Friday, 30 September 2011

M337 TMA04 back and Hume

So got my last TMA for M337 back overall average in the high seventies so looking for grade 2 pass if the exam goes well. Have to say don't really feel I own the subject in the way I do for M208 where my average was in the mid nineties. Still we will see. Not long now D day or should it be E day is the 11th October Complex Analysis in the morning and Pure Maths in the afternoon. This weekend will be exclusively on Complex Analysis revision I hope to work through two papers thoroughly.

Anyway started my Hume course last night. The focus is on Hune's enquiry which is a smaller version of his magnum opus A Treatise on Human Nature. Hume attempts to apply the experimental method so successfully applied by Newton to the study of human nature, in a way it's a precursor to both psychology and sociology and it is arguable that from these perspectives that Hume has been superseded by developments in say cognitive psychology, or sociology. However Hume has an importance in establishing the limits of human knowledge, which Kant was able to develop further.

Hume as is well known is an empiricist, for him the rationalist speculation of Descartes or Leibniz over exagerates what can be achieved by reason alone. They sought to try to base human knowledge on what could be proved purely by reason in order to arrive at absolutely certain knowledge. Hume and other empiricists such as Locke  argue that what cannot be based on human experience, is speculation and they would argue the dangers of exaggerating what can be achieved purely by the use of reason. A bit like the debate that still goes on today between Platonists in mathematicians for whom mathematics uncovers the hidden secrets of a world of which the empirical reality is a mere copy. In contrast to  those who see us using mathematics as an aid to understanding, but would not make want to make the mistake of assuming that to every mathematical concept there must correspond an element of reality.

Hume begins his enquiry by contrasting what he calls the easy philosophy with more abstruse philosophy. The 'easy' philosophy purports to be  an extension of common sense and attempts to describe the importance of say virtue in ways which can easily be understood. By the use of poetry or literature. In Hume's day novelists such as Addison or the poet Pope would be adherents to such philosophy, in our day think of Alain de Boton.

Hume does not dispute the popularity of such philosophy but 'edifying philosophy' has it's limits and indeed there is a tedency for those who prefer 'edifying' philosophy to denigrate the more abstract philosophy because it is obscure and can only be understood by a few people. Hume offers three main arguments against this

1) A knowledge of abstract knowledge can help poets and artists, for example a painter gains much from a knowledge of anatomy.

2) Abstract knowledge satisfies human curioisity and should be encouraged even if it does not benefit mankind directly. Somewhat optimisitically, Hume claims that politicians and lawyers would benefit from a study of abstract philosophy as they would have a better understanding of how government works. Here Hume approaches Plato's ideas that the guardians of the state should be trained in abstract philosophy.

3) Perhaps his strongest argument is that quite often rational principles are misused as a cloak to justify all sorts of superstition. Indeed it is quite surprising that so called analytic philosophers of religion such as eg Plantiga or Peter Geach, see their main task to use modern techniques of analytical philosophy to maintain standard Christian doctrine no matter how obnoxious. For example the specious justifications often given for why God if he is all powerful and knowing allows evils such as Auszchwitz or Tsunami's to happen. (I might sound off about this in another post). For Hume the only way such specious reasoning can be countered is to master the abstruse metaphysics so that it's weaknesses can be exposed for all to see. Hume offers the hope that by enquiring seriously into the nature of Human Understanding it can be shown by an exact analysis of the powers and capacities of the Human mind that it is not fitted for such remote and abstruse subjects. He hopes to undermine the foundations of obscure metaphysics which has in the past served only to shelter superstition and absurdity.

In the next section Hume discusses the Origin of Ideas of which I will give a basic summary of next week.
If I get time this weekend I shall as promised review Richard II. I'll be watching Henry IV part 1 this weekend.   

Tuesday, 27 September 2011

M208 TMA07 back and Gotterdammerung

Got My last TMA for M208 back yesterday just made 90 due to rushing some group theory questions. Think I definitely prefer analysis to group theory or at least to OU group theory. As I've said before the parts that are relevant to physics is representation theory basically concentrating on representing group operations by matrices but this does not seem to play any part in the OU treatment.

Saturday was spent on a last tutorial for M208 Alan my tutor has been wonderfully supportive and I'm lucky to have him. He will be tutoring me for Topology and Group theory next year. Revision for M208 is under control but have to admit M337 needs some attention. I shall focus on this till Monday hopefully I can do two or even three papers by then.

On Sunday as a complete contrast I went to a concert performance of my favourite Wagner Opera
Gotterdammerung played by the Edinburgh Players Opera group.

Of which one of my work colleagues is the Leader. This has been an annual concert in the late summer the players meet for a whole weekend and friends are invited to come along on the Sunday.

It provides an opportunity for both amateur orchestral players and up and coming singers to perform in roles which they would not otherwise have the opportunity to do so. Ok so there were a few squeeks and squawks but there were no hitches. It is an amazing experience and I still have the music ringing in my head.


Friday, 16 September 2011

TMA06 M208 Back

Well got the 6th TMA for M208 back not bad in the 90's but the elusive 100% escapes me it highlighted one point which I had totally missed. Also it just goes to show how counterintuitive analysis can be.

The series

$$\sum_{0}^{\infty}\frac{1}{n}$$  is divergent but the sum

$$\sum_{0}^{\infty}\frac{-1^n}{n}$$ is convergent

to some people on the forums this seems obvious but to me given that the second series has alternating terms I would think it diverges to two different series. Anyway at least I know now.

Started revising my plan is to do 1 paper per week per course under exam conditions at the start of each weekend and then to consolidate my answers revise topics I'm not sure about until, the last few days before the exams. Which I will take off and try and do two papers for each course on the last four days. That will make a total of five past papers per course which should be enought. At least the exams are on the same day so I can divide my time equally on each course before each exam.

Anyway I'll review Richard 2nd later on this weekend and also summarise the first section of Hume's Enquiry.

Sunday, 11 September 2011

M337 TMA04 finished

After a fairly intensive couple of days I've managed to complete the final TMA04 for M337 hooray.
The questions were

1) Questions on conformal mapping alright once one had grasped the basic idea.

2) Questions on Fluid Mechanics
This is actually a continuation of part 1 as a large part of the fluid dynamics of an aereofoil can be seen as a conformal transformation discovered by Joukowski. There were two parts

  a) Some relatively straightforward questions on Complex Potentials and Stream Functions

  b) A quite tricky question on the flow past an obstacle involving the Joukowski transformation
     and the Flow ,mapping theorem.

3) Questions on Complex iteration including the properties of the Mandelbrot set

   Potentially this should be one of the most interesting units. However short of time I had to skim through the  material and did not do justice to the question. Espescially as the question on fixed points seem to give rise to a particularly awful set of fixed points. Also unlike M208 there is no fixed strategy given for say finding the Keep set of a complex function

I think potentially the second unit of this block is the most interesting and I hope to revisit it during revision

On the whole M337 has been a very stimulating course and I'm looking forward to doing the MSc course on Complex Variables. I'll post a full review after the exam.  I have the book for the MSc course already and will try and fit some of it in during down time. Tomorrow I'm taking the day off to finish off the last TMA for M208. Then it's a question of trying to do as many past papers under exam like conditions as possible.

 For now I'm just going to relax and have a few beers


Sunday, 4 September 2011

This and that and a bit on Hegel.

Not much happening really, ended up with a severe cold  on Thursday so brain hasn't been entirely in gear.

Finished TMA06 for M208 and safely posted it away had a wake up call when trying to the revision TMA blind ie with just the handbook in exam conditions. Only managed about 1/2 still this is usual when revision starts should do enough to finish it this week then revision starts.

Bit bogged down on unit D of M337, after the joys of residue calculus, this is rather tedious stuff on conformal transformations and Mobius transformations. Have finally finished the TMA question but had my head scratching quite a while. Doesn't help that key points are buried in the Audio Visual units. Looks like I'll be winging it for the last two units one on fluid dynamics and the other on the Mandelbrot set. A pity really as I was looking forward to the fluid mechanics part.

Other maths projects on hold until end of next week whislt I crack on with the TMA's which have to be submitted.

As a preparation for my projected MA in Contintental philosophy, and to complement my reading of Hume have started to read Hegel's Phenomenology of Mind or Spirit as some translators have it. Must admit to being deeply biased against it as one of my first books I read on Philosophy was Karl Popper's Open society and it's enemies. This remarkable book makes a link between Plato, Hegel and Marx and the rise of totalitarianism Hegel being one of the main targets of Popper. Popper's line if I recall it was that any attempt to see an underlying pattern in history is doomed to failure as it isn't scientific as it can't be falsified. However given Hegel's importance in 19th Century German philosophy he influenced Marx and it is claimed existentialism, it is important to have an understanding of his ideas. Also Popper's idea of science as essentially that of physics narrows the scope of a wide range of19th century  philosophical texts for them science is more like systematic knowledge rather than something which can be quantified. I can't believe it's all to be dismissed simply because it doesn't conform to the standards of physics. Even Hume's main works despite his dictum to consign any thing that didn't contain 'abstract reasoning concering quantitiy and number or experimental reasoning concerning matter of fact and existence' to the flames doesn't conform to the standards he set himself.  

I'll post more later indeed I want to provide a section by section summary of the main philosophical works on this blog however this is just first impressions.  Having skimmed through the preface, it's quite interesting. Hegel thinks he has found a method of breaking the dualisms associated with philosophy up to Kant namely the dualism between subject and object. he seems to want to go back to an Aristotlean notion of substance which he calls Nous and is translated as Notion but this is now a dynamic thing instead of the static thing of the meadival times. A naive interpretation would say that this is similar to the existentialist idea of being indeed Hegel uses terms like being in itself and being for itself which play a part in Sartre's philosophy

For Hegel science and mathematical truths only describe the appearance of things and provides a static view of the world. Nous however is always changing only presenting part of itself to us. The dynamic of history is driven by Nous's attempt to reconcile it's multifarious appearances with it's underlying being. At different times in something aking to a collective conscious Nous manifests itself. However it is never content to reconcile itself with one particular era or epoch. Or at least that was Hegel's view at the time he wrote the Phenomenology. Of course as is well known Hegel 15 years later was to claim (just as Fukyama claimed in the 1990's) that History had reached it's final destiny in the establisment of the Prussian State. He was wrong then and Fukyama has been shown to be wrong now. So I must confess to some ambivalence about Hegel. We'll see.

As a break from maths and philosophy going to watch Richard II tonight with a bottle of wine I'll let you know what I think Derek Jacobi is in the title role so should be worth watching. I hope also to do Henry IV part I and part II
during the rest of September.