This is the best video ever pic.twitter.com/K065H6RJfQ
— Keith (@lad) July 20, 2017
Saturday, 22 July 2017
I don't normally circulate videos but....
Sunday, 15 January 2017
Draw!
Had this happened today in a game between two top players, there would surely be protest from amongst the paying public. Why would you not want to watch this lop-sided position play itself out? The game itself had earlier been a disaster for black, who'd blundered a whole rook just out of the opening. Surprisingly he played on and his persistence paid off. White, who was the author of the games collection, reckoned he was in poor form; that's putting it lightly; even I usually win games against my peers with this kind of extra material.
In case you're interested, the game is Botvinnik - Bronstein, 9th match game, 1951; and I'm referring to Botvinnik's Best Games, Volume 2: 1942 - 1956. Botvinnik was +1 in the 24-game match at the time but the match ended drawn, so Botvinnik retained his title.
For what it's worth, when Komodo and Stockfish played the position, they made a draw. Whether the punters' frustration was expressed in the media of the time, I don't know. But probably not at the match venue itself, which was Moscow; protests by citizens at the time weren't well tolerated by the authorities.
There's a short, grainy video of the match venue here, and if you look a little further, you'll find another video where Yasser Seirawan lectures on this game; I'm just about to give it a go.
Friday, 30 December 2016
On Square Roots and the Number Line
I've recently been thinking that it's time I took another look at
mathematics, which was a subject that occupied a lot my thoughts as a kid right up until my early twenties (when career took over all the available brain space). With that in mind, I recently read Marcus du Sautoy's excellent book on the limits of our knowledge. My attempt at a snack-sized review is here.
One of the nice proofs reproduced in the book was the one to show that the square root of 2 is not a rational number; that is, that that it can't be represented as a fraction (a/b). The proof is short and easy to follow (find it on Wikipedia) and the result is satisfying because of its sheer scope. Despite there being literally an infinite quantity of numbers, you will never find a number that is the exact square root of 2. And you can do that with absolute certainty without even breaking into a mental jog, the proof is that simple.
Anyway, when I was reacquainted with this proof I remembered that many years ago I was really not that impressed by it. There seemed to me to be an obvious intuitive argument that it had to be so. It's all a question of there not being enough space on the number line to fit in all those square-roots.
Think about it: from 1 through 9, say, there are an infinite quantity of intermediate numbers; and if we map each of that infinite multitude to its square-root (or higher root, for that matter), the number line of the roots is squashed up relative to the number line from which is originates (it ranges only from 1 through 3 in the above example). It seemed obvious to me that there simply couldn't be enough room on the number line for every number between 1 & 9 to map to its own unique root in the range 1 to 3. After all, there may be an infinite quantity of numbers between 1 and 3, but the infinite quantity of numbers between 1 and 9 must be greater, mustn't it?
The standard proof that root-2 isn't rational is certainly more definitive than my (admittedly informal) argument; but mine seems to imply that there won't be cube roots, fifth roots and all the way up. Or at least, it seems to be on first glance.
Another way of coming at this question is to consider what the decimal expansion would be of a number that is the square-root of any integer that is not a square number (1,4,9 etc.). Clearly, the root has to end with a non-zero digit after the decimal point. And when squared, the final digit would need to equal zero for the square to be an integer. But when you square all the digits from 1 through 9 you don't find any that maps to zero; the square of any decimal number will in fact have more digits after the decimal point than the putative root itself has. Hence, there are no integers other than square numbers that have a square-root that can be expressed as an exact decimal; and in fact, no number with a single digit after the decimal has its own root either.
Anyway, glad to have got this off my chest after all these years. In writing it down, I suddenly thought about how we express numbers that aren't whole. The whole numbers each have their own symbol(s) that are unique to themselves, whereas the non-whole numbers are expressed only as the output of a computation using whole numbers (a/b); they don't have their own unique symbolic representation and I'm not sure that it would ever be a useful thing to do. Which makes me wonder about how real they really are, or as Leopold Kronecker, a 19th C. mathematician put it: God made the integers, all the rest is the work of man.
AH
One of the nice proofs reproduced in the book was the one to show that the square root of 2 is not a rational number; that is, that that it can't be represented as a fraction (a/b). The proof is short and easy to follow (find it on Wikipedia) and the result is satisfying because of its sheer scope. Despite there being literally an infinite quantity of numbers, you will never find a number that is the exact square root of 2. And you can do that with absolute certainty without even breaking into a mental jog, the proof is that simple.
Anyway, when I was reacquainted with this proof I remembered that many years ago I was really not that impressed by it. There seemed to me to be an obvious intuitive argument that it had to be so. It's all a question of there not being enough space on the number line to fit in all those square-roots.
Think about it: from 1 through 9, say, there are an infinite quantity of intermediate numbers; and if we map each of that infinite multitude to its square-root (or higher root, for that matter), the number line of the roots is squashed up relative to the number line from which is originates (it ranges only from 1 through 3 in the above example). It seemed obvious to me that there simply couldn't be enough room on the number line for every number between 1 & 9 to map to its own unique root in the range 1 to 3. After all, there may be an infinite quantity of numbers between 1 and 3, but the infinite quantity of numbers between 1 and 9 must be greater, mustn't it?
The standard proof that root-2 isn't rational is certainly more definitive than my (admittedly informal) argument; but mine seems to imply that there won't be cube roots, fifth roots and all the way up. Or at least, it seems to be on first glance.
Another way of coming at this question is to consider what the decimal expansion would be of a number that is the square-root of any integer that is not a square number (1,4,9 etc.). Clearly, the root has to end with a non-zero digit after the decimal point. And when squared, the final digit would need to equal zero for the square to be an integer. But when you square all the digits from 1 through 9 you don't find any that maps to zero; the square of any decimal number will in fact have more digits after the decimal point than the putative root itself has. Hence, there are no integers other than square numbers that have a square-root that can be expressed as an exact decimal; and in fact, no number with a single digit after the decimal has its own root either.
Anyway, glad to have got this off my chest after all these years. In writing it down, I suddenly thought about how we express numbers that aren't whole. The whole numbers each have their own symbol(s) that are unique to themselves, whereas the non-whole numbers are expressed only as the output of a computation using whole numbers (a/b); they don't have their own unique symbolic representation and I'm not sure that it would ever be a useful thing to do. Which makes me wonder about how real they really are, or as Leopold Kronecker, a 19th C. mathematician put it: God made the integers, all the rest is the work of man.
AH
Monday, 24 November 2014
Cut my nose to spite my face?
The buy at the end of the month is a reinvested dividend, done automatically and there to taunt me as the share price rose strongly over following weeks. Until Friday. And now, this morning the smug satisfaction as the buyer who took the shares off my hands finally gets their comeuppance. Even though my dividend-in-shares has suffered equally, I feel so much better.
How daft is that?
Wednesday, 15 January 2014
Verona Joyce Bennett, RIP
 |
| Joyce Verona Bennett, 1917 - 2013 |
Today I was at the funeral of my grandmother, who checked out around Christmas time, a few days shy of her 97th birthday. It was a short and unremarkable service, but interesting nevertheless and I'm glad I went.
I'd completely forgotten, for example, that her given name was not in fact Joyce (the name she always used), but was actually Verona. And whilst I knew that she'd travelled fairly widely around the UK and Europe, I didn't know that she had taken her first and only journey by aeroplane - from Exeter to Bristol - aged 93. She'd made the trip just for the experience, apparently. I hope that I can also reach such an age and have new adventures of my own.
I'm not going to labour the point, but I'd guess that 1917 was not an auspicious time to be born as a female to a family of modest means in a small provincial English town. Getting pregnant at 21 by a soldier who then dissappeared off to war (the offspring of this congress being my mother) hardly improved her prospects. Nevertheless, she did prosper. No doubt the widespread upheaval within society that war with Germany precipitated was a good opportunity.
Mum was mostly brought up by her Grandmother, but not without difficulty. Being an unmarried mother in 1940s Britain would have probably been a drab and colourless affair, not helped the inflexible attitudes of the local Christians.
Yet, despite all this, she managed to to steer a life-course that was sufficiently interesting to merit a feature article in the Sunday Independent (more news to me) and a couple of Channel 4 documentaries (which we had all watched, agog, wondering what she might disclose about our hitherto unknown blood relative).
I remember her as a feisty lady of strong opinions, and as my Dad once said, she would likely have made impressive use of the opportunities that being born into a later age would have given her. Not that I think she was in any way dis-satisfied with her lot.
Farewell, Grandma.
Sunday, 27 October 2013
A Season of Cricket, 2013
When Whitchurch on Thames CC suffered some sort of IT failure that resulted in the loss of the whole of last year's averages, I was just a little peeved about it. So this year, I thought I'd keep a record through the season of my performances, just a little something to keep the focus as the season heads through those difficult months of mid-summer when the batsmen are getting themselves into form on flat pitches.
The purpose of this little post is to update myself on how the season went in numbers.
In a great summer of cricketing weather I managed to get in 35 matches; probably some sort of record. Of these, 13 were for Mandarins, the rest for WCC or their opposition (1), who were short.
I bowled in all but one of these games, the one being when I was suffering a cricked neck; and got through 217 overs (phew!). 40 of these were maidens and from the rest 809 runs were given away. The harvest in batsmen for all this was 41 wickets. That's a pleasing economy rate of 3.73 runs per over and averages 19.73 runs / wicket, striking slightly more frequently than once every 32 balls. My best numbers came at Goring on the second played match of the season: 8 - 0 - 15 - 3.
Definitely the secret to a good average is to bowl to passive batters, as the openers frequently are; and try to get yourself a fielding team that can catch and run around a bit. WCC do that creditably, though Mandarins are a little slow on their feet these days.
I collected a rather small number of catches - five - the last one being at the back-end of July. Note for next year: keep a log of drops, half catches and feeble pretences on cold days that "it wasn't quite there".
The batting doesn't need to be gone into much detail. Going in as tail-end-charlie in a run-chase is not always easy an easy place to score from. So maybe an average of 12.46 with the best innings (29*) in October's last fixture is not too dreadful; but then again, there is a reason why I tend to go in this position, and it's not just because I'm opening the bowling.
Looking out for warm days in the spring of 2014.
Tragic Case
The purpose of this little post is to update myself on how the season went in numbers.
In a great summer of cricketing weather I managed to get in 35 matches; probably some sort of record. Of these, 13 were for Mandarins, the rest for WCC or their opposition (1), who were short.
I bowled in all but one of these games, the one being when I was suffering a cricked neck; and got through 217 overs (phew!). 40 of these were maidens and from the rest 809 runs were given away. The harvest in batsmen for all this was 41 wickets. That's a pleasing economy rate of 3.73 runs per over and averages 19.73 runs / wicket, striking slightly more frequently than once every 32 balls. My best numbers came at Goring on the second played match of the season: 8 - 0 - 15 - 3.
Definitely the secret to a good average is to bowl to passive batters, as the openers frequently are; and try to get yourself a fielding team that can catch and run around a bit. WCC do that creditably, though Mandarins are a little slow on their feet these days.
I collected a rather small number of catches - five - the last one being at the back-end of July. Note for next year: keep a log of drops, half catches and feeble pretences on cold days that "it wasn't quite there".
The batting doesn't need to be gone into much detail. Going in as tail-end-charlie in a run-chase is not always easy an easy place to score from. So maybe an average of 12.46 with the best innings (29*) in October's last fixture is not too dreadful; but then again, there is a reason why I tend to go in this position, and it's not just because I'm opening the bowling.
Looking out for warm days in the spring of 2014.
Tragic Case
Saturday, 23 February 2013
How You Know Caissa Has Forsaken You
Strictly between us chess players...
My form on the board has been rather poor of late. My team mates know it, and I know it. This is my self indulgent notes-to-self after Wednesday's debacle...
- My pieces are not the equal of my opponents. My opponent and I are managers of two teams but, on a man for man basis, every piece on my side is a weakling compared to his.
- My pieces get in the way of each other and refuse to work together. It's as though they are all enemies; of each other, and me. Some have clearly gone rogue.
- My opponent's moves seem to happen more frequently than mine. On his turn, he seems to be making more moves than me. My own pieces seem content to stay at home today.
- I know I'm losing, even in positions which to anyone else would be OK. I've seen them in books and know, objectively, they're fine; but at the back of my mind, I know I'm losing, if not already flat lost.
- I struggle for ages to find any move that doesn't lose immediately, and yet my position continues to degrade with every clock tick. On the other side of the board, I see so many resources! It's inconceivable that, bunny though he is, he won't find the easy moves that'll beat me.
- I know that I'm going to lose this evening, even before the clocks have started and no matter how weak my opponent. He simply has to turn up and push some wood. If necessary, I'll help him beat me; and if he's a real patzer, I'll probably selfmate.
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