Tuesday, 23 August 2016

The Germanic Languages and Language History

Speakers of English might also be interested to know a little bit about the history of the Germanic languages.  Contrary to what the average native speaker of English is aware - English is a Germanic language!
So, where did English come from?  Where did German come from?  What other European languages  are  Germanic?  How are they related to each other?  What languages were the roots of the modern Germanic languages?  What was the history and time-frame of the languages that eventually became modern English and modern German?  This article touches on answers to these seemingly simple but actually complex questions  

My sources here are primarily textbooks and notes from language history courses I completed while doing graduate studies in German linguistics at Ohio State University.

The history of documented Germanic languages begins somewhere in the 8th century with the literary works published by Karl the Great.  At that time there existed many more languages than exist today due to the general less mobile nature of the world at that period in history.  We could go further back, but starting in the 8th century is the point at which it is possible to identify languages that are similar to can be correlated to our modern versions.

The Roots of Language in Europe
Around that period there were 8 identifiable language groups in the modern worl  Europe had become, for all intents and purposes, the center of the civilized during that era.  Its languages found their roots in the eastern languages.  The major language groups may be familiar to some readers:

Indo-European Languages - These languages had their origins in the Far East.  The Indian languages come from this group and survive today as Hindi, Bengali, Urdu, and some less defined gypsy languages.  Iranian falls in this family and has links to modern Persian, Kurdish, and Pashtu, the national language of Afghanistan.   Hindi and Sanskrit have been found to have been heavy influences on the development European languages, although nothing like the Indo-European languages exists in Europe today.   All of the languages groups listed below have Indo-European roots.

 Greek – Old Greek belongs to the family of ancient Indo-European languages.  New Greek developed in the post classical time of Greece.  Among other things, it is well known as the language in which the New Testament was written.  Modern Greek is something else again.

Romance Languages – Latin, the language of ancient Rome, was a language comprised of many regional languages from areas conquered by Rome, and more or less forced as an official language.  Its modern descendants include Italian, Spanish, Portuguese, French, Romanian, and Rhetoromansch (still alive but dying in Graub√ľnden in Switzerland).
Keltic Languages – Gaelic and Welsh people were geographically separated from the speakers of Germanic and Roman languages and developed on their won. There still exist a few million speakers of variants of these languages.
Baltic and Slovak Languages - Members of this group still surviving today include Latvian, Russian, Sorbic (spoken in eastern Germany ), Polish, Slavic, Czech, Srbo-Croatian, Bulgarian.  This is not an all inclusive list.
Germanic Languages – Modern Germanic Languages include but are not limited to English, German, Dutch, Swiss German, Fresian, Luxembourgish, Danish, Swedish, Icelandic, Yiddish.  

Non Indo European Languages -  Languages which were imported into Europe through migrations from elsewhere during the time the Indo-European languages were developing into their modern forms include Finnish and its cousin Bulgarian, Basque, Turkish, Lapplandish, Tocharic.

In a follow up blog we will discuss the development of German and English from about the time of Karl the Great to modern times, including Old Saxon, Old High German, Middle High German, Old English, Middle English, and variants of German like Dutch and Swedish

Friday, 19 August 2016

Math in Real Life! Coordinate Geometry in Real Life! Mathematics Lives!

Unlike the majority of math educators, I come from a practical world of using what I learned about mathematics in real life.  As a result of textbooks written by pure educators with no engineering and little or no practical experience, often I hear beginning students complain that they believe there are no real applications for what they are learning.  I’m here to show you that the world actually revolves around the properties of a right triangle!

Stupid Word Problems

Many of the hokey word problems published in the vast majority of mathematics textbooks are really sorry excuses for real practical applications.  I apologize to any readers who might be contributors to the word problem sections on which I am commenting - but come on!  How many of us are going to be tracking elephant migrations for a living, or calculating when airplanes traveling at different speeds from different cities are going to cross paths?  Interesting questions, but such textbook word problems are just obscure oddities.  They just do not reflect what real people do every day with math, and they do not encourage the student to want to learn more math.  Instead, they think of math as some stupid obscure subject.

Real Mathematical Applications

I am here to talk about coordinate geometry.  Students ask “What would anyone ever use this for?”  It is unfortunate that the average educator cannot expound on the simple applications presented in this article.  Have you ever driven past an interstate highway interchange construction site?  Just how does such a complex set of interconnecting curves and lines and bridges all come together into one smooth and continuous system on which automobiles can safely travel at 70 mph?  I suppose that a number of people never think about it.  Many take it for granted.  But that entire road system had to go through a conceptual process in someone’s brain, then transferred to a paper and computer plan, and finally transferred into reality with the aid optical and mechanical layout equipment controlling heavy equipment around massive but precise amounts of dirt, fabricating complex pieces of steel which all must fit together tightly like a jigsaw puzzle.  What wonder of science makes this possible?  Mathematics does!

Coordinate Geometry

Perhaps you have taken an Algebra course where you learned to graph and plot complex curves with names like hyperbola or parabola, spirals of various types, or just more simple shapes like triangles, rectangles or parallelograms.  Perhaps you advanced to 3 dimensional graphing, where various geometric shapes are represented by mathematical functions.  In the highway construction world, everything you see being built is defined on paper and in a computer by such mathematical functions.  And construction engineering is only the tip of the iceberg.  In a continuation of this blog, we will go over a simple street and curve design to show how the lines and functions which you l may have already learned to plot in coordinate geometry in your Algebra class.