Posts Tagged ‘numeracy’


April 29, 2021


The invention of the phonetic script about three and a half thousand years ago enabled humans to suddenly think about a million times better, and they took off. Likewise the invention of a script for thinking quantitatively, that is to say Mathematics , could lead to thinking of a different kind that is just as powerful. In fact it has already: Maxwell’s Equations (ME).

Some arguments are of a purely quantitative nature. For instance in our post “Civilization and Moonpower” we demonstrated that large cities not dependent on slavery only became feasible once tidal energy was harnessed, as was possible in North Western Europe, where it is far more abundant than elsewhere. Here I talk about the most momentous piece of Mathematics ever done, Maxwell’s Equations.

Maxwell’s Equations describe the interaction between Electricity, Magnetism, Space and Time. They were an attempt to write down the experimental findings of the ‘electricians’ Hans-Christian Oersted (1820) and Michael Faraday (1831) but they led to a totally unexpected insight, and thus to the modern world: “Electromagnetic waves can propagate across empty space at the speed of light”.

Out of that insight (1864) there was to come Radio (1887), Transatlantic wireless (1901), Relativity (1904), Electronics (1912), Broadcasting (1920), Television (1930), Code-breaking (1930’s onward), Radar (1935), Microwaves (1940), The Electronic Computer (1943), Communication Satellites (1960), Space Travel (1969), The Internet (1980), Mobile Phones (2000). … while the Second World War could as aptly be called ‘The Radio War’ because it was started by Radio ( broadcast hate propaganda), controlled by radio (e.g. Churchill and Roosevelt talking to their peoples), won by radar in its many guises both in defence and attack, and lost by code-breaking ( e.g. : the battles of Midway and Kursk). A huge operation like the D-Day landing would have been unthinkable without the command and control made possible by radio.

Einstein is rightly famous for his E=mc2 equation (1905) but in a sense he and others (for he was only one of several) were only adding footnotes to Maxwel’s Equations which in themselves prove that Space and TIme cannot be at all as we had thought them to be.

So what are Maxwell’s Equations? There are 4 of them actually and you can write them out in different ways using rather different vocabularies. Textbooks on Electromagnetism can make them look both galumphing and arbitrary, when, as I believe, they are inevitable; the world couldn’t have been constructed in any other way. I find that both beautiful and totally unexpected. They, and the many stories behind them, are certainly worth having a look at even if you have no ambitions to use them yourself. You can regard them like The Rosetta Stone, as a wonder to behold, though they are far far more remarkable and momentous than that iconic stone. If you don’t believe me look at:

Yes they do look unfamiliar, even frightening, but that’s probably because you’ve been put off Mathematics by bad teaching.The world is full of Baducation and bad ideas . And one of the most debilitating , which goes back to the Ancient Greeks, is the notion that “Mathematics is Deductive in Nature”, and therefore quite different from our normal everyday Common Sense Thinking , which is Inductive. But that is a complete misconception. It’s as if the Maths teaching profession have mistaken the grocery- bill for the groceries. Don’t take my word for it: Morris Kline, that most eminent Historian of Mathematics wrote: ” “Mathematics is a human activity and is subject to all the foibles and frailties of humans. Any formal, logical account is pseudo-mathematics, a fiction, even a legend, despite the element of reason.” [‘Mathematics, The Loss of Certainty, ‘ OUP, 1986]

So many of us have been put off maths because we’ve been taught it back to front by the maths- teaching profession: deduction first, intuition afterwards. No wonder so many of us rebel. If you look at the following url you can see the Theorem that “The angles in any triangle add up to two right angles‘ being taught in the two alternative ways so that you can judge which is best for yourself:

The consequence of all this innumeracy are fairly tragic. Most of us are innumerate and, in my opinion, innumerate people can never become wise, not any more, not in the modern world( see all the current confusion over Covid vaccination statistics). The great news is that innumeracy is by no means irreversible. Maths is a subject peculiarly suited to self-instruction over the Internet. I suggest that everyone who earns a certificate of numeracy receives an immediate grant of £15,000 while many prestige professions and jobs be reserved entirely for the numerate. Thus a large fraction of a population could become numerate at a trivial cost by comparison with many infrastructure projects. And surely widespread wisdom is more desirable than say more runways. It’s probably no accident that the most numerate people on Earth (the Japanese) are also the wealthiest (UN figures).

The consequences of all this innumeracy are fairly tragic. Most of us are innumerate, and in my opinion innumerate people can never become wise, not any more, not in the modern world ( see all the current confusion over Covid. vaccination Statistics). The good news is that innumeracy is by no means irreversible. Maths is a subject especially suited to self instruction over the internet. I suggest that everyone who can earn a certificate of numeracy receive an immediate cash award of £15,000, while many prestige jobs and professions should be reserved for the numerate. Thus much of a population could become numerate at a trivial cost: Widespread wisdom is surely more desirable than say more runways. It is probably no accident that the most numerate people on Earth (the Japanese) are also the wealthiest (UN figures).http://Baducation

If you would like to see a wide-ranging discussion of numeracy and innumeracy in the British context, taken from my book ‘History of the Brits’ (Amazon 2020) you might like to click on:

If you want to see a wide-ranging discussion of Numeracy in the British context you might like to click on:

Anyway , for those who can appreciate them, Maxwell’s Equations are every bit as beautiful as great music, prose or poetry . They enable us to hear , in Tennyson’s words “…the horns of elfland faintly blowing….”


December 16, 2020

How innumeracy has led successive British governments into disastrous economic follies.

In 1820 Britain stood, a lone Collossus, above the world. By 1920 a dozen other nations had higher per-capita GDP. In 2020 we seem even closer to the fringe of things: timid, divided, decaying, relatively impoverished and weak. What happened?

I am going to argue here , through specific examples, that having an innumerate ruling (and media) elite, as we have, is akin to being driven by a drunk.

(A) Leverage (The baboons in the reactor)

The banking crash of 2008. halted progress, stalled incomes, led to austerity, closed social programs and libraries, generated misery and uncertainty, and yet was totally avoidable. Because the ex- Chancellor Gordon Brown, and all his high-powered Treasury officials, were ignorant of simple algebra, they had allowed the Leveraging of bank loans to rise from less than 25 in 1995, already far too high as we shall calculate, to over 50 by 2008. Whatever else was going on, that was bound to lead to a crash. If Brown hadn’t been so innumerate [he did have a PhD in ‘economic history’, which probably made him unjustifiably over-confident] he might even have persuaded his US counterpart ( Alan Greenspan, another innumerate) to behave sensibly. But while Brown was boasting about his “Prudence” he had been blindly driving our bus towards the cliff edge.

A leverage of 50 allows investors to borrow 50 times their own invested capital and so, in a rising market, to double their money every year. How clever, how miraculous! But there ain’t no such things as miracles — even Gordon Brown should have known that. If the market falters, such highly leveraged investors, be they banks or individuals, can lose all their money almost overnight and default on their loans. Banks then panic or crash, and ordinary citizens who were either too wise, too moral or too poor to plunge into the fools’ bonanza, were forced to bail the greedies out. All because Brown and his Treasury wise-acres couldn’t do simple sums. If you want to see just how bloody simple that sum was go to:

(B) Malthus’ Essay on Population.

Follies of innumeracy are by no means uncommon, or new. In 1798 the Revd. Thomas Malthus, a don at Cambridge, published his highly influential “Essay on the Principles of Population”. In it he argued that an unrestrained population would always multiply faster than its food resources, leading inevitably to starvation, to misery, and to a “struggle for existence”. In his own words this struggle entailed  “…..every cause, whether arising from vice or misery, which in any degree contributes to shorten the natural duration of human life. Under this head, therefore, may be enumerated all unwholesome occupations, severe labour and exposure to the seasons, extreme poverty, bad nursing of children, great towns, excesses of all kinds, the whole train of common diseases and epidemics, wars, plagues and famine”.

Malthus’ well-intentioned but naïve argument, was that while population increases exponentially (like flies breeding), food production increases only linearly. It was almost puerile because it ignored the fact that hungry people can often find ingenious new forms of alternative sustenance – thus displaced crofters founded the mighty Scottish herring fishery. But many influential people chose to believe Malthus’ essay, with absolutely tragic consequences for the British poor. It excused: work-houses, forcible Land Enclosures, the transportation of juvenile petty thieves, Highland clearances and so on and so on. The rich used it as an excuse for land grabs, the poor were emiserated, deprived of their livings and their homes, and even of their dignity as human beings. The equivalent of 30 % of the entire British population was forced to emigrate. Never did so little algebra generate so much unnecessary misery. It should have been a warning to all: ‘Beware economic theorists.’

This is a different kind of folly from the first in that here the elite were taken in by a naive mathematics-based essay which most of them probably couldn’t understand but which they should have and probably would have questioned had they had been more confidently numerate themselves. Alas this happens all the time: thus Reagan and Thatcher were taken in by Friedman’s fallacious ‘Monetarism’, again with miserable long-term consequences, mostly for the poor.

(C) The Disastrous Folly of Free Trade.

Malthus’ Essay was bad enough — but it was to be succeeded by much worse. In 1814 Parliament introduced the Corn Laws (i.e. imposed high tariffs on cheap imported cereals) — which enriched the landowning classes and the Church, but impoverished everyone else, especially the industrial poor. The laws were repealed in 1846, but not before they had created a weird economic dogma called “Free Trade”. A millionaire speculator in Parliament David Ricardo convinced many contemporaries that Free Trade is always essential for prosperity and progress. His argument was subtle but, like Malthus’s, far too naive in that it ignored vast factors such as employment, and infrastructure-investment. Unfortunately, subsequent academic Economists, who have a rather feeble grasp of mathematics, though they like to pretend otherwise, were wholly taken in, and what is worse, they persuaded even more innumerate politicians all over the Capitalist world, that Free Trade is good for everybody. It isn’t. It simply isn’t. If you do a proper calculation which embraces all the relevant factors, Free Trade is mostly harmful to any advanced nation like Britain .

       As a result all Britain’s great industries have either closed down, or are in the process: coal, steel, ship-building, cotton mills in Lancashire, woollen mills in Yorkshire, cars, motor-cycles, bicycles, trucks, clocks and pottery in the Midlands, white goods, aircraft, computers, electronics,…….going, going, gone. But it isn’t just Britain. Youth unemployment in France is 25%, 40% in Italy and Spain. And look at America: its great manufacturing centres such as Pittsburgh, Detroit, Cleveland….. are now part of that broken rust belt which rose in despair and voted for Trump. What have we all done to ourselves? I will argue that what the academic economists proclaim is so good for us is actually a deadly poison.

An imported commodity may be dramatically cheaper at the point of retail sale than its domestically produced equivalent. Unfortunately though imports can also have large Sunken Costs arising from losses in domestic employment, investment and profits. And none of us can afford to ignore such Sunken Costs because we will all have to stump up for them in the end in the form of extra taxes to pay for unemployment benefits, retraining and relocating workers,  lost capital and wasted infrastructure (factories, roads, schools, shops, hospitals….). And that says nothing of the misery involved in breaking up communities, families and friends. All that should be obvious; but not apparently to our Economist friends.

What needs to be made, commodity by commodity, is a calculation of the benefits of  a particular Free Trade set against the Sunken Costs which we will have to be borne by the wider community as a whole (i.e. the importing nation). That shouldn’t be too difficult – and it isn’t. I won’t bore you with the algebra at this point (which is rather simple) but you can follow it all up in detail via the links provided; and I encourage you to do so. The results though, are both dramatic and shocking — for instance just take one example: importing a car into an advanced country like Britain only makes sense if its price at the point of retail sale is at least 64% cheaper than its domestic equivalent: 64 per cent! That’s huge. But why so? Because any advanced nation like Britain has, by definition, invested a lot of money in its people and their infrastructure, and when you destroy their means of making their livings and maintaining their societies, by allowing cheaper foreign imports in, it will cost us all an awful lot to replace them. By contrast a relatively backward country like China with almost no welfare system can hugely profit from such trades. But don’t blame China; blame the innumerate economists over here who can’t do simple sums and who’s head is still buried in a dogma formed in the 1840’s during the fight over the bloody Corn Laws. The real point here is that, 160 years later, this is a very different world, but economists don’t seem capable of keeping up. The damage they have done to Britain (and elsewhere), and are still doing, is incalculable. I will say no more here because there is a separate post entitled ‘THE FOLLY OF FREE TRADE’ which includes my calculation as a url.

(D) The Immigration Fiasco.

Is a contemporary example of what a numerically ignorant ruling elite is capable, or rather incapable of — recognising a simple perilous truth, and thus doing something about it. So high has been the the immigration rate been over the past 50 years that it is equivalent to 3 British mothers out of 4 raising an extra child. If that is not “swamping” then what is? Since I have written a whole post on this, entitled ‘IMMIGRATION FIASCO’ I will say no more here. But you can see the calculation there and see if you agree.

(E) The nuclear war that hasn’t happened. Yet.

By contrast to the hideous damage innumeracy can wreak upon a nation, let’s look at even more dramatic example where numeracy may not only have saved the day but have actually preserved Life on Earth.

The most important event of the 20th century didn’t happen — Nuclear Armageddon, though it appears we came desperately, desperately close during the Cuban Missile Crisis in 1962.

In 1921 the Quaker mathematician and pacifist Lewis Fry Richardson pointed to the probable cause of the First World War — a mathematical instability in the arms race that preceded it. If nations can arm faster than they can disarm such a race will eventually explode out of control into war. But if they can disarm faster than they can arm, the race need never blow up in such an accidental way. Rightly terrified out of their wits after Cuba, the commanders on both sides, with their experts, recalled Richardson’s analysis and installed a hot-line between the White House and the Kremlin to defuse potential escalations in future. That is probably why you and I are still alive. An innumerate society with The Bomb could still put us all in the grave.


Britain has been, and is being brought low by a ruling and media elite who imagine they are educated. — when they are not . While some cringers are unwilling to look at the truth (viz. on Immigration) I suspect that most of our troubles do not stem so much from cowardice as from what I call ‘Baducation’. For instance most people who have studied ‘PPE’ at Oxford (as so many of our elite have, including the Editor of The Economist ) are simply not numerate enough to grasp salient facts and arguments.

The only good news here is that if we are only willing to face the truth at last we could rapidly put things right because although Innumeracy is a highly debilitating disease it is not malignant. If we paid everyone who made the effort to learn enough to pass a basic test in Numeracy £15,000 ,we could enumerate the entire nation for less than half the cost of a third runway at Heathrow. It is no accident that the wealthiest people on Earth at present, the Japanese, are also the most numerate ( For instance they figured out the Immigration problem long ago).

In the mean time we shouldn’t listen to, and certainly shouldn’t vote for Innumerates, never mind how many PPE degrees and the like they might have got from ancient universities. They’re simply Baducated, and as such dangerous. As the world has become more sophisticated so it needs more sophisticated people to govern it. We wouldn’t accept an illiterate Cabinet; why should we accept an innumerate one?

There is much more on this topic, and possible remedies we can use, in my “History of the Brits (from a scientist’s point of view) “, described elsewhere on this site . For instance it includes chapters entitled Half Baked Economics and Baducation.


October 16, 2020


An immigration rate of about half a per cent a year as we presently have in Britain, sounds innocuous. I certainly thought so. Thus people who object to it are sometimes branded as ‘racists’ or worse by ‘liberals’. But liberals generally don’t understand that half a per cent a year is the equivalent of 3 British mothers out of 4 raising an extra child. So it is dramatic. Even as a very experienced user and teacher of maths myself, I was very surprised indeed when I worked this out last year (2019). Indeed I was so shocked I refused to believe it for weeks until I had re-done the calculation in several independent ways. But it seems there can be no doubt about it.

How could a small percentage lead to apocalyptic growth? Mainly because immigrants arrive every year whilst births and deaths are lifetime events, and Life-expectancy in Europe today is about 80 years. So you have to multiply yearly immigration rates by 80 to appreciate the real scale of it. Then again, only the female half of the existing population breeds, while immigrants come in in both sexes. So that’s another multiplying factor of 2. Now we can begin to see why the current figure of roughly 300,000 immigrants/year is equivalent to 160 times that amount in a lifetime, or 48 Million. It is indeed equivalent to 3 British mothers out of 4 having an extra child. [Alternatively note that the immigration rate is about half the annual birth rate; that should make one think — indeed that’s what started me calculating.]

I don’t think any of us can have a fruitful. discussion of immigration (or population control in general, which was my initial interest) unless we understand the scale of it. There is no avoiding the conclusion that at anything like its present level immigration will swamp Britain. That’s not racism, that is simple algebra. Alas very few of our governing or media elite are numerate enough to comprehend the scale of the problem while residents in certain areas know only too well they are being swamped, or have been already.

I discuss Population and Immigration as impersonally as I can in my recent book History of the Brits (from a scientists point of view), Amazon 2020. It is described elsewhere on this site under ‘My Books’ Category Here is the summary at the end of Chapter 16, which deals only with the numbers:

“Any discussion of population and immigration which doesn’t take numbers into account is worthless. Who sensible would argue that all or any immigration is either wholly good or wholly bad – surely it is a question of how much; and that takes some calculating:

We have found that:

  1. Indigenous Brits have largely descended from a few hundred hunter-gatherers who were stranded here when Doggerland was inundated around 6500 BC. There is thus no way Brits can argue that they are especially talented people who got here because of, for instance, their seafaring enterprise. The silly buggers were simply cut off. Lucky devils!
  2. Subsequent invasions must have been more of ideas than people. Ideas can obviously fly.
  3. The indigenous British population is approximately 400 generations old.
  4. So as to make up for occasional setbacks such as plagues and droughts all animal populations must be able to grow exponentially. Such is the nature of exponential growth however that minute rates of growth or decline can lead eventually to apocalyptic changes in population. We all need an intuitive grasp of this vital process. [See Box]
  5. Many debates about immigration policy are confused, and have led to shouting matches, because educated but innumerate people have confounded immigration rates with population numbers and so have dramatically underestimated the long term effects of immigration. To compare a rate with a number one must first multiply the rate by twice the life expectancy of the existing population – 160 years in Britain. Thus the current rate of roughly 300,000 immigrants a year corresponds to a total number of 48 million migrants! This dramatic multiplier, which was by no means obvious, needs most careful thought – and acknowledgement.

NB The vital Intergenerational Population Multiplier is:

X= (b+B)/2 where b is the average number of children per mother (close to 2.0) while B=2IT/P where I is the net annual immigration rate (about 300,000 at present), T the average life expectancy (about 80 years), and P the existing population (about 67 Million in 2020). If you work it out B comes to about 0.75 extra babies per mother — as claimed above.

(The 2 in B arises because only the female half of the indigenous population breeds so the fair ratio of immigration to breeding has to be I/(P/2) = 2I/P while the T converts a rate into a number.)


Britons are comparatively wealthy; immigrants are comparatively poor – which is mostly why they come. Thus, immigration must necessarily drain the per capita accumulated wealth of a host country. People don’t talk about this. Thus the present immigration rate is halving the UK’s annual accumulation of wealth – which is a very slow process.[Note 3]. Thus each immigrant costs the UK roughly a million pounds, but for some reason people never talk about that This is already showing up in the present housing crisis – the canary in the mine.

The great news is that we can, if we want to, reduce our present population to a sustainable level (less than 20 million?) in only two generations without any need for draconian restrictions such as a One Child policy, provided we now halt immigration almost entirely. Because of the aforesaid 160, small numbers of immigrants arriving per year are , in this context, equivalent to large numbers of extra babiesEvery citizen should understand that. It is not obvious, but it is absolutely spinal!

But the point of this post is simply to help anyone interested in these subjects to understand the Maths, and if possible to check it. To that end I have written a short algebraic essay which you can click on at:

ABOUT MY BOOK : ‘HISTORY OF THE BRITS from a scientist’s point of view’.

September 30, 2020

What we aim for, and what we can achieve, are largely determined by who we think we are, by our self-confidence. And that is as true for nations as it is for individuals. Where we British go in future will be decided by what we think about our past. So this is a history of the Brits with its eye on the future. It is different partly because it is written by a scientist who believes that technology, mathematics and science have been so crucial to history that historians without a scientific background are virtually condemned to miss the point. Think of the following: vaccination, Darwinism, universal sewage and clean water, Calculus, broadcasting, the industrial revolution, representative democracy, the telescope, organised sport, tourism, railways, megacities, the middle class, the jet engine, anti-sepsis, computing, expert committees, the abolition of slavery, electronics, nursing, the electric motor, steel, cement, steam-ships, astronavigation, chemistry, Energy, atomic theory, artificial dyes, television, refrigeration, ATMs, the atomic nucleus, , antibiotics, IVF, …… one could go on and on. They were all British developments or insights which have revolutionised mankind’s life. No other society has left such a legacy – or anything approaching it. Surely it is vital to try and understand how it came about – if only to prevent the magic spring from drying up, and that is what this book is largely about. If Ancient Greece was interesting the evolution of Britain is vastly more.

The technlogy that made civisation possible
Civilisation requires above all the transport capacity to feed and fuel great cities. The Greeks and Romans relied on slaves whose backs and spirits they broke before they were replaced by constant conquest. Not only were they brutal but they were long term unsustainable. But an ingenious alternative was to be found eventually in North Western Europe, Britain in particular: Moon power. You are looking at a Thames Sailing Barge which, with crew of only 2 men and a boy, could easily carry more than a thousand fit slaves, or more than 250 horses and carts. Thus great cities like London, Amsterdam, Antwerp, Glagow, Bruges, Rouen, Bristol and Edinburgh became possible for the first time in history; without slavery. See Chapter 2 ; Civilisation and Moon-power. The sails are mainly used to get in and out of favourable tidal streams. Powell/Alamy Live News

My main qualification to attempt a history is a lifetime spent as a Space scientist and astronomer trying to sift through and make sense of conflicting evidence. A sceptical, outsider’s point of view is essential for that, as well as a willingness to change one’s mind – which is never easy. And It helps that I have lived and worked in a dozen countries, experiences which help me to see Britain in a more impersonal light. My portrait of Britain will show her from a new angle, and so by a rather different light.

According to Einstein there is only one fruitful way to think – and that is to use Common Sense Thinking (CST). CST is essential to winnow sound conclusions out of conflicting evidence. But how does Common Sense work? They don’t teach us at school or university because scholars don’t understand it. So I go into CST in some depth before tackling vital issues which historians have almost entirely neglected. For instance: much of human activity is dominated by simple underlying mathematical principles, but conventional historians don’t ‘do’ mathematics. Thus, for example, they don’t understand why nations, including the British, have been forced into continually warring with one another. If we could understand, we might be able to stop it. Civilisation grows out of great cities, but sustainable cities require vast amounts of cheap power just to feed and fuel themselves. Why did London and Glasgow succeed where Rome and Athens failed? It was Moon-power.Why do people go to hot countries to relax, but risk their lives to come and live in cool ones? It is all to do with Thermodynamics – which dominates all of human existence. It turns out that Britain’s climate is ideal. The Armada and the Luftwaffe were both repulsed by expert committees, Britain’s greatest legacy to civilization? But why do committees work?

Healthy societies must progress; but what is Progress? Our study of CST enables us to pin down its 7 key principles, its Seven Pillars of Wisdom, which turn out to be: Curiosity, Honesty, Adaptability, Numeracy, Tolerance, Literacy and Democracy which then illuminate the whole subject and explain Britain’s uniqueness. But can it remain Progressive? Yes; but only if we thoroughly understand what those Seven Pillars of Wisdom are, and just why they work. So this is about some fundamental and fascinating issues that other historians, because of their background, or rather their lack of scientific background, have left out. Britain’s future could be either very dark; or very bright, depending on our understanding of what Progress entails. George Orwell said: “The most effective way to destroy people is to deny and obliterate their own history”. The author believes that modern Brits have allowed their history to be stolen away. It’s time to put the record straight.

                              TABLE OF CONTENTS,

Preface      Another History; What on Earth For?  p 1

Chapter 1: Geography: This Sceptred Isle    p 6   

Chapter 2: Civilisation and Moon-power     11

Chapter 3: The Royal Navy     16

Chapter 4: A Mathematical Portrait of History     19

Chapter 5: Progress: Why Nice Chaps come in First     29

Chapter 6: Committees     41

Chapter 7: Parasites.    48

Chapter 8: Can History have a  Scientific Method ?    60

Chapter 9: Why Men have  had to Fight.    71

Chapter 10: Britain in the Second World War.    81

Chapter 11: The British Empire: Achievement or Crime?     90

Chapter 12: Escaping its Priestly Chains.     98

Chapter 13: The Baleful Shadow of America.     105

Chapter 14: Half-baked Economics; the Modern Religion.      128

Chapter 15: Numeracy; the Seventh Pillar of Wisdom      146

Chapter 16: Population and Immigration:  the Numbers.     162

Chapter 17: Innovation.    182

Chapter 18 The History of Thinking.    206

Chapter 19 Mass Immigration – the Big Creep.     219

Chapter 20 Baducation.    P 235

                Retrospect and Prospect.    255

                If I had my way. 258

Chapter 21 The Superpowers Aren’t [ on line only at my post HOB&&& ]

                Au Revoir      261

                Acknowledgments   267

The paperback version [ ISBN – 9 – 781086157499] with 77 kilo-words came out on Amazon in June 2020 priced at £10.00 HOWEVER THIS IS A LIVE BOOK WITH MORE STUFF BEING CONSTANTLY ADDED IN MY POST HOB&&&.