One of the great debates in the history of mathematics was that between Isaac Newton and Gottfried Leibniz. Newton had invented (or discovered, if you please) calculus, but did not publish any works on the subject. Some time thereafter, Leibniz also invented calculus, but he had his work published. Newton accused Leibniz of having stolen his idea, while Leibniz maintained that he had reached his conclusions independently.
It is possible, of course, for separate individuals to discover or invent the same methods independently. (In nature, an analogous process exists called convergent evolution, and it is freaking awesome.) Perhaps the most important aspect about language is that it allows humans to advance technologically. Because Leibniz was able to write down his method for calculus and share it with others, every future mathematician is spared the effort of inventing calculus herself.
And this is true of more than just mathematics. How many times must the wheel have been invented, lost, and reinvented until it was effectively passed down to enough people that we will never again have to re-invent the wheel? Likewise, beer may have been independently invented at various times around the world, but if every new batch could only be brewed by re-discovering fermentation, how could we ever have achieved the tremendous selections of beers available today?
The fantasy of an individual human in the state of nature (totally outside of society) is a popular notion. It features prominently in the philosophical works of Locke, Rousseau, and others. It also appears in fictional works such as Kipling’s Jungle Book and Defoe’s Robinson Crusoe. A philosophical and fictional book that is an excellent example of the theme is Philosophus Autodidactus (or Ḥayy ibn Yaqẓān) by Ibn Tufail. The main character of that book is a foundling that is nursed and raised by a female deer. Over time, this man outside of society is able to discover a great deal about the world. But while the story is meant to show the capacity of humans to learn from their surroundings, I think that it unreasonably downplays the greatest advantage that we have when it comes to learning: the ability to learn from others so that each individual does not have to re-discover everything that has previously been learned before he can go any further.
Beer of the week: Carta Blanca – Ibn Tufail’s writing is steeped in the epistemological concept of “tabula rasa”, a Latin phrase meaning “blank slate.” So it seems that Carta Blanca (Spanish for “white/blank card”) should be a good pairing. This Mexican beer is pretty good for what it is. It is a clear, refreshing lager. And, like so many Mexican beers, it really shines with some salt and lime. And home-made fish tacos.
Reading for the week: Philosophus Autodidactus by Ibn Tufail – Considering the fact that this book is about an entirely self-taught man, it is somewhat ironic how much of an influence it has been on so many important thinkers in the generations after it was first published in the early 12th century. In this excerpt, the title character learns about fire and performs crude experiments in biology.
Question for the week: Ibn Tufail’s character discovers not only a great deal in the field of natural philosophy, but he also discovers the precepts of natural religion. How far could an intelligent individual get if he had to start accumulating knowledge independently from the beginning?
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.
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?
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?
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?