Every week, though not every day, I buy a few newspapers, mainly for the puzzles rather than the news. On Friday for instance the Guardian has a sudoku and kakuro that are usually a bit harder than during the week. The Guardian on Saturday always has a good prize crossword, often by Araucaria, but I don't always buy it because it has far too many sections, on subjects such as sport, travel, finance, fashion and so on, that I'm not really interested in.
I also tend to get the Times once or twice a week, mainly for the crossword and the killer sudoku. However this week the Times has started to include a four-page puzzle section every day! This will mean that I have to avoid buying the Times in future, because once I start on the puzzles I have the compulsion to solve them all, and waste most of the day when I should be doing something productive. Why they have changed to this new scheme I don't know, I thought their previous policy was just the right balance.
Friday, 5 March 2010
Saturday, 27 February 2010
More Random Thoughts
I spent most of Thursday journeying to and from Uckfield to attend the East Sussex SACRE meeting on behalf of Hastings Humanists. Since I have a Senior Railcard and a Buspass this was not expensive, just time-consuming. When I returned, and all next day, I had a headache. Whether this was due to bumping about on the bus, or waiting for it in the cold and wet, or some other cause I'm not sure, but at least it seems to have cleared up today. At any rate it stopped me going to the chess club on Friday evening.
While in Uckfield I chanced to go into a Health Food shop and bought a jar of Barley Cup as a possible substitute for drinkng too much Coffee. It doesn't have any distinctive taste that I can detect, just a smooth texture. I did try flavouring it with some Malt Extract, bought at the same shop, but Honey would probably be better. Since I arrived in plenty of time for the meeting I looked around to see what cafes were available and ended up in a Poppins restaurant, which provided a nice lesagna with baked potato and salad.
I'm still working on the knight's tours book. I had hoped to get it finished for my 70 th birthday, but there is still a lot to be done. At present I'm on the chapter dealing with tours on oblong boards. I completely rechecked the tours on the 3x9 board, finding 146 as reported on the KTN website back in year 2000, although there is a minor misprint there, the number of {1,1} tours, with ends a diagonal step apart, is 28 not 29. The next section to check is on the 4xn boards, where I did some work trying to generate recursion relations for the numbers of half-tours, which has never yet been reported on the KTN site.
While in Uckfield I chanced to go into a Health Food shop and bought a jar of Barley Cup as a possible substitute for drinkng too much Coffee. It doesn't have any distinctive taste that I can detect, just a smooth texture. I did try flavouring it with some Malt Extract, bought at the same shop, but Honey would probably be better. Since I arrived in plenty of time for the meeting I looked around to see what cafes were available and ended up in a Poppins restaurant, which provided a nice lesagna with baked potato and salad.
I'm still working on the knight's tours book. I had hoped to get it finished for my 70 th birthday, but there is still a lot to be done. At present I'm on the chapter dealing with tours on oblong boards. I completely rechecked the tours on the 3x9 board, finding 146 as reported on the KTN website back in year 2000, although there is a minor misprint there, the number of {1,1} tours, with ends a diagonal step apart, is 28 not 29. The next section to check is on the 4xn boards, where I did some work trying to generate recursion relations for the numbers of half-tours, which has never yet been reported on the KTN site.
Saturday, 20 February 2010
Random Thoughts
I played another couple of chess games on Friday evening, at a slow rate without clocks, and won both of them against a player who seemed quite strong, so perhaps I'm getting back into the right frame of mind. One ended in a knight checkmate, the other in a queen against rook superiority. The more rapid play games which we played on previous weeks require one to react much more instinctively, rather than contemplate each move carefully.
Why are there no longer any malt-flavoured cereals being produced? I used to like malted shreddies when they were produced by Rowntrees, but as soon as Nescafe took them over they changed the recipe so that the malt taste was far less. I complained at the time, but got no helpful response. Now they have removed the malt altogether! This seems to be part of their policy of claiming that everything is "whole grain".
My article on "Howard Jacobson and the Temple of Darwin" appeared on the new HumanistLife website on my 70th birthday, 8th February, but has not attracted any comments. Perhaps this means that it is perfect as it is and doesn't need any further comments? Probably not! I'm glad to see that more articles are appearing with a greater frequency now. There are strong disagreements between Humanists on a number of issues, for instance the assisted dying question, and whether the burka should be banned. These have attracted the most comments.
Why are there no longer any malt-flavoured cereals being produced? I used to like malted shreddies when they were produced by Rowntrees, but as soon as Nescafe took them over they changed the recipe so that the malt taste was far less. I complained at the time, but got no helpful response. Now they have removed the malt altogether! This seems to be part of their policy of claiming that everything is "whole grain".
My article on "Howard Jacobson and the Temple of Darwin" appeared on the new HumanistLife website on my 70th birthday, 8th February, but has not attracted any comments. Perhaps this means that it is perfect as it is and doesn't need any further comments? Probably not! I'm glad to see that more articles are appearing with a greater frequency now. There are strong disagreements between Humanists on a number of issues, for instance the assisted dying question, and whether the burka should be banned. These have attracted the most comments.
Thursday, 11 February 2010
The Religion of Infinity
I happened to notice that the Horizon programme on BBC2 TV this evening was about "Infinity and Beyond". Hoping to learn of some new research I tuned in but was sorely disappointed. The programme was aimed at about the intellectual level of a five-year-old. The commentary was given by an Aleister Crowley lookalike who was filmed in murky black and white endlessly walking up stairs and reappearing again, Escher-like, on the bottom landing, and making pompous and portentous-sounding statements and poses. Half-way through he even renamed Georg Cantor "Gregor".
All the usual elementary illustrations of infinity were included, such as Hilbert's Hotel, Cantor's diagonal argument and monkeys typing Shakespeare, followed by speculation about whether the universe might be infinite. There was one chap who didn't believe in infinity, but all he could say was that there was a largest number, but no-one knows what it is, and it is followed by zero.
My argument for finitism runs as follows: It is true that we can generate symbols for numbers in a systematic manner using the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and the positional convention, but this does not mean that the set of all such symbols 'exists' already until we actually construct it. Nor does the mere construction of a symbol, such as n+1 for a number imply that the number 'exists' in this sense.
The mathematical term 'finite' applies to sets of things and the numbers of things in those sets: a set is said to be finite if it has the sensible property that it cannot be placed in one-to-one correspondence with a part of itself; a number is finite if it describes the size of a finite set. The Finitist maintains that all sets, and therefore all numbers, are in fact finite.
In order to introduce infinity into mathematics it is necessary to postulate that it exists, or to assume some other axiom that implies this, for instance Peano's axiom that every number has an immediate successor. Further the properties of infinities depend on the axioms that are chosen. For example Paul Cohen proved that, under the usual axioms for arithmetic, it is impossible to say whether there is an infinity between that of the integers and the real numbers.
On the other hand the properties of finite sets and numbers are a matter of physical fact, at least within the 'realisable' realm, where they can be applied to material objects. Statements about 'all' numbers, such as Goldbach's conjecture, may not be realisable.
What do we mean by saying that something 'really exists'? The simplest definition is that something exists if it is material, that is if it has measurable mass. On this basis it might be argued that 'ideas' like numbers do not exist since they are immaterial. But are they? Ideas exist in the minds of people, and presumably therefore they exist materially in the form of electrical or chemical energy in the brains of those who think about them. By Einstein's equation, E = mc², anything that has energy has corresponding mass. So if mathematician's brains really contained the infinite set of all whole numbers they would have infinite mass and implode into a black hole!
By a similar argument, the universe is finite in mass, since if it were infinite there would be infinite gravitational force at every point in the universe (a version of Olbers' paradox).
Even if we discount the argument by weight, so long as we accept that ideas exist in the form of electrical or chemical configurations in the brains of thinkers, there can still only be a finite number of ideas in existence, certainly of human ideas, held by human beings, because there is only a very finite number of human beings extant, and their brains contain only finite numbers of neurons.
EDIT: In contrast to the puerile "Horizon", Melvyn Bragg's "In Our Time" on Radio 4 this morning was an adult-level programme about "unintended consequences" in mathematics, on how ideas developed purely out of mathematical interest later prove to have practical consequences: such as prime number theory in cryptography, complex numbers in alternating electrics, and non-euclidean geometry in relativity. Why does TV have to dumb-down, while Radio does ideas so well?
All the usual elementary illustrations of infinity were included, such as Hilbert's Hotel, Cantor's diagonal argument and monkeys typing Shakespeare, followed by speculation about whether the universe might be infinite. There was one chap who didn't believe in infinity, but all he could say was that there was a largest number, but no-one knows what it is, and it is followed by zero.
My argument for finitism runs as follows: It is true that we can generate symbols for numbers in a systematic manner using the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and the positional convention, but this does not mean that the set of all such symbols 'exists' already until we actually construct it. Nor does the mere construction of a symbol, such as n+1 for a number imply that the number 'exists' in this sense.
The mathematical term 'finite' applies to sets of things and the numbers of things in those sets: a set is said to be finite if it has the sensible property that it cannot be placed in one-to-one correspondence with a part of itself; a number is finite if it describes the size of a finite set. The Finitist maintains that all sets, and therefore all numbers, are in fact finite.
In order to introduce infinity into mathematics it is necessary to postulate that it exists, or to assume some other axiom that implies this, for instance Peano's axiom that every number has an immediate successor. Further the properties of infinities depend on the axioms that are chosen. For example Paul Cohen proved that, under the usual axioms for arithmetic, it is impossible to say whether there is an infinity between that of the integers and the real numbers.
On the other hand the properties of finite sets and numbers are a matter of physical fact, at least within the 'realisable' realm, where they can be applied to material objects. Statements about 'all' numbers, such as Goldbach's conjecture, may not be realisable.
What do we mean by saying that something 'really exists'? The simplest definition is that something exists if it is material, that is if it has measurable mass. On this basis it might be argued that 'ideas' like numbers do not exist since they are immaterial. But are they? Ideas exist in the minds of people, and presumably therefore they exist materially in the form of electrical or chemical energy in the brains of those who think about them. By Einstein's equation, E = mc², anything that has energy has corresponding mass. So if mathematician's brains really contained the infinite set of all whole numbers they would have infinite mass and implode into a black hole!
By a similar argument, the universe is finite in mass, since if it were infinite there would be infinite gravitational force at every point in the universe (a version of Olbers' paradox).
Even if we discount the argument by weight, so long as we accept that ideas exist in the form of electrical or chemical configurations in the brains of thinkers, there can still only be a finite number of ideas in existence, certainly of human ideas, held by human beings, because there is only a very finite number of human beings extant, and their brains contain only finite numbers of neurons.
EDIT: In contrast to the puerile "Horizon", Melvyn Bragg's "In Our Time" on Radio 4 this morning was an adult-level programme about "unintended consequences" in mathematics, on how ideas developed purely out of mathematical interest later prove to have practical consequences: such as prime number theory in cryptography, complex numbers in alternating electrics, and non-euclidean geometry in relativity. Why does TV have to dumb-down, while Radio does ideas so well?
Friday, 5 February 2010
More Chess
More chess this Friday evening, a six-player all-play-all with twenty minutes on the clock. I was given a low grading of 80 and had 13 minutes to 7, or 15 minutes to 5, depending on opponents' gradings. This time I won two, though my opponents in those games were either distracted by the time handicap, or thought I needed a win. Both ended in a straightforward queen checkmate. I did deliberately try to play in a more attacking style compared with last time.
I've been feeling rather tired in the afternoons lately, and unable to rouse myself to get much done. Perhaps I need to keep more regular hours, or perhaps I will come out of hibernation when the weather warms up a bit.
I've been feeling rather tired in the afternoons lately, and unable to rouse myself to get much done. Perhaps I need to keep more regular hours, or perhaps I will come out of hibernation when the weather warms up a bit.
Sunday, 31 January 2010
A Busy Week in London
On Thursday evening I returned from a two-day visit to London, but I haven't been able to report on it until now since my internet connection has been down, due to a fault at Virgin Media.
On the Wednesday afternoon I had booked a visit to the Cocoon at the Natural History Museum, and in the evening went to the 'Evict the Bishops' debate at the Houses of Parliament. These were both something of a disappointment. I've submitted an article to HumanistLife relating to the first topic, and have reported on the second on the Hastings Humanists blog. The cheap hotel room I stayed in overnight was also not to be recommended.
On Thursday afternoon however I had the much more pleasant experience of going to the Albert Hall to see the Cirque du Soleil production called "Varekai". Their show is a sort of mixture of circus, theatre and ballet. To appreciate it best I think you need to book a seat facing the stage and probably on the flat, though these seats are the more expensive for that reason. I was in a box high up on one side. From there you can see all the workings of the stage. They make extensive use of trap doors through which characters regularly appear and disappear. There are all the usual circus attractions, but no animals of course, though many of their costumes resemble strange creatures.
On Friday evening at the chess club I was inveigled into an all-play-all rapid chess tournament, and despite being allowed a handicap of 15 minutes against 5 minutes playing time against strong opponents managed to lose all my eight games, though they all went close to the wire.
So it was a busy week. More on it later perhaps.
On the Wednesday afternoon I had booked a visit to the Cocoon at the Natural History Museum, and in the evening went to the 'Evict the Bishops' debate at the Houses of Parliament. These were both something of a disappointment. I've submitted an article to HumanistLife relating to the first topic, and have reported on the second on the Hastings Humanists blog. The cheap hotel room I stayed in overnight was also not to be recommended.
On Thursday afternoon however I had the much more pleasant experience of going to the Albert Hall to see the Cirque du Soleil production called "Varekai". Their show is a sort of mixture of circus, theatre and ballet. To appreciate it best I think you need to book a seat facing the stage and probably on the flat, though these seats are the more expensive for that reason. I was in a box high up on one side. From there you can see all the workings of the stage. They make extensive use of trap doors through which characters regularly appear and disappear. There are all the usual circus attractions, but no animals of course, though many of their costumes resemble strange creatures.
On Friday evening at the chess club I was inveigled into an all-play-all rapid chess tournament, and despite being allowed a handicap of 15 minutes against 5 minutes playing time against strong opponents managed to lose all my eight games, though they all went close to the wire.
So it was a busy week. More on it later perhaps.
Wednesday, 27 January 2010
Chess, Music and Euthanasia
This is a photo I took on Monday of the Hastings Chess Club premises in Cornwallis Terrace. As you can see, like many places in Hastings, they hardly conform to the requirements of disabled access. The steps up to the front door could hardly be more precipitous!Besides chess I've started to take an interest once more in music, with a view to playing or composing, probably with an electronic keyboard. Besides loking at various keyboards in a local music shop, and searching for details online, I borrowed a book "Play it Again" from the public library. This gave some useful website links and they are now listed on a page of my website devoted to Music.
Last week I also received a bowel cancer test kit through the post from the NHS. Taking smears for the test was not a very pleasant occupation, it must be very embarrassing for people who are unable to do them without assistance. According to the news this morning everyone who attends hospital is now to be tested for liability to thrombosis. Is this determination to keep more people living longer really a good thing? I see Martin Amis is advocating the provision of euthanasia booths on street corners where the decrepit are to be encouraged to end it all!
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