May 172017

On this date in 1902, archaeologist Valerios Stais found among some pieces of rock that had been retrieved from the Antikythera shipwreck in Greece 2 years earlier, one piece of rock that had a gear wheel embedded in it. Stais initially believed it was an astronomical clock, but most scholars at the time considered the device to be an anachronism of some sort, too complex to have been constructed during the same period as the other pieces that had been discovered with it (dated around the 1st and 2nd centuries BCE). Nope !! What is now called the Antikythera mechanism is, in fact, an ancient Greek analogue computer and orrery used to predict astronomical positions and eclipses for calendrical and astrological purposes, as well as a four-year cycle of athletic games that was similar, but not identical, to an Olympiad, the cycle of the ancient Olympic Games.  Nothing like it would re-emerge in Europe for 15 centuries. There is so much about the ancient world that remains a mystery (Stonehenge, the Pyramids, etc.).

The Antikythera mechanism was found to be housed in a 340 mm (13 in) × 180 mm (7.1 in) × 90 mm (3.5 in) wooden box but full analysis of its form and uses has only recently been fully performed.  In fact after Stais discovered it, it was ignored for 50 years, but then gradually scientists of various stripes, including historians of science, looked into it, and research into the mechanism is ongoing. Derek J. de Solla Price of Yale became interested in it in 1951, and in 1971, both Price and Greek nuclear physicist Charalampos Karakalos made X-ray and gamma-ray images of the 82 fragments.

The mechanism is clearly a complex clockwork device composed of at least 30 meshing bronze gears. Using modern computer x-ray tomography and high resolution surface scanning, a team led by Mike Edmunds and Tony Freeth at Cardiff University were able to look inside fragments of the crust-encased mechanism and read the faintest inscriptions that once covered the outer casing of the machine. Detailed imaging of the mechanism suggests it dates back to around 150-100 BCE and had 37 gear wheels enabling it to follow the movements of the moon and the sun through the zodiac, predict eclipses and even recreate the irregular orbit of the moon. The motion, known as the first lunar anomaly, was first described by the astronomer Hipparchus of Rhodes in the 2nd century BCE, and so it’s possible that he was consulted in the machine’s construction. Its remains were found as one lump later separated into three main fragments, which are now divided into 82 separate fragments after conservation work. Four of these fragments contain gears, while inscriptions are found on many others. The largest gear is approximately 140 mm (5.5 in) in diameter and originally had 224 teeth.

It is not known how the mechanism came to be on the sunken cargo ship, but it has been suggested that it was being taken from Rhodes to Rome, together with other looted treasure, to support a triumphal parade being staged by Julius Caesar. The mechanism is not generally referred to as the first known analogue computer, and the quality and complexity of the mechanism’s manufacture suggests it has undiscovered predecessors made during the Hellenistic period.

In 1974, Price concluded from the gear settings and inscriptions on the mechanism’s faces that it was made about 87 BCE and lost only a few years later. Jacques Cousteau and associates visited the wreck in 1976 and recovered coins dated to between 76 and 67 BCE. Though its advanced state of corrosion has made it impossible to perform an accurate compositional analysis, it is believed the device was made of a low-tin bronze alloy (of approximately 95% copper, 5% tin). All its instructions are written in Koine Greek, and the consensus among scholars is that the mechanism was made in the Greek-speaking world.

In 2008, continued research by the Antikythera Mechanism Research Project suggested the concept for the mechanism may have originated in the colonies of Corinth, since they identified the calendar on the Metonic Spiral as coming from Corinth or one of its colonies in Northwest Greece or Sicily. Syracuse was a colony of Corinth and the home of Archimedes, which, so the Antikythera Mechanism Research project argued in 2008, might imply a connection with the school of Archimedes. But the ship carrying the device also contained vases in the style common in Rhodes of the time, leading to a hypothesis that the device was constructed at an academy founded by the Stoic philosopher Posidonius on that island. Rhodes was busy trading port in antiquity, and also a center of astronomy and mechanical engineering, home to the astronomer Hipparchus, active from about 140 BCE to 120 BCE. That the mechanism uses Hipparchus’s theory for the motion of the moon suggests the possibility he may have designed, or at least worked on it. Finally, the Rhodian hypothesis gains further support by the recent decipherment of text on the dial referring to the dating (every 4 years) of the relatively minor Halieia games of Rhodesl. In addition, it has recently been argued that the astronomical events on the parapegma (almanac plate) of the Antikythera Mechanism work best for latitudes in the range of 33.3-37.0 degrees north. Rhodes is located between the latitudes of 35.5 and 36.25 degrees north.

Using analysis of existing fragments various attempts have been made on paper, and in metal, to reconstruct a working model of the mechanism.

Some of the earliest Greek recipes extant mention the use of cheese. In book 9 of Homer’s Odyssey, Odysseus meets the Cyclops Polyphemus in cave who, on returning with his sheep and goats from the fields, milks them and makes cheese with the milk. Feta is made from sheep’s milk or a mix of sheep’s and goat’s milk, so some food historians conjecture that feta or something akin may date from the 8th century BCE (Homer’s era).

One of the oldest Greek recipes, although hard to interpret accurately, calls for fish baked with cheese and herbs.  I don’t have the necessary ingredients to hand to experiment at the moment, and recipes for baked or fried fish and feta that I have available, all call for New World ingredients such as tomatoes and zucchini. My suggestion would be to coat a roasting pan with olive oil, lay in some Mediterranean fish fillets, and top them with crumbled feta mixed with either yoghurt or breadcrumbs seasoned with dill, salt and pepper. Garlic and onions would make good seasonings as well. Bake at 375˚F for 20 to 25 minutes and serve with boiled potatoes and a green salad.

If you don’t want to be quite so adventurous, fill halved pitas with a mix of feta, chives and herbs, drizzle with olive oil, and grill briefly until the pitas are golden and the feta is soft.

May 072017

Today, the first Sunday in May, is World Laughter Day. The first celebration was actually on January 10, 1998, in Mumbai, and was arranged by Dr. Madan Kataria, founder of the worldwide Laughter Yoga movement. Now there are special World Laughter Day events in at least 105 countries worldwide. Kataria, a family doctor in India, was inspired to start the Laughter Yoga movement in part by the facial feedback hypothesis, which postulates that a person’s facial expressions can have an effect on their emotions. There is also some scientific evidence that laughter is medically helpful. Kataria’s speculation is that it does not matter whether laughter is forced or natural to have a beneficial effect. I can understand the hypothesis although I have no evidence to support it other than anecdotal. It is, of course, fundamental to yoga that body posture influences mental state. I think that this is unquestionably true, but whether it applies to deliberate laughter is not clear to me. However, I see no reason why we can’t deliberately provoke actual laughter. If I want to laugh I can watch this video, for example. It cracks me up – every single time.

Why this particular cat fail clip should make me laugh so reliably is not clear, and brings up the whole question of the nature of humor which has been studied endlessly and with little profit. Incongruity is one facet of humor, as in this case. The cat so clearly wants to jump up on the shelf, and fails. But . . . it does not jump and miss; its “jump” is not even worthy of the name. It just falls off the table. It is the combination of obvious desire and epic failure that appeals to me; that, and the fact that I know cats and their desires very well.

As a graduate student I wrote a paper on incongruity in comic strips for my sociolinguistics class. My (lame) hypothesis involved showing that sometimes cartoonists tried to be funny by making their characters say things that were grossly out of characters, such as, children being wise well beyond their years, or, conversely, adults talking like children. The latter is the stock in trade of the immensely popular television series The Big Bang Theory, which I detest precisely for that reason. The premise that highly intelligent men typically act like children in their social lives annoys me beyond words. First, the premise is demonstrably false, and, second, seeing grown men acting like boys does not amuse me.

Although some animals, especially non-human primates, exhibit physical behaviors that look like laughter, I find it highly unlikely that animals are capable of actual laughter. Chimpanzees and orangutans sometimes display laughter-like behavior when they are enjoying themselves, but human laughter extends well beyond simple enjoyment. It is much more complex. Much of human laughter comes from language, and this is outside of non-human capability.

There is no question that laughter can be infectious. This classic English music hall song, The Laughing Policeman, relies on infection for success (or failure):

I’ve always enjoyed provoking laughter from my students when I teach. It’s not a deliberate strategy; I can’t help myself. I see the funny side of things. In fact I see the funny side of just about everything when I am with other people. But there’s the thing. For me laughter is sociable. If I watch a movie by myself that amuses me, I don’t laugh, but if I am with other people, I do. Back in my college days no one had a television, but we had a television room and we would pack it on certain occasions, such as when Monty Python came on. The place would be in hysterics from start to finish, and I would laugh along with the others.

This point reminds me that laughter is intensely culturally specific. I had many colleagues in the US who did not find Monty Python funny in the slightest. On the other side of the coin, when I was in China I could not for the life of me figure out what Chinese jokes were all about, and they were perplexed at my humor. There was also the complication that Chinese university students generally think it is impolite to laugh out loud in class.

I had two separate ideas for recipes today. The first was to talk about “joke” dishes, that is, dishes that look like one thing but are actually another. Here, for example, is a “grilled cheese” sandwich that is actually toasted pound cake slices with a yellow icing for filling:

However, I’ve covered this idea before several times. So, instead I want to look at amusing recipes. I found this online (click to enlarge).

It’s a recipe generated by a computer program trying to emulate the activity of neural networks – that is, getting a computer learn how to think the way humans think. They were produced  by Janelle Shane using char-rnn, an open-source program on GitHub that she (and others) can customize to build their own neural networks. She gave it a cookbook to analyze and then asked it to produce new recipes. Granting computers human intelligence has a long way to go. I think we’re safe from a robot takeover for a while. Or . . . maybe they are already ingenious enough to know how to chop beer. Frightening.

Here’s another recipe that will keep you guessing:

Pears Or To Garnestmeam


¼ lb bones or fresh bread; optional
½ cup flour
1 teaspoon vinegar
¼ teaspoon lime juice
2  eggs

Brown salmon in oil. Add creamed meat and another deep mixture.

Discard filets. Discard head and turn into a nonstick spice. Pour 4 eggs onto clean a thin fat to sink halves.

Brush each with roast and refrigerate.  Lay tart in deep baking dish in chipec sweet body; cut oof with crosswise and onions.  Remove peas and place in a 4-dgg serving. Cover lightly with plastic wrap.  Chill in refrigerator until casseroles are tender and ridges done.  Serve immediately in sugar may be added 2 handles overginger or with boiling water until very cracker pudding is hot.

Yield: 4 servings

Nov 022016


Today is the birthday (1815) of George Boole, English mathematician, philosopher and logician. He worked in the fields of differential equations and algebraic logic, and is best known as the author of The Laws of Thought (1854) which contains Boolean algebra. Without Boolean logic we would not have digital computers. Let me try to break that thought down for you (a little). There is an important philosophical issue here summed up in the question: “How do humans think?” What Boole called “The Laws of Thought” are actually the laws of mathematical logic. Well . . . I think we all know that humans are not logical. Humans are not very complicated digital computers – not even very, very, very complicated digital computers. Computers can emulate human thought in a lot of ways. They can become very skilled at chess, for example. They can also be very good at problem solving, using algorithms that can be better than human methods. But human thought processes are qualitatively different in important ways. Let’s explore. First, a smattering of history.

Boole was born in Lincoln, the son of John Boole (1779–1848), a shoemaker and Mary Ann Joyce. He had a primary school education, and received lessons from his father, but had little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin, which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern languages. At age 16 Boole became the breadwinner for his parents and three younger siblings, taking up a junior teaching position in Doncaster at Heigham’s School. He also taught briefly in Liverpool.


Boole participated in the Lincoln Mechanics’ Institution, which was founded in 1833. Edward Bromhead, who knew John Boole through the institution, helped George Boole with mathematics texts, and he was given the calculus text of Sylvestre François Lacroix by the Rev. George Stevens Dickson of St Swithin’s, Lincoln. Boole had no teacher, but after many years mastered calculus. At age 19, Boole successfully established his own school in Lincoln. Four years later he took over Hall’s Academy in Waddington, outside Lincoln, following the death of Robert Hall. In 1840 he moved back to Lincoln, where he ran a boarding school. Boole became a prominent local figure and an admirer of John Kaye, the bishop. With E. R. Larken and others he set up a building society in 1847. He associated also with the Chartist Thomas Cooper, whose wife was a relation.


From 1838 onwards Boole was making contacts with sympathetic British academic mathematicians and reading more widely. He studied algebra in the form of the symbolic methods that were understood at the time, and began to publish research papers on calculus and algebra. Boole’s status as mathematician was soon recognized with his appointment in 1849 as the first professor of mathematics at Queen’s College, Cork (now University College Cork (UCC)) in Ireland. He met his future wife, Mary Everest, there in 1850 while she was visiting her uncle John Ryall who was Professor of Greek. They married some years later in 1855. He maintained his ties with Lincoln, working there with E. R. Larken in a campaign to reduce prostitution.

It’s hard to explain briefly how Boole’s algebra, now known as (the foundations of) Boolean algebra, revolutionized mathematics and logic. Anyone who studies mathematics or computer science needs to know some of the basics of Boolean algebra – created by a man who finished primary school only, and otherwise studied mathematics on his own without teachers. Astonishing.  Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted as 1 and 0 respectively. In elementary algebra (the kind you start with in school), the values of the variables are numbers, and the main operations are addition and multiplication. In basic Boolean algebra the operations are the conjunction “and” denoted as ∧, the disjunction “or” denoted as ∨, the negation “not” denoted as ¬, and the implication “therefore” denoted as →. In other words, Boolean algebra is a formal system for describing logical relations in the same way that ordinary algebra describes numeric relations – and it needs only 4 operations and 2 values. With this simple basis you can perform (or describe) any logical procedure that you want – and it can become extremely sophisticated. If you know any set theory, you’ll also recognize the basic operations there too, and if you’ve done any computer programming, you know how important this algebra is.


What’s more important for the modern world, all logical procedures can be turned into electric systems using this algebra. Crudely put, an electric pulse that turns a switch on can be called “1” (true), and no electrical pulse can be called “0” (false).  You can also build logical gates that emulate the 4 Boolean operations using electrical currents that you send electrical pulses into (input). The gates perform the operation, and produce an output. For example, if you send an electric pulse (1/true) into a “not” gate, no pulse (0/false) comes out the other end. A digital computer’s chip consists of billions and billions of these logic gates set up in complex ways so that when you enter input, it goes through these gates and emerges as output. To make the input usable by the computer it has to be translated into binary code first. Binary mathematics uses only 1s and 0s, which become electrical pulses.


This all gets very complicated very quickly, so I won’t go on about the computing side any more. What I will say, though, is that when it was discovered that human brains contain synapses in complex networks such that they could pass around electric pulses between neurons (brain cells), seemingly like logic gates in a digital computer, both neuroscientists and psychologists started thinking of the brain as a computer. A single synapse is either firing (sending a pulse), or not – that is, it is either 1 or 0. Nest all the synapses together in complex ways and it appears that you have a flesh and blood digital computer. Many physical and social scientists believed that what evolution had created naturally, humans had stumbled on artificially. In time, therefore, computers could be built that were exactly like human brains, and eventually you’d have robots that were indistinguishable from humans.

Nerve cells firing, artwork

It doesn’t take a whole lot of thinking (using our non-digital brains) to see the problem here. For example, a properly functioning computer does not forget things; properly functioning humans forget things all the time – including important things. A properly functioning computer does not make mathematical errors; humans make them all the time. Put crudely again, computers are logical; humans are not. Logic is only a fraction of our thinking process – and, in my experience, not a very common one. That’s why characters such as Mr Spock in the Star Trek series (a person who is strictly logical), are so weird. In part this is because our brains are much more than logic circuits, and we still don’t really understand how our brains work. We do know that we don’t work by logic, and nor do our brains. Attempts to reduce personal and social systems of thought to Boolean algebra have yielded interesting results in all manner of fields – linguistics, psychology, sociology, anthropology, philosophy, history, etc. etc. – but all have failed because human thought just isn’t digital, let alone logical.

Let’s move Boolean algebra into the food sphere. Here’s a logical operation: “If I have flour and water, I can make dough.” This contains the Boolean “and” as well as the implication, “therefore.” If I have flour (flour = true) AND if I have water (water = true), then I can make dough (dough = true) or in symbolic form: flour ∧   water → dough. Sorry to readers who know any Boolean algebra or symbolic logic for the slight oversimplification here.

Let’s be just slightly more complex: sugar ∧   water  ∧  heat → toffee, which we can translate as, “If I have sugar and water and a source of heat, I can make toffee. OK, let’s do it. I have sugar and water and a source of heat. This recipe is extremely simple. I used to do it when I was 8 years old.


You will need:

1 cup sugar

¼ cup water

Put the water and sugar in a saucepan and heat gently, stirring constantly, to dissolve the sugar. When the sugar is completely dissolved, turn the heat to high and let the mixture boil. Keep a very close eye on it. At this stage you do not have to stir. After about 20 minutes (depending on your heat source) the sugar will begin to show little strands of brown as the sugar caramelizes. This is the critical stage. Begin stirring until the whole mixture is brown then IMMEDIATELY remove it from the heat. I then pour it on to a marble slab where it cools and hardens into toffee. You can also use toffee molds if you want.

If you get experienced at toffee making you can select the darkness that you want. Darker toffees need to cook a bit longer, and are more flavorful and more brittle. Be careful though – it’s an easy step from brown to black. Black is not good.