters of fact.

As I pointed out a couple of years back

http://www.blogger.com/blogger.g?blogID=7897235423812277683#editor/target=post;postID=7025597943261709647;onPublishedMenu=allposts;onClosedMenu=allposts;postNum=59;src=postname

Hume points out that although we use inductive reasoning all the time there can be no rational justification for it as it involves a circular argument. How do I know that if confronted with a glass of claret it will taste the same as another one by an appeal to experience. How do I ground my experiences by an appeal to the uniformity of nature. How do I know that nature is uniform by an appeal to experience. Reasoning based on induction requires many observations to establish a truth and again not every glass of claret will taste exactly the same. On the other hand inductive reasoning is used all the time.

In contrast in the realm of ideas mathematical and logical deductions once proven are true for all time it only needs one demonstration that eg the gap between two prime numbers is less than 7.5 billion to show that this is the case.

When it comes to applying mathematical ideas to the natural world although the laws of physics can be expressed mathematically they are only approximations albeit really good ones for a lot of cases. In what Hume calls mixed maths which we nowadays call Applied maths the laws are grounded in empirical observation. To test a theory requires a lot of hard work in relating the general principles to a concerte prediction. For example the predicition of the properties of the Higg's boson required many calculations by whole teams of people based on reasonable approximations from the Standard model using the techniques of quantum field theory and even more people to test the predctions by measuring the decay rates and scattering cross sections. This involves calculatiing Hundreds of Feynman diagrams and summing up their individual contributions to the given decay rate or scattering cross-section. Messy, tedious prone to error but thats how real calculations are made in physics even then the actual value of the given parameter will only be an approximation albeit a good one.

Another point is that the laws of phyiscs when expressed mathematically will always have an empirical constant associated with it. The accuracy of the application of say Schrodinger's equation which involves the masses and charges of the particles involved will only be as good as the measured values. Even if one day we do reduce everything to 1 coupling constant, that coupling constant will have to be measured and one measurement will not suffice. . All this points to a degree of approximation associated with the laws of physics expressed mathematically and far removed from the pristine unmessy platonic world that du Sautoy and Weinstein live in.

The symmetries of the Standard model are only approximate to take an example the masses of the quarks in each generation are only approximately the same, indeed as I pointed out it here

http://www.blogger.com/blogger.g?blogID=7897235423812277683#editor/target=post;postID=3500862736577281127;onPublishedMenu=allposts;onClosedMenu=allposts;postNum=3;src=postname

It stretches credulity to suggest that the top quark has the same mass as the bottom quark. Or that neutrino's are massless. Nevertheless as an empirical summary of the current status of particle physics the Standard model is probably the most empirically adequate theory we have. Even if trying to predict results from it is quite a messy busimess.

Such a world is far removed from the Pristine Platonic world of Marcus du Sautoy and Weinstein. It is not enough to come up with some elegant mathematics one has to show how it applies to the real world and acknowledge that at best it will be an ideal approximation. What people like Weinstein and Marcus du Sautoy do is confuse two quite separate areas and types of reasoning. Seduced by the elegance of their mathematics they think they have found the ultimate secret of reality. Unfortunately for them the natural world will always end up blowing a great raspberry at their naive idealism as the approximation will sooner or later breakdown.

http://www.guardian.co.uk/science/2013/may/23/eric-weinstein-answer-physics-problems

http://www.guardian.co.uk/science/blog/2013/may/23/roll-over-einstein-meet-weinstein

What is unsual about this is that Mr Weinstein hasn't even published a paper describing his theory not even on ArXiv so that other people can examine it and test it's credibility. It would seem that his friendship with Marcus du Sautoy enabled him to give a highly prestigious lecture. I'm sure the guy has come up with some clever maths but like say the current state of superstrings or the multiverse the fact that the theory can't make any predictions and hasn't even been written down means it's definitely in the not even wrong theory.

It does make one question the credibility of Marcus du Sautoy who seems to be latching onto every possible break through in physics (not that Weinstein's attempt could be seen as a breakthrough) and over egg the pudding to say the least. He claimed in a Horizon programme last year that the alleged violation of the speed of light by neutrino's proved superstring theory and M theory. When in fact the result was shown to be due to a faulty cable. I did not see him eating his boxer shorts as Jim Al Khalili offered to if the result was shown to be correct. Marcus du Sautoy righthly has come in for some intense criticism in the way he has handled this issues some links to which can be seen here

http://blogs.scientificamerican.com/cocktail-party-physics/2013/05/24/dear-guardian-youve-been-played/

Anyway this is not the main point of this post. I want to examine what seems to be a misconception by the likes of Marcus du Sautoy about how physics works. People like him seem to think there is a one-one correspondence betweem mathematical structures and the natural world. However any mathematical construction when applied to the real world can only be an approximation not the real thing.

Hume put the dilemma quite precisely in his Fork. Humans use two types of reasoning deductive and inductive. Deductive reasoning such as mathematics applies to the realm of ideas whereas we use inductive reasoning to apply to matters of fact.

As I pointed out a couple of years back

http://www.blogger.com/blogger.g?blogID=7897235423812277683#editor/target=post;postID=7025597943261709647;onPublishedMenu=allposts;onClosedMenu=allposts;postNum=59;src=postname

Hume points out that although we use inductive reasoning all the time there can be no rational justification for it as it involves a circular argument. How do I know that if confronted with a glass of claret it will taste the same as another one by an appeal to experience. How do I ground my experiences by an appeal to the uniformity of nature. How do I know that nature is uniform by an appeal to experience. Reasoning based on induction requires many observations to establish a truth and again not every glass of claret will taste exactly the same. On the other hand inductive reasoning is used all the time.

In contrast in the realm of ideas mathematical and logical deductions once proven are true for all time it only needs one demonstration that eg the gap between two prime numbers is less than 7.5 billion to show that this is the case.

When it comes to applying mathematical ideas to the natural world although the laws of physics can be expressed mathematically they are only approximations albeit really good ones for a lot of cases. In what Hume calls mixed maths which we nowadays call Applied maths the laws are grounded in empirical observation. To test a theory requires a lot of hard work in relating the general principles to a concerte prediction. For example the predicition of the properties of the Higg's boson required many calculations by whole teams of people based on reasonable approximations from the Standard model using the techniques of quantum field theory and even more people to test the predctions by measuring the decay rates and scattering cross sections. This involves calculatiing Hundreds of Feynman diagrams and summing up their individual contributions to the given decay rate or scattering cross-section. Messy, tedious prone to error but thats how real calculations are made in physics even then the actual value of the given parameter will only be an approximation albeit a good one.

Another point is that the laws of phyiscs when expressed mathematically will always have an empirical constant associated with it. The accuracy of the application of say Schrodinger's equation which involves the masses and charges of the particles involved will only be as good as the measured values. Even if one day we do reduce everything to 1 coupling constant, that coupling constant will have to be measured and one measurement will not suffice. . All this points to a degree of approximation associated with the laws of physics expressed mathematically and far removed from the pristine unmessy platonic world that du Sautoy and Weinstein live in.

The symmetries of the Standard model are only approximate to take an example the masses of the quarks in each generation are only approximately the same, indeed as I pointed out it here

http://www.blogger.com/blogger.g?blogID=7897235423812277683#editor/target=post;postID=3500862736577281127;onPublishedMenu=allposts;onClosedMenu=allposts;postNum=3;src=postname

It stretches credulity to suggest that the top quark has the same mass as the bottom quark. Or that neutrino's are massless. Nevertheless as an empirical summary of the current status of particle physics the Standard model is probably the most empirically adequate theory we have. Even if trying to predict results from it is quite a messy busimess.

Such a world is far removed from the Pristine Platonic world of Marcus du Sautoy and Weinstein. It is not enough to come up with some elegant mathematics one has to show how it applies to the real world and acknowledge that at best it will be an ideal approximation. What people like Weinstein and Marcus du Sautoy do is confuse two quite separate areas and types of reasoning. Seduced by the elegance of their mathematics they think they have found the ultimate secret of reality. Unfortunately for them the natural world will always end up blowing a great raspberry at their naive idealism as the approximation will sooner or later breakdown.

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