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glossary page 88

Eddas:

The Eddas are Medieval Icelandic literary works, the Prose Edda & an older collection of poems, the Poetic Edda; both works were written down in Iceland during the 13th century with roots in the Viking Age.  They are the main sources of medieval skaldic tradition in Iceland & Norse mythology.

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conquering Goths:  * see Endnote 80

Goths or Geats were a North Germanic tribe (today inhabit  S. Sweden).  They spoke the Gothic language.  Their migrations led to considerable political change & dislocation in Europe.  Famously the Visigoths & the Ostrogoths, played an important role in the fall of the Western Roman Empire & the emergence of Medieval Europe.  They dominated a vast area, which at its peak under the Germanic king Ermanaric and his sub-king Athanaric possibly extended all the way from the Danube to the Don, and from the Black Sea to the Baltic Sea.

 

conquering Vikings: * see Endnote 81

Norse seafarers, sailing from homelands in Denmark, Norway & Sweden, raided & traded across wide areas of northern, central, eastern & western Europe during the late 8th to late 11th centuries (the Viking age);  established communities in England (Danelaw, Scandinavian York, Kingdom of Northumbria, Mercia, East Anglia) as well as in the Shetland, Orkney & Faroe Islands; Iceland; Greenland & Newfoundland.  This period of Nordic military, mercantile & demographic expansion constitutes an important element in the early medieval history of Scandinavia, Estonia, the British Isles, France, Kiev & Sicily

 

Gauss (& Euclidean geometry, axiom of parallels): * see Endnote 82

Gauss claimed to have discovered the possibility of non-Euclidean geometries but never published it. This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid's axioms were the only way to make geometry consistent and non-contradictory.  Research on these geometries led to, among other things, Einstein's theory of general relativity, which describes the universe as non-Euclidean.

 

multi-dimensional space:

In mathematics, the dimension of an object is an intrinsic property independent of the space in which the object is embedded.  A point on the unit circle in the plane can be specified by two Cartesian coordinates, but a single polar coordinate (the angle) would be sufficient, so the circle is 1-dimensional even though it exists in the 2-dimensional plane.  This intrinsic notion of dimension shows how the mathematical notion of dimension differs from its common usages.

 

logarithms:

the inverse operation to exponentiation, just as division is the inverse of multiplication and vice versa.  In its simplest form, a logarithm answers the question: how many of one number do we multiply to get another number? Example: How many 2s do we multiply to get 8?  Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2s to get 8, so the logarithm is 3.

Decline of the West, Chapter II: The Meaning of Numbers
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