In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the product of n numbers.
The arithmetic mean of any two different, non-negative, real numbers is always greater than their geometric mean.
Arithmetic comes from the the Greek word ἀριθμός or arithmos meaning “number”.
Ancient Greek had three grammatical numbers: the normal singular and plural, and a third, the dual. The dual form of words was used when referring to precisely two things, generally when they tended to come in pairs e.g. eyes, feet, or were closely related e.g. two brothers. In Sophocles’ Antigone grammatical number is used subtly to represent the rupture between the two daughters of Oedipus, Antigone and Ismene, when Antigone stops talking of herself and her sister in the dual and instead uses the plural.
English still has residual traces of the dual number: both vs all; either vs any; neither vs none.
African numeration system are numerous and varied. The most common are numeration systems based on base 2, 5, 10, or 20, or a combination thereof.
Numeration based on the number two is widespread and unique to African numeration systems. It can be seen in the method of doubling in Divination systems (Ifa, Cedento, and Vodun make use of doubling) whilst the ancient Egyptians continuously used base two for calculations. An example in the Shambaa language of Tanzania express 8 as " ne na ne" or “four and four”.
Other African languages construct numbers by using arithmetic functions of multiplication, addition, and subtraction such that the Bulanda of West Africa (base 6) express 7 as 6 1( six one or six plus one) and 8 as 6 plus 2 etc. The Adele count koro (6), koroke (6+1 = 7), nye (8) and nyeki (8+1 = 9). Adding ki as a suffice add one at the previous number. The Huku of Uganda the number words for 13, 14, 15 are formed by the addition of 1, 2 or 3 to twelve in a similar way that French does for numbers over twenty. The Tschwa express 60 as thlanu wa makuma ni ginwe, “five times ten plus one more (ten)”.
When Winston Churchill went to Africa in 1907, he travelled from Mombasa up country to Nairobi on the fabled Uganda Railway ‘Lunatic Express’. This involved sitting on a bench strapped to the cow-catcher on the front of the engine.
Churchill is infinitely quotable.
One that resonates with me is, “You have enemies? Good. That means you’ve stood up for something, sometime in your life.”
There are two Churchill Counties in the world, neither named after Winston Churchill. The one in Queensland, Australia, was named after Winston’s father, Lord Randolph Churchill. The one in Nevada USA was named after Mexican-American War hero General Sylvester Churchill,
Churchill, a town on the west shore of Hudson Bay in northern Manitoba, Canada, is the prime destination for those who want to view polar bears up close. Large touring vehicles with huge tires to prevent damage to tundra are used to cart the tourists around and keep them from becoming a snack.
The future Admiral Nelson almost became a Polar Bear snack when his musket misfired on an expedition to Spitsbergen in 1773 whilst he was a 15 year old Midshipman.
After his musket misfired he attempted to belabour the beast with the butt end of his Brown Bess. Fortunately for him and perhaps England, he and the bear were separated by a break in the ice. Had the bear been able to engage more closely, we might now be speaking French.
A total solar eclipse will be visible from Spitsbergen on 20 March next year.
Spitsbergen has no immigration formalities, and any person can go there and stay forever with no papers. It is technically under Norwegian sovereignty. There is a modern community there, but the cost of living is very high.
The Norwegian author Sigrid Undset was awarded the Nobel Prize for Literature in 1928, largely in recognition of her three volume work about life in the middle ages in Scandinavia, Kristin Lavransdatter.
Norwegian-American author Ole Edvart Rølvaag is best remembered for his semi-autobiographical novel Giants in the Earth, about settlers in the Dakota Territory, originally published in Norwegian before Rolvaag and Lincoln Colcord translated it into the more-marketable language of English. The opera adaptation by by Douglas Moore and Arnold Sundgaard won the Pulitzer Prize for Music.
Mozart composed his opera *Bastien und Bastienne *when he was only 12 years old.
Frédéric Bastien is a Québécois political scientist and historian who has written “La Bataille de Londres”, arguing that Prime Ministre Trudeau broke the separation of powers in his efforts to ensure the passage of the Patriation package, and therefore the patriation of the Canadian Constituiton is illegitimate.
Mozart’s opera Bastien und Bastienne is alleged to have been commissioned by Franz Mesmer, who first theorized what is now known as hypnotism, whose name is the origin of the word “mesmerize”.
Wolfgang Amadeus Mozart composed his first complete symphony, the Symphony No. 1 in E Flat, when he was only 8 years old. The symphony was composed in 1764 and it was the Mozart’s first complete symphony, containing three parts: allegro molto, andante, and presto.
Mahler’s 8th Symphony is known as the ‘Symphony of a Thousand’ due to the enormous number of musicians and singers required to perform it.
The Thousand Islands is a group of over 1800 islands on the New York-Ontario border where Lake Ontario empties into the St. Lawrence River. To qualify as an island in the count, the last must be above water level year round, Have an area greater than 1 square foot, and support at least one living tree.