Descartes (2)

 

In Rules for the Direction of the Mind, Descartes wrote: “The first principles themselves are given by intuition alone, while, on the contrary, the remote conclusions are furnished only by deduction. . . . These two methods are the most certain routes to knowledge, and the mind should admit no others. All the rest should be rejected as suspect of error and dangerous.” 

Descartes was embracing the Euclidean ideal: Start from self-evident axioms, proceed by infallible deductions. But in his own research, Descartes forgot the Euclidean ideal. Nowhere in the Geometry do we find the label Axiom, Theorem, or Proof. 

In classical Greece, and again in the Renaissance and after, mathematicians distinguished two ways of proceeding—the “synthetic” and the “analytic.” The synthetic way was Euclid’s: from axioms through deductions to theorems. In the analytic mode, you start with a problem and “analyze” it to find a solution. Today we might call this a “heuristic” or “problem-solving” approach. 

In formal presentation of academic mathematics, the synthetic was and still is the norm. Foundationist schools of the nineteenth and twentieth centuries identify mathematics with its synthetic mode—true axioms followed by correct deductions to yield guaranteed true conclusions. 

In his Rules for the Direction of the Mind, Descartes insists on the synthetic method. But his own research, in the Geometry, uses only the analytic mode. He solves problems. He finds efficient methods for solving problems. Never does he bother with axioms. 

Descartes’s conviction of the certainty of mathematics might lead readers to expect that at least Descartes’s own mathematics is error-free. But of course, as we will see, the Geometry, like every other math book, has mistakes. Certitude is only a goal.

**

You won’t find in the Geometry the method we teach nowadays as Cartesian or “analytic” geometry. Our analytic geometry is based on rectangular coordinates (which we call “Cartesian”). To every point in the plane we associate a pair of real numbers, the “x” and “y” coordinates of the point. To an equation relating x and y corresponds a “graph”—the set of points whose x and y coordinates satisfy the equation. For an equation of first degree, the graph is a straight line. For an equation of second degree, it’s a circle or other conic section. Our idea is to solve geometric problems by reducing them to algebra. Nowhere in Descartes’s book do we see these familiar horizontal and vertical axes! Boyer says it was Newton who first used orthogonal coordinate axes in analytic geometry.

**
The conceptual essence of analytic geometry, the “isomorphism” or exact translation between algebra and geometry, was understood more clearly by Fermat than by Descartes. Fermat’s analytic geometry predated Descartes’s, but it wasn’t published until 1679. The modern formulation comes from a long development. Fermat and Descartes were the first steps. Instead of systematically developing the technique of orthogonal coordinate axes, the Geometry studies a group of problems centering around a problem of Pappus of Alexandria (third century A.D.). To solve Pappus’s problem Descartes develops an algebraic-geometric procedure. First he derives an algebraic equation relating known and unknown lengths in the problem. But he doesn’t then look for an algebraic or numerical solution, as we would do. He is faithful to the Greek conception, that by a solution to a geometric problem is meant a construction with specified instruments. When possible Descartes uses the Euclidean straight edge and compass. When necessary, he brings in his own instrument, an apparatus of hinged rulers. Algebra is an intermediate device, in going from geometric problem to geometric solution. Its role is to reduce a complicated curve to a simpler one whose construction is known. He solves third and fourth-degree equations by reducing them to second degree—to conic sections. He solves certain fifth-and sixth-degree equations by reducing them to third degree. A modern reader knows that the general equation of fifth degree can’t be solved by extraction of roots. So he’s skeptical about Descartes’s claim that his hinged rulers can solve equations of degree six and higher. Descartes was mistaken on several points. In themselves, these are of little interest today. But they discredit his claim of absolute certainty. Descartes’s mathematics refutes his epistemology. 

Emily Grosholz and Carl Boyer point out errors in the Geometry. “When he turns his attention to the locus of five lines, he considers only a few cases, not bothering to complete the task, because, as he says, his method furnishes a way to describe them. But Descartes could not have completed the task, which amounted to giving a catalogue of the cubics. . . . Newton, because he was able to move with confidence between graph and equation, first attempted a catalogue of the cubics; he distinguished seventy-two species of cubics, and even then omitted six” (Grosholz, referring to Whiteside).

**

Descartes claimed his Method was infallible in science and mathematics. He was more cautious with religion. He didn’t derive Holy Scripture or divine revelation by self-evident axioms and infallible deductions. When he heard that Galileo’s Dialogue on the Two Chief Systems was condemned by the Holy Church, he suppressed his first book, Le Monde, even though he was living in Holland, safe from the Church. (Galileo was kept under house arrest at first. For three years he had to recite the seven penitential psalms every week.) Descartes wrote to Father Mersenne, “I would not want for anything in the world to be the author of a work where there was the slightest word of which the Church might disapprove.”

**

Like Pascal, Newton, and Leibniz, Descartes may have valued his contributions to theology above his mathematics. His struggle against skeptics and heretics is the major half of his philosophy, more explicit than his battles with scholastics. “In Descartes’ reply to the objections of Father Bourdin, he announced that he was the first of all men to overthrow the doubts of the Sceptics . . . he discovered how the best minds of the day either spent their time advocating scepticism, or accepted only probable and possibly uncertain views, instead of seeking absolute truth. . . . It was in the light of this awakening to the sceptical menace, that when he was in Paris Descartes set in motion his philosophical revolution by discovering something so certain and so assured that all the most extravagant suppositions brought forward by the sceptics were incapable of shaking . . . in the tradition of the greatest medieval minds, (he) sought to secure man’s natural knowledge to the strongest possible foundation, the all-powerful eternal God” (Popkin, p. 72). The essence of the Meditations is a proof that the world exists by first proving Descartes exists, and then, by contemplating Descartes’s thoughts, proving that God exists and is not a deceiver. Once a non-deceiving God exists, everything else is easy.

 

Descartes

 

D’Alembert wrote that it was Descartes who first “dared . . . to show intelligent minds how to throw off the yoke of scholasticism, of opinion, of authority—in a word, of prejudices and barbarism. . . . He can be thought of as a leader of conspirators who, before anyone else, had the courage to arise against a despotic and arbitrary power, and who, in preparing a resounding revolution, laid the foundations of a more just and happier government which he himself was not able to see established.” 

Philosophers of the scholastic persuasion pointed to the dangerous parallel between Descartes’s scientific individualism and the outlawed Protestant heresy. Descartes said individual thinkers could find scientific truth; Protestants said individual souls could find direct communion with the Almighty. But the Holy Roman Catholic Church knew that individual souls and thinkers could be deceived. It took the experience and wisdom of the Church to prevent the seeker from wandering astray. Despite such scholastic criticism, Descartes quickly came to dominate West European intellectual life.

**

Like Galileo, Descartes recognized mathematics as the principal tool for revealing truths of nature. He was more explicit than Galileo about how to do it. In every scientific problem, said Descartes, find an algebraic equation relating an unknown variable to a known one. Then solve the algebraic equation! With the development of calculus, Descartes’s doctrine was essentially justified. Today we don’t say “find an algebraic equation.” We say “construct a mathematical model.” This is only a technical generalization of Descartes’s idea. Our scientific technology is an inheritance from Descartes.


 

Nicholas of Cusa and Theology in Math

 

The son of a fisherman, Nicholas rose to become a diplomat and counselor for the Church. “He was a member of the commission sent to Constantinople to negotiate with the Eastern church for reunion with Rome, which was temporarily effected at the Council of Florence (1439).” In 1448 he became cardinal and governor of Rome. 

Cusa was not a philosopher of mathematics. He was a philosopher whose thinking was imbued with mathematical images, so that he used mathematics to teach theology. He knew that there are different degrees of infinity. He said, amazingly, that the physical universe is finite but unbounded. He showed that a geometric figure can be both a maximum and a minimum, depending on how it’s parametrized. 

Again from the Encyclopedia, “According to Cusa, a man is wise only if he is aware of the limits of the mind in knowing the truth. . . . Knowledge is learned ignorance (docta ignorantia). Endowed with a natural desire for truth, man seeks it through rational inquiry, which is a movement of the reason from something presupposed as certain to a conclusion that is still in doubt. . . . As a polygon inscribed in a circle increases in number of sides but never becomes a circle, so the mind approximates to truth but never coincides with it. . . . Thus knowledge at best is conjecture (coniectura).” 

Cusa was a Platonist at a time when Aristotelians were dominant. “He constantly criticized the Aristotelians for insisting on the principle of noncontradiction and stubbornly refusing to admit the compatibility of contradictories in reality. It takes almost a miracle, he complained, to get them to admit this; and yet without this admission the ascent of mystical theology is impossible. . . . He constantly strove to see unity and simplicity where the Aristotelians could see only plurality and contradiction. 

“Cusa was most concerned with showing the coincidence of opposites in God. God is the absolute maximum or infinite being, in the sense that he has the fullness of perfection. There is nothing outside him to oppose him or to limit him. He is the all. He is also the maximum, but not in the sense of the supreme degree in a series. As infinite being he does not enter into relation or proportion with finite beings. As the absolute, he excludes all degrees. If we say he is the maximum, we can also say he is the minimum. He is at once all extremes. . . . The coincidence of the maximum and minimum in infinity is illustrated by mathematical figures. For example, imagine a circle with a finite diameter. As the size of the circle is increased, the curvature of the circumference decreases. When the diameter is infinite, the circumference is an absolutely straight line. Thus, in infinity the maximum of straightness is identical with the minimum of curvature. . . . 

Cusa denied that the universe is positively infinite; only God, in his view, could be described in these terms. But he asserted that the universe has no circumference, and consequently that it is boundless or undetermined—a revolutionary notion in cosmology. . . . Just as the universe has no circumference, said Cusa, so it has no fixed center. The earth is not at the center of the universe, nor is it absolutely at rest. Like everything else, it moves in space with a motion that is not absolute but is relative to the observer. . . . 

“Beneath the oppositions and contradictions of Christianity and other religions, he believed there is a fundamental unity and harmony, which, when it is recognized by all men, will be the basis of universal peace.”

Plato's mathematics

  

Plato didn’t have a “philosophy of mathematics” as we understand that phrase today. Mathematics is central in his philosophy. His believes the physical world of visible, changeable entities is illusion. What’s real is invisible, immaterial, eternal. Mathematics is real because it’s immaterial and eternal. It’s tied to religion, as a stepping stone in one’s ascent toward “the good,” the loftiest aspect of invisible reality. A challenge to his notion of mathematics would be a challenge to his religion.

Rules for educating "guardians"

  

My dear Glaucon, what study could draw the soul from the world of becoming to the world of being? . . . this, which they all have in common, which is used in addition by all arts and all sciences and ways of thinking, which is one of the first things every man must learn of necessity.” 

“What’s that?” he asked again. 

“Just this trifle, I said—to distinguish between one and two and three: I mean, in short, number and calculation . . .” 

“Number, then, appears to lead towards the truth?” 

“That is abundantly clear.” 

“Then, as it seems, this would be one of the studies we seek; for this is necessary for the soldier to learn because of arranging his troops, and for the philosopher, because he must rise up out of the world of becoming and lay hold of real being or he will never become a reckoner.” 

“That is true,” said he. 

“Again, our guardian is really both soldier and philosopher.” 

“Certainly.”

“Then, my dear Glaucon, it is proper to lay down that study by law, and to persuade those who are to share in the highest things in the city to go for and tackle the art of calculation, and not as amateurs; they must keep hold of it until they are led to contemplate the very nature of numbers by thought alone, practicing it not for the purpose of buying and selling like merchants or hucksters, but for war, and for the soul itself, to make easier the change from the world of becoming to real being and truth.” 

“Excellently said,” he answered. 

“And besides,” I said, “it comes into my mind, now the study of calculations has been mentioned, how refined that is and useful to us in many ways for what we want, if it is followed for the sake of knowledge and not for chaffering.” 

“How so?” he asked. 

“In this way, as we said just now; how it leads the soul forcibly into some upper region and compels it to debate about numbers in themselves; it nowhere accepts any account of numbers as having tacked onto them bodies which can be seen or touched. . . . I think they are speaking of what can only be conceived in the mind, which it is impossible to deal with in any other way.” 

“You see then, my friend, said I, that really this seems to be the study we need, since it clearly compels the soul to use pure reason in order to find out the truth.” 

“So it most certainly does. . . . 

“For all these reasons, the best natures must be trained in it.” 

After arithmetic, Glaucon and Socrates consider geometry. 

Says Socrates, “The knowledge the geometricians seek is not knowledge of something which comes into being and passes, but knowledge of what always is.”

“Agreed with all my heart, said he, for geometrical knowledge is of that which always is.” 

“A generous admission! Then it would attract the soul toward truth, and work out the philosopher’s mind so as to direct upwards what we now improperly keep downwards.” 

After arithmetic and plane geometry, Glaucon proposes astronomy as the third subject in the curriculum of the Guardians. Socrates objects; solid geometry is more appropriate, he says. 

“Quite so,” says Glaucon, “but it seems that those problems have not yet been solved.” 

“For two reasons,” I said, “because no city holds them in honour, they are weakly pursued, being difficult. Again, the seekers lack a guide, without whom they could not discover; it is hard to find one in the first place, and if they could, as things now are, the seekers in these matters would be too conceited to obey him. But if any whole city should hold these things honourable and take a united lead and supervise, they would obey, and solutions sought constantly and earnestly would become clear. Indeed even now, although dishonoured by the multitude, and held back by the seekers themselves having no conception of the objects for which they are useful, these things do nevertheless force on and grow against all this by their own charm, and I should not be too surprised if they should really come to light. . . . 

“Let us put astronomy as the fourth study, assuming that solid geometry, which we leave aside now, is there for us if only the city would support it.”

[The Republic (“Great Dialogues of Plato,” pp. 315–16, 323–31). Plato gave Socrates the first person, “I.”]

Pythagoreans!

 

The number one, they argued, is the generator of numbers and the number of reason; the number two is the first even or female number, the number of opinion; three is the first true male number, the number of harmony, being composed of unity and diversity; four is the number of justice or retribution, indicating the squaring of accounts; five is the number of marriage, the union of the first true male and female numbers; and six is the number of creation. Each number had its peculiar attributes. The holiest of all was the number ten, or the tetractys, for it represented the number of the universe, including the sum of all possible dimensions. [See also Heath, 1981, p. 75.] A single point is the generator of dimensions, two points determine a line of dimension one, three points S (not on a line) determine a triangle with area of dimension two, and four points (not in a plane) determine a tetrahedron with volume of dimension three; the sum of the numbers representing all dimensions, therefore, is . . . ten. It is a tribute to the abstraction of Pythagorean mathematics that the veneration of the number ten evidently was not dictated by anatomy of the human hand or foot.”

Mainstream Philosophies of Mathematics

 

Frege

                                                          

The name “foundationism” was invented by a prolific name-giver, Imre Lakatos. It refers to Gottlob Frege in his prime, Bertrand Russell in his full logicist phase, Luitjens Brouwer, guru of intuitionism, and David Hilbert, prime advocate of formalism. Lakatos saw that despite their disagreements, they all were hooked on the same delusion: Mathematics must have a firm foundation. They differ on what the foundation should be. 

Foundationism has ancient roots. Behind Frege, Hilbert, and Brouwer stands Immanuel Kant. Behind Kant, Gottfried Leibniz. Behind Leibniz, Baruch Spinoza, and René Descartes. Behind all of them, Thomas Aquinas, Augustine of Hippo, Plato, and the great grandfather of foundationism—Pythagoras. 

We will find that the roots of foundationism are tangled with religion and theology. In Pythagoras and Plato, this intimacy is public. In Kant, it’s half covered. In Frege, it’s out of sight. Then in Georg Cantor, Bertrand Russell, David Hilbert, and Luitjens Brouwer, it pops up like a jack-in-the-box.

In the twentieth century, we look at Russell, Brouwer, Hilbert, Edmund Husserl, Ludwig Wittgenstein, Kurt Gödel, Rudolph Carnap, Willard V. O. Quine, and a small sample of today’s authors. Philip Kitcher said the philosophy of mathematics is generally supposed to begin with Frege—before Frege there was only “prehistory.” Frege transformed the issues constituting philosophy of mathematics. In that sense earlier philosophy can be called prehistoric. But to understand Frege you must see him as a Kantian. To understand Kant you must see his response to Newton, Leibniz, and Hume. Those three go back to Descartes, and through him to Plato. Plato was a Pythagorean. The thread from Pythagoras to Hilbert and Gödel is unbroken. I aim to tell a connected story from Pythagoras to the present—where foundationism came from, where it left us. 

Instead of going straight through from Pythagoras, I’ve split the story into two parallel streams—the first section is about the “Mainstream.” The second is about the “humanists and mavericks.” 

For the Mainstream, mathematics is superhuman—abstract, ideal, infallible, eternal. So many great names: Pythagoras, Plato, Descartes, Spinoza, Leibniz, Kant, Frege, Russell, Carnap. (For Kant, membership in this group is partial.) 

Humanists see mathematics as a human activity, a human creation. Aristotle was a humanist in that sense, as were Locke, Hume, and Mill. Modern philosophers outside the Russell tradition—mavericks—include Peirce, Dewey, Roy Sellars, Wittgenstein, Popper, Lakatos, Wang, Tymoczko, and Kitcher (a self-styled maverick). There are some interesting authors who aren’t labeled philosophers: psychologist Jean Piaget; anthropologist Leslie White; sociologist David Bloor; chemist Michael Polányi; physicist Mario Bunge; educationists Paul Ernest, Gila Hanna, Anna Sfard; mathematicians Henri Poincaré, Alfréd Rényi, George Pólya, Raymond Wilder, Phil Davis, and Brian Rotman.

As mathematics changes...

 

As mathematics grows and changes, geometry changes. A more current example. Until the mid-twentieth century, the “derivative” or “slope” of a function at a point existed only if at that point the graph of the function was smooth—had a definite direction, and no jumps. Now mathematicians have adopted Laurent Schwartz’s generalized functions. Every function, no matter how rough, has a derivative.

**

The meaning of differentiation has changed. Newton and Leibniz’s differentiation operator has become something more general. Our generalized differentiation includes the old differentiation, and it’s much more powerful. 

As mathematics grows and changes, functions and operators change.  

A familiar cliché says that while other sciences throw away old theories, mathematics throws away nothing. But the old mathematics isn’t preserved intact. Mathematics is intensely interconnected and self-interactive. The new is vitally linked to the old. The old is revitalized, enriched, and complexified by interaction with the new.

Ten Global Trends

You can't fix what is wrong in the world if you don't know what's actually happening. In this book, straightforward charts and graphs, combined with succinct explanations, will provide you with easily understandable access to the facts that busy people need to know about how the world is really faring.

Polls show that most smart people tend to believe that the state of the world is getting worse rather than better. Consider a 2016 survey by the global public opinion company YouGov that asked folks in 17 countries, "All things considered, do you think the world is getting better or worse, or neither getting better nor worse?” Fifty-eight percent of respondents thought that the world is getting worse, and 30 percent said that it is doing neither. Only 11 percent thought that things are getting better. In the United States, 65 percent of Americans thought that the world is getting worse, and 23 percent said neither. Only 6 percent of Americans responded that the world is getting better.

This dark view of the prospects for humanity and the natural world is, in large part, badly mistaken. We demonstrate it in these pages using uncontroversial data taken from official and scientific sources.

Of course, some global trends are negative. As Harvard University psychologist Steven Pinker says: "It's essential to realize that progress does not mean that everything gets better for everyone, everywhere, all the time. That would be a miracle, that wouldn't progress." For example, man made climate change arising largely from increasing atmospheric concentrations of carbon dioxide released from burning fossil fuels could become a significant problem for humanity during this century. The spread of plastic marine debris is a big and growing concern. Many wildlife populations are declining, and tropical forest area continues shrinking. In addition, far too many people are still malnourished and dying in civil and sectarian conflicts around the globe. And, of course, the world is afflicted by the current coronavirus pandemic.

However, many of the global trends we describe are already helping redress such problems. For example, the falling price of renewable energy sources incentivize the switch away from fossil fuels. Moreover, increasingly abundant agriculture is globally reducing the percentage of people who are hungry while simultaneously freeing up land so that forests are now expanding in much of the world. And unprecedentedly rapid research has significantly advanced testing, tracking, and treatment technologies to ameliorate the coronavirus contagion.

PSYCHOLOGICAL GLITCHES MISLEAD YOU

So why do so many smart people wrongly believe that all things considered, the world is getting worse?

Way back in 1965, Johan Galtung and Mari Holmboe Ruge, from the Peace Research Institute Oslo, observed, "There is a basic asymmetry in life between the positive, which is difficult and takes time, and the negative, which is much easier and takes less time-compare the amount of time needed to bring up and socialize an adult person and the amount of time need ed to kill him in an accident, the amount of time needed to build a house and to destroy it in a fire, to make an airplane and to crash it, and so on." News is bad news; steady progress is not news.

Smart people especially seek to be well informed and so tend to be voracious consumers of news. Since journalism focuses on dramatic things and events that go wrong, the nature of news thus tends to mislead readers and viewers into thinking that the world is in worse shape than it really is. This mental shortcut causes many of us to confuse what comes easily to mind with what is true; it was first identified in 1973 by behavioral scientists Amos Tversky and Daniel Kahneman as the "availability bias." Another reason for the ubiquity of mistaken gloom derives from a quirk of our evolutionary psychology. A Stone Age man hears a rustle in the grass. Is it the wind or a lion? If he assumes it's the wind and the rustling turns out to be a lion, then he's not an ancestor. We are the descendants of the worried folks who tended to assume that all rustles in the grass were dangerous predators and not the wind. Because of this instinctive negativity bias, most of us attend far more to bad rather than to good news. The upshot is that we are again often misled into thinking that the world is worse than it is.

"Judgment creep" is yet another explanation for the prevalence of wrong-headed pessimism. We are misled about the state of the world because we have a tendency to continually raise our threshold for success as we make progress, argue Harvard University psychologist Daniel Gilbert and his colleagues. "When problems become rare, we count more things as problems. Our studies suggest that when the world gets better, we become harsher critics of it, and this can cause us to mistakenly conclude that it hasn't actually gotten better at all," explains Gilbert. "Progress, it seems, tends to mask itself." Social, economic, and environmental problems are being judged intractable because reductions in their prevalence lead people to see more of them. More than 150 years ago, political scientist Alexis de Tocqueville noted a similar phenomenon as societies progress, one that has since been called the Tocqueville effect.

What, though, accounts for progress?

Some smart folk who acknowledge that considerable social, economic, and environmental progress has been made still worry that progress will not necessarily continue.

"Human beings still have the capacity to mess it all up. And it may be that our capacity to mess it up is growing," asserted Cambridge University political scientist David Runciman in a July 2017 Guardian article. He added: "For people to feel deeply uneasy about the world we inhabit now, despite all these indicators pointing up, seems to me reasonable, given the relative instability of the evidence of this progress, and the [unpredictability] that overhangs it. Everything really is pretty fragile."

Runciman is not alone. The worry that civilization is just about to go over the edge of a precipice has a long history. After all, many earlier civilizations and regimes have collapsed, including the Babylonian, Roman, Tang, and Mayan Empires, and more recently the Ottoman and Soviet Empires.

In their 2012 book, Why Nations Fail: The Origins of Power, Prosperity, and Poverty, economists Daron Acemoglu and James Robinson persuasively outline reasons for the exponential improvement in human well-being that started about two centuries ago.

They begin by arguing that since the Neolithic agricultural revolution, most societies have been organized around "extractive" institutions-political and economic systems that funnel resources from the masses to the elites.

In the 18th century, some countries including Britain and many of its colonies-shifted from extractive to inclusive institutions. "Inclusive economic institutions that enforce property rights, create a level playing field, and encourage investments in new technologies and skills are more conducive to economic growth than extractive economic institutions that are structured to extract resources from the many by the few," they write. "Inclusive economic institutions are in turn supported by, and support, inclusive political institutions," which "distribute political power widely in a pluralistic manner and are able to achieve some amount of political centralization so as to establish law and order, the foundations of secure property rights, and an inclusive market economy." Inclusive institutions are similar to one another in their respect for individual liberty. They include democratic politics, strong private property rights, the rule of law, enforcement of contracts, freedom of movement, and a free press. Inclusive institutions are the basis of the technological and entrepreneurial innovations that produced a historically unprecedented rise in living standards in those countries that embraced them, including the United States, Japan, and Australia as well as the countries in Western Europe. They are qualitatively different from the extractive institutions that preceded them.

The spread of inclusive institutions to more and more countries was uneven and occasionally reversed. Those advances and in the University of Illinois at Chicago economist Deirdre Mc Closkey's view, the key role played by major ideological shifts resulted in what McCloskey calls the "great enrichment," which boosted average incomes thirtyfold to a hundredfold in those countries where they have taken hold.

The examples of societal disintegration cited earlier, whether Roman, Tang, or Soviet, occurred in extractive regimes. Despite crises such as the Great Depression, there are no examples so far of countries with long-established inclusive political and economic institutions suffering similar collapses.

In addition, confrontations between extractive and inclusive regimes, such as World War II and the Cold War, have generally been won by the latter. That suggests that liberal free-market democracies are resilient in ways that enable them to forestall or rise above the kinds of shocks that destroy brittle extractive regimes.

If inclusive liberal institutions can continue to be strengthened and further spread across the globe, the auspicious trends documented in this book will extend their advance, and those that are currently negative will turn positive. By acting through inclusive institutions to increase knowledge and pursue technological progress, past generations met their needs and hugely increased the ability of our generation to meet our needs. We should do no less for our own future generations. That is what sustainable development looks like.

We devour each other

 

It all started with my brother, to whom I dedicated the novel. The idea arose from the long evenings I spent at his restaurant Ocho Once in Buenos Aires. Gonzalo Bazterrica is a chef and he works with organic food; but above all, he is a conscious food researcher and, through his cooking and his research I could understand what Hippocrates meant by: “Let food be thy medicine and let medicine be thy food”.

Thanks to my own reading on the topic I gradually changed my diet and I stopped eating meat. When I did, a veil was drawn, and my view of meat consumption was completely changed. To me, a steak is now a piece of a corpse. One day I was walking by a butcher’s shop and all I saw were bodies of animals hanging down and I thought, “Why can’t those be human corpses? After all we are animals, we are flesh.” And that’s how the idea for the novel emerged.

I wanted to write about how, in the near future, cannibalism could be legalised, but I needed a story. And the plot that I imagined is this: there is a so-called virus affecting animals rendering them inedible and cannibalism becomes legal. Humans start being butchered in meat-processing plants. The protagonist runs a meat-processing plant and is gifted a female to butcher or raise. That is, he has a naked woman in his possession. I won’t give away what happens later.

The creative process was visceral, compulsive; but since I am obsessive, there was a preparation process. I had the story quite clear in my head before sitting down to write it. What I did first was research. I read a formidable amount of manuals, instructions, fiction material and essays on cannibalism, on meat industry operations and animal rights. I also watched movies, documentaries and videos. That was the hardest part of the process, the one most difficult to face due to the violence of the imagery. Seeing how chickens get their beaks cut off so they won’t peck each other due to overcrowding is disturbing. Seeing how a wild animal is skinned alive is heartbreaking.

Although my book contains clear criticism of the meat industry, I also wrote the novel because I have always believed that in our capitalist, consumerist society, we devour each other. We phagocyte each other in many ways and in varying degrees: human trafficking, war, precarious work, modern slavery, poverty, gender violence are just a few examples of extreme violence.

Objectivising and depersonalising others allows us to remove them from the category of human being (our equal) and place them in the category of a mere “other”, whom we can be violent to, kill, discriminate against, hurt, etc. One clear example: when we allow a 12-year-old girl to work as a prostitute, it shows that there is a part of society that is indifferent, uninterested in that situation, and that another huge part validates it because it benefits them and in the middle of all that there is this little girl being consumed by everyone.

Hannah Arendt, says in her book Eichmann in Jerusalem, whose subtitle is: “A report on the banality of evil”, that the extermination of Jews in Germany and other European countries was not down to the pure evil in Nazi rulers, but to society’s indifference. This massacre, executed by bureaucrats, would not have been possible without the indifference of “good” citizens.

Thus, we devour each other because we are generally blind to our kinship with others. When faced with their suffering, we look the other way. And we do the same with other sentient beings. It may sound exaggerated, for sure. But to many Argentinians, a meat dish is not seen as a being, but merely as protein. In my country, meat is part of our national identity. Barbecues are basically considered sacred rites. As if they were part of a religious celebration, on Sundays, many Argentinians place pieces of meat on their grills and meet with friends to eat it. The latest official study of 2018 found that the average Argentine eats 118kg of meet a year. There are 45 million Argentinians. That is a staggering amount of meat.

Having said this, I want to make clear that I am not on a crusade to convert carnivores to vegetarianism. I never meant to write a vegan pamphlet. I tried to write the best novel I could possibly write, without trying to convince anyone of anything because, in my opinion, fanaticism is another form of violence.

Despite the fact that I actually am a vegetarian, meat is also part of my identity and I am part of a society that eats meat and unflinchingly accepts animal cruelty with the same brutal indifference shown towards vulnerable groups such as the poor, indigenous populations and women. We are a country that also murders its women. There is one femicide every 18 hours and there are no statistics for deaths related to clandestine abortions since in Argentina it is a crime.

My identity is also pierced, modelled and built by heteronormativity, the deep patriarchy. That boundless weave of oppression that has language as one of its greatest accomplices and supporters. As Heidegger says: “language is the house of being”.

Language gives us an identity; it speaks of who we are. In my country, in my language, a language I share with 22 other nations and 572 million people, we say “dog” – perro – to speak about man’s best friend. When we use the feminine noun perra it becomes synonyms with puta (whore). When we speak about someone who is daring – atrevido – we are talking about a fearless man. When we utter the feminine form atrevida we are referring to a puta (whore). The synonyms we use in Spanish for puta are many (101, to be precise), but there is no negative equivalent to talk about a man who has sex with many women. Because using the masculine form puto constitutes an insult to refer to a homosexual man. Men who have sex with lots of women are considered desirable. There is no derogative word to define them and that is a clear sign of the social construction that is patriarchy.

That is why in Tender is the Flesh I tried to work carefully with language. Creating a new matrix requires new words, new ways of naming new things, like when they call a human that is bred for consumption a “product”. But I also worked with silence, with the unwritten word, which is another form of cannibalism because by not saying certain things we become complicit, we help build and perpetuate that reality. When we do not talk about femicide, for example, we give room to impunity, to thinking that women’s lives are worthless. By naming acts of violence and understanding them, we give them entity and can work towards preventing them.

Language is energy. As Peruvian author César Calvo said: “whoever pronounces words sets potentialities into motion”. Through this book, through these words, I wish to move the energy of a non-violent, caring culture, to think of a world where we respect differences with equal rights, a world where one woman isn’t killed every 18 hours in acts of gender-based violence, a world where symbolic or real cannibalism is just fiction.

 

 

Tender is the flesh

He    had to fire Ency because someone who’s been broken can’t be fixed. He did speak to Krieg and make sure he arranged and paid for psychological care. But within a month, Ency had shot himself. His wife and kids had to leave the neighborhood, and since then Manzanillo has looked at him with genuine hatred. He respects Manzanillo for it. He thinks it’ll be cause for concern when the man stops looking at him this way, when the hatred doesn’t keep him going any longer. Because hatred gives one strength to go on; it maintains the fragile structure, it weaves the threads together so that emptiness doesn’t take over everything. He wishes he could hate someone for the death of his son. But who can he blame for a sudden death? He tried to hate God, but he doesn’t believe in God. He tried to hate all of humanity for being so fragile and ephemeral, but he couldn’t keep it up because hating everyone is the same as hating no one. He also wishes he could break like Ency, but his collapse never comes.

O Zât varlığıyla kainatın yaratılmasına vesiledir

 

 

 

 

 

 

 

 

O Zât

 

“O Zât, pek büyük ve bütün zamanları ve mekânları kapsayan, ezelden ebede uzanan bir davada bulunuyor. Allah ile konuştuğunu, yirmi üç yıl boyunca O’ndan âyetler, sûreler aldığını, O’nun adına hareket ettiğini söylüyor. Yalnız bunları söylemekle kalmıyor. Kimsenin görmediği gaybî meselelerden; pek çoğu zamanla ortaya çıkacak ve çıkmış kâinat gerçeklerinden; kâinatın yaratılış safhalarından; insanın ta başta her bir insanın anne karnında nasıl ve hangi safhalardan geçerek yaratıldığından; insana hilâfet vazifesi verilmesinden; melekler, insan ve şeytan arasında geçen hadiselerden; Hz. Allah’ın İsimleri’nden, Sıfatla-rı’ndan ve icraatından; varlığın tabakaları ve her bir tabakanın hususiyetlerinden; Ruh, melekler ve cinler diye görünmez varlıklardan; geçmiş zamanlardan, yani binlerce sene geriye giden tarihlerden ve bu tarihlerde yaşayan topluluklardan; yakın ve uzak gelecekten; dünyanın yıkılıp ebedî ve yepyeni bir âlemin kurulacağından bahsediyor. Bunlardan bahsederken de hiçbir zaman “Böyle düşünüyorum, sanırım, tahmin ederim.” gibi ifadeler kullanmıyor; bunları kullanmak şöyle dursun, çok kesin, çok net konuşuyor; gelecekten bahsederken bile âdeta olmuş gibi sözediyor. Ve aradan geçen ondört asır içinde gelecekle ilgili verdiği yüzlerce haberin pek çoğu aynen gerçekleşmiş bulunuyor. Bütün bunları tek bir zaman diliminde tek bir topluluk önünde söylemiyor. Bütün zamanlara ve bütün topluluklara hitap ederek söylüyor. Sıradan bir insan bile basit bir meselede küçük bir topluluk önünde yalana dayalı bir iddiada bulunmaktan çekinir. Fakat bu Zât, son derece büyük bir davayı ve sözünü ettiğimiz meseleleri bütün zamanlar, mekânlar ve topluluklar önünde hiç çekinmeden, kesin bir dille ve pervasızca dile getiriyor. Böyle bir Zât’ın, söylediklerinden emin olmaksızın kendinden ve hevasından konuşması mümkün müdür? Bir yanlışı, bir yalanı ortaya çıktığında bütün iddialarının ve davasının yıkılıp gideceği açıkken, her şeyi bilen Allah tarafından konuşturulmadıkça bu kadar meselede bu kadar kesin ve net konuşması mümkün müdür?”