May 2011

Clawson, Calvin C. Mathematical Mysteries. New York: Perseus Books, 1996. ISBN 978-0-7382-0259-4.

This book might be more accurately titled “Wonders of Number Theory”, but doubtless the publisher feared that would scare away the few remaining customers who weren't intimidated by the many equations in the text. Within that limited scope, and for readers familiar with high school algebra (elementary calculus makes a couple of appearances, but you'll miss little or nothing if you aren't acquainted with it), this is an introduction to the beauty of mathematics, its amazing and unexpected interconnectedness, and the profound intellectual challenge of problems, some posed in ancient Greece, which can easily be explained to a child, yet which remain unsolved after millennia of effort by the most intelligent exemplars of our species.

The hesitant reader is eased into the topic through a variety of easily-comprehended and yet startling results, expanding the concept of number from the natural numbers to the real number line (like calculus, complex numbers only poke their nose under the tent in a few circumstances where they absolutely can't be avoided), and then the author provides a survey of the most profound and intractable puzzles of number theory including the Goldbach conjecture and Riemann hypothesis, concluding with a sketch of Gödel's incompleteness theorems and what it all means.

Two chapters are devoted to the life and work of Ramanujan, using his notebooks to illustrate the beauty of an equation expressing a deep truth and the interconnections in mathematics this singular genius perceived, such as:

which relates the sequence of prime numbers (p_i is the ith prime number) to the ratio of the circumference to the diameter of a circle. Who could have imagined they had anything to do with one another? And how did 105 get into it?

This book is a pure joy, and a excellent introduction for those who “don't get it” of how mathematics can become a consuming passion for those who do. The only low spot in the book is chapter 9, which discusses the application of large prime numbers to cryptography. While this was much in the news during the crypto wars when the book was published in the mid-1990s, some of the information in this chapter is factually incorrect and misleading, and the attempt at a popular description of the RSA algorithm will probably leave many who actually understand its details scratching their heads. So skip this chapter.

I bought this book shortly after it was published, and it sat on my shelf for a decade and a half until I picked it up and started reading it. I finished it in three days, enjoying it immensely, and I was already familiar with most of the material covered here. For those who are encountering it for the first time, this may be a door into a palace of intellectual pleasures they previously thought to be forbidding, dry, and inaccessible to them.

 

Gabb, Sean. The Churchill Memorandum. Raleigh, NC: Lulu.com, 2011. ISBN 978-1-4467-2257-2.

This thriller is set in Britain in the year 1959 in an alternative history where World War II never happened: Hitler died in a traffic accident while celebrating his conquest of Prague, and Göring and the rest of his clique, opting to continue to enrich themselves at the expense of the nation rather than risk it all on war, came to an accommodation with Britain and France where Germany would not interfere with their empires in return for Germany's being given a free hand in Eastern Europe up to the Soviet border. With British prosperity growing and dominance of the seas unchallenged, when Japan attacked Pearl Harbor and the Philippines, Britain was able to arrange a negotiated settlement under which the Royal Navy would guarantee freedom of the seas, Hawaii, and the west coast of the U.S.

The U.S., after a series of domestic economic and political calamities, has become an authoritarian, puritanical dictatorship under Harry Anslinger and his minions, and expatriates from his tyranny enrich the intellectual and economic life of Europe.

By 1959, the world situation has evolved into a more or less stable balance of powers much like Europe in the late 19th century, with Britain, Germany, the Soviet Union, and Japan all engaged in conflicts around the margin, but in an equilibrium where any one becoming too strong will bring forth an alliance among the others to restore the balance. Britain and Germany have developed fission bombs, but other than a single underground test each, have never used them and rely upon them for deterrence against each other and the massive armies of the Soviets. The U.S. is the breadbasket and natural resource supplier of the world, but otherwise turned inward and absent from the international stage.

In this climate, Britain is experiencing an age of prosperity unprecedented in its history. Magnetically levitated trains criss-cross the island, airships provide travel in style around the globe, and a return to the gold standard has rung in sound money not only at home but abroad. Britain and Germany have recently concluded a treaty to jointly open the space frontier.

Historian Anthony Markham, author of a recently published biography of Churchill, is not only the most prominent Churchill scholar but just about the only one—who would want to spend their career studying a marginal figure whose war-mongering, had it come to fruition, would have devastated Britain and the Continent, killed millions, destroyed the Empire, and impoverished people around the world? While researching his second volume on Churchill, he encounters a document in Churchill's handwriting which, if revealed, threatens to destabilise the fragile balance of power and return the world to the dark days of the 1930s, putting at risk all the progress made since then. Markham finds himself in the middle of a bewilderingly complicated tapestry of plots and players, including German spies, factions in the Tory party, expatriate Ayn Rand supporters, the British Communist party, Scotland Yard, the Indian independence movement, and more, where nothing is as it appears on the surface. Many British historical figures appear here, with those responsible for the decline of Britain in our universe skewered (or worse) from a libertarian perspective. Chapter 31 is a delightful tour d'horizon of the pernicious ideas which reduced Britain from global hegemon to its sorry state today.

I found that this book works both as a thriller and dark commentary of how bad ideas can do more damage to a society and nation than any weapon or external enemy, cleverly told from the perspective of a world where they didn't prevail. Readers unfamiliar with British political figures and their disastrous policies in the postwar era may need to brush up a bit to get the most out of this novel. The Abolition of Britain (November 2005) is an excellent place to start.

As alternative history, I found this less satisfying. Most works in the genre adhere to the rule that one changes a single historical event and then traces how the consequences of that change propagate and cascade through time. Had the only change been Hitler's dying in a car crash, this novel would conform to the rule, but that isn't what we have here. Although some subsequent events are consequences of Hitler's death, a number of other changes to history which (at least to this reader) don't follow in any way from it make major contributions to the plot. Now, a novelist is perfectly free to choose any premises he wishes—there are no black helicopters filled with agents of Anslinger's Bureau of Genre Enforcement poised to raid those who depart from the convention—but as a reader I found that having so many counterfactual antecedents made for an alternative world which was somewhat confusing until one eventually encountered the explanation for the discordant changes.

A well-produced Kindle edition is available.

 

Fergusson, Adam. When Money Dies. New York: PublicAffairs, [1975] 2010. ISBN 978-1-58648-994-6.

This classic work, originally published in 1975, is the definitive history of the great inflation in Weimar Germany, culminating in the archetypal paroxysm of hyperinflation in the Fall of 1923, when Reichsbank printing presses were cranking out 100 trillion (10¹²) mark banknotes as fast as paper could be fed to them, and government expenditures were 6 quintillion (10¹⁸) marks while, in perhaps the greatest achievement in deficit spending of all time, revenues in all forms accounted for only 6 quadrillion (10¹⁵) marks. The book has long been out of print and much in demand by students of monetary madness, driving the price of used copies into the hundreds of dollars (although, to date, not trillions and quadrillions—patience). Fortunately for readers interested in the content and not collectibility, the book has been re-issued in a new paperback and electronic edition, just as inflation has come back onto the radar in the over-leveraged economies of the developed world. The main text is unchanged, and continues to use mid-1970s British nomenclature for large numbers (“millard” for 10⁹, “billion” for 10¹² and so on) and pre-decimalisation pounds, shillings, and pence for Sterling values. A new note to this edition explains how to convert the 1975 values used in the text to their approximate present-day equivalents.

The Weimar hyperinflation is an oft-cited turning point in twentieth century, but like many events of that century, much of the popular perception and portrayal of it in the legacy media is incorrect. This work is an in-depth antidote to such nonsense, concentrating almost entirely upon the inflation itself, and discussing other historical events and personalities only when relevant to the main topic. To the extent people are aware of the German hyperinflation at all, they'll usually describe it as a deliberate and cynical ploy by the Weimar Republic to escape the reparations for World War I exacted under the Treaty of Versailles by inflating away the debt owed to the Allies by debasing the German mark. This led to a cataclysmic episode of hyperinflation where people had to take a wheelbarrow of banknotes to the bakery to buy a loaf of bread and burning money would heat a house better than the firewood or coal it would buy. The great inflation and the social disruption it engendered led directly to the rise of Hitler.

What's wrong with this picture? Well, just about everything…. Inflation of the German mark actually began with the outbreak of World War I in 1914 when the German Imperial government, expecting a short war, decided to finance the war effort by deficit spending and printing money rather than raising taxes. As the war dragged on, this policy continued and was reinforced, since it was decided that adding heavy taxes on top of the horrific human cost and economic privations of the war would be disastrous to morale. As a result, over the war years of 1914–1918 the value of the mark against other currencies fell by a factor of two and was halved again in the first year of peace, 1919. While Germany was committed to making heavy reparation payments, these payments were denominated in gold, not marks, so inflating the mark did nothing to reduce the reparation obligations to the Allies, and thus provided no means of escaping them. What inflation and the resulting cheap mark did, however, was to make German exports cheap on the world market. Since export earnings were the only way Germany could fund reparations, promoting exports through inflation was both a way to accomplish this and to promote social peace through full employment, which was in fact achieved through most of the early period of inflation. By early 1920 (well before the hyperinflationary phase is considered to have kicked in), the mark had fallen to one fortieth of its prewar value against the British pound and U.S. dollar, but the cost of living in Germany had risen only by a factor of nine. This meant that German industrialists and their workers were receiving a flood of marks for the products they exported which could be spent advantageously on the domestic market. Since most of Germany's exports at the time relied little on imported raw materials and products, this put Germany at a substantial advantage in the world market, which was much remarked upon by British and French industrialists at the time, who were prone to ask, “Who won the war, anyway?”.

While initially beneficial to large industry and its organised labour force which was in a position to negotiate wages that kept up with the cost of living, and a boon to those with mortgaged property, who saw their principal and payments shrink in real terms as the currency in which they were denominated declined in value, the inflation was disastrous to pensioners and others on fixed incomes denominated in marks, as their standard of living inexorably eroded.

The response of the nominally independent Reichsbank under its President since 1908, Dr. Rudolf Havenstein, and the German government to these events was almost surreally clueless. As the originally mild inflation accelerated into dire inflation and then headed vertically on the exponential curve into hyperinflation they universally diagnosed the problem as “depreciation of the mark on the foreign exchange market” occurring for some inexplicable reason, which resulted in a “shortage of currency in the domestic market”, which could only be ameliorated by the central bank's revving up its printing presses to an ever-faster pace and issuing notes of larger and larger denomination. The concept that this tsunami of paper money might be the cause of the “depreciation of the mark” both at home and abroad, never seemed to enter the minds of the masters of the printing presses.

It's not like this hadn't happened before. All of the sequelæ of monetary inflation have been well documented over forty centuries of human history, from coin clipping and debasement in antiquity through the demise of every single unbacked paper currency ever created. Lord D'Abernon, the British ambassador in Berlin and British consular staff in cities across Germany precisely diagnosed the cause of the inflation and reported upon it in detail in their dispatches to the Foreign Office, but their attempts to explain these fundamentals to German officials were in vain. The Germans did not even need to look back in history at episodes such as the assignat hyperinflation in revolutionary France: just across the border in Austria, a near-identical hyperinflation had erupted just a few years earlier, and had eventually been stabilised in a manner similar to that eventually employed in Germany.

The final stages of inflation induce a state resembling delirium, where people seek to exchange paper money for anything at all which might keep its value even momentarily, farmers with abundant harvests withhold them from the market rather than exchange them for worthless paper, foreigners bearing sound currency descend upon the country and buy up everything for sale at absurdly low prices, employers and towns, unable to obtain currency to pay their workers, print their own scrip, further accelerating the inflation, and the professional and middle classes are reduced to penury or liquidated entirely, while the wealthy, industrialists, and unionised workers do reasonably well by comparison.

One of the principal problems in coping with inflation, whether as a policy maker or a citizen or business owner attempting to survive it, is inherent in its exponential growth. At any moment along the path, the situation is perceived as a “crisis” and the current circumstances “unsustainable”. But an exponential curve is self-similar: when you're living through one, however absurd the present situation may appear to be based on recent experience, it can continue to get exponentially more bizarre in the future by the inexorable continuation of the dynamic driving the curve. Since human beings have evolved to cope with mostly linear processes, we are ill-adapted to deal with exponential growth in anything. For example, we run out of adjectives: after you've used up “crisis”, “disaster”, “calamity”, “catastrophe”, “collapse”, “crash”, “debacle”, “ruin”, “cataclysm”, “fiasco”, and a few more, what do you call it the next time they tack on three more digits to all the money?

This very phenomenon makes it difficult to bring inflation to an end before it completely undoes the social fabric. The longer inflation persists, the more painful wringing it out of an economy will be, and consequently the greater the temptation to simply continue to endure the ruinous exponential. Throughout the period of hyperinflation in Germany, the fragile government was painfully aware that any attempt to stabilise the currency would result in severe unemployment, which radical parties of both the Left and Right were poised to exploit. In fact, the hyperinflation was ended only by the elected government essentially ceding its powers to an authoritarian dictatorship empowered to put down social unrest as the costs of its policies were felt. At the time the stabilisation policies were put into effect in November 1923, the mark was quoted at six trillion to the British pound, and the paper marks printed and awaiting distribution to banks filled 300 ten-ton railway boxcars.

What lessons does this remote historical episode have for us today? A great many, it seems to me. First and foremost, when you hear pundits holding forth about the Weimar inflation, it's valuable to know that much of what they're talking about is folklore and conventional wisdom which has little to do with events as they actually happened. Second, this chronicle serves to remind the reader of the one simple fact about inflation that politicians, bankers, collectivist media, organised labour, and rent-seeking crony capitalists deploy an entire demagogic vocabulary to conceal: that inflation is caused by an increase in the money supply, not by “greed”, “shortages”, “speculation”, or any of the other scapegoats trotted out to divert attention from where blame really lies: governments and their subservient central banks printing money (or, in current euphemism, “quantitative easing”) to stealthily default upon their obligations to creditors. Third, wherever and whenever inflation occurs, its ultimate effect is the destruction of the middle class, which has neither the political power of organised labour nor the connections and financial resources of the wealthy. Since liberal democracy is, in essence, rule by the middle class, its destruction is the precursor to establishment of authoritarian rule, which will be welcomed after the once-prosperous and self-reliant bourgeoisie has been expropriated by inflation and reduced to dependence upon the state.

The Weimar inflation did not bring Hitler to power—for one thing the dates just don't work. The inflation came to an end in 1923, the year Hitler's beer hall putsch in Munich failed ignominiously and resulted in his imprisonment. The stabilisation of the economy in the following years was widely considered the death knell for radical parties on both the Left and Right, including Hitler's. It was not until the onset of the Great Depression following the 1929 crash that rising unemployment, falling wages, and a collapsing industrial economy as world trade contracted provided an opening for Hitler, and he did not become chancellor until 1933, almost a decade after the inflation ended. And yet, while there was no direct causal connection between the inflation and Hitler's coming to power, the erosion of civil society and the rule of law, the destruction of the middle class, and the lingering effects of the blame for these events being placed on “speculators” all set the stage for the eventual Nazi takeover.

The technology and complexity of financial markets have come a long way from “Railway Rudy” Havenstein and his 300 boxcars of banknotes to “Helicopter Ben” Bernanke. While it used to take years of incompetence and mismanagement, leveling of vast forests, and acres of steam powered printing presses to destroy an industrial and commercial republic and impoverish those who sustain its polity, today a mere fat-finger on a keyboard will suffice. And yet the dynamic of inflation, once unleashed, proceeds on its own timetable, often taking longer than expected to corrode the institutions of an economy, and with ups and downs which tempt investors back into the market right before the next sickening slide. The endpoint is always the same: destruction of the middle class and pensioners who have provided for themselves and the creation of a dependent class of serfs at the mercy of an authoritarian regime. In past inflations, including the one documented in this book, this was an unintended consequence of ill-advised monetary policy. I suspect the crowd presently running things views this as a feature, not a bug.

A Kindle edition is available, in which the table of contents and notes are properly linked to the text, but the index is simply a list of terms, not linked to their occurrences in the text.

 

Thor, Brad. Blowback. New York: Pocket Books, 2005. ISBN 978-1-4516-0828-1.

This is the fourth in the author's Scot Harvath series, which began with The Lions of Lucerne (October 2010). In this novel, Harvath is involved in a botched takedown attempt against an al-Qaeda operative which, repeated endlessly on cable news channels, brings him and his superiors into the crosshairs of ambitious former first lady and carpetbagging Senator Helen Remington Carmichael, who views exposing Harvath and those who ordered the operation as her ticket to second place on the next Democratic presidential ticket.

As wise people do when faced with the flounderings of a wounded yet still dangerous superpower, Harvath gets out of Dodge and soon finds himself on the trail of a plot, grounded in the arcane science of paleopathology and dating from Hannibal's crossing of the Alps, which threatens a genocide of non-believers in the Dar al-Harb and unification of the Ummah under a new caliphate. Scientists have been disappearing, and as Harvath follows the trail of the assassin, he discovers the sinister thread that ties their work, performed in isolation, together into a diabolical scheme.

Harvath teams up with a plucky lady paleopathologist (Harvath's female companions seem to adapt to commando missions as readily as Doctor Who's to multiverse displacement) and together they begin to follow the threads which lead to an horrific plot based on a weapon of mass destruction conceived in antiquity which has slumbered for millennia in an ice cavern.

What more could you ask for? Politics, diseases in antiquity, ice mummies, evil geniuses in Swiss mountain redoubts (heh!), glider assaults, mass murder with the chosen protected by mass marketing, and a helicopter assault on a terrorist icon in a Muslim country—works for me!

This is a thriller, and it delivers the thrills in abundance. But this is Fourmilab, and you expect the quibbles, don't you? So here we go, and without spoilers! The Super Vivat motor-gliders used to assault the mountaintop are said in chapter 72 to be capable of retracting the propeller into the nose of the fuselage and retracting and extending their landing gear. Neither is correct—the propeller can be feathered but not retracted, and the landing gear is fixed.

This is a page-turner, and it succeeds at its mission and will send you off to read the next in the series. The solution to the chaos in the Islamic world advanced here by the bad guys is, in fact, one I've been thinking about as less worse than most of the alternatives for more than decade. Could the “Arab Spring” give way to an “Ottoman Fall”? Let's talk Turkey.

 

Hamilton-Paterson, James. Empire of the Clouds. London: Faber and Faber, 2010. ISBN 978-0-571-24795-0.

At the end of World War II, Great Britain seemed poised to dominate or at the least be a major player in postwar aviation. The aviation industries of Germany, France, and, to a large extent, the Soviet Union lay in ruins, and while the industrial might of the United States greatly out-produced Britain in aircraft in the latter years of the war, America's P-51 Mustang was powered by a Rolls-Royce engine built under license in the U.S., and the first U.S. turbojet and turboshaft engines were based on British designs. When the war ended, Britain not only had a robust aircraft industry, composed of numerous fiercely independent and innovative companies, it had in hand projects for game-changing military aircraft and a plan, drawn up while the war still raged, to seize dominance of civil aviation from American manufacturers with a series of airliners which would redefine air travel.

In the first decade after the war, Britons, especially aviation-mad “plane-spotters” like the author, found it easy to believe this bright future beckoned to them. They thronged to airshows where innovative designs performed manoeuvres thought impossible only a few years before, and they saw Britain launch the first pure-jet, and the first medium- and long-range turboprop airliners into commercial service. This was a very different Britain than that of today. Only a few years removed from the war, even postwar austerity seemed a relief from the privations of wartime, and many people vividly recalled losing those close to them in combat or to bombing attacks by the enemy. They were a hard people, and not inclined to discouragement even by tragedy. In 1952, at an airshow at Farnborough, an aircraft disintegrated in flight and fell into the crowd, killing 31 people and injuring more than 60 others. While ambulances were still carrying away the dead and injured, the show went on, and the next day Winston Churchill sent the pilot who went up after the disaster his congratulations for carrying on. While losses to aircraft and aircrew in the postwar era were small compared combat in the war, they were still horrific by present day standards.

A quick glance at the rest of this particular AIB [Accidents Investigation Branch] file reveals many similar casualties. It deals with accidents that took place between 3 May 1956 and 3 January 1957. In those mere eight months there was a total of thirty-four accidents in which forty-two aircrew were killed (roughly one fatality every six days). Pilot error and mechanical failure shared approximately equal billing in the official list of causes. The aircraft types included ten de Havilland Venoms, six de Havilland Vampires, six Hawker Hunters, four English Electric Canberras, two Gloster Meteors, and one each of the following: Gloster Javelin, Folland Gnat, Avro Vulcan, Avro Shackleton, Short Seamew and Westland Whirlwind helicopter. (pp. 128–129)

There is much to admire in the spirit of mourn the dead, fix the problem, and get on with the job, but that stoic approach, essential in wartime, can blind one to asking, “Are these losses acceptable? Do they indicate we're doing something wrong? Do we need to revisit our design assumptions, practises, and procedures?” These are the questions which came into the mind of legendary test pilot Bill Waterton, whose career is the basso continuo of this narrative. First as an RAF officer, then as a company test pilot, and finally as aviation correspondent for the Daily Express, he perceived and documented how Britain's aviation industry was, due to its fragmentation into tradition-bound companies, incessant changes of priorities by government, and failure to adapt to the aggressive product development schedules of the Americans and even the French, still rebuilding from wartime ruins, doomed to bring inferior products to the market too late to win foreign sales, which were essential for the viability of an industry with a home market as small as Britain's to maintain world-class leadership.

Although the structural problems within the industry had long been apparent to observers such as Waterton, any hope of British leadership was extinguished by the Duncan Sandys 1957 Defence White Paper which, while calling for long-overdue consolidation of the fragmented U.K. aircraft industry, concluded that most military missions in the future could be accomplished more effectively and less expensively by unmanned missiles. With a few exceptions, it cancelled all British military aviation development projects, condemning Britain, once the fallacy in the “missiles only” approach became apparent, to junior partner status in international projects or outright purchases of aircraft from suppliers overseas. On the commercial aviation side, only the Vickers Viscount was a success: the fatigue-induced crashes of the de Havilland Comet and the protracted development process of the Bristol Britannia caused their entry into service to be so late as to face direct competition from the Boeing 707 and Douglas DC-8, which were superior aircraft in every regard.

This book recounts a curious epoch in the history of British aviation. To observers outside the industry, including the hundreds of thousands who flocked to airshows, it seemed like a golden age, with one Made in Britain innovation following another in rapid succession. But in fact, it was the last burst of energy as the capital of a mismanaged and misdirected industry was squandered at the direction of fickle politicians whose priorities were elsewhere, leading to a sorry list of cancelled projects, prototypes which never flew, and aircraft which never met their specifications or were rushed into service before they were ready. In 1945, Britain was positioned to be a world leader in aviation and proceeded, over the next two decades, to blow it, not due to lack of talent, infrastructure, or financial resources, but entirely through mismanagement, shortsightedness, and disastrous public policy. The following long quote from the concluding chapter expresses this powerfully.

One way of viewing the period might be as a grand swansong or coda to the process we Britons had ourselves started with the Industrial Revolution. The long, frequently brilliant chapter of mechanical inventiveness and manufacture that began with steam finally ran out of steam. This was not through any waning of either ingenuity or enthusiasm on the part of individuals, or even of the nation's aviation industry as a whole. It happened because, however unconsciously and blunderingly it was done, it became the policy of successive British governments to eradicate that industry as though it were an unruly wasps' nest by employing the slow cyanide of contradictory policies, the withholding of support and funds, and the progressive poisoning of morale. In fact, although not even the politicians themselves quite realised it – and certainly not at the time of the upbeat Festival of Britain in 1951 – this turned out to be merely part of a historic policy change to do away with all Britain's capacity as a serious industrial nation, abolishing not just a century of making its own cars but a thousand years of building its own ships. I suspect this policy was more unconscious than deliberately willed, and it is one whose consequences for the nation are still not fully apparent. It sounds improbable; yet there is surely no other interpretation to be made of the steady, decades-long demolition of the country's manufacturing capacity – including its most charismatic industry – other that at some level it was absolutely intentional, no matter what lengths politicians went to in order to conceal this fact from both the electorate and themselves. (p. 329)

Not only is this book rich in aviation anecdotes of the period, it has many lessons for those living in countries which have come to believe they can prosper by de-industrialising, sending all of their manufacturing offshore, importing their science and engineering talent from other nations, and concentrating on selling “financial services” to one another. Good luck with that.