Monday, 6 February 2017

Hard Sudoku

Saturday, 4 February 2017 and the Guardian reports how the EU leadership criticise the US president for his ‘lack of respect’. Earlier this week Jeremy Corbyn had placed a ‘3-line whip’ on Labour MPs to support the 2nd reading of the European Union (Notification of Withdrawal) Bill. Quite a number defied the whip but not enough. Typically only Ken Clarke from the Tory side voted against.

It is sad that so many of the UK’s MPs have forgotten that they were voted into Parliament to act in accordance with the views they presented at the General Election 2015. Of course they are entitled to change their mind, but they must be convinced of the rationale for changing it. I wonder whether they are following what they believe to be the voter arithmetic rather than being persuaded by the argument. If that is the case, they have failed fundamentally in their duty as MPs.

But enough of all that. Hard Sudoku is what this blog is about. I tried the Guardian Sudoku puzzle (No. 3663) and recorded my progress. This record uses the methodology developed in MS Excel about 10 years ago. The methodology is quite weird and long winded but, in this context, it is useful for explaining how and why I got stuck. I describe below the argument I employed for getting unstuck.

I had got as far as here using conventional arguments and methods. Assuming no mistakes in recording, this would represent a valid solution thus far. 

The record shows that I had reviewed all the unsolved positions in the puzzle without making any further progress. This also covered the examination of individual Sudoku Nos. and their relative positions in each of the 3 dimensions of the puzzle. There were only four numbers left (1, 2, 6 and 8) and the reasons for not making progress bears some examination.

Top 3 Rows
Middle 3 Rows
Bottom 3 Rows
Left 3 Columns
Middle 3 Columns
Right 3 Columns
Id 1
No positions fixed
All positions fixed
Only 1 position fixed
2 positions fixed?
All positions fixed
Only 1 position fixed
Id 2
No positions fixed
Only 1 position fixed
All positions fixed
2 positions fixed?
Only 1 position fixed
All positions fixed
Id 6
No positions fixed
Only 1 position fixed
Only 1 position fixed
Only 1 position fixed
Only 1 position fixed
No positions fixed
Id 8
Only 1 position fixed
No positions fixed
2 positions fixed?
2 positions fixed?
No positions fixed
Only 1 position fixed

Both Id’s 1 & 2 have a combination groups of three such that one group is solved completely and at least one other group where two positions are known, but not the third. Unfortunately, the information in the opposing dimension does not help us limit the position of the 3rd ID. For ID 6, there is altogether too little information to make further progress.

ID 8 has 2 groups of three where the location of two of the elements is known. At first glance, the unsolved positions in the first column at rows 4 and 5 look the most promising. After all the sub-grid at the bottom left hand corner is solved completely and the sub-grid immediately above it has only these two elements unsolved. Nevertheless, no amount of examination has revealed a logically provable determination as to which cell should contain which ID.

I’m left with considering the position of ID 8 in the bottom 3 rows of the puzzle. At first glance this looks considerably less promising than the column 1 vacancies discussed above, especially since there are 3 unsolved ID positions for row 9 (see the values highlighted in green below) rather than the just two for column 1. However, in my solution methodology, I highlight cells where the possible solutions is limited to 1 of 2 IDs (see the cells circled in red).

The information available to us is therefore is
  • ·         The location of ID 8 is known to be row 8 in for the bottom left sub-group and in row 7 for the bottom right sub-group, thus ID 8 must appear in one of the 3 cells in row 9 of the bottom middle sub-group. The right most cell of this sub-group row 9 has already been solved.
  • ·         There are 3 unallocated cells in row 9 and 3 unallocated IDs.
  • ·         But column 4 of the puzzle has two cells (named 2_43 and 8_48 in my nomenclature) whose ID values are limited 1 or 6. Logically, if these two values must appear in the two named cells, then they cannot appear anywhere else.

I conclude therefore the cell named 8_49 in row 9 must contain the ID value 8, since that is the ID value left for this column.

This is something of a tortuous argument but it seems to work. Any thoughts?

Sunday, 13 November 2016

Early Musical Influences

Following on from bringing my grandchildren to their firstlive concert, I began to wonder what the impact of my own early musical experiences had been.

Clearly my father’s piano playing and the church played an important part (see Getting into Music). The question here is “to what extent have I guided my own musical taste?” as opposed to having it preordained by early experiences.

My teenage years coincided with the ‘Swinging 60's’. The Beatles, The Rolling Stones and the Kinks permeated my young mind. Some of those influences were surprisingly sophisticated, but by the middle of the 70's I had lost all interest in popular music.

An opposing influence were the long playing records that Cla brought home from the Hendon Record Library. The emphasis was on song, mainly Schubert, but there were other important highlights (e.g. Haydn’s arrangement of “My Mother Bids me Bind my Hair” and Benjamin Britten’s folksong arrangements). Kathleen Ferrier and Irmgard Seefried figured large in this melee.

The records also had an impact on the piano music that Cla bought. These included both Schubert’s song cycles “Die schöne Müllerin” and “Winterreise” as well as the group known as Schwanengesang. There was also a large volume of Schubert’s more popular songs. These represented a wide source of exploration for me looking at the piano accompaniments. (There was a universal hatred of me attempting to sing along with myself.)

My tastes in instrumental music were also influenced heavily by Cla’s acquisitions from the Library. Once again, these were dominated by Schubert the piano sonatas, pieces for 4 hands, the myriad of impromtus and moments musicaux,  the ‘Trout’ quintet (including a wonderful cover cartoon of the string players fishing from a grand piano), the two piano trios Op 99 & 100 and the extra ordinary string quintet (Stern, Schneider, Katims, Casals, Tortelier). The emphasis on chamber music was certainly led by Cla, but I was also introduced to the “Great” C major symphony and the incidental music to Rosamunde.
Hoffnung's Trout Quintet Cartoon

This was quite a narrow fare of influence. It needed some external factors to encourage the expansion of my musical taste.

Two things happened at almost the same time. I began to learn the violin and I joined the Hendon County school choir under the direction of Charles Western. To the casual observer, Charles was a mild mannered man who presented a weak persona together with his sloping shoulders. Much fun was made of him, but he had true intellectual integrity in the way he presented choral music.

Naturally, the choir worked on the major choral works in English – Messiah, the Creation (Haydn). On the lighter side, he schooled us in Gilbert and Sullivan (I certainly remember Iolanthe, but I suspect there were others lost in the mists of my memory). His passion, however, was for the English madrigals. These were both great fun and contain sufficient technical difficulty to keep the choir’s collective nose to the grind stone.

Charles was well respected and influential as a choirmaster. He brought the school choir onto the BBC at least twice during my time. The highlight, for me, was the choir trip to Berlin, where Gertrude Stranz (Head of Chemistry) had contacts in Neukölln. The trip, long before the opening of the Channel Tunnel, was an adventure in itself. Charles never lost an opportunity to promote his choir. We sang from memory on board the cross channel ferry. The choir gave two concerts at the school in Neukölln. We also had the opportunity to explore Berlin. This included a brief strip across the wall into East Berlin (as it was then). To us westerners, this was a strange rather unsettling experience.

Learning to play the violin, was every bit as difficult as one might expect. Those hearing me practise must have had sore ears for quite a while. Curiously, I joined several orchestras but never really joined in. The process of working with other musicians meant that I had to submit to a communal discipline, especially with regard to bowing. This was something I have never quite achieved. I’m not deliberately or intentionally anarchic, it comes quite naturally.

Even so from the fringes of the various groups, got to know a much wider range of orchestral music. The highlights of these were the early Schubert symphonies (in particular 3 and 5), the Mozart A major Piano Concerto (No. 23), Mendelssohn’s Oratorio “Elijah”, Elgar’s “Pomp and Circumstance” marches and, almost inevitably, the orchestral accompaniment to Handel’s “Messiah”. I also took this enforced expansion of my musical horizon into other areas of chamber music.

Two groups of works made a profound impression. These were the Beethoven “Rasumovksy” quartets (Op 59) and perhaps most importantly the Haydn string quartets Op 20 (also known as the Sun Quartets). The name “Sun Quartets” may well be made up, even so it is entirely appropriate. 

These quartets brought the genre out from background salon music into an era where the listener was expected to listen attentively. The form of the music was still in its early stages. The 1st violin was very prominent especially in the slow movements. The more egalitarian employment of all four instruments would develop in Haydn’s later quartet writing. Even so these 6 quartets are all emotionally powerful presentations and clearly a precursor to his “Sturm and Drang” period.

This started on me on a musical exploration that continues to this day.

Friday, 11 November 2016

Getting into Music

For me it began at home. Cla played popular songs from WW2 and Stephen Foster songs from the US on the piano. These were my earliest musical memories, caught on the verge of sleep. Setting dates to early memories is really difficult, but I guess these were when I was between 5 and 8 years old.

Curiously, I never remember my two eldest brothers at piano practice, I guess they must have learnt although neither of them play now. My closest brother, David, is a different matter. David is 5 years my senior. An age gap where the younger sibling can be real nuisance. I fitted that category to a ‘T’.

Initially, David took piano lessons from a teacher near his school in Hendon. While I certainly heard him practice, it made no impression on me. As I reached 10, my father wondered whether I would take to having lessons myself. David at that time was having lessons from Dennis Page at home. Dennis lived in Harrow and arrived at the house on a moped. It’s curious how these memories stick.

There was some doubt as to whether I had either the talent or was suitable for teaching. It turned out that I had very little talent, but plenty of energy and interest in music. When teaching young children that counts for a lot.

The initial stages must have been difficult for Dennis, but over the course of time I learnt my way around a keyboard. Reading music, and in particular sight reading, never came easily. Here my elder brother David was an absolute boon. He, of course, was practising a way at his pieces while I listened. This was not an intentional or surreptitious listening. It was simply part of life at home. I confess, however, when I got bored with practising my own pieces, I grabbed his and learnt them.

This was a cause of deep irritation for David. I gather he complained quite forcefully to Cla and Rose. But I was not very controllable and, in any case, whole episode was one of the primary reasons that I learnt to read music effectively. I have benefited hugely from this learning, in particular from the intimate knowledge of both the base and treble clefs. I still play the piano, albeit, very badly.

Dennis and his sister were both music teachers. Together they provided a platform for us young students to present our progress in performance. I remember being driven to Harrow and waiting with lots of other would be pianists (and the occasional violinist).

One of the most nerve racking experiences was the wait until I was called on stage. We young performers were in the wings of a theatre stage, trying (and in my case failing) to remain calm. I remember going through this process at least twice. At the last of these, I performed the “Gypsy” rondo from one of Haydn’s piano trios arranged for solo piano. (I still have the sheet music in my library of piano music.) Although it looks simple, it really isn’t.

Here I show images of the initial bars of the rondo up to the first recapitulation from two different sources. The first is 18 bars long and the second 26 bars. Broadly speaking rondos have standard structure of A – B – A – C – A. Second source shows the full rondo structure in its full glory, while the first is adapted for students at around grade 5 and entirely misses out two of the sections as well as some of the elements of the musical development.

Simplified version

Full Version

I highlight below some of the more interesting sections omitted from the student version.

Note the rather tricky rhythmic passages in the left hand of the second passage. I have certainly never managed this effectively on the piano. But this is taken up by the cello in the trio version and is much easier.

Notwithstanding that I eventually became a committed atheist, I attended church at Mill Hill until I was 16. Curiously, my weekly dose of hymn singing made very little impact on me. However, I was asked to accompany small children on piano at Watling Free Church during my later teens. This meant that I had to come to grips with a new hymn more or less every other week. This requirement to lead the children in, and to persuade them to sing with me was a very useful skill.

Although perhaps the most useful skill was being able to fudge the difficult bits. I’ve applied it ever since.

Sunday, 6 November 2016

Live Music and Children

About a week ago I attended a workshop for orchestral instrumentalists organised by the Pulham Village Orchestra (PVO). These are biennial events and I attended my first in 1988, when my own children were all 10 or less.

This year the study pieces included Vaughan Williams, Symphony No.8; extracts from Hansel and Gretel, Humperdinck (including a couple of songs) and overture to Semiramide by Rossini. I expected the Vaughan Williams to be very challenging and indeed it was. After three fairly full days of rehearsal work, both as a whole orchestra and with tutors for individual sections we gave a performance. This time three generations of Allens and Walshes attended the concert.

Bryony, Meredith and Simon had their work cut out keeping Molly (8) and Nuala (4) from causing disruption, but they managed it. At least I didn’t notice anything untoward from the depths of the viola section. However, the order of the concert was geared for the benefit of the amateur players and our powers of concentration, rather than the audience.

The Vaughan Williams Symphony came first. It was something of a struggle for both audience and players. However the 3rd slow movement for strings only came over well. It certainly attracted Nuala’s attention. That’s quite a feat for a four year old.

Everybody enjoyed the singing in the Humperdinck but the purely orchestral parts did not come over as well.

Molly’s attention was really engaged by a recently composed duet for percussion. Unfortunately, neither the details of the performers nor the composer were included in the programme. I’ll try and locate these details over the next couple of weeks.

The Rossini overture was also attractive for both the children. Even so, I gather that their attention was beginning to waiver. From their viewpoint it would have been better received at the start of the concert (as implied by its title).

Molly and Nuala were by no means the only youngsters at the concert. It is important that they hear presentations of all sorts of standards. They will be much better able to appreciate what’s really good later on.

Monday, 24 October 2016

The Sore Loser

What is it that I don’t like about Jeremy Corbyn? (October 2016)

At the beginning, I was a Corbyn supporter, so my political tendencies are closely aligned with his. Nevertheless, I believe that his re-election as Labour leader will consign the party to the political wilderness for a decade or more. Since I like his politics, I have to ask myself “why am I so convinced of this?” It does not make obvious sense.

The June EU referendum in which the UK voted to exit from the European political block represents a second strand to this argument. To date I’ve always tried to keep these issues separate, but they are so closely intertwined I don’t think I can make sense of the whole unless I treat them together.

We know the bare facts of the history. Corbyn was elected the Labour Party leader following electoral defeat at the 2015 general election. The Tory Party had promised a referendum on membership of the EU if it won the election. It delivered on that promise. As individual streams of reality there is nothing particularly remarkable but together they have the power to decimate the future of the UK. Why? Because, it leaves no one to speak for the 48% who voted to stay in the EU.

The argument from the Brexit camp seems to be that I and 16 million or so fellow voters were on the losing side so we should put up and shut up. In a normal General Election I would indeed agree, but this was not a normal election. I do not get to vote again in five years’ time.

A further argument might run that I should leave it to our MPs. After all, that’s what they were elected for. Our current Prime Minister, Mrs May, seems to believe that the referendum vote provides her with all the authority she requires to proceed without further scrutiny from Parliament. In fact there has been a wholesale changing of the guard in Her Majesty’s Government (HMG). Was this really a vote to change HMG? Yet that is what has happened. Not only have the personnel changed but significant tranches of government policy have changed. The referendum was not a general election. It conferred no such authority upon the government post referendum, no matter how plausible and rational the changes she proposes. Yet in reality that is exactly what has happened.

At this point, I feel the need to step back again and take a long hard look at what really happened in the context. The members of the UK electorate were given an opportunity to voice an opinion on whether we should remain part of the EU. I’m satisfied that for 90% of the electorate, who voted that is exactly what they did. But I’m not convinced of the remaining 10%. The scope and integrity of the arguments laid before the electorate on both sides lend credence to this view.

The narrowness of the scope of the arguments laid before us and in some respects their downright mendacity suggests that we were being duped for the sake of winning the vote. A feeling of being duped, I suspect was quite widespread and at least some part of the electorate was determined to make their voices known. Is this fanciful thinking on my part? I suspect not. Railing against the government of the day is common place, especially in by-elections.

I have analysed the votes against the government in by-election over the past 4 general election periods. These analyses show a clear protest against the government of the day between general elections. Data source

These tables show clearly that protest against the government of the day is a common feature of by elections, but the sentiment tends to be reversed in General Elections. 

It would be prudent for any government to consider whether this kind of sentiment had affected the result of the referendum. The Cameron administration had invited some pre-eminent voices from the international scene to speak on its behalf. For voters, already predisposed to protest, this could have confirmed their prejudices.

A potent argument against this logic could be that the referendum was a “single issue” topic and therefore not susceptible to the kind of protest so clearly exhibited in by-elections. In truth though this apparently simple question has a multitude of facets. Indeed it is so easy to get lost in the myriad of detail that comprises the EU, I wonder why it was ever considered suitable for a national plebiscite. For that I would have to look into the minds of those who prepared to the 2015 Tory manifesto. This is a task I am determined to avoid.

Unlike our history of by-elections, there is no evidence from similar elections to demonstrate that this was a protest vote. However, I note from Polly Tornbees’s article in the Guardian, 20 October, that the level of regret amongst leave voters was significant around 6%. The equivalent level of regret amongst remain voters (at not being on the winning side) was 1%. On this basis the result of the referendum would have been reversed.

Nevertheless, we have a result that say that the UK should seek to extricate itself from the EU. The new Tory administration is determined to follow the referendum commendation without further consideration. So how should the 48% who voted to remain in the EU react?

Normally, one would jump on the opposition bandwagon and wait for the next general election. This is not practicable. Firstly, the leader of the Opposition (one Jeremy Corbyn) won’t oppose leaving the EU, even though he “said” he was in favour of staying. Secondly, we the electorate, don’t get the chance to reverse the decision in 4 or 5 years’ time.

The “remain campaign” cannot bury its collective head in the sand. It must act now, but how. We desperately need a collective opposition to Brexit. In the absence of Jeremy Corbyn stepping up to the mark, he must be disposed of, since his presence is a positive barrier to effective opposition.

Let us suppose then, that the Parliamentary Labour Party would once again approve a vote of no confidence in Mr Corbyn. That would leave the PLP both leaderless and exhausted from a bruising leadership election over the summer. My advice would be to appoint a caretaker leader until next year’s conference season. That would still leave the “remain campaign” without a focal point or leader.

Curiously, we have a ready-made leader in Nicola Sturgeon of the SNP. Her voter base may appear out on a limb in Scotland, but she is experienced and effective. I wonder if she would be prepared to lead a coalition of that rather disparate opinion that represents the “remain campaign”.

Tuesday, 18 October 2016

A Question of Timing

Quite often I’m alone on my morning walk and my mind has a tendency to wander. On this particular morning I wondered whether there was a clear relationship between the number of steps taken on the walk and the time taken. Of course, I had recently bought a stopwatch and was anxious to get good use out of it.

A moments pondering suggested that there would be an inverse relationship between number of steps and speed. I had measured the distance of our morning walk fairly carefully (see Measurement) so calculating speed was easy. By this time, I thought I’d enough data to evaluate whether there was indeed a correlation.

Excel is not regarded as a good statistical package, but it’ll do for my amateurish approach. I have 26 data points ranging from 5462 steps to 5846 at the high end.

Data points from my Morning Walk
When plotted on a scatter graph it gave a good impression of verifiable statistical relationship.

I have marked two data points that might be regarded as outliers. The problem with outliers is that I really have to justify their classification. Fortunately I maintain a contemporaneous commentary on the morning walks and both these data points had suitable remarks. These remarks provided the justification for their removal from the data set.

Looks may not be everything, but in this case the scatter graph provides a much more convincing case for a correlation between speed and the number of steps.

In fact in statistical terms the correlation coefficient improves from -0.85 to -0.90.

Friday, 14 October 2016

A New Morning Walk Route

On Tuesday, Bryony and I set out for our regular morning walk in aid of getting fit, or at least fitter. The route goes down the gentle slope of the Needham Road out of Harleston. We then turn right into Starston Lane. This has a dip in the road from which water cannot escape and a rather steeoer slope the other side of it – see the gully at the start of Starston Lane (Walking, talking and listening). The dip was completely flooded filling the whole road. There was no route to either side. We gave up and returned home.

Since winter is coming on and we are likely to face more occasions when we cannot use this route. I was determined to find a new route, roughly equivalent to this one.

I first sought to circumvent the gully. This is possible by continuing on towards the roundabout and turning right along the side of the Needham bypass. There is no footpath here but plenty of fairly flat grass. In 200 - 300 yards we reach a footpath (also not paved) going back to Starston Lane.

Adjusting the usual Starston :Lane route
While this isn’t a major diversion, the lack of paved walking is a major drawback. This is not a long morning walk. The only way it can deliver a reasonable contribution to an exercise regime is by taking it reasonably quickly. As winter draws in and the mornings become darker, there is no chance of maintaining a reasonable speed over this portion. Sadly, this route has to be rejected.

I’ve always liked the route to Harleston’s sister community in Redenhall. This has the advantage that it can all be walked on paved roads, which are, mostly, free of traffic.

Route via Redenhall and the Gawdy Hall Estate
There are however some major drawbacks. It crosses the main A143 twice, which means waiting for a gap in the traffic. It is also about 4.3 miles long. This is too long for a morning walk which has to be fitted with our commitments as grandparents. A pity, I liked this route.

The advantage of the north eastern end of town is that it exhibits far fewer steep slopes, so the tendency to get flooded is also reduced. After heavy this also seems a good alternative. The major issue was to find a route that was roughly equivalent to the distance of the Starston Lane route, kept to paved roads and which was relatively free of traffic. Eventually I chose a route as shown below.

Route via School Lane and Lush Bush 

It proved to be a couple of hundred yards longer than the Starston Lane route, but we encounter slightly less traffic. The timings are very similar.