Did The Light Dawn Decades Later?

@JoyfulSilence Thankyou very much for going to all that trouble, especially if you wrote it all by your own memory not copied it from a text-book; but I was describing school-level mathematics, not Degree level!


I know Integration can be illustrated graphically as finding an defined area under a curve that represents the equation being analysed, as I recall adding the areas of lots of very thin strips of that total shape; but that's as far as I managed.


You also introduced right at the top some branch of Maths totally unfamiliar to me, with that " Int( f(x) , x=a..b ) " and the mysterious letter 'k', so I am afraid you lost me immediately!

The introductory calculus we were taught at school in my mid-teens, went straight to the heart of the matter with simple terms like x^n where n is a simple integer, and ordinary equations like y= 3x^2 + 3x +3.

It did not introduce us to natural logarithms, let alone calculus of their equations. We knew ordinary logarithms but only for performing awkward multiplications, divisions and powers. Nor to things called "exp", chain rules, geometric means ,etc. The only numerical Chain I know is the surveyors' unit of length of 22 Yards.


I am sorry, but why are you just blinding me with Degree-level Mathematics? Did you not realise I could never comprehend what you have shown there, even with a full explanation and all in conventional algebra?


I used sometimes to see research papers stuffed with extraordinarily complicated mathematics. I noticed their authors liked to show off by following some extremely complicated, page-width equation, with something like,

"Then by dividing by Eqn. 37 we see that..."

... another line of Equally Hard Algebra.

Oh, of course we do. Don't you?

I saw one with equations prefaced with no less than five definite integral signs in a row, like a stylised sketch of a swannery. I know they were equations by their ' = ' signs in the middle of each jumble of letters and squiggles. I think it described some physics experiment, and with a genuine engineering purpose.

I often wondered how the scientists who write such material know how to design such mathematics when their starting point is probably just several big lists of numbers. They can't just look up a book of standard formula.


So I had no hope of a professional engineering or scientific career. I did at least spend a working life associated with these fields, but at semi-skilled shop-floor level needing no higher than simple mensuration and perhaps a little ordinary trigonometry, with quite basic formulae.

Are you trying to remind me how incapable of learning advanced Maths I am?

@ArishMell

Sorry if it is too much. I thought maybe you had more exposure.

And it is hard to use text to represent curly symbols like integral signs.

Yet you are correct. Integrals are just areas under curves.

For what it is worth, I would be lost in a shop: I could not build anything to save my life. I took my car in because its computer told me to, and I had no clue what it all was. I just paid the man. Then they told me all these numbers, like something was a 3, but if it became a 5, I would have to replace something. I said, I have no clue how to check that, so you will tell me next time, right? He said yes, we check that each time.

I am just good with algebra and programming.

If you want to learn more, look for YouTubes. Many are accessible. I am using them to learn about relativity and quantum mechanics, which is my personal frontier of understanding.

I watched one about power outlets and the dude was speaking about types of things using their trade names and numbers and I had no clue so left.

Oh, the "k" is just an integer.

@JoyfulSilence Thankyou!

I do have a few maths text-books although they can be hard to use because commonly they only give a few definitions, a worked example or two then exercises. No proper explanation - but I suppose that's the tutor's job!

You are not alone in having to rely on garages to repair you car (as I did a few weeks ago). That is becoming almost universal. I used to be able to diagnose and repair moderately difficult faults but modern cars have become so complicated and physically awkward to work on, that there are few things the owner can repair.

The power-outlet video was probably intended for the trade and may even have really been to advertise a manufacturer or major retailer. I do feel slightly out-of-place if I go to my local builders' tool stockist in the working day, and am queuing behind professional customers who all know the proper names and methods for everything, what alternatives they can use if the first choice is not in stock, and so on!

@ArishMell

Everybody has their niche. Everyone is a specialist. Nobody can be good at a lot of things these days. I love a lot of subjects, though. But it is mostly academic, seldom applied.

And one reason I am good at my job is I have been doing it for 26 years! New people come, smarter and more educated, yet they lack the institutional knowledge I have. I know what we do, and used to do, for example. I do not always know why, though. Often it is inherited, and just how it "always had been done."

@JoyfulSilence Oh, yes - I agree!

Experience very often does count more than just the book learning, but I think it needs careful balancing. It's fine if the "always" approach does still work properly, and change for the sake of change is not always a good thing.

Sometimes a newcomer might see a better way without a lot of upheaval, that no-one already there had spotted, but should still accept that the long-term employees have all the experience.

@ArishMell

A young employee with an advanced degree proposed a new method. I am not on board with it yet, mostly because I do not understand it. My brain is so challenged now.

@JoyfulSilence I have noticed what seems a trend in modern businesses to see management as almost an end in itself, rather than providing vital support for the organisation's main role.

There is also a lot more tendency to recruit people to fairly high positions much more on qualifications than experience, rather than a balance of both. It does not happen universally, as we see with the difficulty so many graduates have finding good employment, because even if the work exists they do not have the experience.

I do wonder if one symptom of this is the growth of business fads, pretentious language and over-blown role titles like Chief Cliche Officer.

Or as one I heard of recently, Chief People Officer... no, Personnel Director!

How much of this rhubarb comes from Bright Young Things who gain degrees in "Business Studies" but have never run a business or worked behind a shop counter or in a factory?


A couple of years ago I examined the official web-site for Britain's very own vanity project, the "HS2" Railway. Its Board of Directors had the specialists you'd expect: Personnel (probably called Human Resources... urrrgh!), Finance, Legal, etc.. And a "Director of Strategic Partnerships". No, I don't know what one of those does either but I expect it is Very Important and every company should have one. This is a huge and desperately expensive civil, mechanical and electrical engineering project.... with not a single Chartered Engineer on the Board!

@ArishMell

Yeah, lots of meddling managers. And regular meetings even if there is nothing new to report.

Meetings for the sake of meetings.

Spend time documenting what you plan to do, rather than just doing it. The plan never survives the demands of action. I hate Gannt charts. Nobody ever sticks to them, they just do what they want when they want, or at least do what was planned, only when they can. Real life is messy, and real people are stubborn, uncooperative, and/or lazy. Collaboration is hard. Communication sloppy. I prefer to work alone!

@JoyfulSilence I think I was lucky! For a start I was never in any sort of supervisory role, and most of our managers were sensible and experienced, having gained their roles by promotion rather than intake.


I think the oddest incident was when the Directors found some daft fad, apparently invented among Japan's car manufacturers, called "TQP". I forget what it stood for, probably something like "Total Quality Practices" or similar.

Its glossy publicity leaflet given to each of us, and a "home-made" video so naff it could be used as an advertising-course lesson in what not to do, told us nothing much beyond it would supposedly give us all more freedom and initiative in our work.

We all trooped back from the presentation muttering, "It'll never work. We can only do as we are told, on time, in the way we are meant to!"

It didn't work. We noticed nothing new at all.

Within weeks we'd all forgotten about it, but about a year later it was overturned anyway because our main customer made us seek ISO9001 registration. That, as I expect you know, was sold as a "quality assurance" scheme, but is really a management-accreditation system predicated on top-down management and rigid adherence to written "Procedures". No initiative, individuality, inventiveness or other "Evil Is".

Only our lot went overboard, so much so that the external accreditation authority said we'd gone far too far in inventing masses of surplus bureaucracy because the top managers had not taken the trouble - or had been too nervous - to ask such auditors what was actually necessary!

Once that was sorted, we did indeed gain ISO9001.

@ArishMell

I work for a US federal government bureaucracy. So I understand. It is the fourth branch of government. I have served 5 presidents. They arrive with plans, that never materialize once they hit the wall of custom, intertia, and Congress. Yet Kamala will be my last, most likely.

@JoyfulSilence I fear Public Inquiries sometimes end up the same way: lots of recommendations, followed by lots or prattling about "leaning lessons and putting procedures in place to ensure it can never happen again".

Sometimes that does happen but I wonder how many "lessons" become forgotten in a pile of later work or just inertia.


We started this exchange about mathematics.

I have encountered something that seems to defy any known arithmetical analysis yet appears to be a special type of circular slide-rule for some long-ago trade or measurements-conversion; and take some comfort for people with more numerate brains than mine being unable to work out any pattern to it!

Now, my work sometimes involved Excel so I became moderately fluent with that, at a fairly simple arithmetical level, and now wonder if shovelling this "slide-rule" into a spreadsheet and testing the scales with various sums might reveal anything.

I can still use a conventional slide-rule, with a bit of revision, but this one, made in 1908, defies all logic!

@ArishMell

I saw that other post, with the round thingy. I have no clue what it is, either

But I have never even held a slide rule. I would have no clue how to use it. We all had hand held electronic calculators when I was young. I still have my Texas Instruments solar powered scientific calculator from high school. Still works!

But for my job I use Excel, or else write a program (usually in a language/application) called SAS, which is itself a dinosaur.

@JoyfulSilence Ah well, I am a generation older than you!

Electronic calculators were just beginning to appear at about the time I left school in 1970, so we were all accustomed to using slide-rules and log. tables for awkward calculations in Maths and Physics homework.

I still have two slide-rules. One was my own anyway, and I inherited the other from my Dad, who had been a Chartered Electrical Engineer so much of his work was highly mathematical. (I don't know what he actually did in detail because that was all confidential, but he did have a Degree and I have seen some of his course notes and text-books.)


That type of slide-rule is not longer made as far as I know, but special ones for particular trades are, and many of those are circular rather than linear like a general-purpose arithmetical slide-rule.

It amused me a bit when I see things described as "dinosaurs". The real dinosaurs as an entire group were very successful animals indeed, and their eventual demise was by forces far beyond their control or ability to handle!

If Excel or the SAS language still work as you intend for your purposes, they are hardly "dinosaurs" just because they were developed a few decades ago.

@ArishMell

I will only use SAS as long as my employer does, and pays for it. It ain't cheap. There are newer, even open source stuff, but I am still a novice.

I can also write Visual Basic programs in Excel. It has a feature where you hit record, do something manually, then hit stop. It then shows Visual Basic code for the task. Then I modify it. It is how I learned, along with Google searches.

@JoyfulSilence SAS is a new one to me.

I know of Visual Basic but have only a rudimentary knowledge of BASIC generally, self-taught and I've probably forgotten most of it.

I found it moderately easy to lean but for one thing. I could not work out at all how to make it write and read files, and the tutorial book I was using did not really tell me! Still, CHR$ commands for manipulating simple lines of text were fun to create.

I've just tried what you suggest! I switched on "Record macro", wrote two columns of letters, only 5 deep, then in Col.C a simple formula to concatenate them. That works and if I select the cell it shows me the equation; but I'd obviously not understood the technique you describe. Either it is something different or I was not using the record tool properly.

I never needed use macros or Visual BASIC in any spreadsheet I created at work or elsewhere.


The hardest software I ever tried to learn was Microsoft 'Access', on an Introductory course from work. The tutor did say it is a very hard to learn, but lets you create databases that are very easy to use. It is not helped by most of its terms being totally un-intuitive, unlike most MS Office applications, it is full of traps for the unwary, and I did not progress very far. Then the development at work for which this was for, did not materialise anyway!

As far as I can tell MS no longer makes 'Access' as a database-creator, but seems to have used the name for something else; and anyway only in the "Professional" editions of its 'Office' software.

@ArishMell

I have never used Access.

As for VB macros, hit "stop recording", and then look for the code. I do not recall off the top of my head exactly where I clicked. I think I right-clicked on the tab. Yet maybe there is a way to view macros in the same place you hit record.

@JoyfulSilence Oh yes! Found it! Thankyou!

Going back to school maths courses and exams, in my forties I think it was I took one of the standard secondary-school courses, in adult-education evening-classes, culminating in the proper exam. This was as a sort of refresher for work reasons, with an idea to then go onto the Advanced-level course.

Called the GCSE (I think standing for 'General Certificate of Secondary Education') it was significantly different from the General Certificate of Education 'Ordinary Level' of my school days.

Some topics were the same, including Trigonometry I think. I forget exactly as I think I no longer have the text-book. It seemed objectively simpler and slimmer than the GCE course. I do remember it had dropped Euclidean Geometry and Calculus, but introduced something totally new to me, called 'Matrices'.

Could I understand matrices? Could I heck! They seemed merely boxes of very simple sums and strange moves with peculiar names that did not convey their meanings; too abstract to have any link to any other branch of mathematics, let alone any possible use in the real world!

I told an acquaintance this, knowing she is a professional mathematician. She told me her work involved Matrices to solve giant blocks of simultaneous equations with as many as a hundred unknowns (sounds a bit like that famous remark by a politician). The computer does the number-milling but she still needs understand the method. Then she asked me an example of one of these strange moves. "Oh, that's... " and rattled off a short lecture, then sat back and beamed at me.

"Thank you," I replied, "but I am none the wiser because you've told me only what the teacher and book say, so I still don't know what it does and why, so I still don't understand it!"

She looked a bit put out by that. I was secretly amused that I had baffled a Doctor of Mathematics by asking a question of introductory level.

The problem of course was that she did not understand that I could not learn matrices because I could not "see" what they do and how. Only that you add or times little numbers together for no reason. I did learn they do have practical uses, in certain very advanced engineering calculations (my friend's work) and computer graphics programming. So I am puzzled why such a specialised and difficult topic should be in an ordinary school maths syllabus. Also that they have a very ancient history and one of their main developers was Prof. Charles Dodgson (Oxford University) in the 19C. Rather apt I thought, given his moonlighting as "Lewis Carroll" by writing dream-fantasies for children.

And the exam?

There was not a single Matrix question in it, and I passed it with high marks!

I did go on to attempt the Advanced Level course but totally failed. It was just too much and too difficult for me; but I also recognised that when the education system was re-organised, the designers had failed to maintain the previous, fairly close progression from Ordinary to Advanced Level. So in Mathematics at least, there was a now a huge leap in technical difficulty between the two syllabi.

@ArishMell

In the most general interpretation, an (M by N) matrix A is a way to represent linear transformations L between N-dimensional vectors and M-dimensional vectors.

An N-dimensional vector V is just an ordered list of N numbers. If N=M <= 3, we visualize it as a point in space, or else an arrow between the origin (center of space) and the point.

A transformation L is a function mapping V to a new vector L(V). For example if you rotate, rescale, shear, or translate (shift) space, then you move V so it has a new tip endpoint (yet whose tail os still anchored to origin)

The translation L is called linear if
L(x*V+y*U)
= x*L(V) + y*L(U)
for all scalars (numbers) x and y and vectors V and U. Rotations, rescalings, and shears are linear, but translations are not.

The product x*V just means multiply the length of V by x, yet keep its direction. W=U+V is a new vector formed by appending the tail of U to the front tip of V, and drawing a vector from the origin to the tip of V.

Suppose L maps from 2-D to 2-D. To see what L does, it is sufficient to see what it does to unit column vectors E2=(1,0) and E2=(0,1).

Suppose A1=L(E1) and A2=L(E2). Suppose we have a vector
V=(x,y). Then
V =x*E1+y*E2, so
L(V)=x*L(E1)+y*L(E2)
=x*A1+y*A2

If you make a a matrix A out of column vectors A1 and A2, then
A*V=x*A1+y*A2

So L(V) = A*V.

Neato!

@JoyfulSilence Very Neato! LOL! I'm afraid you've plunged me in the deep end again!

I don't know if I can represent it in SW's very simple text-editor, but this is the level I was taught.....

[a b c] [h]
[d e f ] X [i ] = [ a third box, holding some abstruse mixture of all eight letters]

(Combining the [ ] marks vertically.) I forget what the answer would look like, and never knew the purpose anyway.


I do know what real-life vectors are, such as the course of a ship across a tidal stream, or a resultant of two forces. Those are real navigation and engineering calculations amenable to real mathematics like geometry, co-ordinates, trigonometry and Pythagoras.

Matrices, as far as that maths course was concerned, are just bundles of random numbers.

We were never given any handle on what matrices "do", nor "how" they do it (only how to make it do it), what they are for, what words like "transform", "determinant" and "identity matrix" mean and why you need them. Nor where matrices might meet other mathematics. Nor any real-world examples of their use. They were taught as total abstractions all on their own.

The text-book introduced them by an odd, very feeble example. It supposed a domestic-appliances retailer writing his weekly sales in a grid, something like this:

Item........... Number sold

Fridges ...... 10
Toasters......6
Kettles.........9

With prices and totals columns as well. The text followed this by saying he realises he need not label the rows and columns, as long as he keeps the items in the same order.

Then it abruptly abandoned the shop-keeper and launched into those boxes of numbers and strange technical terms, nothing whatever to do with selling fridges.

So I was never able to learn them!

....

As an illustration of a "handle", many years after I left school not understanding what is Differentiation, I attended a geology lecture about rivers.

It involved a very simple formula, which if I remember rightly is something like { (A-a) / L }, the numerator being the change in altitude over a measured length L of the stream's course.

Something - I have no idea what - made me write it as { ∂A / L } and I suddenly realised that we were differentiating that stretch of the river! The only reason for no (∂L) is that though the altitude is obtained from the contours on the map, the length of that stretch is determined from a map-measurer, so no subtraction involved.

It was that handle, a real river we could measure from a map, that broke through the fog of abstraction.

The calculation, by the way, is part of a technique for finding geological boundaries hidden below the river and its valley floor sediments, vegetation, etc., by plotting its gradient as a graph that can reveal the boundaries as steps not obvious in the scenery.

@ArishMell

Sorry, I cannot help myself. It is hard to talk about math without using its language.

Physics is expressed in terms of vectors, and changes of coordinates, for example, are often calculated using matrices. They are not essential: just people noticed patterns in formulas that had terms that could be nicely organized into grids and rows and columns. It proved to be a useful tool for calculation. Just like learning how to add. The concept of addition is independent of representation, but to do calculations it is helpful to line up the digits and follow an algorithm, etc.

I think one main problem with math education is people get all hung up on the language and implimention, and miss the logic, flow, and concepts.

Like a derivative is just the slope of a curve, the integral is the area under it, and matrices are just ways to record how a type of function acts on vectors.

You start with concepts and logic, then you use the language of math to write it down, and build. Of course, to be useful, it must be quantized, and algorithms must be developed to implement them. Yet the concepts are more important to me, because it allows me to shift if the implementation changes.

For example, in the 1800's mathematicians invented ways to talk about the curvature of surfaces, and tension and twisting of them. Then decades later, Einstein was trying to model gravity, and he realized it was not a force but actually the curvature of space, and masses just followed it where it took them, yet at the same time mass curves the space around it. It is a dance.

Einstein had friends who knew the earlier work and shared it, and he applied it to his new ideas of gravity, and came up with his equations of general relativity.

Progress requires both the insight of new concepts, the rigor of calculations and detail, and the ability to make connections.

And yes, a slope at a point is the derivative. That what the definition of the of derivative is!

Have fun with math (maths).

@JoyfulSilence Thankyou!

I wonder if the way mathematics is taught at school means things like concepts and patterns are missed. Certainly I don't recall anything more than a long series of instructions on how to work out the problems set in exercises and examinations rather than any deeper exploration.

The ultimate aim was to pass examinations in various subjects - Maths, French, Geography, etc. - with little real link to the outside world beyond impressing potential employers with lists of qualifications. So perhaps understanding an abstract subject like much of mathematics was less important than being able to "do" it.

Unfortunately I can't learn it if I can't understand it, and you can go only so far with rote-memory and trying to match exercise questions to the text-book's worked examples.

....

At around the same time as I took that maths course as a refresher, and found it had these pesky matrices in it, I took the parallel course in physics. At that level the maths was very simple, not even maths really, just basic arithmetic.

I passed the standard exam in each then tried the General Certificate of Education's "Advanced Level" courses in both subjects. In the British school system A-Levels are normally studied from ages 16-18 and as entry qualifications to university, so they are quite intense, but worse, changes to the system discarded the previous smooth progression from the old GCE 'Ordinary Level' to A-Level.

So I floundered. Though taking a cut-down version called "Additional Mathematics" I think, of the maths A-level syllabus, it was still very hard. It included calculus, matrices to a higher level, and another subject new to and equally incomprehensible to me, called "functions", which appeared to be a fancy replacement for ordinary equations. The tutor described it as of the same technical level but smaller volume of contents - which included . I took the exam but performed so badly my result was "U", meaning "Ungraded"!

I also struggled with the A-Level Physics, which does have more maths, and gave up part-way through the course.

I still have the A-Level Physics book so looked to see what it says about Vectors and Matrices.

Very little. It explains simple resultants of vectors, and shows a worked example of the tensions in two "light inextensible strings" unsymmetrically suspending a mass. (Physics courses seem to have an inexhaustible supply of massless, inelastic cord.) However the calculations invoke only Pythagoras and simple trigonometry, though the suspended mass problem does involve a simultaneous equation. A difficult one at that because the co-efficients are trigonometrical values, so decimal fractions, not neat integers!

There are no matrices anywhere in the book, so presumably they were not in the standard school A-Level Physics syllabi of about 30 or 40 years ago.

''''''''

I have sometimes turned the tables on the mysteries of Mathematics.

Some years ago I regularly used Wikipedias' Answers, which is an all-knowledge Q&A site.

Its section on Maths and Arithmetic often included American users' appeals for help on converting between SI and American units of measure. These were mainly in two categories.

One was private swimming-pool owners trying to calculate the correct additive quantities for the water, having bought the chemicals in metric packaging with metric instructions. Most knew they needed know the water volume: some already did, some needed help to calculate it, and one or two muddled volume and area. I would supply the answer but complete with carefully walking them through the necessary method and conversions. I had to remember my UK Gallon differs from the US Gallon.

The other questions were simple conversion in one dimension: Gallon to Litres, Miles to km, Pounds to kg., apparently from schoolchildren's homework. I was not going to help them cheat, so I would show them how to do it but I don't think I always gave the specific answers!

.
That second group were plagued by two clowns who loved to cause havoc. I did complain but the administrators let them carry on. They would take a simple question like "How many kilometres in 40 miles?", then give several screenfuls reducing the miles and km to inches and cm then back again, naming "Algebra" without using it and "Dimensional Analysis" which it isn't - and frequently making mistakes in their own arithmetic. I felt sorry for the unfortunate child transcribing this waffle into an exercise-book, and for the poor teacher faced with it.

@ArishMell

When I want to do a conversion, I just type it into Google. Like if I were going to tell you the temperature here, and it were 60 F, I would type "60 F" in the search, or least "60 F to C". I just didyhe former and this immediately popped up:


Below it was a mini form to add in any value F and get a value C.

Sort of like Googke translate, to switch between languages.

OMG, they must have AI now.

Just for fun, I searched


It returned what looks like an AI result. It converted my text into proper notation, that looked perfect, then proceeded to explain how to solve it, in two steps, and what rule to use. Then it said the solution: 2*x (but as symbols, not text).

So neat. I will have to play with their AI someday!

@JoyfulSilence Interesting exploration!

My computer is host to a no-frills, direct converter a bit like a little database in appearance, covering far more than all measurement units I'll ever want. I don't know its origins - someone gave a copy to me on a disc, at work, quite some years ago now.

I used that 40miles -> km example quite deliberately because for most practical purposes, the factor 8/5 is close enough and easy enough for mental arithmetic. After all, when we drive from one town to another we very rarely travel from one mapping-point to another. We might start somewhere in the suburbs and end in the other's suburbs, possibly some miles (or km) from the sign-post distance. So it's 64 miles.

One distance sign that struck me as a bit odd, is in Norway, which I've visited several times on holiday. It says "Narvik 999" (km). Perhaps they thought if they rounded it to 1000 it would look so much further away!

Well, 999 looks awkward to turn into miles mentally, but 5/8 X 1000 is a bit easier. It comes to 625 - but I know that from a very different calculation, in mechanical engineering! (Vulgar to decimal, fractions of an inch.)

That sign is in a rather curious road-side location as if the surveyors actually chose a point exactly 999km from the centre-point of Narvik. As if anyone's going to notice the difference on a drive that long.

@ArishMell

I always think of speed limit signs. Typical rural highway limits are about 65 mph. Yet in Canada I recall 100 kph. Also, my car had both on the dial. Yet my recent cars are digital, so you just toggle a button. My car was actually made in Canada.

At least the US was smart enough to use base ten currency! Of course there still are coins for 25 and 5 cents. Yet ever since the pandemic, I stopped using bills and coins. First, because of distancing, then because of shortages due to low circulation.

I am clueless about British currency. Strange words for strange things.

@JoyfulSilence
Although the UK has been metric for most things for decades now, we have retained the Statute Mile and Yard for road and railway distances and speeds; and miles-per-gallon for road fuel consumption even though the fuel is sold by the litre. So our road signs are still all Mile based.

I think the railways also still use the Chain for distances, including curve radii. I have noticed this on bridge and level-crossing signs.

...

Why do you say you are "clueless" about the British currency? It differs from yours only in unit names and relative international value.

The British currency has been decimal for more than fifty years - we changed to it in 1971!

We kept the Pound Sterling (£) as the base unit, divided into 100 Pence.

Why "strange" words? They have to be called something! Are the words Pounds and Pennies any stranger than "Dollar" and "Cents", or "Franc" and "Centimes"? Or "Yen", or "Rouble", and whatever are their divisions?.

Actually the French currency has gone too, replaced by the European Union's bloc-wide "Euro". Well, almost bloc-wide, of course, because the UK kept out of the Euro. I am not sure if any other EU country did.


There would be a major social difficulty in Britain if cash disappears. Even if it was easy for everyone including the disabled or very poor to use bank-card or telephone payments even for the most trivial purchases - as the no-cash enthusiasts seem to want.

British society is extremely rich in voluntary arts, sports, hobby and general social clubs, church groups, local museums and charities; the last both local and national. Many of these are supported by amateur-run social events like carnivals, village fetes, coffee-mornings, small-scale exhibitions, film showings, public lectures, "open gardens", and bring-and-buy sales. Many events include side-sales of, e.g., light refreshments - many of the larger ones rent space to refreshment or other relevant traders who rely heavily on cash.

There are also many, many private sales by individuals, of surplus, low-value possessions.

These all generate vast numbers of very small cash sales or donations that cannot sensibly be paid other than by cash - it would be costly and physically impractical to use digital means for these.

Costly for the payees, due to the equipment costs but also because the banks charge to handle card and 'phone-reader transactions. If via a "smart"-'phone, is there also a "middle-man" fee charged to the buyer by the bank or 'phone company for making that?


The real financial value is probably incalculable but the typical annual total turn-over by all these small-scale cash-only payments nation-wide, may be some millions of Pounds.

However we should also examine the social value of this money-flow. Removing cash would destroy very many of these voluntary social activities and organisations, leaving big holes in many people's lives and communities; as well as costing charities significant income.


The only ones who gain from a cashless society are the supermarkets, mail-order retailers and the banks, the latter two are already trying to destroy any concept of customer service.

Possibly, indirectly, also the Treasury. That by wiping out a lot of the criminal cash-only "trade". Not just money-laundering by foreigners buying homes and land in Britain. I mean here tax-evading by so-called "travellers" (few of whom are Roma - a Romany told me), dishonest cash-in-hand trades-people and exploitative back-street "sweat-shops". All fees and wages would have to be between bank-accounts only, receipted and with wages on the PAYE tax system, so all audited and traceable. It would also make life harder for outright criminal activity like metal-stealing and fly-tipping by gangs who cannot even use cheques without being traceable.