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?

Stop losing weight! Don’t you know how bad exercising is for the environment?

Ever since Al Gore won a bunch of awards for his PowerPoint presentation on global warming, carbon emissions have been one of the biggest environmental hot topics. Proposed solutions for excessive carbon emissions include carbon credits, hybrid cars, and local sourcing. But people continue to ignore their personal carbon emissions. They really ought to consider this startling equation from an article in The British Medical Journal:


Well, it is not startling for anybody who hasn’t had high school chemistry for a few years. I’ll translate for those readers whose chemical notation is rusty: one fat molecule (a triglyceride in this example) combines with and 78 oxygen molecules to produce 55 carbon dioxide molecules, 52 water molecules, and energy. Even more simply: whenever your body burns fat, you take in oxygen and literally breathe away the pounds in the form of carbon dioxide. (Water is also released and excreted from the sweat glands or… elsewhere.) Every pound of fat you burn results in 2.8 pounds of CO2 emissions.

Frankly, I do not find any of that surprising. I have always thought it was awesome how plants take in CO2, separate the carbon from the oxygen, and turn it into fruit and leaves and all manner of plantstuffs. Trees turn air into wood. That’s amazing.

Some 250 years ago, Antoine Lavoisier showed that animal respiration is basically the opposite of that; animals consume plant matter, combine the carbon in it with oxygen, and breathe it out as CO2. However, distressingly few people understand this simple biological process. According to that BMJ article, most family doctors, dietitians, and personal trainers surveyed did not know where the fat goes when people lose weight. Most of them answered that fat is simply converted into heat or energy. As if the law of conservation of matter doesn’t apply to beer guts!

Obviously, carbon emissions from losing weight are not the same as carbon emissions from burning coal or gasoline. The carbon in fossil fuels has been locked away for millions of years, and the carbon in your paunch has only been locked away since the last holiday season. Also, it is likely that there are significantly more important factors in climate change than carbon emissions. However, feel free to use this as an excuse for skipping leg day.

Wachusett Light IPA

Beer of the week: Wachusett Light IPA – If you insist on losing weight, you may be tempted to drink “light” beer. The brewers of Wachusett Light IPA claim that it is America’s first light IPA. The beer is hazy orange and has a malty aroma with some of the typical IPA hops. The flavor is a bit more subdued than most IPAs, without the strong punch of hops that one expects from American IPAs. The finish is a bit on the watery side. After swallowing, there is a bit of bite from the hops, but this beer generally light on the flavor. Overall, however, I think this is a decent beer. I get why they call it a light IPA, but I think I would call it it a session pale ale. Of course, I’m not in marketing.

Reading for the week: Elements of Chemistry by Antoine Lavoisier – This excerpt from Lavoisier’s greatest work is somewhat dry, but it presents a few interesting features. First, Lavoisier explains why ice stays ice cold until it is completely melted even though almost every other substance we know of will warm up (or cool down) gradually. Secondly, he introduces a device called a calorimeter for the measuring of heat. The device is interesting in itself, but the name is also worth a bit of thought. Lavoisier defends mixing Latin (calor – heat) and Greek (metron – measure) because “in matters of science, a slight deviation from strict etymology, for the sake of giving distinctness of idea, is excusable.” He then shoves a guinea pig inside a sphere of ice to measure how much heat it produces.

Question for the week: Lavoisier’s word calorimeter is not the only Latin-Greek hybrid out there. Notable hybrid words include homosexual, television, automobile, and claustrophobia. Is there really something objectionable about mixing and matching root words this way?

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?

Le Début et la Fin du Monde

As the days get sunnier and warmer, I am reminded of a classic urban legend:

A woman went shopping for groceries. After she finished at the grocery store, she placed her purchases on the back seat of her car in the parking lot. She had a few more errands to run, so she left the groceries in the car while she went about her business. When she returned and entered the car, which had been warmed considerably by the midday sun, she heard a loud BANG and suffered a blow to the back of the head. She reached back to feel the point of impact and found find a gooey mass. Naturally she started to panic. With both hands she attempted to hold her brains in place and screamed for help. When other shoppers came to see what was wrong, she said that she had been shot in the head and that her brains were exposed. Upon closer examination, her brains were safely in place, but she was desperately pressing warm biscuit dough into her hair. Apparently, the heat in the car had caused a tube of biscuit dough to pop, splattering its contents on the woman. One of the “rescuers” told her, “Ma’am, you will be alright. You’ve been shot by the Pillsbury Doughboy.”

This story is a rather amusing little farce, but it says something important about sensory perception and the disconnect between our personal experience and external stimuli. The lady in the story felt warm dough on her head, but her senses did not convey to her mind the reality of the situation. The sense of touch, even when functioning properly, never totally captures the nature of the thing touched.

Descartes used a similar, although far less amusing story to make this very point. A soldier returning from the field feels a sharp pain in his side and thinks that he has suffered a wound that he did not notice in the heat of battle. Upon closer inspection, however, a strap on his armor simply became twisted, causing a buckle to dig into his side. If senses accurately and fully conveyed the nature of stimuli, then the soldier would have known immediately that the pain in his side was caused by the buckle.

To be fair, our senses are pretty trustworthy most of the time and we combine all sorts of additional context and sensory input to determine what is really going on. We are constantly and effortlessly making judgments based on our perceptions and that frees up our limited brainpower to work on more complicated questions. Questions such as what beer to drink.


Beer of the week: Fin du Monde – French-Canadian brewery Unibroue makes some very well regarded beers. Fin du Monde is probably their best known brew, a Belgian-style tripel. It smells of yeast and cider. The body is remarkably smooth and the taste is outstanding. There are hints of pepper and the considerable alcohol content (9%) makes itself known at the end. The aftertaste is similar to that of a dry cider, encouraging sip after sip.

Reading of the week: Le Monde by Rene Descarts – Although Descartes apparently intended to write a complete philosophy of the world, his work was never completed. Instead the title Le Monde (“The World”) was attached after his death to the first part of that project, Treatise on Light.

Question of the week: Humans are extremely visual, and our trust in sight as a reliable source of information is evident in the idiom “seeing is believing.” But we have all experienced optical illusions, so we know that sight cannot always be trusted. Descartes writes that “Of all our senses, touch is the one considered least deceptive and the most secure.” Is he right? Which sense most reliably presents our mind with the reality of the outside world?

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: