In Hospital

 On 24 March I went into Leighton Hospital for an operation to remove stnes from my bladder. I expected to be out in a couple of days, but was kept there for two weeks. They successfullylaseredon of the stones, but I have to go in again on 19 May for the other stone to be removed.

After coming out of hospital I had a period where I could hardly eat without throwing up, but gradually this has improved until I now enjoy my food once again.

I've also had trouble seeing clearly.. This was partly due to being given antihistamine in hospital. This is takinga  long while to clear up. .

The 19 ay date proved to be another pre-op assessmant. A date for the operation has not been set. I have a CT scan scheduled for11 June.

Algebraic Numbers

For my Numberlore book  I've been looking into the subject of Algebraic numbers. These are numbers that are the (real) solutions of algebraic equations with integer or rational coefficients. They include all rational numbers and expressions involving nth roots (square roots, cube roots etc), known as radicals. Thee are sufficient to solve all equations up to the fourth degree.

They do not include transcendental numbers like the circular constant, pi, or the exponential constant, e, which require infinite series

There are, however, further algebraic numbers between radicals and transcendentals. Little seems to have been written about them. They are solutions of quintic or higher equations and are known as ultra-radicals. One such is the solution to x^5 - x = 1. which is 1.1673... to four places of decimals. This and similar numbers were studied by a Swedish mathematician, Erland Bring (1736 - 1798). This information is from Wickipedia. I would be interested to know more.

 

In the News

 I found this Polar map projection among my History files. I copied it from somewhere years ago. It shows the location of Greenland, which is in the news, very clearly.

The quality of videos on You Tube seems to have deteriorated considerably lately, due to inferior productions based on Artificial Intelligence, and the automatic generation of mis-spelt captions, which often translate the same word or name in different ways in the same article. A lot of them also have the same didactic style of presentation.

We had a bit of snow on 5th January and since then it has been very cold here in Crewe. However the two named storms didn't reach this far north. Here's a photo I took from my front porch.

 

Medical Chaos

 I'm having difficulty communicating with the medical staff at Leighton Hospital departments and in the local General Practice. There are too many people involved who all seem to have their own idea of what should be done.

My long term problem has been prostate blockage which means I have to use self-administered catheters to empty my bladder of urine. I was advised in the past not to have the prostate operation because it might result in incontinence. However I came to the conclusion that this was the wrong advice and have asked for several years for the operation to be done. Maybe I could get it dome privately if the NHS will not do it.

Meanwhile stones have developed in the bladder and the Urologists proposed operating to remove them before operating on the prostate. They are now proposing to do an operation to drain off fluid from the  kidneys at the back before removing the stones. A further alternative is dialysis which I do not want. 

The renal doctor that I have been seeing prescribed some tablets called "Sevelamer Hydrochloride". I only took two tablets but they immediately upset my bowels resulting in constipation and episodes of diarrhoea  This took a month or so to recover from.

Most recently the the urologists fitted me with a fixed catheter. This fell out after one day, and they fitted me with another, but this has also come out. Rather that to submit to more of this torture I have reverted to using the self-administered catheters which work perfectly well.  

However the GPs keep arranging for extra leg bags and other equipment to be sent to me every  week that I cannot use. I'm no longer sure how I am supposed to communicate with the GPs. It is difficult to find the appropriate form on their website and I can't get the NHS "App" to work on my Laptop.

Trip to Blackpool

I tend to forget to report things on these diary pages, so here I am catching up on last month. On 13 - 16 October I managed to organise two days away in Blackpool.. 

The flats I was interested in were both gone already before I got there. . 

It is difficult to arrange such things from a distance. 

 

It was al a bit dull and overcast. but at least it didn't rain

and I had some long rides on the trams with a one-day ticket.

However my left knee seized up from too much walking,

so I was hobbling on the way home.

 

Maybe I'm not as frail as the doctors seem to think.

I ought to get out more like this.

 

Website Update

 I've started to update my website

Mayhematics

My photo is replaced by a new one with a hat. You may need to refresh the page.

I have deleted the Social link at the bottom since I found Bluesky was too US oriented. I don't want to go back to Twitter (X). I may be tempted to try mathstodon again, which I tried for a while but found too highly mathematical. Maybe they have a recreational branch?

I have noticed a few "comments" on my posts here. They aren't sent on to me and I tend to forget to look at them. Maybe I should check them more regularly and reply.

More updates to follow I hope.

Computer Problems

 I'm having a number of problems with my current computer set-up.

First my "btinternet . com" email address has been hacked so instead please use

jeepyjay @ who . net (close up spaces)

until further notice.

I'm also considering changing over to an alternative internet connection instead of BT.

I will also need to get a new computer with Windows 11 since Windows 10 is no longer being supported after October this year apparently. 

Probably my landline phone will no longer work so I will have to use a mobile phone. 

This is a lot of hassle that I don't really need in my present state of health!

Hospital Visit

 On Tuesday at 5:30 pm I got a phone call from one of the GPs to say that because of the results of a blood test I had on the previous Saturday, they were sending an ambulance to take me to hospital for tests.  The ambulance arrived at 7:15 and after doing blood pressure and sugar level tests to me to the Leighton Hospital where I arrived at 8:30 pm, and was given further Triage tests. 

After this I was sent to the Waiting Room, where I was expecting to see a doctor and to be sent home that evening. However nothing happened. A spent all night without being able to get any sleep. There were only hard seats. People were trying to sleep across several of the seats or on the floor. In the morning I was offered a bed in the corridor, but still no doctors.

Fortunately I was rescued from this situation when a doctor arrived who was setting up a new facility for treating elderly patients in a separate ward (18). This room included just five other elderly patients. This new department was evidently just being set up, so was still a bit disorganised. However I did get a comfortable seat and some food. Though I was tired out due to sleep deprivation.

Eventually I was given discharge and caught the bus home arriving a 4:30 pm on Wednesday. 

It seems I will be asked back to the same department for checking in future and they will be liaising with other departments such as Urology and Renal. I have declined to have any dialysis, but prefer to have palliative care, which virtually means I look after myself. 

I am also supposed to have an operation to remove two stones from my bladder, though when this can be done is unclear. Personally I would also like to have the operation to remove my prostate blockage, but the Urologists are reluctant to do this because of the risk of incontinence.

Numberlore

 Some years ago I produced a little PDF on Figurate Numbers, which I have continued to expand over the years in various forms. It is now coming together under the title "Numberlore" which as the name suggests covers a much wider range of topics.

Recently I have come across this website: Numbers Aplenty which includes lists of numerous classes of numbers that I have not come across before. Some seem rather trivial, but others are interesting..

Another website I've long been familiar with is Math Day of the Year Facts: Number Facts for Every Year Day ((1-30)) from "On This Day in Math" which has a similar eclectic selection of properties of numbers.

I would be interested to learn of other websites of this nature. The Numberphile pages on YouTube are another source of miscellaneous number lore. Also the Online Encyclopedia of Integer Sequences (OEIS).

My main interest is in whole numbers rather than irrationals, though they are of course related and turn up as limits of ratios of whole number terms in sequences. 

A curious book on numbers with a rather bombastic title is Numbers, Their Occult Power and Mystic Virtues by W. Wynn Westcott (1911) but its mathematical content is disappointing. The subject being mainly the occurrence of numbers in Bible texts and commentaries.

Rapid PLay Chess

 Our waste bins were not collected on Monday. I reported this to the Cheshire East council on the Wednesday but the bins have still not been emptied. They replied, giving me a code number to cite if nothing happens, but it is unclear how this is to be used. 

I took part in the Crewe Chess Club rapid play tournament which concluded with two rounds on Tuesday. I was placed in the lowest section but only managed to score 3 out of 6. A couple of photos I took of the event turned out to be too fuzzy to use. 

I'm not playing in the main Crewe Chess Tournament beginning today at the Mornflake stadium, since I haven't been feeling fit enough for three days play. 

I'm not looking forward to the weekend, if it s going to be really hot. The heat seems to be attracting a lot of little flies into my flat. It is necessary to keep the windows open at times to allow air to move through.

What Storm?

 No sign of the thunder storm we were supposed to get at 5pm today. It's been sunny for most of the day so far.  My front room gets hot in the afternoon. I've had to put up an extra blind. The house next door has been playing jungle drum music at the back, so I had to close the window. 

My GPs or their "assistant practitioner" has refused to allow ne any more antibiotic for UTI, so I've had to resort to paracetamol to control the pain. I hope this isn't a permanent decision. They don't seem to understand that a urine sample given through a catheter doesn't show the state of the urinary tract 

 

In the Alley

 I've been taking a walk along the alley at the back of my flat. 

There is extensive clearance going on at the back of several houses 

in Delamere Street, from the old Nunnery to No.59. 

It looks as though they may be planning to build something there. 

I took the photo through a gap in the high fence. 

The other photo is of a street light that is on at irregular times. 

At night it shines directly into my bedroom window. 

I did try a few years ago to get it moved but nothing happened. 

First Signs of Spring in the Park

I took a walk via Flag Lane and the Valley brook to Queens Park this sunny morning and took a few photos to cheer me up.

 

Circulating Chess Tours

I seem to have forgotten about this diary page for a while. Probably I've been too distracted with hospital check-ups and appointments. 

It was my 85th birthday early in February. It may be noted that 85 is a sum of two squares in two ways. It also has an interesting pattern in binary notation.

I've had one of the infrequent exchanges of messages with Prof Donald Knuth. He was interested in the E. W. Bennett problem of a circulating knight tour, which I solved with four symmetric tours, back in 1995. The tours are shown on the Knight's Tour Notes PDF #6 page 32.

Thanks to research by Arnaud Lefebvre (Rouen) it was possible to establish some biographical details: The original author was Edward William Bennett (1899 - 1979) who was President of the Otago Chess Club (New Zealand) in 1938 and champion there 1941, moving to Australia in 1945. 

I've been trying to convert material on my website into books of some kind, possibly a series of "Guides" on various subjects. The problem with making a Guide to Knight Tours is editing down the material to a manageable form. It would be necessary to keep referring to the website for more extensive details.

 

Chess Activities

 Since November last year I have resumed submitting some chess problem compositions to the BCPS for The Problemist and its Supplement. These revisit old pieces like Moose, Eagle and Equihopper where I think I should have done more work years ago. I have now found out how to use the computer program Popeye to test compositions in these pieces. Though there are still pieces that it does not test such as Ski-Pieces or L-hoppers where I have some unpublished ideas. Also it seems single-line compositions such as Helpmates in three are out of fashion and need to be enhanced with a second solution or twin to merit publication.

I've also been debating with myself as to whether to carry on playing over the board chess, since my health problems have been preventing my playing regularly. I think I will carry on after all.

Here are my two most recent wins, with interesting checkmate endings.

Crewe Chess Congress 2024

White G. Jelliss Black O. Bell

1.Nf3 Nc6 2.d4 Nf6 3.c3 h6 4.Bf4 d5 5.Nbd2 Bf5 6.e3 Qd7 7.Nb3 Ne4 8.Bd3 e7 9.OO OOO 10.Qe2 Re8 11.Ne5 NxNe5 12.BxNe5 f6 13.Bg3 a6 14.Na5 NxBg3 15.fxNg3 BxBd3 16.QxBd3 c6 17.b4 r5 18.a4 e4 19.Qe2 h5 20.h3 Rh6 21.Rab1 f5 22.b5 cxb5 23.axb5 Qc7 24.Qa2 Ree6 25.Rxf5 Be7 26.Rxd5 Bd8 27.Rc5 Kb8 28.RxQc7 KxRc7 29.Qd5 Rb6 30.Qc5+ Kb8 31.Rb4 Rbe6 32.c4 BxNa5 33.Qf8+ Ka7 34.Ra4 Bd2 35.Ra3 a5 36.c5 g5 37.b6+ Ka6 38.Qf1#

Wallasy v Crewe Match 2024

White M. Cockerill Black G. Jelliss

1.d4 e6 2.c4 b6 3.Bf4 Bb7 4.Nc3 d6 5.e3 Nbd7 6.Nf3 Be7 7.Be2 c5 8.OO h5 9.Rc1 g5 10.Nxg5 BxNg5 11.Bxd6 N2f6 12.dxc5 bxc5 13.Bxc5 Qc7 14.Ba3 Ne7 15.Qc2 Ng4 16.BxNg4 hxBg4 17.g3 f5 18.Nb5 Qc6 19.Nd6+ Kf8 20.NxBb7 QxNb7 21.Rcd1 Kf7 22.Qd4 Rxh2 23.f3 Rah8 24.Rd7 Bxe3+ 25.Rf2 Rh1+ 26.Kg2 R8h2#

This last was quite an aggressive game on my part with a nice forced mate at the end.

////////////

Is there an Election on?

 I bought a local paper today thinking it might have details of the candidates in the General Election on 4th July, but there is no mention of anything there! Aren't local "hustings" held here?

The BBC website has a list of eight candidates standing here, in Crewe and Nantwich, but so far I have only had one leaflet from the Labour Party candidate Connor Naismith. 

I suppose people are expected to vote on Party lines rather than by assessing the virtues of the individual candidates.  

Visit from Ayliean

 On 3 June I had a visit from Ayliean MacDonald, who publishes a number of videos on YiuTube and in Numberphile on knight's tours and other mathematical topics. 

Ayliean was interested in acquiring my "Archive on Knight's Tours", consisting mainly of photocopies of old documents and correspondence relating to the subject, accumulated over fifty years or more. 

We loaded them into her Renault for the long journey to Inverness. 

This video in her series includes my results on magic knight tours on the 16x16 board with biaxial symmetry using my "split and fix method".

More Magic Knight’s Tours, Hidden Inside Magic Knight’s Tours (youtube.com)    

==================

Photo added to post 25 August

Crewe Bus Station

 The Crewe Bus Station and multi-storey car park now appear to be completed. 

Though the area all round is still just wasteland. 

Presumably that area will be landscaped. I've not seen any plans to do more building there.

8x12 Symmetric Magic Knight Tour

 Guenter Stertenbrink reports that after a computer search 

there are no symmetric magic knight tours on the 8x10 rectangle.

 8x10 magic knight tours - ChessProblem.net

He provides this example of a rotationally symmetric magic tour 8x12.

First half numbered 1 to 48 (instead of 0 to 47).

Rank sum 582 (6x97). File sum 388 (4x97).

New Years Moan

The Christmas to New Year period is my least favourite time of the year. 

Over Christmas all the radio stations I normally listen to are taken over by Christian propaganda in the form of carols, which being a secular humanist unbeliever I find annoying. I tend to go into hibernation and put on my own CD music collection. I'm also not keen on the consumerist advertising, since I like a simple life of plain food without alcohol. 

The other main annoyance is that everything closes down every few days, not excluding strikes by doctors and train drivers. This morning I was thinking of changing my method of payment of my energy supply from pay-as-you-go to direct debit, since finding a functioning Pay Point anywhere near is increasingly difficult. However I couldn't find any way of doing this online. I suppose I will have to phone tomorrow, if it is possible to get through. 

I also checked my bank account online, but found I was not allowed access until they had phoned me and I had given them a four-digit code (this was after signing in with my ID, Password and four letters of my Special information). I tried opening a saver account that was on offer, but got a message that something went wrong and I should try visiting the bank! I clicked on a message that was indicated, but it resulted in signing me out. So I couldn't make the transfer of money from my current account to my ISA that I intended. So it was all a waste of time and effort. 

It seems that BT is threatening to close down land lines. Since I don't have  a mobile phone this would leave me incommunicado. I rely on it for communication with the medical profession. Now it seems it would also cut me off from my bank account.

Happy New Year?