Proofs of Prophesy

It seems that primitive peoples had a god for practically every natural phenomenon. Even the culturally and academically advanced Greeks and Romans had a literal pantheon of gods to explain everything from the daily rising of the sun to the changes of the seasons. (To be sure, there were certainly ancient philosophers who did not believe in the literal existence of the Olympians. But one of the charges against Socrates was refusal to recognize the official gods of the city, so they still took that stuff seriously.) It may well be that the eventual predominance of monotheism in the western world was in part due to advances in natural philosophy.

As we humans came to understand the world better, fewer and fewer gods were needed to explain all of the individual aspects of our reality. The more we learn about the nature of our universe, the less we need myths to explain the world around us. Inevitably, some people take this line of thought to its logical limit: as human understanding increases, we find that there is no need for any theistic explanations at all.

A counter argument that has been advanced is that our growing understanding of the world is itself proof of God’s assistance. The eighth century theologian Abu Hatim al-Razi asserts that all of the great thinkers throughout time were actually prophets. Divine inspiration, he argues, is the only way to explain the genius that created Euclid’s geometry or Ptolemy’s astronomy. Knowing his own intellectual powers, he cannot believe that such tremendously insightful works can be the work of unaided humans. There is some serious appeal to that argument; I don’t see how I could ever produce something as great as Ptolemy’s Almagest.

Still, we are constantly learning more and coming to greater and greater understandings. Consequently, all great geniuses in natural philosophy are doomed to be overtaken. In the face of non-Euclidean geometry and modern astronomy, Euclid and Ptolemy look like poor prophets indeed. What good are is the prophets Newton or Darwin if their systems are sure to be found defective down the line? Can it really be divine inspiration if it invariably comes up short of later human understanding?

The final rejoinder must be that prophets never tell the whole truth or explain everything clearly. Each generation must have its own sages and prophets to build upon the divine revelations of their predecessors.  So who can say that Lobachevsky or Stephen Hawking are not also divinely inspired?


Beer of the Week: Odyssey Imperial IPA – Throughout Homer’s Odyssey, storms, shipwrecks, deaths, and other events are attributed to the wills of the gods. So a beer called Odyssey seems like a good choice for this post. This Imperial IPA from Sly Fox Brewing Company is delicious. The lighting in this photo is a bit off; the beer is actually more amber in color. It has a nice thick head that leaves plenty of lacing on the glass. Odyssey is quite bold, with strong, flavorful hops that totally dominate the flavor. And the hops has to be strong to cover the 8.4% alcohol. Anybody who drinks enough of this beer is surely in for an adventure.

Reading for the Week: The Madman by Friedrich Nietzsche – The famous quote “God is dead” comes from this reading. This parable(?) from The Gay Science hints at the problems of a post-religious society. The atheists in the story do not understand the ramifications of the death of God, hence the messenger of God’s death is called “the madman.”

Question for the week: Is there anything compelling about Abu Hatim al-Razi argument that all of our geniuses are divinely inspired? Or is he just moving the goalposts?

Heavy Lifting

Plenty of people advocate physical exercise in the morning. Exercise in the morning has a way of waking up the body. After a morning run or weight lifting session, one feels energized and alert and ready to face the day.

My morning routine of late has included not only physical exercise, but also mental exercise. After I run and shower, I sit down with my copy of The Bones. The Bones is a pocket companion to Euclid’s Elements of Geometry. It contains all of the propositions and diagrams of the Elements, without the extended proofs. Without the proofs in front of me, I am forced to remember (if I am lucky) or work though how the propositions function and build upon each other. It is occasionally quite difficult, but always a great mental exercise to prepare my mind for an active day.

In the introduction to his famous translation of the Elements, Oliver Byrne claims that the “sublime science” of geometry is “better calculated than any other to call forth the spirit of inquiry, to elevate the mind, and to strengthen the reasoning faculties.” Is it any wonder that starting the day with a few propositions serves as the perfect intellectual exercise to invigorate the mind?


Beer of the week: La Trappe Quadrupel – The International Trappist Association certifies beers as “Authentic Trappist Products.” To qualify the beers must be brewed inside the walls of a monastery, any proceeds that go beyond maintenance of the monks and the monastery must go to charity, and the beer has to be of “irreproachable quality.” And this beautiful, red/amber ale is the first “Authentic Trappist” reviewed for this blog. As a quadruple, this ale has an alcohol content of 10%. The flavor is rich and full, with notes of very ripe fruit. The alcohol does make itself felt in the end, but not in a harsh way.

Reading for the week: The First Six Books of the Elements of Euclid, translated by Oliver Byrne – Like Trappist beer, Oliver Byrne was born in the Netherlands. In his introduction Byrne explains that his intention in translating Euclid is to “assist the mind in its researches after truth.”

Question for the week: There are also those who advocate exercise at other times of day, are there advantages to performing the mental labor of geometry at the end of the day?

Linguistic Anarchy

I have become something of a linguistic anarchist. The way I see it, the English language does not have rules. Moreover, it does not need rules. As a matter of fact, the most popular “rule book” for English writing is Strunk and White’s Elements of Style, the very title of which indicates that it is not a book of rules but a stylistic guide. One is not “wrong” if he does not follow Strunk and White, he is simply “unfashionable.”

That said, children ought to be taught “proper spelling” and “proper grammar.” Before one can be a free thinker and an innovator, one must have a firm grasp of what they are rebelling against. This opinion of mine extends to the fine arts as well. I have a deep-seated distrust of extremely novel painters and musicians who did not first demonstrate their ability to master more conventional forms. Dali and Picasso are both extremely interesting to me and they are made much more so by the fact that they established themselves as traditionally talented before their work became more heterodox. It shows that their art is not simple novelty, but innovation.

As it turns out, the same principles may apply to mathematics. Euclid’s geometry is every bit as artificial as any attempt to construct an “English grammar.” Whereas the concepts of number seem inherent (eg. the number 2 can correspond with two “real” objects,) The principles of Euclidean geometry do not correspond with anything other than definitions and axioms. As Einstein writes in his book Relativity, “The concept “true” does not tally with the assertions of pure geometry, because by the word “true” we are eventually in the habit of designating always the correspondence with a “real” object;” there are no tangible “straight lines” or “points” or “circles” as defined by Euclid.

And yet, it is essential that an education in geometry start with these “artificial” constructs in the same way that an education in English should start with grammar and spelling, or an education in music should start with scales. Eventually, the most gifted mathematical minds can move beyond Euclid, but it is impossible to make any serious headway as an innovator without knowing what one’s jumping off point is.

Beer of the Week: Viru – This beer comes in an octagonal pyramid bottle. Not a “true” octagonal pyramid, but pretty cool none the less. I have no reason to think that I had ever seen or touched anything from Estonia before purchasing this beer. In fact, the extent of my knowledge about Estonia consists of being able to identify the flag (it is black, blue and white) and the knowledge that they are often grouped with Latvia and Lithuania. Now I know one more thing: their beer is of a rather middling quality.  It is very, very pale and exhibits no extraordinary features. It is nothing but a standard macro-brew in a very silly bottle. It is hard not to judge a country by the quality of their beer, but I’ll give Estonia a pass since they were under Soviet rule for so long… I think.

Reading for the Week: Relativity by Albert Einstein, Section 1 – The beginning of this book is a great teaser for what is to come. Einstein refers to Euclid as “the magnificent structure, on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers.” And then he questions the “truth” of that edifice and indicates that by the time he is done, “we shall see that this “truth” is limited, and we shall consider the extent of its limitation.”

Question for the week: Do you believe that English has rules? Maybe Steven Fry can help free you from that: