Saturday, January 10, 2015

Reading List: Enlightening Symbols

Mazur, Joseph. Enlightening Symbols. Princeton: Princeton University Press, 2014. ISBN 978-0-691-15463-3.
Sometimes an invention is so profound and significant yet apparently obvious in retrospect that it is difficult to imagine how people around the world struggled over millennia to discover it, and how slowly it was to diffuse from its points of origin into general use. Such is the case for our modern decimal system of positional notation for numbers and the notation for algebra and other fields of mathematics which permits rapid calculation and transformation of expressions. This book, written with the extensive source citations of a scholarly work yet accessible to any reader familiar with arithmetic and basic algebra, traces the often murky origins of this essential part of our intellectual heritage.

From prehistoric times humans have had the need to count things, for example, the number of sheep in a field. This could be done by establishing a one-to-one correspondence between the sheep and something else more portable such as one's fingers (for a small flock), or pebbles kept in a sack. To determine whether a sheep was missing, just remove a pebble for each sheep and if any remained in the sack, that indicates how many are absent. At a slightly more abstract level, one could make tally marks on a piece of bark or clay tablet, one for each sheep. But all of this does not imply number as an abstraction independent of individual items of some kind or another. Ancestral humans don't seem to have required more than the simplest notion of numbers: until the middle of the 20th century several tribes of Australian aborigines had no words for numbers in their languages at all, but counted things by making marks in the sand. Anthropologists discovered tribes in remote areas of the Americas, Pacific Islands, and Australia whose languages had no words for numbers greater than four.

With the emergence of settled human populations and the increasingly complex interactions of trade between villages and eventually cities, a more sophisticated notion of numbers was required. A merchant might need to compute how many kinds of one good to exchange for another and to keep records of his inventory of various items. The earliest known written records of numerical writing are Sumerian cuneiform clay tablets dating from around 3400 B.C. These tablets show number symbols formed from two distinct kinds of marks pressed into wet clay with a stylus. While the smaller numbers seem clearly evolved from tally marks, larger numbers are formed by complicated combinations of the two symbols representing numbers from 1 to 59. Larger numbers were written as groups of powers of 60 separated by spaces. This was the first known instance of a positional number system, but there is no evidence it was used for complicated calculations—just as a means of recording quantities.

Ancient civilisations: Egypt, Hebrew, Greece, China, Rome, and the Aztecs and Mayas in the Western Hemisphere all invented ways of writing numbers, some sophisticated and capable of representing large quantities. Many of these systems were additive: they used symbols, sometimes derived from letters in their alphabets, and composed numbers by writing symbols which summed to the total. To write the number 563, a Greek would write “φξγ”, where φ=500, ξ=60, and γ=3. By convention, numbers were written with letters in descending order of the value they represented, but the system was not positional. This made the system clumsy for representing large numbers, reusing letters with accent marks to represent thousands and an entirely different convention for ten thousands.

How did such advanced civilisations get along using number systems in which it is almost impossible to compute? Just imagine a Roman faced with multiplying MDXLIX by XLVII (1549 × 47)—where do you start? You don't: all of these civilisations used some form of mechanical computational aid: an abacus, counting rods, stones in grooves, and so on to actually manipulate numbers. The Sun Zi Suan Jing, dating from fifth century China, provides instructions (algorithms) for multiplication, division, and square and cube root extraction using bamboo counting sticks (or written symbols representing them). The result of the computation was then written using the numerals of the language. The written language was thus a way to represent numbers, but not compute with them.

Many of the various forms of numbers and especially computational tools such as the abacus came ever-so-close to stumbling on the place value system, but it was in India, probably before the third century B.C. that a positional decimal number system including zero as a place holder, with digit forms recognisably ancestral to those we use today emerged. This was a breakthrough in two regards. Now, by memorising tables of addition, subtraction, multiplication, and division and simple algorithms once learned by schoolchildren before calculators supplanted that part of their brains, it was possible to directly compute from written numbers. (Despite this, the abacus remained in common use.) But, more profoundly, this was a universal representation of whole numbers. Earlier number systems (with the possible exception of that invented by Archimedes in The Sand Reckoner [but never used practically]) either had a limit on the largest number they could represent or required cumbersome and/or lengthy conventions for large numbers. The Indian number system needed only ten symbols to represent any non-negative number, and only the single convention that each digit in a number represented how many of that power of ten depending on its position.

Knowledge diffused slowly in antiquity, and despite India being on active trade routes, it was not until the 13th century A.D. that Fibonacci introduced the new number system, which had been transmitted via Islamic scholars writing in Arabic, to Europe in his Liber Abaci. This book not only introduced the new number system, it provided instructions for a variety of practical computations and applications to higher mathematics. As revolutionary as this book was, in an era of hand-copied manuscripts, its influence spread very slowly, and it was not until the 16th century that the new numbers became almost universally used. The author describes this protracted process, about which a great deal of controversy remains to the present day.

Just as the decimal positional number system was becoming established in Europe, another revolution in notation began which would transform mathematics, how it was done, and our understanding of the meaning of numbers. Algebra, as we now understand it, was known in antiquity, but it was expressed in a rhetorical way—in words. For example, proposition 7 of book 2 of Euclid's Elements states:

If a straight line be cut at random, the square of the whole is equal to the squares on the segments and twice the rectangle contained by the segments.

Now, given such a problem, Euclid or any of those following in his tradition would draw a diagram and proceed to prove from the axioms of plane geometry the correctness of the statement. But it isn't obvious how to apply this identity to other problems, or how it illustrates the behaviour of general numbers. Today, we'd express the problem and proceed as follows:

    (a+b)^2 & = & (a+b)(a+b) \\
    & = & a(a+b)+b(a+b) \\
    & = & aa+ab+ba+bb \\
    & = & a^2+2ab+b^2 \\
    & = & a^2+b^2+2ab

Once again, faced with the word problem, it's difficult to know where to begin, but once expressed in symbolic form, it can be solved by applying rules of algebra which many master before reaching high school. Indeed, the process of simplifying such an equation is so mechanical that computer tools are readily available to do so.

Or consider the following brain-twister posed in the 7th century A.D. about the Greek mathematician and father of algebra Diophantus: how many years did he live?

“Here lies Diophantus,” the wonder behold.
Through art algebraic, the stone tells how old;
“God gave him his boyhood one-sixth of his life,
One twelfth more as youth while whiskers grew rife;
And then one-seventh ere marriage begun;
In five years there came a bounding new son.
Alas, the dear child of master and sage
After attaining half the measure of his father's life chill fate took him.
After consoling his fate by the science of numbers for four years, he ended his life.”

Oh, go ahead, give it a try before reading on!

Today, we'd read through the problem and write a system of two simultaneous equations, where x is the age of Diophantus at his death and y the number of years his son lived. Then:

    x & = & (\frac{1}{6}+\frac{1}{12}+\frac{1}{7})x+5+y+4 \\
    y & = & \frac{x}{2}

Plug the second equation into the first, do a little algebraic symbol twiddling, and the answer, 84, pops right out. Note that not only are the rules for solving this equation the same as for any other, with a little practice it is easy to read the word problem and write down the equations ready to solve. Go back and re-read the original problem and the equations and you'll see how straightforwardly they follow.

Once you have transformed a mass of words into symbols, they invite you to discover new ways in which they apply. What is the solution of the equation x+4=0? In antiquity many would have said the equation is meaningless: there is no number you can add to four to get zero. But that's because their conception of number was too limited: negative numbers such as −4 are completely valid and obey all the laws of algebra. By admitting them, we discovered we'd overlooked half of the real numbers. What about the solution to the equation x² + 4 = 0? This was again considered ill-formed, or imaginary, since the square of any real number, positive or negative, is positive. Another leap of imagination, admitting the square root of minus one to the family of numbers, expanded the number line into the complex plane, yielding the answer 2i as we'd now express it, and extending our concept of number into one which is now fundamental not only in abstract mathematics but also science and engineering. And in recognising negative and complex numbers, we'd come closer to unifying algebra and geometry by bringing rotation into the family of numbers.

This book explores the groping over centuries toward a symbolic representation of mathematics which hid the specifics while revealing the commonality underlying them. As one who learned mathematics during the height of the “new math” craze, I can't recall a time when I didn't think of mathematics as a game of symbolic transformation of expressions which may or may not have any connection with the real world. But what one discovers in reading this book is that while this is a concept very easy to brainwash into a 7th grader, it was extraordinarily difficult for even some of the most brilliant humans ever to have lived to grasp in the first place. When Newton invented calculus, for example, he always expressed his “fluxions” as derivatives of time, and did not write of the general derivative of a function of arbitrary variables.

Also, notation is important. Writing something in a more expressive and easily manipulated way can reveal new insights about it. We benefit not just from the discoveries of those in the past, but from those who created the symbolic language in which we now express them.

This book is a treasure chest of information about how the language of science came to be. We encounter a host of characters along the way, not just great mathematicians and scientists, but scoundrels, master forgers, chauvinists, those who preserved precious manuscripts and those who burned them, all leading to the symbolic language in which we so effortlessly write and do mathematics today.

Posted at 22:08 Permalink

Friday, January 2, 2015

Reading List: The Strangest Man

Farmelo, Graham. The Strangest Man. New York: Basic Books, 2009. ISBN 978-0-465-02210-6.
Paul Adrien Maurice Dirac was born in 1902 in Bristol, England. His father, Charles, was a Swiss-French immigrant who made his living as a French teacher at a local school and as a private tutor in French. His mother, Florence (Flo), had given up her job as a librarian upon marrying Charles. The young Paul and his older brother Felix found themselves growing up in a very unusual, verging upon bizarre, home environment. Their father was as strict a disciplinarian at home as in the schoolroom, and spoke only French to his children, requiring them to answer in that language and abruptly correcting them if they committed any faute de français. Flo spoke to the children only in English, and since the Diracs rarely received visitors at home, before going to school Paul got the idea that men and women spoke different languages. At dinner time Charles and Paul would eat in the dining room, speaking French exclusively (with any error swiftly chastised) while Flo, Felix, and younger daughter Betty ate in the kitchen, speaking English. Paul quickly learned that the less he said, the fewer opportunities for error and humiliation, and he traced his famous reputation for taciturnity to his childhood experience.

(It should be noted that the only account we have of Dirac's childhood experience comes from himself, much later in life. He made no attempt to conceal the extent he despised his father [who was respected by his colleagues and acquaintances in Bristol], and there is no way to know whether Paul exaggerated or embroidered upon the circumstances of his childhood.)

After a primary education in which he was regarded as a sound but not exceptional pupil, Paul followed his brother Felix into the Merchant Venturers' School, a Bristol technical school ranked among the finest in the country. There he quickly distinguished himself, ranking near the top in most subjects. The instruction was intensely practical, eschewing Latin, Greek, and music in favour of mathematics, science, geometric and mechanical drawing, and practical skills such as operating machine tools. Dirac learned physics and mathematics with the engineer's eye to “getting the answer out” as opposed to finding the most elegant solution to the problem. He then pursued his engineering studies at Bristol University, where he excelled in mathematics but struggled with experiments.

Dirac graduated with a first-class honours degree in engineering, only to find the British economy in a terrible post-war depression, the worst economic downturn since the start of the Industrial Revolution. Unable to find employment as an engineer, he returned to Bristol University to do a second degree in mathematics, where it was arranged he could skip the first year of the program and pay no tuition fees. Dirac quickly established himself as the star of the mathematics programme, and also attended lectures about the enigmatic quantum theory.

His father had been working in the background to secure a position at Cambridge for Paul, and after cobbling together scholarships and a gift from his father, Dirac arrived at the university in October 1923 to pursue a doctorate in theoretical physics. Dirac would already have seemed strange to his fellow students. While most were scions of the upper class, classically trained, with plummy accents, Dirac knew no Latin or Greek, spoke with a Bristol accent, and approached problems as an engineer or mathematician, not a physicist. He had hoped to study Einstein's general relativity, the discovery of which had first interested him in theoretical physics, but his supervisor was interested in quantum mechanics and directed his work into that field.

It was an auspicious time for a talented researcher to undertake work in quantum theory. The “old quantum theory”, elaborated in the early years of the 20th century, had explained puzzles like the distribution of energy in heat radiation and the photoelectric effect, but by the 1920s it was clear that nature was much more subtle. For example, the original quantum theory failed to explain even the spectral lines of hydrogen, the simplest atom. Dirac began working on modest questions related to quantum theory, but his life was changed when he read Heisenberg's 1925 paper which is now considered one of the pillars of the new quantum mechanics. After initially dismissing the paper as overly complicated and artificial, he came to believe that it pointed the way forward, dismissing Bohr's concept of atoms like little solar systems in favour of a probability density function which gives the probability an electron will be observed in a given position. This represented not just a change in the model of the atom but the discarding entirely of models in favour of a mathematical formulation which permitted calculating what could be observed without providing any mechanism whatsoever explaining how it worked.

After reading and fully appreciating the significance of Heisenberg's work, Dirac embarked on one of the most productive bursts of discovery in the history of modern physics. Between 1925 and 1933 he published one foundational paper after another. His Ph.D. in 1926, the first granted by Cambridge for work in quantum mechanics, linked Heisenberg's theory to the classical mechanics he had learned as an engineer and provided a framework which made Heisenberg's work more accessible. Scholarly writing did not come easily to Dirac, but he mastered the art to such an extent that his papers are still read today as examples of pellucid exposition. At a time when many contributions to quantum mechanics were rough-edged and difficult to understand even by specialists, Dirac's papers were, in the words of Freeman Dyson, “like exquisitely carved marble statues falling out of the sky, one after another.”

In 1928, Dirac took the first step to unify quantum mechanics and special relativity in the Dirac equation. The consequences of this equation led Dirac to predict the existence of a positively-charged electron, which had never been observed. This was the first time a theoretical physicist had predicted the existence of a new particle. This “positron” was observed in debris from cosmic ray collisions in 1932. The Dirac equation also interpreted the spin (angular momentum) of particles as a relativistic phenomenon.

Dirac, along with Enrico Fermi, elaborated the statistics of particles with half-integral spin (now called “fermions”). The behaviour of ensembles of one such particle, the electron, is essential to the devices you use to read this article. He took the first steps toward a relativistic theory of light and matter and coined the name, “quantum electrodynamics”, for the field, but never found a theory sufficiently simple and beautiful to satisfy himself. He published The Principles of Quantum Mechanics in 1930, for many years the standard textbook on the subject and still read today. He worked out the theory of magnetic monopoles (not detected to this date) and speculated on the origin and possible links between large numbers in physics and cosmology.

The significance of Dirac's work was recognised at the time. He was elected a Fellow of the Royal Society in 1930, became the Lucasian Professor of Mathematics (Newton's chair) at Cambridge in 1932, and shared the Nobel Prize in Physics for 1933 with Erwin Schrödinger. After rejecting a knighthood because he disliked being addressed by his first name, he was awarded the Order of Merit in 1973. He is commemorated by a plaque in Westminster Abbey, close to that of Newton; the plaque bears his name and the Dirac equation, the only equation so honoured.

Many physicists consider Dirac the second greatest theoretical physicist of the 20th century, after Einstein. While Einstein produced great leaps of intellectual achievement in fields neglected by others, Dirac, working alone, contributed to the grand edifice of quantum mechanics, which occupied many of the most talented theorists of a generation. You have to dig a bit deeper into the history of quantum mechanics to fully appreciate Dirac's achievement, which probably accounts for his name not being as well known as it deserves.

There is much more to Dirac, all described in this extensively-documented scientific biography. While declining to join the British atomic weapons project during World War II because he refused to work as part of a collaboration, he spent much of the war doing consulting work for the project on his own, including inventing a new technique for isotope separation. (Dirac's process proved less efficient that those eventually chosen by the Manhattan project and was not used.) As an extreme introvert, nobody expected him to ever marry, and he astonished even his closest associates when he married the sister of his fellow physicist Eugene Wigner, Manci, a Hungarian divorcée with two children by her first husband. Manci was as extroverted as Dirac was reserved, and their marriage in 1937 lasted until Dirac's death in 1984. They had two daughters together, and lived a remarkably normal family life. Dirac, who disdained philosophy in his early years, became intensely interested in the philosophy of science later in life, even arguing that mathematical beauty, not experimental results, could best guide theorists to the best expression of the laws of nature.

Paul Dirac was a very complicated man, and this is a complicated and occasionally self-contradictory biography (but the contradiction is in the subject's life, not the fault of the biographer). This book provides a glimpse of a unique intellect whom even many of his closest associates never really felt they completely knew.

Posted at 14:29 Permalink

Wednesday, December 31, 2014

Books of the year: 2014

Here are my picks for the best books of 2014, fiction and nonfiction. These aren't the best books published this year, but rather the best I've read in the last twelvemonth. The winner in both categories is barely distinguished from the pack, and the runners up are all worthy of reading. Runners up appear in alphabetical order by their author's surname.


Winner: Runners up:


Winner: Runners up:

Posted at 14:00 Permalink

Reading List: How Ronald Reagan Changed My Life

Robinson, Peter. How Ronald Reagan Changed My Life. New York: Harper Perennial, 2003. ISBN 978-0-06-052400-5.
In 1982, the author, a recent graduate of Dartmouth College who had spent two years studying at Oxford, then remained in England to write a novel, re-assessed his career prospects and concluded that, based upon experience, novelist did not rank high among them. He sent letters to everybody he thought might provide him leads on job opportunities. Only William F. Buckley replied, suggesting that Robinson contact his son, Christopher, then chief speechwriter for Vice President George H. W. Bush, who might know of some openings for speechwriters. Hoping at most for a few pointers, the author flew to Washington to meet Buckley, who was planning to leave the White House, creating a vacancy in the Vice President's speechwriting shop. After a whirlwind of interviews, Robinson found himself, in his mid-twenties, having never written a speech before in his life, at work in the Old Executive Office Building, tasked with putting words into the mouth of the Vice President of the United States.

After a year and a half writing for Bush, two of the President's speechwriters quit at the same time. Forced to find replacements on short notice, the head of the office recruited the author to write for Reagan: “He hired me because I was already in the building.” From then through 1988, he wrote speeches for Reagan, some momentous (Reagan's June 1987 speech at the Brandenburg gate, where Robinson's phrase, “Mr. Gorbachev, tear down this wall!”, uttered by Reagan against vehement objections from the State Department and some of his senior advisers, was a pivotal moment in the ending of the Cold War), but also many more for less epochal events such as visits of Boy Scouts to the White House, ceremonies honouring athletes, and the dozens of other circumstances where the President was called upon to “say a few words”. And because the media were quick to pounce on any misstatement by the President, even the most routine remarks had to be meticulously fact-checked by a team of researchers. For every grand turn of phrase in a high profile speech, there were many moments spent staring at the blank screen of a word processor as the deadline for some inconsequential event loomed ever closer and wondering, “How am I supposed to get twenty minutes out of that?“.

But this is not just a book about the life of a White House speechwriter (although there is plenty of insight to be had on that topic). Its goal is to collect and transmit the wisdom that a young man, in his first job, learned by observing Ronald Reagan masterfully doing the job to which he had aspired since entering politics in the 1960s. Reagan was such a straightforward and unaffected person that many underestimated him. For example, compared to the hard-driving types toiling from dawn to dusk who populate many White House positions, Reagan never seemed to work very hard. He would rise at his accustomed hour, work for five to eight hours at his presidential duties, exercise, have dinner, review papers, and get to bed on time. Some interpreted this as his being lazy, but Robinson's fellow speechwriter, Clark Judge, remarked “He never confuses inputs with output. … Who cares how many hours a day a President puts in? It's what a President accomplishes that matters.”

These are lessons aplenty here, all illustrated with anecdotes from the Reagan White House: the distinction between luck and the results from persistence in the face of adversity seen in retrospect; the unreasonable effectiveness and inherent dignity of doing one's job, whatever it be, well; viewing life not as background scenery but rather an arena in which one can act, changing not just the outcome but the circumstances one encounters; the power of words, especially those sincerely believed and founded in comprehensible, time-proven concepts; scepticism toward the pronouncements of “experts” whose oracle-like proclamations make sense only to other experts—if it doesn't make sense to an intelligent person with some grounding in the basics, it probably doesn't make sense period; the importance of marriage, and how the Reagans complemented one another in facing the challenges and stress of the office; the centrality of faith, tempered by a belief in free will and the importance of the individual; how both true believers and pragmatists, despite how often they despise one another, are both essential to actually getting things done; and that what ultimately matters is what you make of whatever situation in which you find yourself.

These are all profound lessons to take on board, especially in the drinking from a firehose environment of the Executive Office of the President, and in one's twenties. But this is not a dour self-help book: it is an insightful, beautifully written, and often laugh-out-loud funny account of how these insights were gleaned on the job, by observing Reagan at work and how he and his administration got things done, often against fierce political and media opposition. This is one of those books that I wish I could travel back in time and hand a copy to my twenty-year-old self—it would have saved a great deal of time and anguish, even for a person like me who has no interest whatsoever in politics. Fundamentally, it's about getting things done, and that's universally applicable.

People matter. Individuals matter. Long before Ronald Reagan was a radio broadcaster, actor, or politician, he worked summers as a lifeguard. Between 1927 and 1932, he personally saved 77 people from drowning. “There were seventy-seven people walking around northern Illinois who wouldn't have been there if it hadn't been for Reagan—and Reagan knew it.” It is not just a few exceptional people who change the world for the better, but all of those who do their jobs and overcome the challenges with which life presents them. Learning this can change anybody's life.

More recently, Mr. Robinson is the host of Uncommon Knowledge and co-founder of

Posted at 00:56 Permalink

Saturday, December 27, 2014

Tom Swift and His Submarine Boat updated, EPUB added

All 25 of the public domain Tom Swift novels have been posted in the Tom Swift and His Pocket Library collection. I am now returning to the earlier novels, upgrading them to use the more modern typography of those I've done in recent years. The fourth novel in the series, Tom Swift and His Submarine Boat, has now been updated. Several typographical errors in the original edition have been corrected, and Unicode text entities are used for special characters such as single and double quotes and dashes.

An EPUB edition of this novel is now available which may be downloaded to compatible reader devices; the details of how to do this differ from device to device—please consult the documentation for your reader for details.

It's delightful to read a book which uses the word "filibuster" in its original sense: "to take part in a private military action in a foreign country" but somewhat disconcerting to encounter Brazilians speaking Spanish! The diving suits which allow full mobility on the abyssal plain two miles beneath the ocean surface remain as science-fictional as when this novel was written almost a century ago.

Posted at 01:53 Permalink

Wednesday, December 24, 2014

Reading List: Hidden Order

Thor, Brad. Hidden Order. New York: Pocket Books, 2013. ISBN 978-1-4767-1710-4.
This is the thirteenth in the author's Scot Harvath series, which began with The Lions of Lucerne (October 2010). Earlier novels have largely been in the mainstream of the “techno-thriller” genre, featuring missions in exotic locations confronting shadowy adversaries bent on inflicting great harm. The present book is a departure from this formula, being largely set in the United States and involving institutions considered pillars of the establishment such as the Federal Reserve System and the Central Intelligence Agency.

A CIA operative “accidentally” runs into a senior intelligence official of the Jordanian government in an airport lounge in Europe, who passes her disturbing evidence that members of a now-disbanded CIA team of which she was a member were involved in destabilising governments now gripped with “Arab Spring” uprisings and next may be setting their sights on Jordan.

Meanwhile, Scot Harvath, just returned from a harrowing mission on the high seas, is taken by his employer, Reed Carlton, to discreetly meet a new client: the Federal Reserve. The Carlton Group is struggling to recover from the devastating blow it took in the previous novel, Black List (August 2014), and its boss is willing to take on unconventional missions and new clients, especially ones “with a license to print their own money”. The chairman of the Federal Reserve has recently and unexpectedly died and the five principal candidates to replace him have all been kidnapped, almost simultaneously, across the United States. These people start turning up dead, in circumstances with symbolism dating back to the American revolution.

Investigation of the Jordanian allegations is shut down by the CIA hierarchy, and has to be pursued through back channels, involving retired people who know how the CIA really works. Evidence emerges of a black program that created weapons of frightful potential which may have gone even blacker and deeper under cover after being officially shut down.

Earlier Brad Thor novels were more along the “U-S-A! U-S-A!” line of most thrillers. Here, the author looks below the surface of highly dubious institutions (“The Federal Reserve is about as federal as Federal Express”) and evil that flourishes in the dark, especially when irrigated with abundant and unaccountable funds. Like many Americans, Scot Harvath knew little about the Federal Reserve other than it had something to do with money. Over the course of his investigations he, and the reader, will learn many disturbing things about its dodgy history and operations, all accurate as best I can determine.

The novel is as much police procedural as thriller, with Harvath teamed with a no-nonsense Boston Police Department detective, processing crime scenes and running down evidence. The story is set in an unspecified near future (the Aerion Supersonic Business Jet is in operation). All is eventually revealed in the end, with a resolution in the final chapter devoutly to be wished, albeit highly unlikely to occur in the cesspool of corruption which is real-world Washington. There is less action and fancy gear than in most Harvath novels, but interesting characters, an intricate mystery, and a good deal of information of which many readers may not be aware.

A short prelude to this novel, Free Fall, is available for free for the Kindle. It provides the background of the mission in progress in which we first encounter Scot Harvath in chapter 2 here. My guess is that this chapter was originally part of the manuscript and was cut for reasons of length and because it spent too much time on a matter peripheral to the main plot. It's interesting to read before you pick up Hidden Order, but if you skip it you'll miss nothing in the main story.

Posted at 15:39 Permalink

Saturday, December 13, 2014

Reading List: The Science of Interstellar

Thorne, Kip. The Science of Interstellar. New York: W. W. Norton, 2014. ISBN 978-0-393-35137-8.
Christopher Nolan's 2014 film Interstellar was eagerly awaited by science fiction enthusiasts who, having been sorely disappointed so many times by movies that crossed the line into fantasy by making up entirely implausible things to move the plot along, hoped that this effort would live up to its promise of getting the science (mostly) right and employing scientifically plausible speculation where our present knowledge is incomplete.

The author of the present book is one of the most eminent physicists working in the field of general relativity (Einstein's theory of gravitation) and a pioneer in exploring the exotic strong field regime of the theory, including black holes, wormholes, and gravitational radiation. Prof. Thorne was involved in the project which became Interstellar from its inception, and worked closely with the screenwriters, director, and visual effects team to get the science right. Some of the scenes in the movie, such as the visual appearance of orbiting a rotating black hole, have never been rendered accurately before, and are based upon original work by Thorne in computing light paths through spacetime in its vicinity which will be published as professional papers.

Here, the author recounts the often bumpy story of the movie's genesis and progress over the years from his own, Hollywood-outsider, perspective, how the development of the story presented him, as technical advisor (he is credited as an executive producer), with problem after problem in finding a physically plausible solution, sometimes requiring him to do new physics. Then, Thorne provides a popular account of the exotic physics on which the story is based, including gravitational time dilation, black holes, wormholes, and speculative extra dimensions and “brane” scenarios stemming from string theory. Then he “interprets” the events and visual images in the film, explaining (where possible) how they could be produced by known, plausible, or speculative physics. Of course, this isn't always possible—in some cases the needs of story-telling or the requirement not to completely baffle a non-specialist with bewilderingly complicated and obscure images had to take priority over scientific authenticity, and when this is the case Thorne is forthright in admitting so.

Sections are labelled with icons identifying them as “truth”: generally accepted by those working in the field and often with experimental evidence, “educated guess”: a plausible inference from accepted physics, but without experimental evidence and assuming existing laws of physics remain valid in circumstances under which we've never tested them, and “speculation”: wild and wooly stuff (for example quantum gravity or the interior structure of a black hole) which violates no known law of physics, but for which we have no complete and consistent theory and no evidence whatsoever.

This is a clearly written and gorgeously illustrated book which, for those who enjoyed the movie but weren't entirely clear whence some of the stunning images they saw came, will explain the science behind them. The cover of the book has a “SPOILER ALERT” warning potential readers that the ending and major plot details are given away in the text. I will refrain from discussing them here so as not to make this a spoiler in itself. I have not yet seen the movie, and I expect when I do I will enjoy it more for having read the book, since I'll know what to look for in some of the visuals and be less likely to dismiss some of the apparently outrageous occurrences by knowing that there is a physically plausible (albeit extremely speculative and improbable) explanation for them.

For the animations and blackboard images mentioned in the text, the book directs you to a Web site which is so poorly designed and difficult to navigate it took me ten minutes to find them on the first visit. Here is a direct link. In the Kindle edition the index cites page numbers in the print edition which are useless since the electronic edition does not contain real page numbers. There are a few typographical errors and one factual howler: Io is not “Saturn's closest moon”, and Cassini was captured in Saturn orbit by a propulsion burn, not a gravitational slingshot (this does not affect the movie in any way: it's in background material).

Posted at 22:38 Permalink

Saturday, December 6, 2014

Reading List: A Troublesome Inheritance

Wade, Nicholas. A Troublesome Inheritance. New York: Penguin Press, 2014. ISBN 978-1-59420-446-3.
Geographically isolated populations of a species (unable to interbreed with others of their kind) will be subject to natural selection based upon their environment. If that environment differs from that of other members of the species, the isolated population will begin to diverge genetically, as genetic endowments which favour survival and more offspring are selected for. If the isolated population is sufficiently small, the mechanism of genetic drift may cause a specific genetic variant to become almost universal or absent in that population. If this process is repeated for a sufficiently long time, isolated populations may diverge to such a degree they can no longer interbreed, and therefore become distinct species.

None of this is controversial when discussing other species, but in some circles to suggest that these mechanisms apply to humans is the deepest heresy. This well-researched book examines the evidence, much from molecular biology which has become available only in recent years, for the diversification of the human species into distinct populations, or “races” if you like, after its emergence from its birthplace in Africa. In this book the author argues that human evolution has been “recent, copious, and regional” and presents the genetic evidence to support this view.

A few basic facts should be noted at the outset. All humans are members of a single species, and all can interbreed. Humans, as a species, have an extremely low genetic diversity compared to most other animal species: this suggests that our ancestors went through a genetic “bottleneck” where the population was reduced to a very small number, causing the variation observed in other species to be lost through genetic drift. You might expect different human populations to carry different genes, but this is not the case—all humans have essentially the same set of genes. Variation among humans is mostly a result of individuals carrying different alleles (variants) of a gene. For example, eye colour in humans is entirely inherited: a baby's eye colour is determined completely by the alleles of various genes inherited from the mother and father. You might think that variation among human populations is then a question of their carrying different alleles of genes, but that too is an oversimplification. Human genetic variation is, in most cases, a matter of the frequency of alleles among the population.

This means that almost any generalisation about the characteristics of individual members of human populations with different evolutionary histories is ungrounded in fact. The variation among individuals within populations is generally much greater than that of populations as a whole. Discrimination based upon an individual's genetic heritage is not just abhorrent morally but scientifically unjustified.

Based upon these now well-established facts, some have argued that “race does not exist” or is a “social construct”. While this view may be motivated by a well-intentioned desire to eliminate discrimination, it is increasingly at variance with genetic evidence documenting the history of human populations.

Around 200,000 years ago, modern humans emerged in Africa. They spent more than three quarters of their history in that continent, spreading to different niches within it and developing a genetic diversity which today is greater than that of all humans in the rest of the world. Around 50,000 years before the present, by the genetic evidence, a small band of hunter-gatherers left Africa for the lands to the north. Then, some 30,000 years ago the descendants of these bands who migrated to the east and west largely ceased to interbreed and separated into what we now call the Caucasian and East Asian populations. These have remained the main three groups within the human species. Subsequent migrations and isolations have created other populations such as Australian and American aborigines, but their differentiation from the three main races is less distinct. Subsequent migrations, conquest, and intermarriage have blurred the distinctions between these groups, but the fact is that almost any child, shown a picture of a person of European, African, or East Asian ancestry can almost always effortlessly and correctly identify their area of origin. University professors, not so much: it takes an intellectual to deny the evidence of one's own eyes.

As these largely separated populations adapted to their new homes, selection operated upon their genomes. In the ancestral human population children lost the ability to digest lactose, the sugar in milk, after being weaned from their mothers' milk. But in populations which domesticated cattle and developed dairy farming, parents who passed on an allele which would allow their children to drink cow's milk their entire life would have more surviving offspring and, in a remarkably short time on the evolutionary scale, lifetime lactose tolerance became the norm in these areas. Among populations which never raised cattle or used them only for meat, lifetime lactose tolerance remains rare today.

Humans in Africa originally lived close to the equator and had dark skin to protect them from the ultraviolet radiation of the Sun. As human bands occupied northern latitudes in Europe and Asia, dark skin would prevent them from being able to synthesise sufficient Vitamin D from the wan, oblique sunlight of northern winters. These populations were under selection pressure for alleles of genes which gave them lighter skin, but interestingly Europeans and East Asians developed completely different genetic means to lighten their skin. The selection pressure was the same, but evolution blundered into two distinct pathways to meet the need.

Can genetic heritage affect behaviour? There's evidence it can. Humans carry a gene called MAO-A, which breaks down neurotransmitters that affect the transmission of signals within the brain. Experiments in animals have provided evidence that under-production of MAO-A increases aggression and humans with lower levels of MAO-A are found to be more likely to commit violent crime. MAO-A production is regulated by a short sequence of DNA adjacent to the gene: humans may have anywhere from two to five copies of the promoter; the more you have, the more the MAO-A, and hence the mellower you're likely to be. Well, actually, people with three to five copies are indistinguishable, but those with only two (2R) show higher rates of delinquency. Among men of African ancestry, 5.5% carry the 2R variant, while 0.1% of Caucasian males and 0.00067% of East Asian men do. Make of this what you will.

The author argues that just as the introduction of dairy farming tilted the evolutionary landscape in favour of those bearing the allele which allowed them to digest milk into adulthood, the transition of tribal societies to cities, states, and empires in Asia and Europe exerted a selection pressure upon the population which favoured behavioural traits suited to living in such societies. While a tribal society might benefit from producing a substantial population of aggressive warriors, an empire has little need of them: its armies are composed of soldiers, courageous to be sure, who follow orders rather than charging independently into battle. In such a society, the genetic traits which are advantageous in a hunter-gatherer or tribal society will be selected out, as those carrying them will, if not expelled or put to death for misbehaviour, be unable to raise as large a family in these settled societies.

Perhaps, what has been happening over the last five millennia or so is a domestication of the human species. Precisely as humans have bred animals to live with them in close proximity, human societies have selected for humans who are adapted to prosper within them. Those who conform to the social hierarchy, work hard, come up with new ideas but don't disrupt the social structure will have more children and, over time, whatever genetic predispositions there may be for these characteristics (which we don't know today) will become increasingly common in the population. It is intriguing that as humans settled into fixed communities, their skeletons became less robust. This same process of gracilisation is seen in domesticated animals compared to their wild congeners. Certainly there have been as many human generations since the emergence of these complex societies as have sufficed to produce major adaptation in animal species under selective breeding.

Far more speculative and controversial is whether this selection process has been influenced by the nature of the cultures and societies which create the selection pressure. East Asian societies tend to be hierarchical, obedient to authority, and organised on a large scale. European societies, by contrast, are fractious, fissiparous, and prone to bottom-up insurgencies. Is this in part the result of genetic predispositions which have been selected for over millennnia in societies which work that way?

It is assumed by many right-thinking people that all that is needed to bring liberty and prosperity to those regions of the world which haven't yet benefited from them is to create the proper institutions, educate the people, and bootstrap the infrastructure, then stand back and watch them take off. Well, maybe—but the history of colonialism, the mission civilisatrice, and various democracy projects and attempts at nation building over the last two centuries may suggest it isn't that simple. The population of the colonial, conquering, or development-aid-giving power has the benefit of millennia of domestication and adaptation to living in a settled society with division of labour. Its adaptations for tribalism have been largely bred out. Not so in many cases for the people they're there to “help”. Withdraw the colonial administration or occupation troops and before long tribalism will re-assert itself because that's the society for which the people are adapted.

Suggesting things like this is anathema in academia or political discourse. But look at the plain evidence of post-colonial Africa and more recent attempts of nation-building, and couple that with the emerging genetic evidence of variation in human populations and connections to behaviour and you may find yourself thinking forbidden thoughts. This book is an excellent starting point to explore these difficult issues, with numerous citations of recent scientific publications.

Posted at 15:23 Permalink

Sunday, November 30, 2014

Reading List: The Martian

Weir, Andy. The Martian. New York: Broadway Books, [2011] 2014. ISBN 978-0-553-41802-6.
Mark Watney was part of the six person crew of Ares 3 which landed on Mars to carry out an exploration mission in the vicinity of its landing site in Acidalia Planitia. The crew made a precision landing at the target where “presupply” cargo flights had already landed their habitation module, supplies for their stay on Mars, rovers and scientific instruments, and the ascent vehicle they would use to return to the Earth-Mars transit vehicle waiting for them in orbit. Just six days after landing, having set up the habitation module and unpacked the supplies, they are struck by a dust storm of unprecedented ferocity. With winds up to 175 kilometres per hour, the Mars Ascent Vehicle (MAV), already fuelled by propellant made on Mars by reacting hydrogen brought from Earth with the Martian atmosphere, was at risk of being blown over, which would destroy the fragile spacecraft and strand the crew on Mars. NASA gives the order to abort the mission and evacuate to orbit in the MAV for an immediate return to Earth.

But the crew first has to get from the habitation module to the MAV, which means walking across the surface in the midst of the storm. (You'd find it very hard to walk in a 175 km/h wind on Earth, but recall that the atmosphere pressure on Mars is only about 1/200 that of Earth at sea level, so the wind doesn't pack anywhere near the punch.) Still, there was dust and flying debris from equipment ripped loose from the landers. Five members of the crew made it to the MAV. Mark Watney didn't.

As the crew made the traverse to the MAV, Watney was struck by part of an antenna array torn from the habitation, puncturing his suit and impaling him. He was carried away by the wind, and the rest of the crew, seeing his vital signs go to zero before his suit's transmitter failed, followed mission rules to leave him behind and evacuate in the MAV while they still could.

But Watney wasn't dead. His injury was not fatal, and his blood loss was sufficient to seal the leak in the suit where the antenna had pierced it, as the water in the blood boiled off and the residue mostly sealed the breach. Awakening after the trauma, he made an immediate assessment of his situation. I'm alive. Cool! I hurt like heck. Not cool. The habitation module is intact. Yay! The MAV is gone—I'm alone on Mars. Dang!

“Dang” is not precisely how Watney put it. This book contains quite a bit of profanity which I found gratuitous. NASA astronauts in the modern era just don't swear like sailors, especially on open air-to-ground links. Sure, I can imagine launching a full salvo of F-bombs upon discovering I'd been abandoned on Mars, especially when I'm just talking to myself, but everybody seems to do it here on all occasions. This is the only reason I'd hesitate to recommend this book to younger readers who would otherwise be inspired by the story.

Watney is stranded on Mars with no way to communicate with Earth, since all communications were routed through the MAV, which has departed. He has all of the resources for a six-person mission, so he has no immediate survival problems after he gets back to the habitation and stitches up his wound, but he can work the math: even if he can find a way to communicate to Earth that he's still alive, orbital mechanics dictates that it will take around two years to send a rescue mission. His supplies cannot be stretched that far.

This sets the stage for a gripping story of survival, improvisation, difficult decisions, necessity versus bureaucratic inertia, trying to do the right thing in a media fishbowl, and all done without committing any howlers in technology, orbital mechanics, or the way people and organisations behave. Sure, you can quibble about this or that detail, but then people far in the future may regard a factual account of Apollo 13 as largely legend, given how many things had to go right to rescue the crew. Things definitely do not go smoothly here: there is reverse after reverse, and many inscrutable mysteries to be unscrewed if Watney is to get home.

This is an inspiring tale of pioneering on a new world. People have already begun to talk about going to Mars to stay. These settlers will face stark challenges though, one hopes, not as dire as Watney, and with the confidence of regular re-supply missions and new settlers to follow. Perhaps this novel will be seen, among the first generation born on Mars, as inspiration that the challenges they face in bringing a barren planet to life are within the human capacity to solve, especially if their media library isn't exclusively populated with 70s TV shows and disco.

A Kindle edition is available.

Posted at 23:48 Permalink

Wednesday, November 26, 2014

Reading List: Liberators

Rawles, James Wesley. Liberators. New York: Dutton, 2014. ISBN 978-0-525-95391-3.
This novel is the fifth in the series which began with Patriots (December 2008), then continued with Survivors (January 2012), Founders (October 2012), and Expatriates (October 2013), These books are not a conventional multi-volume narrative, in that all describe events in the lives of their characters in roughly the same time period surrounding “the Crunch”—a grid down societal collapse due to a debt crisis and hyperinflation. Taking place at the same time, you can read these books in any order, but if you haven't read the earlier novels you'll miss much of the back-story of the characters who appear here, which informs the parts they play in this episode.

Here the story cuts back and forth between the United States, where Megan LaCroix and her sister Malorie live on a farm in West Virginia with Megan's two boys, and Joshua Kim works in security at the National Security Agency where Megan is an analyst. When the Crunch hits, Joshua and the LaCroix sisters decide to team up to bug out to Joshua's childhood friend's place in Kentucky, where survival from the urban Golden Horde may be better assured. They confront the realities of a collapsing society, where the rule of law is supplanted by extractive tyrannies, and are forced to over-winter in a wilderness, living by their wits and modest preparations.

In Western Canada, the immediate impact of the Crunch was less severe because electrical power, largely hydroelectric, remained on. At the McGregor Ranch, in inland British Columbia (a harsh, northern continental climate nothing like that of Vancouver), the family and those who have taken refuge with them ride out the initial crisis only to be confronted with an occupation of Canada by a nominally United Nations force called UNPROFOR, which is effectively a French colonial force which, in alliance with effete urban eastern and francophone Canada, seeks to put down the fractious westerners and control the resource-rich land they inhabit.

This leads to an asymmetrical war of resistance, aided by the fact that when earlier faced with draconian gun registration and prohibition laws imposed by easterners, a large number of weapons in the west simply vanished, only to reappear when they were needed most. As was demonstrated in Vietnam and Algeria, French occupation forces can be tenacious and brutal, but are ultimately no match for an indigenous insurgency with the support of the local populace. A series of bold strikes against UNPROFOR assets eventually turns the tide.

But just when Canada seems ready to follow the U.S. out of the grip of tyranny, an emboldened China, already on the march in Africa, makes a move to seize western Canada's abundant natural resources. Under the cover of a UN resolution, a massive Chinese force, with armour and air support, occupies the western provinces. This is an adversary of an entirely different order than the French, and will require the resistance, supported by allies from the liberation struggle in the U.S., to audacious and heroic exploits, including one of the greatest acts of monkey-wrenching ever described in a thriller.

As this story has developed over the five novels, the author has matured into a first-rate thriller novelist. There is still plenty of information on gear, tactics, intelligence operations, and security, but the characters are interesting, well-developed, and the action scenes both plausible and exciting. In the present book, we encounter many characters we've met in previous volumes, with their paths crossing as events unfold. There is no triumphalism or glossing over the realities of insurgent warfare against a tyrannical occupying force. There is a great deal of misery and hardship, and sometimes tragedy can result when you've taken every precaution, made no mistake, but simply run out of luck.

Taken together, these five novels are an epic saga of survival in hard and brutal times, painted on a global canvas. Reading them, you will not only be inspired that you and your loved ones can survive such a breakdown in the current economic and social order, but you will also learn a great deal of the details of how to do so. This is not a survival manual, but attentive readers will find many things to research further for their own preparations for an uncertain future. An excellent place to begin that research is the author's own Web site, whose massive archives you can spend months exploring.

Posted at 23:37 Permalink