There was a concert of light music, of which I am a fan, due to be held at St George's Church in Beckenham this evening. So I thought I would look into the possibility of travelling there by public transport. According to the National Rail Enquiries website, which I've found to be reliable previously there was a train at 4:55 that would get me to Beckenham Junction by 17:15 with one change at East Croydon.
However, when I tried to buy such a ticket at Hastings station I was told such a trip was "impossible"! Also that the National Rail Enquiries were now run by a bus company who didn't understand the railways. Apparently the link from East Croydon to Beckenham Junction is via a Tram line. This appears to be correct: it is on something called the London Tramlink, which I've never heard of before, though it has been around for ten years.
So, lacking a clear route, I aborted the trip and decided to listen to a concert on Classic FM. This was a Prokofiev concert introduced by Howard Goodall. The first item announced was his Classical Symphony, number 1. However the music played bore little resemblance to previous performances of that work I had heard. I suspect it was some other of his symphonies, in far more modern style. The second item was announced as the music from Romeo and Juliet, including the "Dance of the Knights". However, unless I fell asleep, this was not the music played.
Tomorrow apparently it's time to put the clocks back, or is it forward? I'm not sure if I'm coming or going.
Saturday, 26 March 2011
Tuesday, 8 March 2011
A Magic Knight Rectangle
Back in 2003 I was able to prove that magic knight's tours were not possible on boards 4n+2 by 4m+2, but a proof for the 4n by 4m+2 case eluded me. I now see that that is because there is no such proof! Thanks to a suggestion by John Beasley, that since there is a simple magic knight+wazir tour on the 2x4 board, a magic knight tour should be possible on a sufficiently large 4n by 4m+2 board, I looked at the subject again and found two 12x14 examples last night, of which this is the first:
141 122 143 038 139 124 127 042 045 030 131 026 047 028
144 037 140 123 128 039 044 125 130 041 046 029 132 025
121 142 035 138 119 126 129 040 043 050 031 134 027 048
036 145 120 063 034 137 014 155 032 135 106 049 024 133
011 064 061 118 013 154 033 136 015 156 051 108 105 158
146 117 012 151 062 059 016 153 110 107 018 157 052 023
065 010 115 060 149 152 111 058 017 020 109 054 159 104
116 147 150 009 114 057 094 075 112 055 160 019 022 053
091 066 007 148 093 074 113 056 095 076 021 162 103 078
006 069 092 073 008 003 082 085 168 161 096 077 100 163
067 090 071 004 083 088 167 002 081 086 165 098 079 102
070 005 068 089 072 001 084 087 166 097 080 101 164 099
It is constructed by the "rolling pin" method that I devised for 12x12 magic tours. It's surprising I hadn't thought of trying this before. It's just a matter of widening the board. The files add to 1014 = 169x6 and the ranks add to 1183 = 169x7. Each file consists of three pairs adding to 127 and three pairs adding to 211. The ranks are made up of pairs of complements adding to 169.
141 122 143 038 139 124 127 042 045 030 131 026 047 028
144 037 140 123 128 039 044 125 130 041 046 029 132 025
121 142 035 138 119 126 129 040 043 050 031 134 027 048
036 145 120 063 034 137 014 155 032 135 106 049 024 133
011 064 061 118 013 154 033 136 015 156 051 108 105 158
146 117 012 151 062 059 016 153 110 107 018 157 052 023
065 010 115 060 149 152 111 058 017 020 109 054 159 104
116 147 150 009 114 057 094 075 112 055 160 019 022 053
091 066 007 148 093 074 113 056 095 076 021 162 103 078
006 069 092 073 008 003 082 085 168 161 096 077 100 163
067 090 071 004 083 088 167 002 081 086 165 098 079 102
070 005 068 089 072 001 084 087 166 097 080 101 164 099
It is constructed by the "rolling pin" method that I devised for 12x12 magic tours. It's surprising I hadn't thought of trying this before. It's just a matter of widening the board. The files add to 1014 = 169x6 and the ranks add to 1183 = 169x7. Each file consists of three pairs adding to 127 and three pairs adding to 211. The ranks are made up of pairs of complements adding to 169.
Friday, 18 February 2011
Knight's Tour Notes website gone
I've just noticed that my old Knight's Tour Notes website has vanished into the ether. This is not unexpected, since it was housed on a dial-up site which I have been unable to access for several years. I will now have to relaunch it on my Mayhematics site, or start up a new URL. This may take some time. I will probably want to put it into a revised format and improve some of the diagrams.
Tuesday, 15 February 2011
Outing to London and Leicester
On Saturday morning I decided on something of an impulse to combine a trip to London to attend the Conway Hall talk by Jim Moore on "Darwin and the Sin of Slavery", with a trip to Leicester to attend the lecture by Ken MacLeod on "Darwin Dawkins and the Left". This was just about possible in the time by using booking.com to locate a Hotel and the National Rail Enquiries to book the trains, using a debit card and collecting the tickets from the machine at Hastings station. The machine was a bit recalcitrant but finally came up with the tickets.
One of the interesting points from the Moore lecture that I'd not been aware of was the role of Louis Agassiz (now best known for his work on ice ages) in diverting Darwin's efforts into countering Agassiz's strange theory of multiple 'creations' of separate human races known as polygenism.
Ken McLeod's thesis was that many people on the political Left have deliberately misunderstood Richard Dawkins, or the implications of his "Selfish Gene" idea, though it seems to me that many of other persuasions have been equally free in criticising Dawkins without having apparently read his books.
I was hoping also to fit in a Gresham Lecture by Christopher Hogwood, given at the Museum of London at 1pm today (Tuesday). But this was scuppered since my train was over half an hour late arriving at St Pancras, due apparently to signaling problems. It was also raining, so I used my bus pass to get the No.17 to London Bridge, but managed to get there just in time to miss the first Hastings train.
One of the interesting points from the Moore lecture that I'd not been aware of was the role of Louis Agassiz (now best known for his work on ice ages) in diverting Darwin's efforts into countering Agassiz's strange theory of multiple 'creations' of separate human races known as polygenism.
Ken McLeod's thesis was that many people on the political Left have deliberately misunderstood Richard Dawkins, or the implications of his "Selfish Gene" idea, though it seems to me that many of other persuasions have been equally free in criticising Dawkins without having apparently read his books.
I was hoping also to fit in a Gresham Lecture by Christopher Hogwood, given at the Museum of London at 1pm today (Tuesday). But this was scuppered since my train was over half an hour late arriving at St Pancras, due apparently to signaling problems. It was also raining, so I used my bus pass to get the No.17 to London Bridge, but managed to get there just in time to miss the first Hastings train.
Friday, 4 February 2011
Twittering
Well the beard didn't last very long. I'll have to change my photo again. It felt too uncomfortable, and was just as much trouble to maintain as shaving every day or two, as well as making me feel old. Srangely three people complimented me on the beard, but unfortunately after I'd already got rid of it.
I joined Twitter a few days ago. As if I need more ways to waste my time. Somehow I have already acquired five followers and sixteen subjects to follow, and posted two tweets, all this mostly related to humanism.
I joined Twitter a few days ago. As if I need more ways to waste my time. Somehow I have already acquired five followers and sixteen subjects to follow, and posted two tweets, all this mostly related to humanism.
Saturday, 22 January 2011
Nostalgia Apologia
I thought I'd let my beard grow during the cold spell over the Winter Solstice, thinking that I would probably shave it off when the weather changed, but it seems I have now become attached to it, at least until any really warm weather should come along. I've also updated my photo here and on facebook accordingly.
This evening, having seen it previewed in the local paper, I went to the White Rock Theatre for an evening of nostalgia, where the Glenn Miller Orchestra was performing. The tunes were good, and some of the individual performers, but it was just far too loud. After the interval I tried moving further back in the Gallery but couldn't escape the sheer blast of sound. It was getting almost painful. So when they started playing something from The Sound of Music, which I certainly don't associate with the Glenn Miller era, I decided I'd had enough.
This evening, having seen it previewed in the local paper, I went to the White Rock Theatre for an evening of nostalgia, where the Glenn Miller Orchestra was performing. The tunes were good, and some of the individual performers, but it was just far too loud. After the interval I tried moving further back in the Gallery but couldn't escape the sheer blast of sound. It was getting almost painful. So when they started playing something from The Sound of Music, which I certainly don't associate with the Glenn Miller era, I decided I'd had enough.
Sunday, 2 January 2011
Queen Victoria in Warrior Square
There was a spectacular sunset this evening around 4:30. I went out with my camera to try to capture an image, but by then the view had changed, first the sun came out from behind the clouds, then it quickly set. I got some images, but they were similar to others obtained before. I ended up on the sea-front by Warrior Square and noticed that the statue of Queen Victoria was illuminated with a spotlight and that the plinth seems to have been cleaned. Hence the photo shown here.I did very poorly in the Weekend Chess Congress, playing in the Minor tournament, since I managed only a draw, and that was against the youngest competitor, where I ended up with a knight and pawn against two knights and pawn. The middle game of the five, played in the evening of the first day, was weird. I made a muddle of the opening and was well down, then somehow revived to fight back to a winning position, and then went to sleep again in the end game and threw it away. Sheer tiredness I think. There are another five games to go in the New Year tournament, which I suspect will be against stronger opposition.
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