While browsing an old bookstore, my wife stumbled upon this gem and knew instantly that it would be a fit for me. I typically find it very enjoyable to read stories that describe the pop-culture of ancient times, especially when it’s evident that humans have not changed much in the past few thousand years. This particular book, originally titled Philogelos, describes a particular aspect of our species that seems to have permeated the ages. That’s because, for all intents and purposes, it is the oldest joke book in existence!

This collection of humorous quips is attributed to two fourth-century wise cracks named Hierocles and Philagrios. Though the Romans had ruled the whole known world for a thousand years, our (presumably) drunken duo were unmistakably Greek. Apparently the Greeks expressed themselves quite literally in common speech, and found verbal contradictions or alternative connotations to be tremendously funny. Understandably, this particular style of humor does not always stand the test of time very well. At first glance, we would probably dismiss a large number of jokes as youthful slapstick, whereas our forefathers would be cracking up merely at their notion. It is actually quite common for old books to be laced with humor that we are completely oblivious to because the local inside-jokes are lost in time. What we still have with us today though, are the subjects of all these jokes: idiots, foreigners, smart-asses, and fat people.

Hairdresser: How shall I cut your hair sir?
Client: In silence please.

Though Gottlob Frege might not be a popular or mainstream thinker, he laid down the foundation for one of the most important philosophical  movements in history, namely, analytic philosophy. While Aristotle’s logic couldn’t even represent trivial inferences in Euclidean geometry, Frege’s work lead to the formalization of Russel’s Principia Mathematica, Gödel’s incompleteness theorems, and Tarski’s theory of thruth.

Frege wrote Die Grundlagen der Arithmetik in 1884 with the intent of laying down an a priori analytic-based treatise on what we refer to as numbers. We now know in retrospect that logicism as a singular way to reduce all of mathematics to pure logic did not survive the test of time. However, its rigorous logical formalism did.

Using words to describe mathematics certainly is difficult. Saying that the number 1 is a thing is like defining a definite article in terms of its indefinite article. In Grundlagen, Frege defines numbers as objects that assert something about a concept. What does this mean? In daily speech, we usually use numbers much in the same way we use adjectives: “I see five ants” or “I see red ants”. While both properties may be regarded as objective, the difference is that every ant is red, but not every ant is five. Numbers are not properties of the ants themselves. This becomes more apparent when we convert the sentence to, “The number of ants I see is five”, where the word five is used as a singular term rather than adjectivally. The number five then belongs to a concept of ant that I see. So what is a natural number?

Frege defines ‘the number that belongs to a concept Φ’ as the extension of ‘equal to the concept Ψ’. Equality is defined as: a mutual univocal correlation of the extensions of concept terms. Zero, in turn, would be the concept of being non self-identical. Another way of expressing zero would be as the extension of a concept that has no objects falling under it. I’m not entirely certain if Frege was aware of it or if we all simply have misunderstood his ideas, but to understand the notion of univocal (one-to-one) correlation, we must first define the natural number 1. He’s given us a circular argument! A bit disappointing but not fatal to his legacy.

While Grundlagen leaves out definitions for complex numbers, imaginary numbers, infinitesimals, and more, it sets the bar on other important matters. I particularly enjoyed Frege’s long digressions psychologism which he strongly disliked. The inductive proofs that fancy calculus mathematicians pulled out of their hats seemed to irritate him especially. I would recommend this book to someone that’s interested in mathematical philosophy but doesn’t actually want to learn too much mathematics.

Besides simply being lengthy, this book was a formidably difficult read — unless it was utter nonsense, in which case it was laughably easy. I can’t really decide which because the language was used in such an obscure way that it was extremely difficult to follow the lengthy lines of reasoning and maintain whether or not they were actually consistent. The book is further clouded by the gratuitous use of home-made words which already sound odd in German, “Zuhandenheit”, but even more so in English, “Ready-to-Hand”. Perhaps this is done on purpose, as the author is fond of the hermeneutic circle and feels this is the only way to approach the main topic of the book: What is the true nature of Being?

Being and Time, which is considered one of the premier philosophical works of the 20th century, was written my Martin Heidegger to address a question which he felt had been overlooked in philosophy. He believed that while most philosophers had been chiefly concerned which things that exist, they’d never given a satisfactory definition of what it actually means to exist. The fact that Being seems self-evident to us is exemplified by how easily it is overlooked in quotes such as “I think, therefore I am”. Even the question “what is being?” contains a form of Being in it. While Martin had originally planned on addressing the whole issue in six parts spread out over two books, he was only given time to finish two parts before having to prepare the material for publication. In these two parts he discusses three subjects, namely the meaning of Being, a being called Dasein, and Temporality.

In Martin’s ontological structure, the meaning of Being is grasping how something becomes intelligible, which necessarily precedes things like propositions or science, and may be viewed as a destruction of traditional meta-physics.  Since there is no way to access Being other than via beings themselves the next step is asking a being about its own Being. The one chosen to answer these questions is Dasein. By quantifying a set of characteristics that a being interested in its own existence might have, such as angst and care, Martin reaches the prerequisite of those characteristics which is temporality, because Dasein is mortal. To truly grasp the meaning of his own Being, Dasein must first authentically embrace the fact that it will die. The book ends with questions concerning the nature of temporality itself which were supposed to be answered in the continuation of his project.

I picked up this Times Bestseller at an airport pocket-book store while waiting for a connecting flight. Normally I stay away from shelves with a “bestseller” sign since they only contain banal things like stories about teenage vampires falling in love or never-before-told secrets on how to get rich fast / be happy / loose weight. This book however, had a title which was hard for me to resist. I was skeptical at first because on the cover it stood “understanding philosophy through jokes”, which made me wonder how much philosophy such a small book could contain. I picked it up, flipped to a page in the middle, and started laughing at the jokes. As I paid for the orange paperback I thought, “One bestseller can’t hurt…”

This amusing book explains the most famous ideas in philosophy using comical anecdotes, and one thing it does very well is transition from philosophy to humor in a seamless and unstrained manner. In fact, philosophy seems to lend itself perfectly to humor since the subjects it often discusses are  meant to flip reality, define morals, and single out (often uncomfortable) truths of life. Here are some short gags.

Empiricism, or what data can we trust:
Morty comes home to find his wife and his best-friend, Lou, together in bed.
Just as Morty is about to open his mouth, Lou jumps out of the bed and says,
“Before you say anything, old pal, what are you going to believe, me or your eyes?”

Heidegger’s existentialist anxiety:
A customer in a restaurant asks, “How do you prepare your chickens?”
The cook answers, “Oh, nothing special really. We just tell them they’re gonna die”

In 1884 an English schoolmaster penned a groundbreaking novella called Flatland. The book’s protagonist and narrator is a square living on a vast two-dimensional plane inhabited by a plethora of geometric shapes. As Mr. Square walks the reader through what life in his dimension is like, it's easy to be fascinated with how foreign their universe seems when viewed from the “inside”. For instance, to us a square is easily distinguishable from a circle, but to a Flatlander both look like straight lines. In fact, to a Flatlander, everything looks like a straight line! One evening, the square was visited by a being with extraordinary powers. The guest appeared straight out of nowhere and was at first as small as a point, but grew quickly into a magnificent circle. When the awe-struck square demanded to to be told what he was looking at, the mysterious being obliged by introducing himself as: The Sphere.

In the beginning, the square could not fathom a dimension which rose “out of” his space. It would have to be an infinitely small dimension he decreed. Well, the sphere explained, for Flatlanders it might seem that way, but to us, the third dimension is infinitely big. Still not convinced, the square asked which direction the third dimension was in. Not knowing what words to use, the sphere could only explain that it points orthogonally from the square’s insides! Realizing that words would not suffice to explain the true nature of flatland, the sphere tore the protagonist out of his universe and took him on an extraordinary journey into the 3rd dimension, pushing the limits of his imagination.

The second half of this volume is a sequel called Sphereland where the square’s grandson continues exploring intriguing spatial concepts. The main characters inadvertently discovered non-Euclidean geometry when they found that the sum of angles on very large triangles amounted to more than 180 degrees. After working their grey matter for a long time they postulated that Flatland might be bent in an unseen direction. This turned out to be the case as Flatland was in fact stretched out along the surface of a giant sphere.

A fun thing for me to do while reading the book, was trying to imagine the equivalent of what the square was experiencing except in our dimension. Which direction is the fourth dimension pointing in? I suppose, just like for the square, it points out orthogonally from our own insides but in a direction that we can’t see. What happens when we move around in this new direction? If flipping a Flatlander results in him being “reversed”, then flipping a right-shoe 180 degrees in the fourth dimension should result in a left-shoe. Consequently, if a person were spun the same way, the individual would  feel unaltered but everything from books to cars would be backward. A fourth dimensional being could do things like remove objects from boxes without opening them, and untie knots without touching the ends of the rope. And maybe our world, just like Flatland, is folded into a 4th dimensional sphere so that if we had a big enough telescope, we could see ourselves from behind.

While reading Flatland, I couldn’t help but feel sorry for the inhabitants who could only “see” straight lines in every direction, but upon further reflection, the same limitation applies to us. We can only see a thin two-dimensional surface in every direction, and just like Flatlanders, we have to infer the thickness of a solid. When I see another person standing a bit away, I can’t be one hundred percent certain that they are not just a very well made cardboard cut-out. A fourth-dimensional being however, could see all of a person, including his insides and must view our human existence as infinitely mundane. What would the eye-ball of such a being look like!? I suppose that if our iris is a concave plane in the back of our eye, the iris of a 4D being would have to be a solid, except curved in the 4th dimension. Pretty spaced out! 

As one might guess from the title, this book offers a critique of religion and a particularly scathing one at that. Unfortunately, I don’t feel at liberty to delve into the specific topics covered in the different chapters, and an anecdote used early on in the book illustrates the author’s opinion on the matter. During a panel debate, Hitchens was asked to imagine himself in a strange city with the evening coming on and a large group of men steadily approaching. He was then asked whether he would feel more or less safe if he were to learn that the approaching men were returning from a prayer meeting. Hitchens answered that he had found himself in precisely that situation when visiting Belfast, Beirut, Bombay, Belgrade, Bethlehem, Baghdad, and many other cities. In most cases, it was proper to fear for ones life.

What irks me is that even well-meaning criticism on a topic relating to religion risks being viewed as being disrespectful. This is because people divide their values and beliefs into two categories: one based on their faculty of reason, and one based on faith which is not subject to questioning. While secular ideas can always grow and improve, religious ones are written in stone. If religion were a private phenomenon, like having an “invisible friend”, it would be one thing, but it permeates our relationships, schools, medicine, governments, militaries and much more.

As little as one hundred years ago, the majority of the world’s religious leaders quoted holy scriptures in support of slavery. Today they are actively preventing vaccination of the horrible child maiming disease polio. Their condemnation of contraceptive use is certainly not helping the eradication of AIDS either, and if the HIV virus is god’s punishment for homosexuality then it seems heavily biased toward the male variety. One of the most fantastic and promising forms of medical research, that of embryonic stem-cells, has unfortunately also been hampered by religious activists. Throughout history, from Aristotle, to Galileo, to Darwin, the castigation of science by religious leaders has been relentless.

Hitchen’s book not only discusses how religion ruins entire countries, but also how it can poison the individual. Holy books dictate what we may eat, whom we may love, how to treat our bodies, and even how to cut the body parts of babies. Walking on eggshells an entire lifetime might be possible if these sacred laws were limited to sinful physical actions, but that’s never where it ends. We are imposed with a particularly horrible form of dictatorship, namely one where thought crimes are forbidden. To say you’re not allowed to steal your neighbor’s wife is one thing, but if you even think that you would like to have one of your neighbor’s possessions, you’re on a path to eternal damnation. This type of restriction on reasoning exists by force in all religions, otherwise their dogma would not be able to persist. What is most unfortunate is that children are inoculated with these beliefs before they reach the age of reason, though perhaps that is the entire point.

Many evil things have been done in the name of god, and many good people are believers. Still, their good actions do not require the existence of an omnipotent being to be justified. When forced into a corner, people of religious conviction default to saying that if god does not exist, all evil is permissible. Perhaps though, what they’re really saying, is that to them all evil would be permissible.

Undoubtedly, one of the coolest Samurai of all time is the dual-blade wielding Shinmen Musashi, who went undefeated in over 60 duels and survived 6 wars. At age sixty, having ascended Mount Iwato, he faced the Buddha and decided to write a book on the art he had created in his Individual School of Two Swords.

Go Rin No Sho, as it was originally named, is divided into five scrolls reflecting five elements of combat. The Earth scroll discusses martial arts as a concept and strategy. Musashi expands on why he finds the katana to be an ideal weapon and that the core principle in battle is correct timing. In the Water scroll, correct spiritual alignment, physical bearing, and a unique style of sword fighting are explained in detail. Apparently, correctly gazing at an enemy and executing a flawless crimson leaves strike requires tremendous amounts of practice. As a complement, the Fire scroll discusses how to assess a situation in order to make the best use of one's tools. Things like shouting before attacking, standing with the sun behind you, and knocking an opponent into obstacles are appropriate tactics for gaining an advantage. The Wind scroll is concerned with finding wrongs, not only in alternative styles but more importantly, within yourself. Lastly, the scroll of the Void describes Musashi’s Zen-influenced thoughts on the warrior mindset.

The Book of Five Rings was quite fun to read because I found myself constantly conjuring up intense and picturesque Samurai battles in my mind, wondering how they might have played out in reality four-hundred years ago in feudal Japan. The way in which the seemingly unbeatable Musashi describes sword based combat to the death is fodder for the imagination!

“In single combat, if the enemy is less skillful than ourselves, if his rhythm is disorganized, or if he has fallen into evasive or retreating attitudes, we must crush him straight-away, with no concern for his presence and without allowing him space for breath.”

~ Shinmen Musashi no Kami Fujiwara no Genshin (1578 - 1645)
   新免武蔵守藤原玄信

In 1980, one year after being published, “GEB” won the Pulitzer Prize for general nonfiction and found itself on The New York Times bestseller list for several weeks running. Already then it had gained the reputation of being a book that  only “smart people” read which meant, naturally, everyone had to buy a copy. Unfortunately for them, I am convinced that there is absolutely no way the majority of GEB readers actually have the patience required to understand its mathematics, and consequenly most of its other content. So what is this book about? I would say it is a technically and aesthetically impressive attempt to explain the essence of consciousness.

The book is organized into twenty chapters, with each one preceded by a dialogue between “The Tortoise and Achilles”. Through charming wordplay and sophisticated analogies, these dialogues give an intuitive and tangible feel to the material that is examined by the author in the following chapter. Bach plays a large role in the content and the physical form of these dialogues. Many of his musical works were modulations of the same musical theme and serve to illustrate how many levels of information can permeate the same object. Escher paintings are even more explicit in their direct isomorphism to the concepts that Dr. Hofstadter discusses. For instance, in chapter XV the Dragon painting by MCE shows a powerful dragon trying to defeat his two-dimensionality by ripping a hole in his own picture and sticking his head through it. Unfortunately for the dragon, since he is illustrated in the form of a wood engraving he still ends up being two-dimensional despite his efforts. This serves elegantly to depict how a powerful formal system, no matter how hard it tries to defeat its ω-incompleteness by acquiring more axioms, will always contain a theorem which can not be proven within it.

What makes this book really unique is how it approaches the concept of sentience from so many angles.  Because it goes through such motley topics ranging from Zen Buddhism to the foundations of arithmetic, it might be tempting to dismiss the content as pseudo-scientific speculation, but to do so would be folly. Neuroscience has interesting insights into the brain but we need to distance ourselves from the notion that intelligence is directly related to the way we as human-beings function and interpret symbols. The author begins by examining self-reflection, or self-referencing, which seems to be something that a conscious being should be able to do. From the perspective of propositional calculus, we quickly find limitations in how accurately a system can describe itself; an arithmetic law which Kurt Gödel describes in his incompleteness theorems. This raises the question of whether our own minds might be built on simple formal rules and are “incomplete” in a similar manner? After all, neurons are quite simple in how they interact with the outside world. On a given stimulus they either fire a signal or don't.

To many, the flexibility of the human mind seems irreconcilable with the notion that it resides on rigid hardware. Though, if our self-understanding can't ever be truly complete then perhaps it's not so strange to feel that way. To make a logical example, assume you propose to someone “you can not consistently assert this sentence”. Whether the person asserts it or denies it, they would inevitably admit that they are not able to assert every single truth about themselves. Now if we make this example more concrete, more complex emergent phenomena which come from lower hierarchies of your brain, such as an intimate feeling of choice or want, would be equally inexplicable from within your own consciousness (formal systems). This fits well with the observation that we simply can’t force ourselves to describe the neural or even symbolic functions from whence something like ambition emerges from; it’s just there. So if we as humans are not able to deductively infer where these things come from, would we hold an AI at fault because a programmer could backtrack through sophisticated code to find some deterministic function at its core? The AI itself might describe a very profound feeling of free will, even though it does not understand exactly where it stems from...

While the complexity of the sentient mind is astounding, GEB does an absolutely fantastic job of discussing it. It’s not often you find a book that is both such a great pleasure to read and leaves you feeling motivated to read more math books!

What is the substance of happiness and how can it be attained? These questions have been debated for as long as recorded history, and in this short book Johan Norberg tries to shed light on the topic from two vantage points, a history-of-ideas perspective, and a modern research view.

If we look back at how our philosophical precursors talked about happiness, there's not so much of an evolution in theory as there is a constant lateral shifting of opinion. The two sides of thought in this case are whether happiness is attainable (on earth) or not. Buddhists, Christians, and even many individuals widely regarded as geniuses have all condemned life on earth as perpetual suffering. Lord Byron, wrote in 1850 that he felt sorry for his time’s “young goths” who lived depressed lives on purpose, hoping it would lead to some of that genius.

Well, life is not so bad. According to modern research, genes make up for about 50% of our predisposition towards happiness. The remaining 50% are up to you, and it seems as though the bulk of it more often produced rather than consumed. For instance, a fantastic athlete doesn't consume happiness solely in the form of a gold medal being awarded. He produces it the entire time while training hard and especially in fierce competition with opponents.

So remember, you are the forger of your own happiness.

In the year 335 B.C. lived a man so wise that for a thousand years he was simply referred to as The Philosopher. Aristotle (Ἀριστοτέλης) made such significant contributions to biology, physics, logic, politics, and more that it has been suggested he was the last person to know everything there was to be known in his own time.

While there probably exists enough literature on "the master of those who know" to fill a small library, this book includes selected works which were especially influential or are still being debated today. Included among others are chapters on metaphysics, logic, physics, psychology, ethics, politics, and poetics.

Aristotle sought to define the highest degree of abstraction concerning existence. In his opinion, objects of universal truth are the most difficult for people to understand because they are furthest removed from natural senses. This type of philosophy was a development away from a scientific picture centered in biology toward one based on mathematics, and is probably best exemplified in his chapters on logic. While Aristotle's predecessors placed much importance on dialectics and the correct use of words, Aristotle was the first person to formalize the syntax of logic. For instance, to show that circular reasoning can not be used as the basis of knowledge he argued in a way that computer science students today will instantly recognize. Circular reasoning holds that A→B and B→A are true. If we try to prove something new such as C, on the premises of A, then A→C is true. In other words, our original circular statement could be rephrased as, C→B and B→C are true. If we combine our previous C→B and B→A it follows that C→A. Lastly, if both C→A and A→C then A→A. This is essentially saying A is true because A is true.

Some modern individuals might still not be impressed and claim that as a species we have progressed far since those days and have more complicated issues to think about than the simpletons of the ancient world. Fortunately for those interested in history, Aristotle also wrote extensively on “softer” subjects.  Typical issues back in the day used to be how the youth was being irreversibly corrupted, how troublesome it was to have to exercise, that honorable men were increasingly hard to find, and that women had a long and selective memory in relationships. Sounds familiar! In all seriousness though, concentrated in the ideas of Aristotle are two thousand years worth of dinner-table discussions concerning the nature of happiness, morals, religion, and politics. While I think many of his ideas are still relevant today, what's more important is to understand and appreciate exactly how far he advanced the art of critical thinking. My key take-away from this book will be:

Knowledge is the understanding that something is the case.
Wisdom is the understanding of why.