Nov 162016


Today is Icelandic Language Day (Dagur Íslenskrar tungu), a day commemorating the Icelandic language and drawing attention to its potentially endangered status. This date was chosen to commemorate the birthday of Jónas Hallgrímsson, a locally famous Icelandic poet and naturalist of the 19th century. Icelandic Language Day was first celebrated in 1996 in response to research showing that Icelandic was one of four major European languages that are losing ground. I think this is somewhat alarmist in comparison with minor languages. There are around 250 languages spoken in Europe, 225 of which are endangered (139 languages from the past are already extinct). To be classified as endangered a language must be restricted to grandparents of the present generation, and rarely spoken outside the home. Usually children and grandchildren of the older generation can understand the language, but few speak it or have any interest in passing it on. Icelandic is the official language of Iceland, so I doubt there is any real threat to its existence, but there are only about 330,000 native speakers, the vast majority of whom live in Iceland.

The real problem with Icelandic (along with Latvian, Lithuanian and Maltese) is not with the spoken language but with digital support in the computer age. Ever tried finding an Icelandic keyboard? Digital support includes phone apps, spell checkers, automatic translators, and the like. You might be inclined to scoff, but these are genuine problems in the digital age when more and more people in younger generations rely on this kind of support.


Icelandic has an interesting history. Icelandic language began in the 9th century when the settlement of Iceland, mostly by Norwegians, brought a dialect of Old Norse to the island. The oldest preserved texts in Icelandic were written around 1100. The majority of these texts are poems or laws, preserved orally for generations before being written down. The most famous of these, written in Iceland from the 12th  century onward, are the Icelandic Sagas, the historical writings of Snorri Sturluson, and the Eddas.

The language of the era of the sagas is known as Old Icelandic, a dialect of (Western) Old Norse, the common Scandinavian language of the Viking era. Old Icelandic was, in the strict sense of the term, Old Norse with some Celtic influence. The Danish rule of Iceland from 1380 to 1918 had little effect on the evolution of Icelandic, which remained in daily use among the general population: Danish was not used for official communications. The same applied to English during the British (and later US) occupation of Iceland during World War II.


Though Icelandic is considered by linguists to be more archaic than other living Germanic languages, especially in its morphology and other grammatical aspects, as well as in its lexicon, the language has nevertheless been subject to some important changes. The pronunciation, for instance, changed considerably between the 12th and 16th centuries, especially that of vowels. Nevertheless, written Icelandic has changed relatively little since the 13th century. As a result of this, and of the similarity between the modern and ancient grammar, modern speakers can still understand, more or less, the original sagas and Eddas that were written about 800 years ago. This ability is sometimes mildly overstated by Icelanders themselves, most of whom actually read the Sagas with updated modern spelling and footnotes—though otherwise intact.

During the 18th century Icelandic authorities implemented a stringent policy of linguistic purism. Under this policy, a group of writers and linguists was put in charge of the creation of new vocabulary to adapt the Icelandic language to the evolution of new concepts, without resorting to loan words as many other languages had done. A few old words that had fallen into disuse were updated to fit in with the modern language, and neologisms were created from Old Norse roots. For example, the word rafmagn (“electricity”) literally means “amber power” – a calque of the Greek elektron (“amber”). Similarly the word sími (“telephone”) originally meant “wire,” and tölva (“computer”) is a portmanteau of tala (“digit” or “number”) and völva (“female fortuneteller”).


My interest in Icelandic (in translation) concerns the two Eddas (commonly called the Poetic Edda and the Prose Edda) and the Icelandic Rune Poem. The Poetic Edda, also known as Sæmundar Edda or the Elder Edda, is a collection of Old Norse poems from the 13th century Icelandic medieval manuscript Codex Regius (“Royal Book”). Along with the Prose Edda, the Poetic Edda is the most expansive source on the Norse gods. The first part of the Codex Regius preserves poems that narrate the creation and foretold destruction and rebirth of the Old Norse realm of the gods as well as individual stories about the Norse deities. The poems in the second part narrate legends about Norse heroes and heroines, such as Sigurd, Brynhildr and Gunnar.

The Prose Edda, sometimes referred to as the Younger Edda or Snorri’s Edda, is an Icelandic manual of poetics which also contains many stories of the gods. Its purpose was to enable Icelandic poets and readers to understand the subtleties of alliterative verse, and to grasp the allusions behind the many kennings that were used in the poetry of the skalds (professional Viking court poets). A kenning is a type of circumlocution, in the form of a compound, that employs figurative language in place of a more concrete single-word noun. Kennings are common in Old Norse and later Icelandic and Anglo-Saxon poetry. They usually consist of two words, and are often hyphenated. For example, Old Norse poets might replace sverð, the regular word for “sword”, with a more abstract compound such as “wound-hoe” or a genitive phrase such as randa íss “ice of shields.” The skalds also employed complex kennings in which the determinant, or sometimes the base-word, is itself made up of a further kenning: grennir gunn-más “feeder of war-gull” = “feeder of raven” = “warrior” or eyðendr arnar hungrs “destroyers of eagle’s hunger” = “feeders of eagle” = “warrior” (referring to carnivorous birds scavenging after a battle). Where one kenning is embedded in another like this, the whole figure is said to be tvíkent “doubly determined, twice modified.” Some kennings require an understanding of the history of the gods, hence the use of the Prose Edda – for example, mög-fellandi mellu “son-slayer of giantess” = “slayer of sons of giantess” = “slayer of giants” = “the god Thor.”

Kennings are rare in British English, but are fairly common in American English: rug rat, fender bender, bean counter, and my personal favorite, First Lady, because its Italian translation, prima donna, is used as a loan word/phrase and is also a kenning.


The Prose Edda was written by the Icelandic scholar and historian Snorri Sturluson around 1220. It survives in four known manuscripts and three fragments, written down from about 1300 to about 1600. The Prose Edda consists of a Prologue and three separate books: Gylfaginning, concerning the creation and foretold destruction and rebirth of the Norse world of the gods; Skáldskaparmál, a dialogue between Ægir, a Norse god connected with the sea, and Bragi, the skaldic god of poetry; and Háttatal, a demonstration of verse forms used in Norse descriptions of the gods.

Apart from the information about the Norse gods in the Eddas I am interested in the Old Icelandic rune poem. Runes were used as the alphabet for a number of Old Germanic languages, including Old Icelandic, before the adoption of the Latin alphabet. There is a great deal of nonsense going the rounds about runes these days because they have been popularized in two distinct ways. First, a disparate group of people from neopagans to New Age devotees have latched on to runes as ancient systems of magic and divination even though there is almost no primary evidence of these practices. To be sure, runes were used for carving spells and incantations, but it is reasonable to presume that it was the spells and not the runes themselves that were magical. Nonetheless, non scholars, notably Ralph Blum, have written texts on how to use the runes for divination simply by inventing the rules from scratch. Blum used Tarot and I Ching as his guides because he had no knowledge of runology or Medieval Germanic cultures. Second J.R.R. Tolkien used runes as his models for the alphabets of his created languages of Middle Earth in his Lord of the Rings trilogy, giving runes a mysterious, magical or fantasy quality.

Apart from this nonsense there are actually a few things we know for certain about runes. For one thing, the runes had names and not just phonological values. The names were different in different languages and were explained in rune poems where each stanza starts with the name of a rune and then explains its meaning. The Old Icelandic rune poem is the oldest of the three extant poems (the others are in Old Norse and Old English).  Here’s a sample, the first three verses representing runes for F (Fé), U (Úr ), and TH (Þurs):

Fé er frænda róg
    ok flæðar viti
    ok grafseiðs gata
    aurum fylkir.

Úr er skýja grátr
    ok skára þverrir
    ok hirðis hatr.
    umbre vísi

Þurs er kvenna kvöl
    ok kletta búi
    ok varðrúnar verr.
    Saturnus þengill.

    source of discord among kinsmen
    and fire of the sea
    and path of the serpent.

    lamentation of the clouds
    and ruin of the hay-harvest
    and abomination of the shepherd.

    torture of women
    and cliff-dweller
    and husband of a giantess.

I have used these rune poems to create my own system of divination  It too is nonsense, but it’s credible nonsense. For certain, Icelandic runes were used to create graphics known as rune staves that were used for good luck.

ild12 ild13

This website is great. It tells the would-be tourist to Iceland what sentences in Icelandic not to be bothered with. A few favorites of mine are . “Hvar byrjar röðin?” / “Where does the line start?” which is not utterly useless, but Icelanders are as notoriously ill mannered as the Chinese or Italians when it comes to forming an orderly queue, such as at bus stops, in shops, or at bars.  Then there’s “Hvar er næsta lestarstöð?” / “Where’s the closest train station?” – useless because there are no trains in Iceland (there are no MacDonald’s either – hooray). Finally, “Hvernig verður veðrið í kvöld?” / “What will the weather be like tonight?” The weather in Iceland is legendarily unpredictable, and changeable at a moment’s notice.

I’ve dealt a little with Icelandic cuisine before. For protein, historically, Icelanders depended on fish, sheep, and hunted game birds. Subsistence farming focused on cold weather cereals, such as barley, and vegetables. The cuisine is heavily Scandinavian, of course, with notable Danish influences. Here’s a recipe for skyr – homemade curds which can be eaten with cream and fruit as a dessert. It’s a bit of a rigmarole but I’m all for revamping home cheesemaking, the way my mum used to when I was a little boy. Commercially made skyr is readily available in markets in Iceland, much as yoghurt is in other countries, so few people make it at home these days.




1 gallon whole milk
½ pint sour cream
½ rennet tablet


Scald the milk by bringing it to a boil and then immediately turning off the heat and allow it to cool to blood temperature (98°F/37°C).

Whip the sour cream is whipped and add some of the warm milk until it is thin and smooth. Then pour the cream into the milk and mix thoroughly.

Dissolve the rennet in about a tablespoon of cold water and add to the milk. Mix thoroughly again.

Let the mixture stand at room temperature for 24 hours.

You now have skyr (curds) and whey. The simplest method of separating out the whey is to make several bags out of multiple layers of cheesecloth (its original purpose), fill them with the skyr and whey and let them hang until the whey drains off. My mum used to hang it on the bath taps.

I gallon of milk should make about 3 pints of skyr, so you can adjust the recipe accordingly.

When serving, whip the skyr well with a whisk to a smooth ice-cream-like consistency. It should not be grainy or like cottage cheese. Serve with cream, sugar and fresh berries.

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.