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. 

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)
     

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.
 

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    

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

http://www.youtube.com/user/theonlinepianotutor

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


http://www.youtube.com/watch?v=u3V-0iS8JMY

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.

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.

Seasons Greetings and Plans for the New Year

Well another year has passed and it’s that time of the year when one starts to think about the future. This year promises to be a busy one although I shall be reducing my OU commitments to at the most one 60 point course per year.

I’m currently doing the Number Theory and logic course and completion of that will conclude my second open degree. If I get grade 2 it will put me on line for a 2:1. I then want a break of at least a year from OU work.

The courses will consist of

Level 1 MST121      Introducing Mathematics                      Pass       

Leve 2 MST221      Exploring Mathematics                            Distinction
            M208          Pure Maths                                                 Grade 2
           A208          Philosophy and the Human Condition        Distinction
           A224          Music                                                             Grade 3

Level 3    M338         Topology                                                    Grade 4
             MST324     Waves Diffusion etc                                     Grade 3
             SM358       Quantum Mechanics                                     Grade 2

Then M381 number theory and logic

The only thing that would persuade me to change my mind is if A303 Philosophy of the Mind gets a reprieve and is presented next year. I wont know till about March. I could replace MST324 and M338 with it and would hopefully get a better grade we’ll see.

Not that I wont be busy I want to concentrate on music and my own physics and maths studies for a while. I intend to finally get a piano tutor with the aim of doing grade 1 piano in June and possibly Grade 2 by the end of the year. Also to practice the theory doing grade 5 and 6 theory this year alongside the OCA composition courses

http://www.oca-uk.com/subjects/music.html

I like the idea that eventually I’ll be able to compose a symphony (construct is probably a more accurate term). As I said before A224 is fine for an overview, but it is short on hammering the basics. grade 5 theory whilst quite simple harmonically is quite demanding in terms of getting transposition, the names of the keys and intervals at your finger tips. All necessary pre-requisites for a budding composer. One of the most reliable methods of workling out intervals and transpositon is to use modulo aritthmetic which I will expand on in another post

I also want to get on with my physics I left hanging in the air about 18 months ago the derivation of the Friedmann equations which govern the expansion of the universe from General relativitry and I’m taking the current break as an opportunity to get back into it. Any calculatiion in general relativity, even the most simplest such as those for the expansion of the universe or the Schwarzschild metric involves pages and pages of tedious algebra and it nearly broke my heart round about June of last year. Still having done the spade work I can now get on to the physics, watch this space.

Also I need to crack on with the second part of number theory and logic the computablity part of which awaits me. Given Duncan’s and Daniel’s experiences of it I’m not looking forward to it. Still as it is an important part of maths then it is necessary.

I’ll be in two minds whether to continue with the Open University after June. Part of me wants to do the Maths MSc, the new third level course in music and philosophy and the new pure maths course. The other part wants to concentrate on my maths physics and music. Finish the big bang calculation, then get up to speed with modern cosmology, do the three Peskin and Schroeder research projects, understand the functional analysis formulation of quantum mechanics and also the Hawking and Penrose singularity theorems. I’m in my mid fifties and if I want to do all that and get to grade 8 piano and compose a symphony or two before I die then time is ticking on.

Anyway seasons greetings to you all and I hope 2014 brings you nearer to your goals.

Best wishes Chris