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.

A Team Player

Not every chess team has one, but those captains who have access to one prize them highly; they have some rather rude names, but one polite one: The Draw Specialist.

They are usually in the older age bracket. In their youth they may have been unpredictable, exciting, volatile, with wild attacking games, imaginative sacrifices and disastrous opening strategy. Now they have one opening against each of the two major opponent's moves, e4 and d4, generally obscure, stodgy and devastatingly simple, which they routinely wheel out. The Caro-Kan, say. Or something vaguely sound but which no-one has heard of, let alone plays anymore. The Chigorin Defence to the Queen's Gambit. As White they play something sound and strategic (ie c4 or d4 or both) so that no tactical surprises can occur while they are watching other people's games.

Some play Nimzovitch over-protection; make sure everything is solidly protected and wait for something to happen. Defend doggedly until the opponent over-reaches and offer a draw while he is shell-shocked at the defensive technique. Some just seem to be lucky, or clearly offer a draw too soon, at the psychological moment. "Perhaps I should have played for the win, but I didn't see it coming through."

The captain respects them, though. They play Board 2 or 3. The top boards will play their interesting theoretical stuff and that will go one way or another. But one of the opposition's threats is carefully neutralised, so that the bottom boards, playing down one, have that extra edge to give them the win. Three wins at the lower end and a draw on board 2 will do. They sacrifice their interesting ideas to the team's victory.

It does depend of course on the rest of the team doing their job, of course. But they have great (if misplaced) faith.

And when the rest of the team all lose, honour is upheld. Five and half against is not a whitewash. Today two and a half for - and someone drew a game he should have won, surely? (thought that in earlier weeks, too). Nearly there.

Three games, three draws; two solid and one rather lucky. One third of the whole team's game points (one half before today!). At least it's better than last season which started with four straight and appallling defeats (and the one where the play wasn't too bad came up against Mighty Megan, who exploits older men's weaknesses to an extent that a £200-per-hour lapdancer would be proud of).

A team player.

Abundance

Find the next number in the sequence:

2, 4, 6, 12, 24, 60, 120 ...

I believe I know the next three but there seems to be a big gap later on so I'm doubtful whether 840 really is on it. And is there really nothing between 2520 and 27720 (assuming these are on it)? Research continues.

A slightly easier related (provably expanded?) sequence goes:
2, 4, 6, 8, 10, 12, 18, 20, 24, 30 ...

Edit: Discovered an error in the top sequence. To be updated later.

Hypothetical

What would happen if the designated worship leader didn't have an order of service? (I mean really didn't have one, not just hadn't written it down?)

Would anyone mind?

What should happen when we go to worship? Do we expect it to?

The R Word

This blog was started to help process the overload, in various ways, that was coming in while I was at College, which is why it slowed down in holidays and has been absent lately. So it was a bit reactive and didn't in fact do what it said on the tin. Perhaps it now can be a bit more proactive and initiating. (This is as close to a statement of intent as I can get right now.)

I won't change the name as there was precious little theology in it anyway (an issue in itself, ho-hum). Let's see if we can do better. But it's likely to be a grab-bag (that's the polite term, I believe) of what I'm working on at any given moment. Let's not make promises we can't keep. But we will see if anything can be revisited. Don't hold your breath.

Aspirational TV

I've discovered a wonderful new TV programme called Jane and the Dragon. It's about (ostensibly) a girl who wants to train to be a knight when everyone else, including her mother and father, wants to pigeonhole her into being a lady-in-waiting like her mother. Even her friends aren't sure about her ambition, but at least the rules are applied fairly by Sir Theodore, although he is a daft old ... knight. So she sets out to kill the dragon but instead befriends it and brings it back to the castle. Which isn't always appreciated as it should be.

Why she wants to be a knight when the examples around are less than honourable beats me, but I suppose it's better than being a lady-in-waiting, even if the young princess who smells of lavender is quite nice really.

There's a website although Jester hasn't fully finished it, so no link here. Google it and you'll find it. Programme is Saturday and Sunday mornings on Five.

In other news, I'm hoping to meet a man with seven wives.

Rock Your World

According to New Scientist, researchers have been making recordings to show what sounds come out like on other worlds, in preparation for sending recording equipment there. Atmosphere density and composition changes the harmonics. So now they know what Smoke on the Water sounds like on Venus and Titan. ("I should have doen thunder, but I couldn't resist" says the producer.)

On Venus it's much deeper and punchier and on Titan it's much louder. So that's next holiday sorted.

A British Champion

Who says chess isn't exciting?

This afternoon is the last day of the British Championship and I doubt it's ever been so tense in the last round. The two leaders are the number 8 and 12 seeds, by half a point over numbers 1, 3, 4, 7, 10 and 11. 5 and 9 are half a point behind those two and number 2 seed is off the pace (!) a further half point behind. Now 12 is playing 10, 7 v 8, 1 v4 and 3 v 11. Any of these can therefore finish up first or equal first if the results go their way.

I've been watching live the last few days as Jacob Aagaard (12) has tried to blow a colossal lead. At 6.5 out of 7 he looked like a winner all the way; after 1 point from the next 3 games he's been demoted to Board 2, but is still guaranteed at least a share of first place (with up to one other) if he wins, and a draw will do it unless the game on board 1 is a win for White (potential for up to a four-way tie, if boards 3 and 4 are decisive one way or the other. A draw can't give him the title outright). Another defeat will leave him nowhere, relatively.

I note that Jacob has played (including this afternoon's game) the players currently lying in positions 2, 3, 4, 5, 7, 8, 9 and 10. So I think he'll deserve it if he wins. Averaging the gradings of opponents, he has played the highest average of anyone, equal with the number 4 seed, Nick Pert. Jacob drew with the number 1 seed and beat numbers 3, 4, 5 and 9.

Jacob plays under the Scottish flag. The Scots do seem to have a lock on the championship in recent years .... (Famous last words.)

UPDATE:
Well every bit as thrilling as anticipated. No short draws with so much at stake. Aagaard won a pawn at the cost of an open g-file to his king, and contrived to lose the exchange. Pawn for the exchange then, but pressure against his king-side ....

Rowson beat Pert, so that's one player on 8. Hebden plugging away, but lost his a-pawn and facing an advanced passed d-pawn ... (which disappears with surprising speed)

On board one Gordon, needing a win for 8.5 to overtake Rowson, had a pawn for the exchange ... but I was never convinced his attack was going anywhere. Aagaard I felt could always resist the pressure but one slip and it would be over. Much tense manoeuvring.

Suddenly Kosten gets two rooks round the back of Gordon's defence, whose bishop is pinned to his queen and behind that the king. But the Black king is suddenly exposed ....

Howell beats Williams with 25 seconds left on his clock. (You can make a lot of moves in 25 seconds.)

I don't understand all the pawn captures in Hebden-Haslinger but it looks drawish, two bishops v bishop and knight. Yes, there it goes, in 62 moves. And Aagaard has two passed rook pawns. Now you don't see that too often. He must win, surely? Yep, thought so. Resignation after the second time control, move 60. Both players down to last two or three minutes before that. So can Gordon break through? I didn't think so. Drawn on move 61 - Haslinger can repeat moves and Gordon can't afford not to.

The winner is Aagaard, after all. I'm pleased for him.
Second equal, Gordon, from Oldham, and Rowson from, er, Aberdeen?

Strange Echoes

Well it isn't exactly a pick-up truck, but I have this curious feeling that I should get a pink carnation and drive to the levee ...