Is God a Mathematician? - Mario Livio

Is God a Mathematician? Is Mathematics the language of the universe? Is it an invention or a discovery? Mario Livio tries to present arguments for and against these questions with chapters from mathematical history, concepts from the umpteen branches of mathematics, anecdotes from the lives of great Mathematicians and verbatim quotes from their journals in a 252-pager thriller. The story-telling in the book is fantastic and I found the latter half of the book particularly gripping. A note of trivia about the author - Mario Livio is the same author who wrote about the "golden ratio", a book and the ratio that got a mention in Dan Brown's Da Vinci Code.

The first half of the book presents the mathematical views of the ancient world like the Pythagorean mathematicians and the works of Euclid and Plato. He talks about the Tetraktys and Gnomons, tools developed by the Pythagorean mathematicians that proved certain theorems by inspection. Mario Livio then dwells into the 4 people whom he considers as the giants in Mathematical progress, in chronological order, giving historical insights into their lives and work. The author talks about Archimedes, who quoted “Give me a place to stand, and I will move the Earth”, for his genius in designing pulley-based contraptions, his work on displacements of liquids and his work on finding volumes of 3-d objects in an age where integral calculus was not known. He then moves to Galileo and his work on the acceleration of falling bodies, his evangelism of astronomy and the invention of the telescope. Then on the work of Rene Descartes, that led to the unification of algebra and geometry with concepts what we call as "Analytical Geometry", a breakthrough in math that made the very foundations of geometry stronger and provable. The fourth great one is of course Newton, for his work on gravity that changed not only the perspective of how we view the falling apple but also it changed the way we looks at the solar system and the universe. As a by product, Newton independently gave us calculus along with Leibniz. Mario Livio goes to exhibit the platonic view these mathematical giants had almost convincing the reader that Math had to be a discovery rather than an invention. But hold on, now there is a twist to this tale.

Till this time in history, Euclidean geometry was considered the ultimate truth and the perceived universe seemed to be behaving consistently with these postulates. Euclid's 5th postulate, the parallel postulate, was taken for granted till geometries of curved surfaces came into existence. Curved surfaces posed a new difficulty, it put Euclidean geometry in a fix as it did not behave consistently with the Euclidean postulates. These new-Euclidean surfaces and geometries gave way in the belief that after all Math is an invention, a figment of human thought. Mario Livio goes into the lesser known mathematicians of the non-Euclidean geometries and mentions names like Gauss and Riemann and skims through their work, the latter's geometry forming the building block for Einstein's theories in the future.

The author moves onto Logic and Mathematics, their relationship, discussing the works of George Boole (Boolean algebra), Bertrand Russell (Russell's paradox) and Kurt Godel (Incompleteness theorem) among others. He briefly writes about Godel's "Incompleteness theorem", another shock that rocked the Platonists. Godel showed that any formal system that is powerful enough to be of any interest is inherently either incomplete or inconsistent.

The last few chapters talk about some examples that show the difference between "active" and "passive" applications of Mathematics. Mario Livio covers Knot theory, a mathematical theory that was studied ages before it's application was found, in decoding DNA knots and strands (passive application). He gives a brief description of string theory too in this context. The theories of relativity - special and general are also discussed and their applications in adjusting clocks onboard satellites is given. The author then discusses the opinion of cognitive scientists on the same, which is mostly that Mathematics is an invention of the human intellect. Mario Livio concludes with the answer "it depends", there is math that occurs in nature whose characteristics we have conceptualized in our minds and there is math that purely occurs as thought.

Overall, an interesting read that showcases mathematics - invented or discovered. The book concludes with a paragraph from Bertrand Russell's essay The Problems of Philosophy -
Philosophy is to be studied, not for the sake of any definite answers to its questions since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation; but above all because, through the greatness of the universe which philosophy contemplates, the mind also is rendered great, and becomes capable of that union with the universe which constitutes its highest good.

The Meaning of it all - Richard Feynman

The demand for certainty is one which is natural to man, but is nevertheless an intellectual vice. - Bertrand Russell

A compilation of a series of 3 lectures delivered by Richard Feynman at the University of Washington, Seattle, in 1963, this book delivers profound ideas with a very simple style that can be understood and imbibed by anyone, scientist or not alike. The three lectures are titled, "The Uncertainty of Science", "The Uncertainty of Values" and "This Unscientific Age". The first two lectures have a very good build up and are in continuum, talking about the importance of being uncertain, both in science and in morals or values. The third lecture is a little bit more adhoc as the person delivering the lecture admits and deals with some of the problems we are facing in the current age. Feynman covers both the glaring issues and those that are pretty subtle in nature, potentially harmful nevertheless.

The first lecture is about how uncertainty is important in science inorder to discard older scientific beliefs and embrace newer and more precise ones. Feynman gives the 3 views of the meaning of science, science seen in application of inventions and discoveries (also called technology), science as a body of knowledge arising out of certain inventions and discoveries and the very traditional definition of Science, as a method of inventing and discovering new things. He talks about how scientific statements have to be stated in a precise fashion, leaving very less vagueness and a low tolerance for interpretation, or worse, misinterpretation.

The second lecture is much more interesting as Feynman explores the differences between religious views and scientific views, how uncertainty in values is important, how a "certain" leader is more harmful than an uncertain one, how democracy stems from uncertainty and so on. He makes it a point that "if something cannot be disproved it has to be true" is the most dangerous assumption to be making. This is the same point that the Russell's teapot (see The God Delusion review) analogy explains.

The last lecture is the longest one and deals with a list of problems in this age that makes this age an unscientific one. Here he talks about how quoting probability in experiments after an event has occurred rather than before is not right, how sampling needs to be done for any kind of statistical experiment, how gullible people are by falling for advertising, a skeptic outlook on some of the space missions, questions the need for English teachers and spelling rules, how mind-reading and astrology need to be disowned and so on.

Overall, an engrossing and entertaining 120+ pages, by one of the greatest Physicist and Nobel prize winner in the past century. Though it may not give you the meaning of it all, it does make you a little more uncertain, a little more skeptical and helps you avoid the biggest intellectual vice, Certainty.

Animal Farm - George Orwell

"All animals are equal, But some animals are more equal than others"

A breezy read, George Orwell's Animal Farm is one of the well known satires on the former Soviet Union's political state under Stalin. This book was written around the time of the 2nd world war and covers the fall of the Tsars and the rise of Stalin. Each powerful leader who influenced the former Soviet Union is represented by an animal, with 2 main characters - Snowball, a pig, alludes to Trotsky and Napolean, another pig, interpreted as Stalin. Napolean is the central character in the whole book.

The story is about a farm, Manor Farm, whose animals rebel (Russian Revolution) against Jones (Nicholas II) the owner of the farm under the leadership of Snowball and Napolean. Old Major's (Lenin or Karl Marx, an old boar in the book) speech is supposed to have spurred the rebellion. The idea behind the rebellion was that all human beings are villains, that led to an opinion, "Four legs good, two legs bad", and was engraved in the minds of all beasts on the farm. The first few chapters are pretty hilarious as the animals take control of the farm, manage it and see a lot of improvements as a consequence. But then, Napolean sidelines Snowball, drives him out of the farm and rises to become a tyrannical leader in the farm. Typical political games like opaqueness in policies, changing government agenda and high handedness by violence are played by Napolean to keep his monopoly as a leader.

There are a couple of wars, once an attack by Jones and company and the other by Mr. Fredrick (neighboring farm owner, alluded to Hitler), both of which are won by the animals, but by incurring a lot of loss and significant fatalities. As the book goes by, you feel bad for the other animals under the autocratic rule of Napolean and his fellow accomplices (other pigs). The story comes to an end with a party where Mr. Pilkington (Americans, another neighboring farm owner) having a party in the farmhouse along with the pigs and the other animals just watch on, quite opposite to the philosophy that led to the inception of Animal Farm.

A nice read, highlighting the consequences of power wielding dictators, communism and the suffering of the proletariat. Though the book talks about the dirty world of politics, the story is well told and brings out the moves of the government each citizen needs to be aware of. Another highlight of the book is that it gives an historical perspective into the state of the former Soviet Union for a good 30 years starting from the Russian Revolution in 1917 till the World War II (1945)

Candide - Voltaire

A classic along the lines of Gulliver's travels by Jonathan Swift, Voltaire's Candide is a fast-paced chronicle about a simple, naive and pleasant man in pursuit of his beloved, Cunegonde. Like Gulliver's travels, Candide is also a satire, ridiculing ideologies of the 17th century - Leibnizian optimism, the church and religious fanaticism among other contentious issues. When Voltaire came out with this book, it was banned all across Europe and only a few copies remained as they were smuggled out of the continent.

Leibnizian optimism talks about we being in an ideal world where everything happens in the best possible way for the good of the people. Voltaire, an ardent and vocal critique of this view presents the evil in the world, it's suffering and the prevalent tyranny in this story about Candide, who has to travel around the globe in search of his love, a reason for which he was banished from the place he grew up in West Germany. Voltaire is brutal on optimism and the story is pretty depressing as Candide sees omnipresence of evil, that makes him abandon his teacher's (Pangloss) optimistic views, views similar to Leibniz.

Voltaire also attacks the church and it's conservative views. He brings forth the sufferings of slavery and the genocide of natives in Latin America. Islam and Judaism are not spared as Candide travels through Constantinople. Voltaire does cover an utopian El Dorado, perhaps his views of an ideal state, where rationalism rules over wealth and power. Candide also discovers the wave of power, with it's crests and troughs as he meets 6 monarchs in an inn, all bereft of their power and in exile or travelling. After 130-pages of misery, all ends well as Candide is united with his love, his teacher and his confidants.

Voltaire ends the novel with "we must cultivate our garden", after seeing a happy and content farmer and his family at Constantinople. This particular statement is pretty open ended and has attracted many interpretations. Some say it is Voltaire's deistic views, that is God doesn't interfere in our daily activities, it is we who have to cultivate the garden given to us and it is in our hands to make our living the "best of all possible worlds". There are other interpretations like "Work keeps away three great evils: boredom, vice, and need."

Overall, a breezy read with messages well delivered and driven to a point of boredom. But it has a Orwellian hypocritical and depressive air to it.

ABC Of Relativity - Bertrand Russell

Science is a powerful potion whose consumption converts a dogmatic to a sceptic, and like travel, is fatal to prejudice and pride. But much of science is not popularized and it's depth and concepts are accessible to only unkempt haired, bespectacled, equation-wielding, greek alphabet ace stereotypes whom we brand as scientists. Bertrand Russell, a thinker, philosopher and mathematician, in this book attempts to explain the mysteries of Einstein's theory of Relativity to the common man, a person who has the thirst for this knowledge, but doesn't have the depth or expertise to understand the mathematical intricacies behind it. The 200 pager ABC of Relativity is one of a series of books written by Russell on different topics in science. This 1925 book, written 7 years after Einstein's General theory of relativity, is a credit to Russell's open-mindedness and foresight, personal attributes that are far ahead of his times.

Russell starts off the book by urging the reader to give up thinking in terms of Euclidean geometry and Newtonian physics that we are so used to on earth, a pre-requisite for understanding the theory of relativity. He moves on to explain the misconceptions about the theory of relativity and to describe the properties of light, particularly it's velocity. Russell introduces the Michelson-Morley experiment to measure the velocity of light, whose results called for a new theory, the special theory of relativity. In the middle chapters of the book, the author introduces concepts like the constancy of the velocity of light, time dilation, object length alteration in the direction of motion, Lorentz contraction and space-time, essential concepts behind the Einstein's special theory of relativity.

Russell's explanation of concepts is neither rhetorical nor mathematical, making it very powerful as it can be understood by anyone. His examples are very "earthly", involving objects that we see everyday. After explaining the special theory of relativity, Russell moves to harder concepts like gravitation, formed by space-time hills leading to the general theory of relativity. Personally, I felt concepts around accelaration and gravity a little harder to understand. Perhaps the concepts here are a little more abstract and hard to visualize and imagine. The author also explains the vastness of our expanding universe, sowing seeds of humility in the reader. The book concludes with some philosophical insights.

Overall, a fantastic attempt at popularizing the theory of relativity. After reading the book, I did some research on the web for more attempts at simplified explanation of the theory and here is an article that attempts to explain the theory in 4-letter words or less.

Good Critic, Bad Critic

I am often asked why I like to read book reviews, and what it is that they really do. I mean: why not read the original book, for God's sake? It's a hard question and the best answer is, as it often is , the pragmatic one. With non-fiction, book reviews often serve as a substitute for the book itself. With fiction, it is harder to justify. But life is short, so is time and when one has a pile of books to read, it only makes sense to be judicious when adding to it.

I bring this up because I read three reviews of a book recently and taken together, they all bring out the fine line between book reviews that function as, well, just book reviews and book reviews that manage to be works of genuine criticism.

The book in question is the latest sensation from France: Jonathan Littell's The Kindly Ones.

For a book review that is truly nothing more than book review, see Michiko Kakutani's review in the New York Times.

For a review that rises to the level of criticism, see Daniel Mendelsohn's fine, searching analysis in the New York Review of Books.

And for a review that is written in the spirit of criticism but doesn't quite make it primarily because it follows the fairly predictable arc of the New Republic takedown, see Ruth Franklin's review for the New Republic. (I knew what she was going to say even before I started reading the first paragraph and true to form, she didn't disappoint.)

(Interestingly, both Franklin and Mendelsohn make some of the same points, but they both take them in different directions. In Kakutani's defence, she has to summarize the book and evaluate it in just 2 pages so she really doesn't have that much space to produce genuine criticism.)

The God Delusion - Richard Dawkins

When one person suffers from a delusion, it is called insanity. When many people suffer from a delusion, it is called Religion. - Robert Pirsig, Author of Zen and the Art of Motorcycle maintenance.

The God Delusion, a 400 page best-seller by one of the world's most passionate atheists and renowned biologist is an eye-opener into the realm of religion, creationism and intelligent design. Richard Dawkins, a Darwinian at soul, asks the hard questions about existence of God and religion, that most of us dare not ask with fear. Though the book may not convert a theist into an atheist, it definitely influences you in becoming a deist or makes you ponder about the other options (other than being creationist) or at least makes you think twice the next time you follow something that is indoctrinated on you.

The book starts off by clarifying the misconstrued word "God", when used by Einstein and other scientists ("God does not play dice" -Einstein). The book gets riveting as Dawkins proposes different arguments justifying the existence of God. Some of the arguments are truly intriguing and the author refutes all of them pretty systematically. The best arguments are,

The Ultimate 747 Gambit - "probability of life originating on Earth is no greater than the chance that a hurricane, sweeping through a scrapyard, would have the luck to assemble a Boeing 747"

The Pascal Wager - "even though the existence of God cannot be determined through reason, a person should "wager" as though God exists, because so living has potentially everything to gain, and in theory nothing to lose"

Irreducible complexity - "A single system which is composed of several interacting parts that contribute to the basic function, and where the removal of any one of the parts causes the system to effectively cease functioning."

Dawkins brings forth the infinite regress of "who is the creator of the creator?" as a counter-argument. He also feels that the proposer of a particular dogma should prove it logically rather than claiming it as proved just because it cannot be disproved. Bertrand Russell's teapot logic is used to humorously present this idea. The author then moves on to show that morals don't stem from the scriptures, for people who believe that for a human being to act morally fear of God/religion is very important. Dawkins criticizes the scriptures, drawing examples from both the new testament and the old testament as well as religions like Islam to show that the scriptures are devoid of morals. He talks about the moral zeitgeist by citing examples of changing moral standards over time to prove this point. He ends the book by talking about religion for consolation and inspiration and discussing their importance. Dawkins feels that the world of science, with it's infinite unknowns and truth seeking is inspiration enough to lead a motivated life making religion unnecessary.

A good read that opens up our minds into the limitations of our mind, the possibilities of science and the pitfalls of religion. Dawkins is very meticulous in his research and his presentation is commendable. He doesn't cover oriental religions in depth and feels that Buddhism is more of philosophy rather than a religion, with which I concur. I loved the theme that Dawkins reiterates, "There is no Catholic child or a Muslim child, rather there is a child born to Catholic parents or Muslim parents". Religion should be a prerogative of the child. The ten commandments of humanism is pretty impressive and is quoted in the book. I am yet to read and gather from the critics of this book, which will be my exercise over the next few month.

Here is an excerpt from the preface that is very compelling,

“Imagine, along with John Lennon, a world with no religion. Imagine no suicide bombers, no 9/11, no 7/7, no Crusades, no witch-hunts, no Gunpowder Plot, no Indian partition, no Israeli/Palestinian wars, no Serb/Croat/Muslim massacres, no persecution of Jews as 'Christ-killers,' no Northern Ireland 'troubles,' no 'honour killings,' no shiny-suited bouffant-haired televangelists fleecing gullible people of their money ('God wants you to give till it hurts.')”