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?

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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?

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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: