Saturday, 19 December 2020

"Exponential Growth"


I recently heard someone say in a television interview that incidence of the corona virus was increasing, but not increasing exponentially. That is an absurd claim.

"exponential" is being misused to mean 'fast' by people who do not know what it means, but use it because they hear clever people using it and think that if they use it they too will appear clever.

A quantity q changes exponentially  when:

qt =q0*kt where q0 is the initial value of q,

qt is the value of after t time units, and k is a constant. Positive k corresponds to exponential increase, and negative k to exponential decrease.

Increases of the incidence of the corona virus will always be approximately exponential until near the very end of the epidemic when most people will be immune. Until then the rate at which people catch the virus will be roughly proportional to the number already infectious. That implies exponential growth or decay

Friday, 4 December 2020

What Could we Buy for 4p ?


I was intrigued by the price in the following extract from the latest newsletter from the District Council.

"Our large waste items for collection service allows for up to three large household items or 12 sacks of waste to be collected for a charge of £35.04."

I wonder how someone arrived at that figure ?

Wednesday, 2 December 2020

What Became of Burton's ?


In the 1960 s and 70 s I used to buy suits from Burton's. They measured me and after a while I would be summoned for a fitting. The clothes fitted, lasted for a good while, and were not particularly expensive, but then Burton's shops seemed to disappear. I don't recall seeing one in the last thirty years. I thought the company had faded away until I saw the news of the collapse of the Arcadia group, which apparently owned Burton's. Where was the company hiding in the years since I last patronised it?

Tuesday, 1 December 2020

The Garden in December

 Flowers still abound in the garden. I don't remember ever seeing so many in December. Apart from the yellow Winter Jasmine and the hardy cyclamen that usually flower around this time, there are the white Summer jasmine, blue campanulas, begonias, feverfew, fuchsias, Mexican daisies, rudbekia, a couple of late flowers on the hydrangea, some zonal pelargoniums, often miscalled 'geraniums' and some flowers on old strawberry plants.

I usually try to avoid repetition in this blog, and worry that this post is very similar to one I posted last month, but think the difference between November flowers and December flowers is big enough to justify saying much the same thing twice.

Saturday, 28 November 2020

Praising Solitary Shopping


I try to shop as quickly as possible to minimise my exposure  to infected droplets emitted by other shoppers. Serious obstacles are groups of people blocking aisles. I can usually navigate my way past solitary shoppers quite easily. The great problems are the blockades constructed by people shopping in pairs.

Couples tend to have prolonged seminars about the tensile strength of the cucumbers. Sometimes they block not only the shelf containing whatever it is they contemplate buying, but several other shelves too. There will be their trolley, with one of them behind the trolley, often with a bottom sticking out behind them, and the other in front of the trolley waving about a sample of whatever it is they might eventually decide to buy. Sometimes one of the pair minds the trolley on one side of the aisle, while the other inspects the opposite side, contorting themselves so that there is too little space for anyone to pass between their buttocks and the trolley. I suspect that many people are not aware of themselves as physical objects

 Shopping should not be a social occasion.

Thursday, 26 November 2020

The Last of the Homegrown Tomatoes


For the first time for several months I bought some tomatoes today. Apart from a few unripe fruit that may or may not ripen indoors, I've now used up all the crop from my own plants. They ripened rather later than usual this year - I attribute that to a shortage of sunshine at the time they should have started to ripen, but I still had plenty of fruit in the end. I have saved seed for next year.

Saturday, 21 November 2020

Praising Virtual Firework displays


We didn't hear a great many fireworks this year. Despite the cancellation of the usual town display in the park individual efforts seemed quite restrained though they were spread over several days.

I did wonder though whether actual displays of arial chemistry are needed. Spectacular displays in many places have been filmed in recent years. Those could be made available on the Internet, or even broadcast on television on special occasions.

It should be possible to write a program to simulate a firework display, at a virtual location chosen by the user.

Pets need not be terrified, spectators need not be injured. Let all fireworks be virtual.

Wednesday, 18 November 2020

A Floriforous November


Even though it is now the second half of November, less than five weeks before the shortest day, there are still quite a few flowers in the garden - two sorts of jasmine, begonias, Mexican daisies, zonal pelargoniums, blue campanula, cyclamen, feverfew, and several others whose names escape me.

Friday, 30 October 2020

Immortality ?


A while ago I boasted that I'd killed my mint by neglect - something few gardeners achieve. Now I have to withdraw that boast.  This morning I noticed small sprigs of mint where the old plant used to grow.

It's back!!

Thursday, 29 October 2020

A Reminder of Old Money

I recently saw an advertisement for gold coins, described as one eighth of a sovereign. They cost £69.

That is equivalent to a sovereign costing £552, When my parents were children sovereigns were still in use as currency and were valued at one pound.  An eighth of a pound was a half crown. Moderately distant relatives sometimes gave me a half crown as a Christmas present. £69 would have been much more exciting!

Wednesday, 28 October 2020

Check Bank Statements Carefully


 Before the lock down in March I almost always paid for shopping with cash. Since then I've usually used a bank card like a magic wand, nonchalantly waving it over the shop's machine. After a while I decided to compare deductions from my account with receipts from shops. In one case I noticed a deduction 99 pence more than the sum shown on the receipt, so DON'T TRUST THE SYSTEM !!!

Sunday, 25 October 2020

Nudity in Wales


I read that during the current 'lock down' in Wales shops will be allowed to sell only goods officially considered 'essential' and that that does not include clothes.

Is that official approval for people to shop in the nude?

Wednesday, 21 October 2020

David Hume

I notice that the University of Edinburgh has changed the name of a building that used to be named after David Hume, one of Britain's greatest philosophers. It has been alleged that he was a racist.

I have read a great deal of Hume's writings without ever encountering any remarks about race. I thought this remark on the BBC website significant.

"Elizabeth Lund, who started the online petition, wrote alongside it that Hume "wrote racist epithets not worth repeating." "

Thus she declines to refer us to the passages to which she objects. Without such a reference I shall treat the objections as frivolous, a case of the intellectually insignificant jealous of a mind superior to their own.

Saturday, 10 October 2020

Zooming Again


On Thursday I hosted a Zoom meeting. Although I'd used Zoom before that was the first time I'd hosted a meeting. There were only four of us so it was easy to experiment without confusing each other. We pressed every button we could find so I now have quite a good idea how the software works. I plan to hold regular virtual, meetings henceforth, replacing the monthly meetings the U3A Science and Technology Group used to hold on Age UK premises.

Friday, 2 October 2020

Misplaced Faith


Depressing stories have emerged about Post Office staff convicted of alleged crimes that had never been committed either by themselves or by anyone else. What had actually happened was that the Post Office computer systems made errors. Gullible managers had assumed that the computers could not have erred. 

Ever since computers came to be used widely there have been cases of people making the absurd assumption that computer systems cannot err.  No one making that assumption should be allowed to hold any senior post in any organisation.

Wednesday, 30 September 2020

Double Counting


I just heard a comment that all the money people spend on cigarettes would suffice to pay for inoculating the entire world population against the corona virus. In Britain at least most of the money people spend on tobacco goes to the Government in taxes and so is already available for whatever good deed the Government is inclined to perform, so persuading smokers to give up, though in itself highly desirable, would not solve the problem of corona virus.

Tuesday, 29 September 2020

10 pm Closing


A uniform closing time is producing crowds of garrulous people outside recently closed pubs and restaurants. Total closure of such establishments would make things difficult for people who travel for work or other good reasons. I suggest that we should instead allow eating places to remain open as long as they like, but forbid them to sell alcohol. I believe that sober people would behave less recklessly than tipsy revelers.

We do have alcohol limits for drivers. Why not for everyone in a public place? Those wishing to drown their inhibitions could do so at home, and have virtual pub crawls in a specially designed computer game. 

Saturday, 26 September 2020

Rationing Toilet Paper


I spotted a news item to the effect that some supermarkets are restricting customers to at most three packets of toilet paper. I wonder how they measure the quantity. Toilet paper seems to be sold in packs  ranging in size from two rolls to at least 16. It would be strange to condemn someone buying four packets of two rolls as greedier than someone else who buys one packet of 16.

 Buying four small packets would indeed be odd. but odd cases are often good tests of rules.

Friday, 25 September 2020

Da Home Sexy


Thus did the BBC sub-title algorithm transcribe 'The Home Secretary' . I've often wondered whether the algorithm is embodied in an AI or a human. Whichever it is, it provides me with a good deal of amusement.

Tuesday, 22 September 2020

Paising HTML

I've recently been brushing up my Maths by reading old text books. A great obstacle to understanding is the need to follow references of the form:

'see example 4 following theorem 2 in section 9'

Usually such references contain no page numbers, and section numbers are shown only on the first page of each section, not at the heads of individual pages. I need a bookmark to keep my place, and even then by the time I've shuffled through numerous pages to locate the reference I've often forgotten why I needed it.

In an html document one simply clicks on the reference, and there is it. The BACK key returns on to the original. There are many reasons for publishing online, but the ease of cross referencing is rarely mentioned.

Thursday, 17 September 2020

Bibulous Loquacity


I worry about the likely consequences of reopening public Houses. The core activity of those institutions is the consumption of alcoholic drinks, and many people drink in pubs to meet people they don't meet elsewhere.

Alcohol reduces inhibitions and slackens self control making 'social distancing' harder to maintain. Voices are often raised and raucous laughter is common. The louder the talk and laughter, the more copious the accompanying emissions of infected droplets. 

Pubs are best avoided. Drink only in your bubble!

Saturday, 29 August 2020

Infuriated by Microsoft


When I logged on to my computer after the last update to Windows 10 the screen was filled with a Microsoft Edge window, with buttons telling me where to put files of various sorts, and an incitement to explore the alleged wonders of a new version of Edge.

The buttons that ought to have closed or minimised the Edge window had been disabled, and I had to resort to summoning Task Manager with ALT&Ctrl&Delete to close the offending disutility.

I find Microsoft's tendency to try to tell me how to organise material particularly infuriating. I have devised a filing system that arranges material where I can find it easily. When I get a new computer I copy the accumulated material onto it and I don't want any interference, yet still the operating system tries to put downloaded files to places where I can't find them.

Thursday, 27 August 2020

My Website


I've brought several pages of my website up to date, so those eager for enlightenment are invited to look at and follow the links on that page to garden and books.

Monday, 24 August 2020

Praising Quadratic Equations


It irritates me when people who know little mathematics refer to quadratic equations as examples of very difficult mathematics.

I still remember when I was taught how to solve quadratics by completing the square. I was twelve years old  at the time and was most impressed by the ingenuity of the method. I think that was the first time I found Mathematics exciting. To me those who shudder at the mere thought of a quadratic are identifying themselves as intellectually pre-adolescent.

Quadratics are the key to solving polynomials of higher degree and thus to finding the eigenvalues of a linear transformation - at the heart of quantum theory- and to solving the differential equations governing electrical circuits and the oscillations of the wings of an aircraft. Quadratics are wonderful, and they are also easy.

Saturday, 22 August 2020

Paperless Frustration.


Yesterday I tried to check recent contactless electronic payments to various shops.

I sorted out accumulated receipts, found my bank account on line and started to check. After just a few minutes I was automatically logged off. Having made three attempts, and vainly tried to persuade the bank to increase the five minute  limit for reading the account I decided to download.information and check it offline.

 Paperless banking is less delightful than we are led to believe.


Poor Timing

I thought it strange that examinations boards adhered to the original dates for publishing A level and GCSE grades. Those dates were chosen to allow time for examinations papers to be marked. With no examinations the estimated grades could have been published earlier, leaving time for any appeals to take place before universities allocated places.

I interpret the confusion as yet another example of incompetence in high places.

Wednesday, 19 August 2020

A Ton of Water


After a wet spell I now have five water butts full of water. Each holds 230 litres, so I have rather more than a ton of rainwater to quench the thirst of any needy plants.

I don't recall ever hearing anyone else boast of having a ton of rainwater, so perhaps I'm the first.




Thursday, 30 July 2020

Zooming out of Isolation

This afternoon I attended my first virtual U3A meeting, by courtesy of Zoom. Eight of us were present. It was more than five months since I'd seen any of the others , so it was a happy occasion for me.

Friday, 24 July 2020

The Ponderous Activity of an Ancient Brain.

I have rewritten the books page of my website. For the benefit of anyone wondering what I'm doing in these strange times, here's a link

Thursday, 23 July 2020

A Joyful Day

I had my hair cut today !! It was only my second haircut of the year. I think the last time was either in January or very early February. I'm enjoying feeling light headed!

Monday, 20 July 2020

A Dubious Achievement

I seem to have killed my mint plant. Mint tends to expand into any part of the garden in which one plants it, so cautious gardeners confine their mint to a container.

My mint, so contained,  has died. Should I be proud ?

Saturday, 18 July 2020

Wearing My Mask

Yesterday I wore a face mask while shopping. I decided that if it's necessary to wear masks at the end of next week, it must be necessary to wear them now.

I was surprised that very few shop assistants were masked, though around a fifth of my fellow shoppers were. I also discovered a snag. When masked I couldn't use my spectacles because the lenses were fogged by breath directed upwards by the mask.

Sunday, 12 July 2020

The Congested Middle Ground

Food packaged for oven cooking almost always bears an instruction to cook it in the middle of the oven.

What do these people expect one to cook in the top, or the bottom, of the oven ?

Saturday, 4 July 2020

A Sad Day

Our cat died today. We used to have two, a mother and her daughter. The mother died in 2017, and her daughter died today.  She was twenty years old, which I understand to be very old for a cat, and she'd been in poor health for a while. Today the vet said she would not live for long whatever we did, and she was in pain, so we chose a merciful injection. We miss her very much.

Wednesday, 10 June 2020

A Strange Reaction

I was very surprised when the Houses of  Parliament recently stood in silence in memory of  an American who died while restrained by police.

Minneapolis is not subject to British jurisdiction, and investigations have been undertaken by the local authorities there, where criminal proceedings are underway.

Several years ago members of our own Metropolitan Police shot dead a plumber who had committed no crime and was not even suspected of committing a crime.. There was no minute of silence for him yet he was killed deliberately, unlike the American whose death  followed an inept and excessive effort to restrain him. The senior officer who supervised the plumber's killing was subsequently promoted to the post of Chief Commissioner of the Metropolitan Police. Members of Parliament might sort our our own policing before offering advice to our former colony.

Sunday, 7 June 2020

Relics of Bygone Days

Various relics remind of our past, statues prominent amongst them. I'm annoyed when people call for the removal of a statue because it commemorates someone now considered 'bad'. Recently rioters in Bristol pulled down a statue of Edward Colston, a seventeenth century slave trader, and threw it into the river, whence it will, I expect, have to be removed at considerable expense.

In the seventeenth and early eighteenth centuries slavery was generally accepted, endorsed  by John Locke, the philosopher whose writings inspired the American Constitution, so Colston  was not evil when judged be the standards of his day. His statue was a useful reminder of how things used to be.

Tuesday, 2 June 2020

A Welcome Discovery

Intending to arrange a virtual meeting I looked for my microphone. Alas, it was so ancient that its plug would not fit any of my computers. A friend suggested that one or more of my computers might have a built in microphone, but none was mentioned in either of the computers' lists of devices. Desperate, I opened the utilities to configure a microphone. While the desk top machine just told me no microphone was connected, the laptop suddenly found a microphone. I confirmed its existence by recording myself congratulating myself on having one.


Sunday, 31 May 2020

Contradictory Instructions

In late march we were bidden to stay at home as much as possible and to avoid social gatherings, conducting our social lives through the Internet or by telephone. Yet shops selling the electronic equipment we need for such communication were forbidden to open.

Assess the intelligence of our rulers in the light of that contradiction.

Saturday, 30 May 2020

No More Late Nights

I've noticed that the street lights are switched off earlier than they used to be. They used to go off at midnight, but now they are always off by the time I go to bed, which is almost always between 23 hours and midnight.

I guess that is because late night adventures are rare under present conditions.  So far as I recall, I haven't been out after  19 hours for at least two years, and have never been out after 22 hours since moving into this house more than five years ago.

Thursday, 28 May 2020

Some Advantages of being Anti-Social

I haven't had a cold for a very long time, and wonder if the precautions against the corona virus have helped. I suppose they must have blocked other infections too, and while colds were rarely fatal they were a great nuisance. It would be good to avoid them.

We can't stay locked away indefinitely, but a great deal of social interaction could be avoided. We need to work, and shop, and many of us would find it hard not to encounter others in the process, though the 'lock down' has taught us to reduce the number of those encounters.

Leisure activities involve a great deal of unnecessary interaction. We could easily dispense with crowded places of entertainment. Theatrical performances, films, concerts and sporting events could all be watched on line. Tourism could be replaced by an augmented Google Earth. With less travel there could be fewer visits to restaurants - eating together must involve an exchange of bacteria and viruses, especially when the eating is accompanied by conversation, a potent way of generating infectious aerosol droplets.

Friday, 22 May 2020

A Simple Deterrent

I notice the police are said to be finding it hard to deal with people illegally camping overnight and using local residents' gardens as lavatories..

Why not just pop a few lumps of sugar in the culprits' petrol tanks? As a child I was told that was one way members of the French resistance used to disable German Vehicles. I guess it would still work against most modern vehicles,

Tuesday, 12 May 2020

Sheltered from Vectors of Infection

I haven't had a cold this year. Avoiding the infection we all dread may be protecting us from other infections. For the past few years I have only rarely had visitors and my outings have consisted of daily walks to the shops and fortnightly bus journeys to Leicester for U3A meetings. I haven't been to Leicester or travelled on any public transport since late February and have been to the shops only three times in the last six weeks.

When the health crisis is over we may consider how often we need to meet large numbers of other people. Apart from work, shopping, and visits to doctors or dentists, we rarely need to be in close proximity to other people except to engage in carnal relations, and even they could be replaced by artificial insemination by post. We can exchange thoughts and ideas by email or by reading each other's web sites and blogs.

Sunday, 3 May 2020


We rightly wince when someone refers to some object, event or person as 'more unique' than another, but often overlook less patently absurd uses of the word.

Applied to any particular individual object or event 'X is unique' is vacuously tautological. Provided we take into account all properties, including temporal and spatial, there cannot be two individuals with precisely the same properties, since to assert there are two individuals meetings a certain description implies there is some way of distinguishing them, because we need to distinguish them in order to count them.

If "unique" is to be used to assert anything untrivial it must apply not to an individual but to a particular description of an individual. For instance compare:
(1) Boris Johnson is unique in being a British Prime Minister living with his mistress in Downing Street
(2) Boris Johnson is unique in being Boris Johnson

(1) and (2) are both true, but only (1) is informative.

Wednesday, 29 April 2020

Ungrammatical Imperative

When agents of the Government enjoin me to 'stay home!' my immediate reaction is to regret the absence of a preposition. When people use language so ineptly I hesitate to trust anything they say.

'stay!' without a preposition refers to a state of affairs, as in 'stay awake!' 'stay dry'. Without a preposition one can't tell whether one is supposed to stay away from home or stay at home.

Thursday, 9 April 2020

Living in Slow Motion

This morning I arose promptly when my alarm clock awoke me at 7:00, had what I considered to be a quick bath and dressed. By the time I got downstairs ready to prepare breakfast it was 7:50.

How can it have taken me so long to do so little ? A few decades ago I could have done all that in at most half an hour.

Tuesday, 7 April 2020

A Ridiculously Redundant Statement

"Power is no protection from harm" various ministers and spokesfolk have said of the Prime Minister's admission to hospital. I fear that anyone foolish enough to have thought otherwise would not be open to persuasion.

Wednesday, 1 April 2020

Dyeing the Countryside

I worry about the news that Derbyshire police put dye in a lake to make it unattractive to visitors.

Dyes are complex chemicals that need to be handled with caution. People often wear protective clothing when using them. Could water from the lake migrate though rivers or streams and reach reservoirs? Might the dye poison wildlife? If it makes the water look black it is absorbing light and that would make the upper layers of the water warmer and the lower levels colder than usual, and that could affect aquatic plants and animals.

Did the police concerned know the answers to those questions? Did they even ask the questions?

Sunday, 29 March 2020


As I arose this morning I looked out of the window and saw flakes of snow in the air.

Fortunately they were small and few in number and soon gave way to sunshine, but seeing them reminded me how fickle the weather can be.

Tuesday, 24 March 2020

Delayed Enlightenment

About seven years ago I bought a tablet computer more out of curiosity than need. I bought a fairly cheap one; paying about £70 so far as I can remember.

It could do lots of things, but the accompanying instructions were so scanty as to be almost negligible. In particular there was no indication of how one might delete something, and there was a lot that I wanted to delete. The device came with a library of e-books, most of them in Russian or other Slavic languages.

Today I investigated the device again, searching the web for instructions, and got to the point of being able to conjure up a 'delete' button, but for a while I couldn't get it to do anything, until I discovered that while pressing the button just once achieved nothing however long I pressed, two short presses conjured up a menu offering deletion as an option. I no longer have Russian books on my tablet!!

Monday, 23 March 2020

I Am Alive and Well

The health crisis has reached a stage where people will begin to check who is still alive.

To save people the trouble of asking , I declare that I'm alive and well. We've found a milkman who delivers milk, bread butter, eggs, bacon and other essentials three times per week, so we should be able to survive without needing to eat the cat, though I'd rather starve than do that.

I post here quite frequently. I shan't mention my health in every post, but assume I'm well if I post without saying otherwise.

Sunday, 22 March 2020

A Small Horticultural Trumph

Usually people dig up their wallflower plants once they've finished flowering. Last year I didn't. Instead I cut off the old flowering stems, and any other straggly bits and let the plants stay where they were.

 They all survived the Winter as healthy compact little shrubs and are now flowering profusely.

Saturday, 21 March 2020

A Sign of Spring

Today I dried my washing on the washing line in the garden. It was the first time I've done that this year. Until now the few weekends that weren't wet were so windy that I feared that anything I put on the line would blow away and end up wrapped around someone's chimney stack.

Wednesday, 11 March 2020

A Sinister Sight

When I was out shopping today I saw someone wearing a white face mask. It looked very uncomfortable. That was the first time I've ever seen anyone wearing a face mask in the street, though builders have worn them while doing dusty work around the house. I hope the wearing of such things while shopping  doesn't become a custom one is expected to follow.

Saturday, 7 March 2020

Shopping in the Sunshine

Today I set out for the shops wrapped in my Winter clothes, but soon felt so warm I removed my scarf and left my overcoat buttons undone. It was an agreeable foretaste of Spring.

Tuesday, 3 March 2020

A Redundant Reference Book

A new telephone directory arrived recently. As I threw away the old one I realised I'd never used it, or any of its recent predecessors. On the rare occasions I need a telephone number I get it from the Internet.

How our habits have changed!!

Saturday, 29 February 2020

A Puzzling Sleep Pattern

Often I feel sleepy in the afternoon, suspect that I may not be getting enough sleep at night and resolve to go to bed earlier. Yet, as bed time approaches, I feel wide awake as I potter away on the computer. If I compel myself to go to bed before about 23:30 I usually wake up every couple of hours or so during the night, while if I defer bed till midnight I usually sleep through the night until around 06:00, and sometimes don't wake till my alarm wakes me at 06:50.

How strange !!

Saturday, 22 February 2020

Don't Shake Hands

When I was teaching, a colleague with a medical background told me that one way colds circulate is by people shaking hands. Even people considerate enough to wash their hands after using the WC often do not do so after blowing their noses. Indeed, even people like me who wash their hands when they can, often need to wipe their noses when no washing facilities are available. Therefore


Wednesday, 19 February 2020

A very high price

I've just noticed that the price on the Daily Telegraph is now £2-50.

In the mid 1950's I usd to buy a copy on the way to school. It cost 2d making it the third most expensive daily newspaper. The Guardian cost 3d and the Times cost 4d, while the lesser papers cost 1 1/2 d.

In those days there were 240 pence in the pound, so 2d was 1/120 of a pound, and at £2-50 the price is now 300 times as much as it used to be. Few prices have risen by so great a factor.

Friday, 7 February 2020

The Undefined

When I listen to the media I often hear people say 'by definition' without indicating what definition they are referring to.

I think that people often pick on phrases that they believe are used by clever people, and use them hoping to appear clever. They frequently fail.

Friday, 31 January 2020

A sad moment

This will be my last contribution to this blog as a citizen of the European Union. Britain is to leave in about ten minutes time.


Wednesday, 22 January 2020

Confused vegtation

Flowers we usually associate with the approach of Spring are blooming in my garden at least a month earlier than usual. Miniature irises were the first to come into flower, but crocuses are now following suit.

Usually snowdrops flower first, but so far they haven't even produced buds.

Wednesday, 15 January 2020

The First Spring Bulb of the Year

An iris is flowering in the garden, in a tub it shares with a clematis.

I don't recall ever before having Spring flowers bloom so early.

Wednesday, 1 January 2020

Boldness Rewarded.

In Sainsbury's a few days before Christmas I checked the bundle of vouchers they send me from time to time and found one that nearly matched one of my purchases. It offered points for a purchase from the delicatessen counter. It wasn't quite a match because it required me to spend £2-50 and I'd spent only £2-33, and it was more than a week out of date, but I decided to try it anyway, and the machine accepted it, giving me 150 points, worth 75 p.

Timid readers should heed my example.