## Saturday, 29 November 2014

### True Patriotism or Nationalism

This rant is a lot less objective than  I usually am but I am getting really sick of politicians and the press appealing to a bogus sense of patriotism and I despair of parties that should know better such as the :Labour party for abandoning core values of the basis of socialism such as that what ever country you come from shouldn't matter as to how you are treated.

Dr Johnson a person, who given my instintively left wing sympathies I would not have had any sympathies with, summed the current situation up precisely, when he claimed that patriotism was the last refuge of a scoundrel. It seems to me that both Alex Salmond and his successor Nicola Sturgeon and Nigel Farage are all scoundrels in that respect. Their so called arguments are essentially appeals to the lowest denominator of tribal instincts.

None of them appeal to what has actually made Britain great (and  I use that word delibrately as opposed to Scotish or English) the Britain that  makes me proud is the contribution to the intellectual and aesthetic contribution to the world not the flag waving nationalism of those who thought it right to display a saltire during the referendum or a St George cross in rochester.

No, the Britain that makes me proud is the scientific acheivements of Newton, James Clerk Maxwell, Charles Darwin, Crick and Watson, and Fleming and Peter Higgs, the mathematical achievements of Napier, Hamilton, and Wiles, The poetry of Shakespeare,. Dryden, Milton, Pope, Byron Shelly Keats Coleridge, Wordswith and Burns. The novels of Austen,. the Bronte sisters, Charles Dickens, Robert Louis Stevenson, Thomas Hardy and George Orwell. The philosophy of Locke, Berkely Hume, J S Mill, and Bertrand Russell. The music of Purcell, Handel (who spennt most of his compostional life here), Elgar, Vaughan Williams, Benjamin Britten. (And I am sure there are plenty of others who I have missed)

How many of those idiots who feel it necessary to drap a Saltire or a St George cross outside their windows even know who most of the people I have mentioned above are or even appreciate what the afoerementioned people have achieved.

No it's all a bogus appeal to the lowest common denominator of tribal instinct to enable the scoundrels who dress themselves up in the nationalist flag of whatever country be it Scotland or England without any appreciation  of the people in their countries who have achieved lasting achievements which will transcend the vagaries of the current political situation, as opposed to an appeal to the lowest common denominator of flag waving nationalism of the worst kind.

If that makes me snobbish  I don't give a monkeys.

## Sunday, 23 November 2014

### Piano Grade 1 result Pass

This is just a short post to let those lknow that I passed my Grade 1 piano exam with 110 marks. A respectable pass but nothing great. I think I'll have to postpone my booking for the Usher hall :)

My main problem is that I find it difficult to maintain a steady pulse and two hand co-ordination this is only going to get more difficult as time progresses. I am handicapped by not having a natural sense of rhythm which some people seem to have. I was never good at dancing, I don't buy the idea as some people seem to think that you either have it or you don't. I believe firmly that by training you can gradually improve. Although I do find trying to follow a metronome really tedious and boring. Obviously it's more difficult but I believe you can actually get there. I must have improved my sense of basic pulse from last time as I was able to do the hand clapping example without any problem whereas at my last resit. I was unable to do so.

I am now faced with a dilemma, as the ABRSM syllabus for grade 2 has changed but you are allowed to do the past syllabus for the next time round which would be in March. I have been studying the three pieces on and off and am reasonably confident about two of them, so I could put myself forward for the grade 2 exam but unless I get my rhythm sorted out then it would be marginal whether or not I pass. I will make the decision in the next two months or so

On another topic I want to make a few remarks about Duncan's comment to my last post that we don't know anything about the nature of dark matter or dark energy. That's not entirely true, we know their equations of state and also their ratios. Also we can use the Friedmann equations to predict the future expansion rate of the universe. In a way the situation is similar to the classical ideas of gravity, electromagnetic fields and entropy. It was never possible to get an idea of what these entities actually were however just like dark matter and dark energy their effects on other objects were able to be predicted and measured. To some extent it doesn't really matter that we don't know what dark energy or dark matter actually are because as inputs to cosmological models their effects on the universe can be calculated. Just as say knowing that the gravitational force between two bodies obeyed an inverse square law enabled planetary motions to be predicted. I would say this is more important, given the lack of experimental evidence, than a fruitless attempt to undestand the true nature given  the lack of experimental evidence as to the nature of dark matter or dark energy.

It seems to me that physics has made great strides in developing our understanding of nature works, without getting bogged down in trying to understand the actual nature of some of the important entities that it has used. I'll leave the speculation to those cleverer than me in the mean time I want to focus on the uses of physics which is more than enough to keep us busy for a long time.

## Thursday, 6 November 2014

### Grade 1 piano Resit

Hi first of all apologies for not posting for a while. I guess without the pressure of OU TMA's there is not that much to post about

Anyway today I resat my grade 1 piano exam. I felt a lot more comfortable than before and think I've done enough to pass but it won't be a great one. So how do I feel slightly ambivalent to say the least. I know on a good day I can knock off the pieces set for grade 1 no problem, but in a different environment it's not so easy. I still had problems adjusting to the feel of the piano in the church as opposed to my home one. Maybe I should ask the church if I can spend a few hours practisinng on their piano.

So I stumbled on most of the tasks I was asked to do but unlike last time I was able to recover. Is that enough to pass who knows hopefully yes but for me piano playing isn't a natural thing. I'll persist in practice and see how far I can go, until I really do hit a brick wall.

As for other stuff I have been trying to understand the cosmological revolution of the late 1990's where it was established that the current universe is

a) Accelerating

b) Appear's to consist of 70% dark energy and 30% matter of which 26% is so called dark matter and only 4% is baryonic matter

c) Flat

I hope to finish my write up of this by the start of the new year until then watch this space

Best wishes Chris

## Sunday, 24 August 2014

### Orbitals

In another round of the 'quantum wars' on the OU fora we have got round to discusssing orbitals and what they mean. It wasn't till I started thinking about it that I realised the usual picture of an electron orbiting the nucleus in an orbit of fixed radius like a mini-solar system, and that if it loses energy it 'jumps' from one to another is totally misleading to say the least. The latter view is definitely true of the Bohr model and I guess most people carry this over to their thinking  when (if) they study quantum physics further.

However it is just not correct, When you solve Schrodinger's equation for the hydrogen atom what, one ends up with for each energy level is  a 3 dimensional  probability density function which gives the probability of finding an electron in a given region. This means that the electron in a given orbital can be anywhere in principle allowed by the particular orbital (better called probability density function) so there is a small but finite probability that it could be 1 m, 10m and so on away from the nucleus. Of course it will be closer to the average of the probabiity density function.

The crucial point is however that when the electron either gains or loses energy that loss or gain in energy is fixed (quantised). However the electron does not 'jump' from one orbital to another  what happens is that the probability density function changes in accordance with the appropriate function for that energy level.

Thus the misleading picture given by the Bohr model is totally inadequate to do justice to the picture presented by the solution to Schrodinger's equation.

Matter's aren't helped by the depiction of the energy level diagrams with their pictures of arrows going from one energy level to another giving the impression that the particle is actually jumping from one energy level to another. But those 'jumps' are changes in energy not position.

Finally it is important to remember that those pictures of orbitals shown in chemistry or physics textbooks are pictures of probability density functions. The usual convention when drawing the boundary surfaces is to draw the boundary marking off the region where the electron is likely to be found 95% of the time they do not represent the fixed distance of the electron from the nucleus of the atom. 95% of the time the electron will be inside the so called 'shell' but there is also a 5% probability that it will be outside the shell.  Here are some pretty pictures of hydrogen atom probability density functions for you you to drool over.

https://search.yahoo.com/search?ei=utf-8&fr=ytff1-yff22&p=Pictures%20of%20hydrogen%20atom%20orbitals%20&type=

And here is the first experimental observation of the probability density function of the hydrogen atom

http://io9.com/the-first-image-ever-of-a-hydrogen-atoms-orbital-struc-509684901

## Monday, 4 August 2014

### Yet More Quantum madness the so called Cheshire cat

For those like me, who despair at the increasing tendency to the irrationality of the world, even in science. The recently published claim that it has been possible to separate out the spin component of a quantum object from it's spatial component can only cause one to wonder whether the world has gone mad.

For those who aren't aware this BBC post is typical of the hype

http://www.bbc.co.uk/news/science-environment-28543990

and the original paper is here

http://www.nature.com/ncomms/2014/140729/ncomms5492/full/ncomms5492.html

So the claim at first appears to be  by a special arrangement of beam splitters it is possible to disembody a particles spin from it's location. So that in one path only the location of the particle can be determined on another part it's magnetic moment which seems to have magically been disentangled from the particle. A literal interpretation of this is just not credible.

First of all spin has no spatial properties so it can't move anywhere. Spin is a vector which is allowed quantum mechanically to take a number of fixed directions usually up or down. it is a property of a quantum object. So if the authors of the paper are claiming what the hype says they are then that would require a rewriting of the whole of quantum mechanics of spin and as far as I can tell the authors are not seeking to challenge the standard quantum mechanical concept of spin.

So what exactly have the authors shown? The key to interpreting the experiment is the concept of quantum superposition there are essentially two interpretations

The first beloved of the popular literature, and it would seem journalists who want to peddle the alleged mysterious aspects of quantum mechanics, is called the ontic (short for ontological)  interpretation.

The ontic view is that quantum superpositions are real namely that a cat really is in limbo between being alive or dead or in the case of interferometer experiments each particle really does travel down both paths simultaneously or in the two slit experiment passes through both slits simultaneously.

The solution to Schrodinger's equation is a real wave and something physical (even though it doesn't actually affect anything (for example exert a force on a particle as an electric fiield does), For an N  body problem, it is some sort of field in 3N + 1 configuration space as opposed to our 3+1 dimensional space time. Also when a measurement is made the solution to Schrodinger's eqaution collapses into one of the states. This is usually  called wave-packet collapse but it really should be called the solution to Schrodinger's equation collapse.

On the ontic view, it is only by measurement that a system jumps from it's state of limbo of possible states into a definite state. Extrapolating (slightly unfairly I admit) this means the moon really isn't there when one looks at it. It would seem from the language used by the authors talking of the wavefunction travelling down both paths simultaneously they subscribe to the ontic view.  On this view in this experiment, it really does seem that the spin part of a qauntum objects solution to Schrodinger's equation can be detached from it's spatial part. But just what disembodied spin means hasn't really been explained and if it really was disembodied then all the text books on quantum mechanics would have to be rewritten.

Conversely from an epistemic (statistical) point of view, the solution to Schrodinger's eqaution is a probability amplitude who's modulus squared gives when suitably normalised gives rise to a probability density function. The Born interpretation, on this view the superposition of states represents the lack of knowledge of an observer about a given situation and nothing physical. As the solution to Schrodinger's equation is primarily a statistical quantity, applying it to work out the behaviour of one particle is just as meaningful, as trying to predict the roll of a single dice or a spin of a roulette wheel. When the solution to Schrodinger's equation 'collapses' all that happens is that one of the possibilities is realised. Albeit in order to get the correct probabilities for a given situation one has to use complex numbers which accounts (mathematically at least) for all the interference effects associated with many quantum phenomenon.

I have discussed how this works for two state systems in previous posts

http://chrisfmathsphysicsmusic.blogspot.co.uk/search?q=Two+state+

Where I also point out that the Dirac notation can also be applied to classical systems. But in order to explain many quantum phenomenon, one has to extend our notion of probability to include complex numbers.

On this epistemic\statistical view then when a beam of particles passes through a beam splitter, a single particle, does not travel through both paths simultaneously, but the solution to Schrodinger's equation represents the probability amplitude that it will traverse one path or the other. On this view in the Cheshire Cat experiment, if the neutron passes one path it's location, will be measured on the other it's magnetic moment will be measured. There is no disembodiment  of the spin part of the neutron's solution to Schrodinger's equation  from it's spatial part. That realtively prosaic account of course won't attract attention and so would be ignored by most people.

The epistemic view and the ontic view, as they are interpreting the same mathematical object, namely the Solution to Schrodinger's equation cannot be empirically distinguished from each other. However given the more modest claims of the epistemic view vis a vis our notions of quantum wierdness I know which one I prefer. All the epistemic (statistical view) is asking is that we extend our notions of probability to include complex numbers. In contrast the ontic view would claim that wavepacket collapse is real, that spin's can be dismbodied from their constituent particles and that act's of measurement do create reality. Of course some people would find the epistemic\statistical view  unsatisfactory, accusations of instrumentalism etc but if there are no hidden variables then there can be nothing behind the statistics.

I really do have to ask why is there such a hunger for irrational explanations of quantum phenomenon. I really do despair some times.

## Tuesday, 17 June 2014

### Grade 1 piano exam result

Well I just failed got 94 out of 150

When it came to the exam I just freaked out

Whilst I don't want to make excuses the fact that the piano was an actual piano as opposed to a digital one meant it was a totally different experience to my normal clavinova. And even in the warm up room there was only a digital piano. So despite having gone through the routine 2 or 3 times in the warm up room I was totally unprepared and it was a downward spiral I fluffed a note on the first scale that made me tense and nervous then I fluffed the first piece and the second and so on. It was about the most ghastly ten minutes I've spent in a long time

Ok so I became dis-orientated but at least I know what it is to expect and I would hope next time around I'll do much better

In the mean time I'm plowing my own furrow with the help of stuff on the internet

https://www.webpianoteacher.com/

His approach is amazing he writes out the notes on a white board and copying them onto  a bit of paper definitely helps in the initial stages of learning a pieve. Going to try and learn the first movement of the moonlight sonataover the next few weeks,  following his approach here is the first lesson (which is free)

For budding pianists his site is definitely the best

## Monday, 2 June 2014

### Grade 1 Piano Exam

Well the culmination of almost two years since I started getting an interest in learning the piano has arrived I have my grade 1 piano exam tomorrow. I feel reasonably confident I'll pass but I'm not sure I will get to either merit 130/150 or distinction 140/150

It's kind of weird really, to get an idea of what I'll be doing here is a link to the ABRSM site which shows the sort of thing I'll be asked to do

I hope the examiner is as kind as the examiner in the video

Anyway I'll let you know how I get on

For interest the pieces I've chosen are

Fugue No 4 Alec Rowley

Sailor's Song Felix Swinstead

Thursday R R Bennett

and if you do a serch for grade 1 piano pieces on you tube you should be able to hear what they sound like

Good luck to anyone taking ABRSM exams tomorrow whatever your instrument.

## Thursday, 22 May 2014

### dangers of OU fora

Hi this is more of  a warning to myself and others about the dangers of the OU fora. I have effectively  wasted  a large amount of mine and other peoples time getting involved in a long running dispute which has been continuing for about 2 years with my bete noir.  Those who read the fora especially the philosophy ones will have been the victim of this dispute. It's not important what the actual details are but safe to say my sparring partner is one of those people who evades the issue, keeps twisting and turning and so makes it difficult to answer his points.

Anyway as I say I have wasted so much time getting sucked in to the so called debate. that I really don't want to discuss it further. I will do my best to ignore this person and I want to apologise to any one who got sucked into the debate

## Monday, 28 April 2014

### Do Virtual particles exist

Well been having a ding dong with my bete noir on the physics forums about whether or not virtual particles exist. In my opinion they don't but unfortunately the popular physics literature abounds with such ideas and so the myth is generated that they actually do exist.

A really good overview of why they can't really be said to exist is given here

http://www.mat.univie.ac.at/~neum/physfaq/topics/virtual

I'll just summarise the salient points

What do we mean by a virtual particle ? Let's start by describing what they are not they are not tempory resonances detected at places like CERN those are real particles.

A virtual particle is one which is said to be exchanged during a particle interaction, the story goes because of the Uncertainty principle applied to energy and time.

$$dE dT >= \frac{h}{2\pi}$$

In a particle interaction there is the possibility of a temporal violation of the conservation of energy and so a particle can be formed which then gets immediately absorbed by the other particle.

The classic example is QED where electrons are said to exchange a virtual photon between them when they scatter off each other. And because of the uncertainty principle a positron can be seen equivalent to an electron moving backwards in time. Those phrases should be enough to raise the suspicions of any one who seeks a rational basis for physics. It's all a bit of fudge really.

The whole idea of virtual particle exchange particles is an artefact of the use of Feynman diagrams. A Feynman diagram is a term in a perturbation series expansion because we have no other tool to calculate
with. Essentially in quantum field theory one has a set of propagaters (Green Functions) representing the free particles and  a set of vertices to represent the interaction between them..  A Feynaman diagram is essentially a graphical representation of a complicated mathematical expression representing the interaction.

The simplest are the Tree diagrams essentially an H combined by putting two vertices together. This gives a second order contribution to the scattering process the external legs of the H represent the electron or other particle and the internal line represents the 'exchanged photon' But the internal line can also split to give more complicated diagrams involving loops such as ----O--- or even ----O-----O---- that would be the virtual photon dissociating into an electron and a positron and recombining to form a photon and so forth.

The total contribution to a Feynman diagram expansion is a sum over all possible diagrams the contribution to which decreases as the number of loops increases. Whilst the Feynman diagram expansion is intuitive it should be stressed we are not talking about actual processes. If we were then the infinite series would have to be summed up. As a literal interpretation that would mean that in each particle interaction there would be an infinite number of processes that occur and so the interaction could just not happen.

So a virtual particle is simply an internal line in a Feynman diagram nothing more, it is an artefact of the need to use perturbation theory and so cannot be real. Yes electrons and photons interact with each other and yes the use of Feynman diagrams gives rise to some of the most accurate results in physics for at least QED anyway. But I do find it worrying that what is essentially a metaphor is taken literally, a bit like fundamentalist religion I guess. Hopefully sooner rather than later someone will find a way to solve Quantum Field theory non-perturbatively and the Feynman picture will vanish until that day however we are stuck with it.

## Wednesday, 2 April 2014

### ABRSM Grade 5 Theory result

Well just got my result for  the ABRSM grade 5 theory exam equates to 82% which is a merit, feeling reasonably chuffed, put myself forward for grade 1 piano in June doubt whether I'll get such a good result still 2 months to focus.

More later

## Sunday, 30 March 2014

### Saylor ECON 101 Microeconomics

As my followers will know I have embarked on the excellent (and free !!) courses from Saylor.

http://www.saylor.org/

I'm currently studying Microeconomics. 101

http://www.saylor.org/courses/econ101/

as I want to expand my limited knowledge about this subject. I've just finished the first three units

The Saylor course\provides a free pdf course book specially commisioned from the course which you can download and also links to various on line videos such as those provided by the Kahn academy  and a few others. The aim of Saylor courses is to utilise  on line resources to provide the equivalent of a college or university education in the subject area at the appropriate level and also to provide some form of assessment usually a two hour final exam. These are slowly being recognised by outside institutions and this trend can only grow.

Here is a review of the first three units

1) On production possibility curves and their implication for trade. A production possibility curve represents the total amount of goods or time one can spend on a given activity. Suppose for example I can spend 20 hours a week studying and I'm studying either music or maths. I can spend all the time studying maths or all the time studying music. However if I do so I wont progress on maths if I focus solely on music and vice-versa. Suppose I have an exam in both subjects coming up and I decide that an hour studying music will get me 2% extra marks whilst an hour studying maths (as I'm quite good at that already) will only get me 1% extra marks and suppose I can at present average 50% for music and 60% for a maths exam then I have to do a trade off. Clearly I have to spend more time on music than maths. to bump up the marks. There is a greater opportunity cost in maths  as for each hour I spend studying maths I give up 2 marks in the music exam whilst for each hour I spend studying maths I give up only 1% maths.
The study of this leads to some quite interesting results in terms of trade (due to Ricardo) namely that although one country may have an absolute advantage over another in producing two or more goods both countries can expand the amount of goods by specialisation in one form of good. .

2)  This covered the subject of Supply and Demand and what causes it's shift. Also more contentiously the arguments for abandoning rent controls, or a  minimum wage or taxation are given. On the neo-classical model, (Adam Smith's free hand) the market is generated by each person selfishly pursuing his or own self interests eventually an equilibrium price will emerge where the amount demanded by consumers is equal to the amount suppliers are willing to produce.  In the usual and fairly simplistic way  as prices rise demand falls and as prices rise supply increases and the equilibrium price is at the intersection of the two curves normally represented by two straight lines.

Setting a floor allegedly interferes with this equilibrium  and causes a shortage in the supply or at least so the argument goes. However this is based on a number of dubious assertions. Namely that there is a stable equilibrium price something impossible when more than one good is considered. It ignores the time delay inherent in a change in price and it would seem to justify a fairly obnoxious right wing agenda.
It's a bit worrying that right wing institutions such as the institute for fiscal studies, have based what is a totally unfair set of policies on a fairly naive view of markets. Fortunately there is an antidote to all this given in this wonderful book  by Stephen Keen

http://www.amazon.com/Debunking-Economics-Revised-Expanded-Dethroned/dp/1848139926

and for a detailed critique of the current state of economic theory it can't be bettered. Although I would prefer a more mathematical account. Stephen Keen was one of the few people to predict the current recession by modelling the economy using ideas from chaos theory . I hope to understand his models a lot better in the coming years watch this space.

Unit 3 continues the effects of supply and demand by studyiong what is called consumer and producer surplus. This is essentially the total area made between the supply and demand curves  and the equilibrium point and the price axis (the y axis). If government taxes goods then the supply curve shifts upwards and the area decreases. Also so it is claimed a band is taken out of the area which is government revenue. But this leads to another area called 'dead weight loss'. The terminology is really quite perjorative first of all we are not just consumers and producers. Secondly all this argument ignores the benefits of taxation in terms of provision of public services, health, public transport etc. It is claimed that as these are 'free' and do not respect private rights these will necessarily be inferior to anything the private sector can produce. Nothing is mentioned of the fact that the private sector rips off people as their concern is profit. But in more general terms the picture of humanity depicted by neo-classical economists  is really quite depressing. Yes we all like a good bargain, but do we have the time to seek out the bargain. Even if you do get a bargain you might not get the quality of goods offered is not likely to be optimum or it might cause you inconvenience. For example I regularly buy books at bargain price from Amazon but about 1 times in 10 I never receive the goods as the company does not use regular mail service but some fly by night courier company who seem incapable of putting their depots in a reasonable place accessible to people after work. I also note that for a government which is allegedly based on free-market principles they have not failed to increase taxes on goods, Perhaps George Osborne should do a course similar to economics 101.

I may have given the impression that I'm not enjoying this course that is wrong. I'm actually enjoying finding out where the arguments that are regularly given in the press and right wing media come from and I always have Stephen Keen to help me take the wilder claims of neo-classical economics with  a pinch of salt. It is worrying that what is essentially an ideology is being presented as scientific fact. The coursre as it stands isn't that mathematical but more meatier courses await.

As far as assessment goes this isn't quite ideal you are referred to tests on a micro-economics book published by Pearson and sometimes this covers topics not covered yet. There will be a final exam which you can take when you feel you are ready. You have to get 70% or over and then you get a certificate,but you can resit as many times as you like with a two week gap. As the course is free (in contradiction to the principles that would seem to underly the ideology of neo-classical economics )  then one can hardly complain and I thank Saylor for saving me £750 and rising in OU fees. I really would recommend people to take up Saylor courses

Next post I'll review the other Saylor course I'm doing namely calculus of a single variable.

Bye for now.

## Wednesday, 5 March 2014

### ABRSM grade 5 theory exam post match analysis

Grade 5 Theory Post match analysis

Well today I sat my first ABRSM theory exam. This was grade 5 theory the questions tend to form a fairly set pattern of questions with a few minor variations

Question 1 first part is usually a question on rhythm either as in the case today putting bar lines in various tricky combinations of quavers, semiquavers and hemisemiquavers or alternatively (slightly harder) deducing the time signature as it varies across the melody. Think I got this correct

Question 1 second part gives a passsage and you have to ask various questions about identifying chords quite often they throw a wobbly in that they will sneak a treble clef in the bass line or vice versa. This question seeemed relatively straightforward so again think I got most of this correct.

Question 2 can either be a question identifying 5 intervals or rewriting a piece in open score in short form or vice versa. The latter although straightforward provided you ensure that the tenor part in open score is usually wrtten an octave higher that it would sound is really tedious fortunately the question was
of the former type and provided you are careful making sure that you take into account the key signature can be reduced to modulo 12 arithmetic something I'll expand on in another post.

Question 3 is usually a series of questions on a piece of music identifying various terms such as Adagio or more obscure one's such as Zart (German for play it tenderly yeah right sounds more like fart :) ) still . Fortunately the terms weren't that difficult but I interpreted sforzando as play the note suddenly loud as opposed to forced. So probably lost two easy marks there.

Question 4 is usually a transpositon which can be quite tricky still following my fail safe method outlined a few posts ago I feel I got this one correct . We had to transpose a piece in F major up a major second. Once you realise that the new key is G major and that Eb transposes to F natural whilst E transposes up to F# but the key signature of G major takes this into account so you don't need to put the acccidental in then this is straightforward but tedious as they say in the books. I tend to leave this question till second last

Question 5 is a question on various scales so you are given a starting note and you had to write the ascending harmonic or melodic minor on that note. This time the note was the lower F on a bass clef it's relative major is Ab and it was the ascending harmonic minor that you had to write. This is the same as the notes of Ab major but the leading note in this case Gb is raised a semitone to G natural. The second part asked us to identify a key with 5 sharps (B major) and write a descending scale starting from B easy once you have identified the correct key. So again I think I got most of this out

Question 6 you had to complete a melody given a few starting notes. Normally you have to make sure you reach the dominant note at the end of the first phrase and find a way back to the tonic note in this case D. In between I tend to use a logical chord progession either IV or VI chords unfortunately my melodies tend on the whole to be a bit boring essentially ascending or descending scales with an occasional leap. Still if the melody is logical harmonically then I can't see the problem. Also you have to add dynamics and tempo directions. Who knows how much I got say 10 out of 15

Question 7 the one I find the easiest and the one I normally do first namely identify appropriate chords to fit a melody. You only have 4 to choose from namely 1, II, IV and V and usually this is quite straightforward once you have identified the key of the piece.

So overall take off a few marks for untidyness, and the melody I feel I'm reasonably confident of getting a merit ie > 80 % maybe distinction but one can never realise if you have made a silly mistake fingers crossed I haven't but this is very much a subjective view point so who knows.

Do I feel that doing grade 5 theory is worth it after having studied music at allegedly degree level via the open university. You betcha the grade 5 exams are good at checking you know the basics and I feel a lot more confident about how scales are constructed and how to identify intervals. Yes  the OU is conceptually more advanced than grade 5 but it didn't really reinforce the basics. So they are complementary and I feel the better for it.

Bring on grade 6 (by the end of the year hopefully)

## Monday, 17 February 2014

### Hello Saylor Bye Bye OU

A week ago searching for alternatives to the Open University courses on logic a search led to this wonderful institution

http://www.saylor.org/

This offers a  range of Free Online courses which are equivalent to courses studied at American Universities. Unlike coursera or Future learn which are examples of MOCC's the courses available can be accessed at anytime. Also they can be put together to earn the equivalent of a full degree provided you stay the course.

What is really impressive are the maths courses

http://www.saylor.org/majors/mathematics/

Having looked at the course content I think it's fair to say that they are at least equivalent to the OU and some such Abstract Algebra II and Real Analysis II go further than the OU do.

I have always wanted to understand politics and economics better and so am aiming to do at least the core sections in these disciplines.

http://www.saylor.org/majors/economics/

I've registered for microeconomics and also calculus of a single variable I which has a really good explanation of the epsilon delta definition of continuity. The great thing is that you can take your time there is no scrambling to complete a TMA Anyway hopefully I can zip through a lot of the maths courses in the next two years I'maiming for 1 module in maths every three months or so.

The great thing is that all this is free and the courses are being recognised as equivalent to having studied equivalent to that in an American universities. It can only be a matter of time before this becomes more and more widespread. When the OU is becoming more and more inflexible and restricted in the options they offer and the prices they charge unless it get's it act together institutions like Saylor will rightly supersede them.

As a bit of light relief I'm also doing the Future learn course on the Higg's boson

https://www.futurelearn.com/courses/higg

The lectures seem a bit more advanced than the assessment. the second lecture on the derivation of conservation laws such as momentum from imposing translational invariance on Newton's law is really neat. However the assessment is confined to a few multiple choice questions on general principles.

Anyway it's hello Saylor the way to go.

## Sunday, 19 January 2014

### ABRSM Grade 5 Theory Transposition by Numbers

One of the most difficult parts of the grade 5 theory exam is to get the intervals correct OK we can probably tell that it's a fifth but is it a perfect fifth or a diminished fifth or what?  Similarly with transposition again yes transposing a piece up or down by a minor 3rd say means that the notes are displaced up or down a line or space but what about the accidentals, even worse what if it asks for a key signature change. A while ago when I was first studying music with the OU I hit on the idea that a lot of the confusion could be clarified by using numbers instead of letters. This works really well for intervals and transposition

First number the notes of the Chromatic scale starting with middle C as zero

So we have the table

Db     Eb        Gb     Ab     Bb
C C# D D# E F F# G G# A A# B

0  1   2   3   4 5 6    7  8   9 10 11

Each number is the number of semitones above middle C that the corresponding note is.

Then for transposition for grade 5 the main ones are

Up or down a major 2nd (2 semitones) simply add or subract 2 modulo 12 to the numbers then use the first line to work out the notes

Up or down a minor 3rd (3 semitones) simply add or subtract 3 modulo 12 to the numbers then use the first line to work out the notes

Finally up or down a perfect 5th (7 semitones)

So for example suppose we want to transpose a given melody down a perfect 5th we subtract 7 then add
12 if the new number is less than zero or subtract 12 if the new number is greater than 12.

Db     Eb        Gb      Ab     Bb
C C# D D# E F F# G G# A A# B

0  1    2  3   4 5 6    7   8  9 10  11

Performing the arithmetic gives for C 0 -> -7 then add 12 to get 5 (you only have to do this once)
then just start from 5 to give

Db     Eb       Gb      Ab      Bb
C C# D D# E F F# G G# A A# B

0 1  2 3  4  5  6   7   8  9 10 11
5 6  7 8  9 10 11 0   1  2 3  4

So that we see eg that C goes down to F (5) or Ab goes to D (2) and so forth.

So writing this table out and doing the appropriate arithmetic will give you a fail safe method of
transposing accurately especially for those tricky accidentals.

Of course you have to remember if the original melody has a given key signature to take into account
the key notes. Thus for Bb major the accidentals are Bb and Eb so every time you see a B or an E remember
these are Bb and Eb

This also works for key signature changes so suppose I start in Eb and I want to go up a major second
Eb is 3 according to the table add 2 to give me 5 the key signature is now that for F major ie simply with Bb

In the next post I will show how a similar technique can be used for intervals

## Tuesday, 14 January 2014

### On line piano tuition for Grade 1 and above

Well tomorrow I take my first official piano lesson with the aim
of doing grade 1 by June. I have been practicing on and off
for about 18 months now and I can't say it has been smooth sailing
to say the least. Inded I felt in a bit of a rut as I was playing
the Grade 1 pieces badly and never really completing them.

However over Christmas I found these amazing
on line videos by Alison Sparrow who has some really useful tips

Plus being very attractive to look at. Could be the Nigella
Lawson of piano and violin teaching.

Anyway her tip on practicing really helped me get to grips with
three of the Grade 1 pieces. When you try and set up a practice
session the temptation is to try to and play the piece as
a whole with the inevitable stumbling. Alison's method for which
I cannot thank her enough is to break it down.

At grade 1 the pieces are usually 16 bars what Alison suggests
is play the first 4 bar phrase 4 times. Then play the second
4 bar phrase 4 times then play the first and second phrases
together 4 times. Then move onto the third phrase play that
4 times, then the 4th phrase 4 times. Then put the 3rd and fourth
phrases together 4 times. Then finally play the piece 4 times
repeat this for about 2 weeks and you should have the piece
under your belt. Anyway it certainly seems to have helped me.

This is so obvious when pointed out to you but not at all obvious
when you are practicing on your own.

Another good website I have found is that of Shawn Cheeks
especially his 'boot camp' sight reading course. Shawn points
out that most musicians rely on their ear and memory. What
this misses is actually engaging with the music as it is written
as his career progressed he found it more and more difficult to
tackle the more difficult pieces. So he decided to go back to basics
and really learn the music. Have a look at his introduction
on You tube. Again I have been following his boot camp and
can see the improvement. Certainly spelling out the notes whilst
learning a new piece is really helpful

His philosophy is outlined here

and you can follow the links to the other parts.

I've also put myself forward for grade 5 music theory this march

What i haven't done is any number theory or logic. I have
given myself 4 days  this weekend to complete the assignment
if i don't then I will probably quit I can't really say I'm
enjoying the course OK I haven't really put much effort into
learning it. Right now though my musical interests are
dominanting if I can achieve grade 5 and 6 theory and grade
1 and 2 piano by the end of the year and get back into general
relativity then I wont feel so bad about abandoning M381.

I guess the non stop deadline of assignments exams, followed
by going straight back to other assignments over the past two
yeara has taken it's toll there is a small chance I'll continue
but I can't see it.

## Friday, 3 January 2014

### Instrumentalism or Why we should Shut up and calculate.

Prior to the festive season, I got myself in one of my perenial debates on the physics forum about the meaning or not of quantum mechanics. My main protaganist will be well known to those who follow the debates. He claims to endorse the Copenhagen Interpretation but also denies that he is an instrumentalist. A somewhat inconsistent opinion in my view. Anyone it’s not my job to help him see the contradictions in his position.

I do want to make a defence of instrumentalism however, that is some what missed by self styled philosophers of physics, but is in fact the current practice of most physicists.

OK what is instrumentalism ? essentially it is the view that the main aim of science is to provide empirically adequate models of nature without bothering to much about how the underlying concepts used to make the predictions correspond to reality.

What do I mean by empirically adequate, it is essentiallly the condition that the predictions of the theory when instantiated in a concrete model give reasonable agreement with experiment. For the quantative sciences such as physics this makes the theory testable or at least a given model of a given phenomenon predicitable. If the model does not give reasonable agreement with experiment then one can try and make the model more accurate by including more terms in the model or trying another approach.

It is important to make a distinction between theories and models this distinction is often blurred. A theory is a set of general principles in physics, there are about 8 sets of general principles which have been discovered

Classical physics

Newton’s Laws of motion.
The macroscopic laws of thermodynamics.
Maxwell’s equations.

Modem Physics

Special relativity.
General relativiry.
Non relativistic quantum mechanics.
Statistical physics.
Quantum field theory.

Note I do not include speculative theories such as superstrings because so far there is not one concrete prediction that has come out of it. At this stage it is ‘Not even wrong’

In order to describe natural phenomenon, one takes one of the above set of principles appropriate to the phenomenon in question. Then with the aid of mathematics and empirical information, such as the masses of particles involved sets up the appropriate equations and solves them either analytically or for complicated problems one has to resort to computers.

So for example to model the properties of stars as they collapse, one needs a combination of Statistical physics and General relativity along with an appropriate equation of state. To model planetary motion one would use either Newton’s laws of motion or for say mercury one has to resort to General relativity. A simple model would neglect the interactions between the planets a more complicated model would include these. Deciding on what approximations are appropriate is a necessary skill of a good physicist.

As we apply the above general principles to more and more phenomenon we gradually begin to understand how nature works and whats more with the aid of mathematics can predict how systems will behave. We can predict the energy levels of a molecule or solid. We can predict the orbits of planets, we can predict the decay rates or scattering cross sections of particles. We can even predict the rate of expansion of the universe from it’s early stages by a combination of Einstein’s general theory of relativity. relativistic statistical physics and a knowledge of the basic particles involved.

All of this is so obvious to a practicing physicist, but so called self styled philosophers of science aren’t happy with this. For them the aim of science is not to make concrete predictions of phenomenon but to describe reality as it is initself. They want to concentrate on the meaning of the general principles but therein lies a problem because some of the concepts used can be quite obscure.

For example in classical physics the nature of gravitation remained obscure all one could say about it was that it obeyed an inverse square law. In thermodynamics the concept of entropy also remained obscure although it had a perfectly precise meaning in terms of a measure of heat transfer . Also whilst Maxwell’s equations involved electrical and magetic fields their real nature remained obscure and all sorts of weird and wonderful ideas about the ‘real nature’ of an electric field involving vortices and eddy currents in the Aether were prevalent at the time. However more concrete these models appeared rather than Maxwell’s equations they didn’t really add much to the understanding of electromagnetism and these were ultimately shown to be wrong as the Aether was proven not to exist. The situation in intepreting the nature of an electric field so exasperated Helmholtz that when asked what Maxwell’s theory was he replied that Maxwell’s theory was Maxwell’s equations. Quite similar to the attitude which I favour of ‘Shut up and calculate’ when it comes to interpreting quantum mechanics.

My protaganist in the OU debates on the fora doesn’t like the above view for him and many others like him such as Karl Popper this reduces physics to engineering (as if that were  a bad thing). Well I’ve got news for him and Karl Popper and other anti-instrumentalists most of what is published in physics journals today is an application of one of the 8 above sets of general principles to model a given phenomenon. Indeed it is only by continuing the process of detailed modelling that we understand how nature works. If that’s ‘just’ engineering so what ?

The rest arguing about the nature of gravitation, the wave function, whether or not particles are real or waves are, really doesn’t move us forward and to some extent it doesn’t matter, as I can still use the general principles coupled with empirical information to make concrete predictions about natural phenomenon. What other means of understanding nature do we have ? It is only by shutting up and calculating that we will get any where. The attitude prevalent amongst certain people that one should always be looking for more new general principles is misguided, the need for new general principles will be forced upon us when we are able to probe nature at more and more higher energies or shorter length scales.. Until then we should all shut up and calculate.