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.