The R-word

The most feared word in magazine publishing, at least according to the film "13 Going on 30". So we won't even whisper it. We just do it. Seems the time for it (probably should have been done long ago).

Hanging on the Telephone

The telephone is ringing off the hook with calls from beautiful blondes, and when it's not then I'm calling out, selecting from options, being re-routed to the person who actually knows something (sometimes) or can do something (less often) or can actually sort out the problems caused by other people (very rare). It takes three or more goes of course before someone answers and even then "your call is very important to us" well why don't you bloody answer it then is the sort of response you might give "our lines are very busy" I'm not surprised with the standard of service you generally get.

I've been threatened with debt recovery procedures by npower, Darlington Borough Council and Carlyle Finance, notwithstanding the fact that the first two of these don't actually know how much I owe them (or indeed whether they in fact owe me) and the last has a different figure to me and can't explain why in a way that I can understand. Certainly none of them can provide accurate statements of account, invoices, receipts or any of the documentation that you might expect from a company that knows what it's doing day-to-day. Oh and Angela had a letter threatening to cut off the gas, don't know who that's from, but it's because they can't get the address right or realise that sometimes people move house (I'm not making this up).

In addition there's the banks. There was a man (true story, this, it was on Radio 4 and everything) who got so pissed off with the Yorkshire Bank that he changed his name by deed poll to Yorkshire Bank Are Fascist Bastards plc and got it put on his Yorkshire Bank cheque book. He was wrong, of course, in that he should have changed his name to All Banks are Fascist Bastards plc especially Northern Rock (and you'd think they were into customer service lately having made all our shares worthless through unadulterated greed). When they realise what a balls-up they've made of everything, who ends up bailing them out? You and me. It's enough to make you go back to keeping it in a sock under your bed, at least it might be safer there. So the rules on mortgages have all been switched even when you've been promised that everything will work out. The canard that the banks are there to help the customer (and it looks like it is all banks) has been well and truly found out.

Anyway back to the telephone. Most of the time you get through to a very nice Customer Service Assistant who explains very politely that no he/she can't do anything about it, the computer's in charge and he/she can't override it, but he/she can explain exactly what the computer is thinking (no-one else there does any, obviously) and if you're lucky he/she says "oh don't worry about the gas getting cut off" which is all very well for him/her and James in fact couldn't say that this time despite what the previous girl (Fiona?) had said last month. So you have to do their work for them because clearly they can't get anyone to read the meter (they're all on the phone instead) but 250 miles is quite a long way to go just for that.

To be fair to Darlington Borough Council and their James (there's two, keep up) he did phone back with a much reduced figure which might even be claimable back at some unspecified point in the future (still no invoice, but hey I can get a receipt) and even Alison is a person in her own right who can make arrangements on the spot and is not a mouthpiece for the computer, even if letters arrive somewhat unexpectedly when you thought a Direct Debit would naturally keep things under control. (I'm still waiting for an invoice from Social Services which doesn't seem to be forthcoming.) On the other hand, to sort anything out you have to speak to a minimum of three different people in three different offices with different phone numbers (and not the one they tell you to ring on the letter) because they don't communicate with each other. It's called division of responsibilities, at least that's the polite name for it.

And I still have to ring back the Management Officer of Rockwell House (promise unfulfilled) - so that I can ring npower and go round that loop again - and Carlyle Finance haven't come up with a receipt to show that yes it is all paid off despite the best efforts of Northern Rock. Oh and where's my cheque from BT? (This time I do have a letter saying they owe me, strewth, talk about small mercies.) So it's back to more Vivaldi how much can one man write?

Hymn

Give us this day all that you showed me.
The power and the glory
till my kingdom comes.

Give me all the storybook told me
The faith and the glory
till my kingdom comes.

And they said that in our time all that's good will fall from grace.
Even saints would turn their face in our time.
And they told us that in our days
Different words said in different ways
Have other meanings from he who says in out time:

Give us this day all that you showed me

And they said that in our time we would reap from their legacy
We would learn from what they had seen in our time.
And they told us that in our days
We would know what was high on high
We would follow and not defy in our time.

Give us this day all that you showed me

Faithless in faith
we must behold the things we see.
Give us this day all that you showed me . . .

Cross/Cann/Currie/Ure

Do You Know Where You're Going To?

There used to be an old military joke:

Q: What's the most dangerous situation you can face?
A: An officer with a map.

The modern civilian equivalent:

Q: What's the most dangerous thing on the road?
A: A lorry with a sat-nav.

Do You Feel Like We Do?

I'm feeling vibrant today. This is a good thing. We should all feel vibrant and we should be vibrant in what we do. I hope you are all vibrant and that the things around you and the places you go are vibrant.

I hope that you know when you are vibrant and when the things around you are not vibrant and that you can be vibrant despite not everything being vibrant and that you can help everything to be vibrant because then everything will be all right.

And when you know that you are vibrant please find out what it means to be vibrant and why that is not just the same as thrilling (which is the poor old dictionary's best attempt, unless you want to feel resonant or vibrating, which I think are completely different things) and then be sure that you want to be thrilled all the time and not be old and tired once in a while.

And then come and tell me - but when trying to tell me what vibrant means you are not allowed to use words that don't mean anything or mean all different things to all different people.

It's All In the Game

Time to catch up on three more results before the final game of the season on Tuesday.

Blundering a pawn on move 11 is not the best thing to do. However I get a surprising amount of counterplay and the basis of an attack. The Draw Specialist does what he does best. Has to be said that the opponent was a bit cautious.

Winning a pawn is much better. What was supposed, after 1. c4, to be a quiet strategic game turns into into a wild tactical melee in the centre of the board with his knights dodging all over the central files and me giving myself a backward e-pawn in a desperate attempt to avoid a crushing attack down the e- and f-files. Well in the end it looks to me like I can take his weak central pawn and if he can see better through it than I can he deserves to win. But he can't. So a pawn up in the centre of the board - force the queens and knights off (OK not quite forced but awkward to avoid) to a rook ending. But all rook endings are drawn? Not this one. Carefully advance the backward pawn till it is the front one, swop off to make it passed, the rooks come off and the king is far enough forward so that the opposition makes the win. Job done. Pity that we still lost the match 2.5 to 3.5.

And then one that really is a positional game. Good for the Chigorin Defence to the Queen's Gambit. The key move, the winning move is 5 ... B x f3 - because he gets a doubled pawn. So that when we get to a same-bishop endgame my 3v2 on the Q-side is mobile and his 4v3 on the kingside is crippled - not helped by the fact that all through I have slightly had a lead in development which turns into initiative which turns into a king slightly further up the board. Finally with the threats available (good old Nimzovitch, a threat is stronger than its execution) 3v2 becomes 1v0 and 4v3 gets completely stopped on the same colour the bishops are on. And one drops off and even though the bishop looks trapped, there's a safe maneouvre to get it out and the when the bishops are forced off the king has to take the outside passed pawn which leaves me enough time to take all his. Always put your pawns on the opposite colour square to your bishop. My word, two wins in a row. +4 in division 2 and +2 in division 4.

The Visitors

Since we got a name-check on Ruby's blog, I thought I should finally add the link that I've been meaning to do for ages.

Don't Take Away My Music

People have different things that they consider important in a car. It can be the engine power and the 0-60 time. It can be a go-faster stripe and alloy wheels. It can be space in the boot and leg-room in the back, or a packet of sweets in the glove compartment and air-conditioning. It can be enough headlights to light a film set. I like to have a heated rear window for cold mornings and a sound system for every morning.

Well the heated rear window still works.

But tomorrow we shall again be able to play Ensiferum so that the windows rattle. Happy is the man who has a warranty.

The Hunter

Some results the Draw Specialist get are achieved easily (too easily, even). Some take a bit more work.

Yes, another draw on board 3. This one a bit different. I sacrificed a rook (R x b2+, he didn't see that coming) on move 21 for what I hoped would be a winning attack with a perpetual in hand. It wasn't a winning attack and he managed to find the way out of the perpetual. So I played on a rook down.

A glorious king-hunt, chased the White King from b1 to h3.

At one point the other rook was hanging, too, for at least 3 moves. Threats of mate in 2 (there might have been a mate in 1) were ignored, mainly because there was no way to defend them. Initiative is everything.

At the death he has a pawn ready to promote with check. (My king is on g5 by this point, his pawn is on g2 and g1 is guarded by his rook.) And then I finally forced a perpetual. Draw agreed on move 51; all I have left is queen and a few pawns, in just the right places.

Thirty moves played a rook down (a pair did get swopped at one point) achieves a draw. Is this a record?

My team-mates said I was lucky. I said I always had the draw. You just have to know how to play it.

Sadly, the team lost - to the bottom of the division, see last week - as Boards 5 and 6 yielded only half a point and Glen on 4, despite playing well (their board 4 got a bit distracted by the fireworks on 3), winning at one point, misplayed the ending and eventually lost a piece. 2-4. Heigh-ho.

Still, it was fun.

Bicycle Race

On the news today, a story about how Britain's cyclists are to be helped in their Olympic efforts (sigh) by technology designed for the Eurofighter. A helmet will give them a Heads Up Display while they are competing, showing info to help them in their quest for a medal. Mentioned was the power they are producing so they can find the "sweet spot" behind the leader. Other details I didn't catch, or possibly they didn't want to name.

Hang on. Is anyone else a bit disturbed by this?

Surely the Olympics are about the best athletes not about who has access to the best technology? (I leave aside the area of drugs for the time being.) There's already sufficient technology in the fact of the equipment available - the bike - to make competition an uneven playing field. (Compare motor racing: the best drivers are the best - but they have a huge technological advantage, everyone knows it, and the sport is diminished by it.)

I daresay there is an uneven playing field in the area of training facilities, nutritional advice (I'm still not talking drugs but I might be) and I daresay that the athletes of some countries which are poorer than GB are already at a disadvantage. And we are adding to this?

Now if the cyclists by training discover the sweet spot, fine, more power to them. If training improves their skills on pacing themselves and whatever else, good. The pursuit of excellence.
If the technology helps train them to know the sweet spot, well maybe, they still have to do it themselves to some extent, I suppose. (Thinks: this might have been the intention. Not clear.)

But if this is to be used in a race, no. Unless it is freely available for all athletes to use (or not, if they prefer not to).

I call on the British Government to put pressure on Team GB (or whoever is organising this initiative) to make this technology available to anyone who wishes it. In the interest of fairness.

We don't want to be a nation of cheats, do we? Oh.

Sing When You're Winning

Yesterday's chess match was one of the most thrilling ever. This is my report on it.

Background info: we are second bottom in the division. Our opponents, Clevedon, are second top, relegated last season from division 1. Promises to be a toughie. However our captain, Steve, points out that there are a lot of teams in the middle very close together and that if we win, we go third. I point out that actually we go fifth on board count. We compromise on "equal third" not worrying that other teams will also be playing tonight and some of them have to score points ...

Our team is:
Board 1: Andy, most improved player last season, stepping up to the mark again
Board 2: Steve, with no wins this season
Board 3: me, undefeated but mostly draws
Board 4: Glen, currently with the best grading performance in our club this season
Board 5: Phil, who gets into and out of positions you wouldn't believe
Board 6: Anthony, the smart one (but not today)

Odd board numbers are playing black, as usual.

I get to watch quite a few openings since my opponent is really taking his time (and seems to have had a tough day at work, given by his yawns). Glen has a strong centre, Andy seems to have a loose kingside, a shortage of space and no desire to castle; his opponent's king is also remaining in the centre, with an h-pawn advance. I play the usual Caro-Kan but in response to Nf6 I get not NxN ch doubling my pawns (I of course would play gxf6 like Miles against Karpov) but the retreat Ng3. Which seems to leave my white-square bishop a problem. I lock it in with e6 and start thinking about a Q-side fianchetto.

Meanwhile Andy has played Qxb2 and declines to play Qxa2 in response to Rb1. I can't see the trap ... still a pawn up is a good start.
I get in c5 and cxd4 rather easily and have to think what to do next. Nc5 looks good, forcing Bc2. What now? Develop the Q-side what a good idea. Nh5 really forces g6 but seems to do no harm - he doesn't even force off the dark bishops.

However Nc5 seems to lead inevitably to a threat of a rook on the seventh. Just as he's about to achieve it though, after a bit of swapping off, he offers the draw that I hadn't expected. I accept with alacrity. I wouldn't have offered one there, even with opposite bishops. This time it wasn't the Draw Specialist making the running in splitting the point. All done by half-nine and time to watch some others.

Andy is still a pawn up with a George Crockart-type structure and rooks going to be doubled on the c-file. Still squashed but looking like breaking out. Anthony is dominating the board with a massive space advantage but as pieces get swopped the defence looks easier and counter-play seems easier. Phil wins a pawn and looks comfortable. Steve has a nice-looking centre, but what to do? Is the sacrifice playable? Oh, there go a pair of bishops, perhaps not. Glen's opponent refuses a draw offer, quite a fair one I thought what with Glen's passed pawn securely blocked.

Richard is watching with me and I say prophetically "we could win this with four and a half or lose by the same" and he agrees. The match is heating up nicely. Anthony still looks like he is winning but if that passed e-pawn moves there will be mate threats (after some Q manoeuvres it does and there are, but he has it covered). 1-0.

Phil and Andy both have opposing Qs in their defence. Andy gets rid of his but Phil has to play very delicately, not taking a pawn until the second opportunity, but this seems to be his opponent's last desperate throw and suddenly Phil is a knight up with only rooks on in addition. Careful play and he closes it out. 2-0.

Andy is short on time. He's broken out, bits everywhere, particularly the knights look to have had sone fun, but he's repulsed although his opponent seems relieved. 2-1. Steve is losing. The sacrifice didn't work although I thought he missed a chance to win the piece back (surely Qe5+ works?) and he's got not just a Q in his defence but a rook too. So I go to watch Glen.

I'm not sure where it came from but his opponent misses some tactics and Glen goes a pawn up in a same-bishops ending. That pawn secures the sacrifice of the bishop so it's two v two all on one side but Glen has a bishop. Slightly behind in the race to the Q-side he plays the B to a3 where I would have gone to f6. But it seems to work - I don't think I would have advanced the black pawns, I think Kb1 was the way to go - and when Black resigns against a lone pawn and bishop with his K stranded I say "You've just won us the match, Glen." "Have I?" he says when Steve says "Excuse me, but I won it a few seconds ago". And he did too. Apparently there wasn't the mate his opponent thought and Steve has won with sixteen seconds left on his clock. A captain's performance. Even he can't quite believe his first win this season. Four and a half to one and a half against one of the strongest teams in the division.

So we are third. Or fifth. Or third equal. Or somewhere. And as Richard points out, if we lose next week we'll be back to second bottom. Still that's another day.

Merry Christmas Everyone

Well the shopping is all done now, I do like to do it in good time, and the tree was up a few days ago. Points West want me to be really "festive"; when I find out what that means perhaps I'll have a go. However when they are so relentless it's easy to see that the Puritans may have had a point.

Grumpy, moi? No.

Merry Christmas to all, peace, goodwill etc. Normal service resumed in the new year (maybe). Busy, busy, busy.

Go Wild in the Country

(observ8n)

i c u
i .
u c me
u .
we . . .
u x no me
i wil x hrt u
.
u r cool
u rn & jmp
ur frenz r ther
find cheez

bye

Chalk Mark in a Rainstorm

Oh Lord why have you abandoned me?
You have cast me aside.

Why do you allow my enemies to prosper?
They have influence and power.

Where are you hiding?

I looked to the hills but I did not see you there.
I went to the end of the motorway but I did not find you.
I wander along the hedgerows and you are not there.
I do not see you in your temple.

I know you are there, but you are not here. I cannot hear you.

Ch-ch-changes

It's right to stutter over this word. Not all change is for the better but all change is scary hard work.

But it has to be done. Even if you can't see what the result will be.

The theme of this evening was change. Looked for, resisted, uncertain, and too difficult. And particularly when it doesn't end up in paradise.

Doesn't make you want to do it, does it?

Don't Make Promises (You Can't Keep)

1000 years of monasticism.
500 years of paternalism.
200 years of Dissent.
A decade of evangelism.

20 years of incomprehension.
20 years of blindness.
10 years of wilful blindness.
30 years of avoidance.
15 years of dementia and false hope.
How many years of terminal decline?

The Song Remains the Same

In the absence of winning a ticket to the real thing, went last night to see Whole Lotta Led at the Fleece. (Still might win a ticket?)

The vocalist was not Robert Plant, and didn't quite have his vocal range - but he had his style and his heart and he sang blues and rock with passion and power. 9/10. Since I've Been Loving You was fantastic.

The bassist played a wonderful No Quarter and the drummer played Moby Dick like you've never seen. He could have played all night, and I think he wanted too. Both 9/10. Maybe that's harsh.

But the guitarist was astonishing. No-one is Jimmy Page, but this is as near as you could want. He was ferocious, tender and exciting. The players may change but the song remains the same. Off the scale.

And if the song is good enough and still relevant, the song can remain the same. Only if the song is dated does it need to change. But which songs should remain the same and which need a new riff? A 12-inch remix? A live version? (We can always use a live version.)

No D'yerMak'er, alas. To lament it would be to quibble, to ask too much.

Everything that's small has to grow. And it has to grow!

Dinosaurs

You can imagine the sort of comment the early mammals made while waiting for the comet to strike.

"I don't mind them being so big and stupid, but why do they have to eat all the fruit? There'll be none left when they've finished."

And the dinosaurs saying "When we've gone you can eat what you like. Until then, leaves and branches was good enough for my grandfther and it's good enough for me." (The dinosaurs are too stupid to put it so coherently, but hey that's artistic licence for you.) And of course they were bigger, if not faster, so it was difficult to shove them out of the way.

But these days not only do the dinosaurs eat all the fruit but they uproot all the trees and they don't give you space to plant any more. So not only will the next generation not have any fruit to eat but they wouldn't know what it was if you gave it them.

Mathematics

Define F(N), the factor-sum of N, on integer N, as the sum of the proper factors of N. Formally F(N) = Σi, i divides N, i = 1 to N-1.

Further define Q(N), the quotient-factor of N, Q(N) = F(N)/N.

In common usage:
Q(N) = 1, N is perfect
Q(N) < 1, N is deficient
Q(N) > 1, N is abundant.

Previously existing result:
N is perfect if N = 2^n x (2^(n+1) - 1), provided (2^(n+1) - 1) is prime.
It is not known whether all perfect numbers are of this form.

Preliminary results:
If P is prime, F(P) = 1 and Q(P) = 1/P. Clearly, for e, there exists N s.t. that Q(N) < e.
Primes are maximally deficient.

If N = P^n, where P is prime, F(N) = (P^n - 1)/(P - 1), Q(N) = (N-1)/N(P-1)
For particular P, Q(P^n) tends to 1/(P-1) as n tends to infinity.
In the case P = 2, F(2^n) = 2^n - 1 and Q(2^n) tends to 1.
Integers of the form 2^n are minimally deficient.

Question: Are there other N such that F(N) = N - 1?

If N is abundant, any multiple of N is abundant with greater factor-quotient. (See following lemma; more fractions are added when a multiple is derived.) Formally, if M divides N, then Q(N) > Q(M).

Lemma
For all n, there exists N s.t. Q(N) > n. (Abundancy increases without limit.)
Proof
Q(N) is the sum of fractions of the form 1/n. Since Σ1/n diverges (well-known result), Q(N) is unbounded.

Therefore it is possible to define N is abundant-S if Q(N) >= S and assert that there exists an infinity of abundant-S numbers, whatever the value of S. For instance, 120 is abundant-2 (the smallest such).

Question: Find for each integer N, find the smallest M such that Q(M) ³ N

Further Result:
Since the sum of the odd fractions can also be shown to diverge[1], there is also an infinity of odd abundant-S numbers. The first odd abundant number is 945 and the smallest odd abundant-2 number is believed to be 1 018 976 683 725, which has Q-value 2.0107.

Define N is super-abundant if Q(N) > 1 and Q(N) > Q(n) if N > n. (Informally, a new record is set.)
The first super-abundant number is the first abundant number, 12. Q(12) = 1.33. (The record-holders that are not abundant are 2, 4 and 6.) The set of super-abundant numbers has infinitely many members. (A record-holder will be beaten by any multiple, from result above.)

Question: Find the super-abundant numbers.

[1] The proof is similar to that of the full series. Consider the series 1/3 + 1/5 + 1/7 +1/9 ... If we successively group 1, 3, 9, 27 ... terms ie 1/3 + (1/5 + 1/7 + 1/9) + (1/11 + ... + 1/27) + ... it is clear that the series is greater than 1/3 + 1/3 + 1/3 +1/3 ... and therefore diverges (slowly).

It has been necessary to replace some symbols unsupported by this font by words in the above.

On the Road Again

I've been catching rays
On motorways
Listening to tunes
In afternoons

A big 90 is a trip to the north.

Now a quick return for one of two calls from Chesters.