Music

This page has several hours of YouTube videos of peaceful and serene music distributed over several playlists. Click on “continue reading” to show all playlists. Single click on a playlist to start playing. After that, double click on the playlist to make it full screen. Double click again to change it back. Several of the Continue reading »

A Net Assessment of Europe

Last week I began this series with a Net Assessment of the World, in which I focused on the growing destabilization of the Eurasian land mass. This week I continue the series, which will ultimately analyze each region in detail, with an analysis of Europe. I start here, rather than in the Middle East, because while the increasing successes of the Islamic State are significant, the region itself is secondary to Europe in the broader perspective. The Middle East matters, but Europe is as economically productive as the United States and, for the past 500 years, has been the force that has reshaped the world. The Middle East matters a great deal; European crises can destabilize the world. What happens between Greece and Germany, for example, can have consequences in multiple directions. Therefore, since we have to start somewhere, let me start with Europe.

Religious Freedom is the Issue in the Middle East

We post a new essay by Paul Merkley.. We present this essay reprinted by permission of Paul and from The Bayview Review. See the links at the end for direct access to the rest of Paul’s work.

There are Assyrians and there are Assyrians

Recently the western press has been bemoaning the devastation by ISIS in Iraq and Syria of artifacts and monuments from the Neo-Assyrian Empire (See my essay, “A Meeting of Kindred Spirits In Iraq,” www.thebayviewreview.com, May 1, 2015.)

But the proper name “Assyrian” has been appearing with even greater frequency in quite another context and with quite a different meaning. Among such items is one originating with Newsweek, and distributed by AINA (ASSYRIAN International News agency(aina.org/news): “Fleeing ISIS Into Exile, Assyrian Christians Sing the Oldest Music on Earth, ” April 16, 2015.) It describes the exodus in panic of hundreds of thousands of Christians from Iraq and Syria following the capture by ISIS of Mosul and other major centres since January of this year.

A few days after capturing Mosul … ISIS issued its infamous decree: convert to Islam, pay a tax on unbelievers or die…. [The fleeing Christians] leave behind the bodies of brothers and fathers, and the shelled–out ruins of their shops and houses. They also leave behind much of what it meant to be a Syriac Christian. The ancient cities of Nimrud and Nineveh that they visited proudly to show their children the glories of the Assyrian empire from which they claim descent [emphasis added] — soon these will be bulldozed by ISIS. They leave behind the treasures of Assyria in the Mosul museum — ISIS will loot the smaller antiquities for the black market and smash the statues too big to sell.… From the steeple flies the black flag. In a few months, it will be destroyed.

The Global Water Problem

This is a widely discussed topic of which we have been peripherally aware. We have decided to start collecting references in the same manner as we are doing with automation and robotics (Robotics In the Labour Market). These are large transformative issues that will be major drivers of change in our society in the near future.

We have been tracking the drought in the US southwest. The latest essay is California is the Canary should have enough of a bread crumb trail that you can find out many previous essays on the topic.

The motivational article that prompted this post is from Zero Hedge: Jim Rogers On The Coming Water Wars. This gives a brief introduction to the problem. Below we have a chronology of references.

Introduction to Arithmetic Operators

What Is an Operator?

An operator is a person who does some kind of work, often between two people. If your computer breaks and you phone the company for help you may reach a switchboard operator who will connect you to the right person to speak to. In mathematics we have many operators. You will meet four in this section.

The operators used  in arithmetic are addition or “plus“, subtraction or “minus“, multiplication and division. We’re mathematicians and don’t like writing so we invent symbols to represent our operators. The symbols for addition and subtraction are {+,-}. An example of 3 plus 2 would be 3+2 and an example of 3 minus 2 would be 3-2.

The symbols for multiplication and division, {x,÷}, cause us problems, however.  The “x” would be OK for multiplication in arithmetic but won’t work for algebra that you will learn soon enough, because in algebra we use “x” to represent an unknown quantity.

The Kahn Academy uses a special kind of dot, “•”, not to be confused with a period “.”. But the “•” symbol does not appear on a computer keyboard. Instead it has to be looked up in a special table, something that is time consuming and may not be possible for you. Computer programmers who type all day use the asterisk, “*”, as a multiplication symbol and that is what we will use. An example of 3 multiplied by 2 would be 3*2.

Division presents even more problems. The standard symbol used as the division operator is “÷”.  Like the dot this is not on your keyboard. Text books represent long division by a symbol that looks like this: “)¯¯¯¯”. We can’t even fully express a problem with this symbol. The symbol that is on the keyboard that we will use for division is the forward slash, “/”. An example of 3 divided 2 would be 3/2.

Properties of Operators

Operators have a special word that identifies them, the word “operator”. Like the switchborad operator, the arithmetic operators do

Arithmetic Expressions

An operator is a person who does some kind of work, often between two people. If your computer breaks and you phone the company for help you may reach a receptionist or operator who will connect you to the right person to speak to.

In arithmetic our 4 operators do work that applies one number to another. The statement for the operation of subtraction that we wrote about above was 3-2. Such statements are called expressions. We will use this term a lot.

Key Points

In the lists below, ant text in red is for informational purposes only and the student need not remember them in this course.

New Words
  • digit: a
New Symbols:
  • digi
New Rules
  • buil

An Introduction to Algebra

  1. Equations
    1. The use of Variables
    2. Solving One Equation in One Unknown
    3. Key Points
      1. New Words
      2. New Symbols
      3. New Rules
      4. Conventional Practices

Negative Numbers

What Are Negative Numbers?

Today I was watching the weather report on TV. It said the high for today will be 0 degrees Celsius. It also told me that the high yesterday was 6 degrees above zero or+6 and that tomorrow the high will only be 6 degrees below zero or -6. You are probably familiar with such reports and may even have a thermometer outside that you can read yourself.

But why did the weatherman on TV say plus 6 and minus 6 instead of just saying 6? The high yesterday was just as many degrees away from zero by 6 degrees as the high tomorrow will be away from zero by 6 degrees. We can’t just say the value of the distance from zero but we have also to say the direction away from zero, plus or minus, or with symbols, + or -. Numbers with a sign of + are called positive numbers and numbers with a sign of – are called negative numbers.

Until now, numbers for us have been adequately represented by their value. Now we have to add a new property of numbers and that is called sign. We also now want to be a bit more precise and qualify the value of a number as its absolute value. The idea of absolute value is important in computer programming and higher mathematics but not so much for us now.

A Few Things About Signs

When used to denote the sign of a number the symbols {+.-} are acting as operators. They have only one operand however, and are therefor called unary operators.

Further we have another unary operator,, the absolute value symbol, “| “, that operates on a number to give just its value without any sign. An example is the expression | -6= 6.

You may have noticed that all the numbers we have used until now have shown no sign. Since most numbers we use are positive numbers, by convention, that means by agreement by most mathematicians, we don’t write the + sign for positive numbers. After all, we are mathematicians and don’t like extra writing. This causes a bit of possible confusion when we use the absolute value operator. We have to remember that the expression above is meant as it is written and does not stand for | -6= +6.

Updating the Number Line

Addition and Subtraction of Negative Integers

Multiplication and Division of Negative Integers

Integers

What Are Integers?

The numbers that we made in Introduction to Numbers are called integers or whole numbers. In that section we counted our cats. The numbers we made counted whole cats since we don’t have any partial cats – say a half of a cat – walking around. We also have pies in our house, but someone keeps eating pieces of the pies. We can’t count our pies because we do have half pies in the cupboard. We therefore need some way to count parts of pies and we will explore these ways later in Fractions and

The Integers (Whole Numbers) and the Number Line

  1. counting cats and pies.
  2. The numbers we have talked about are the numbers {0,1,2,…,10,11,12,…,20,21,22,…} these are called integers or whole numbers. Supposing you had half a pie left from supper. What kind of a number would a mathematician use to represent half a pie? We will find out later, but if our integers represent pies, the number to represent half a pie isn’t among them. Hence the integers represent the numbers of whole pies or whole numbers.
  3. Take a ruler marked in centimeters, draw a line from one end of the ruler on the left  to the other and mark on it the integers shown up to 10.
  4. The first thing you may notice is that there is no number at the beginning of the ruler which is the first mark on the ruler. This is actually the number 0.
  5. The next thing you may notice is that between any two numbers on the ruler there are 9 marks in between. We will talk about their meaning later.
  6. Depending on the length of the ruler, the line you draw may allow up t0 30 marks that are numbered and evenly spaced. Longer rulers would allow us to mark more numbers on a longer number line. To be able to mark 1,000 on the number line, we would need a ruler possibly longer than the room you are in. Another characteristic of mathematicians I forgot to tell you is that big numbers don’t scare them. In fact some get excited over the size of really, really big numbers that they invent.

Addition and Subtraction of Integers

Multiplication and Division of Integers

Comparison of Integers

Key Points

A number has the following properties:

  1. It has a representation consisting of the ten digits.
  2. It represents a quantity or value.
  3. The position of each digit in the number is a place value with a distinct name.

Fractions

Fractions

Proper and Mixed Fractions

A proper fraction has both numerator and denominator as integers (whole numbers). Since most fractions that we work with are proper fraction we will drop the “proper” in the name and just call them fractions.

Every integer can be expressed as an equivalent fraction composed of the integer as the numerator and 1 as the denominator. For example 3 = 3/1.

A mixed fraction has two parts, an integer part and a proper fraction part. Example: 2 2/3 is composed of the integer 2 and the fraction 2/3. We sometimes use mixed fractions as a way of expressing fractions that have a numerator larger than the denominator. For example, the fraction 413/17 can be expressed as the mixed fraction 24 5/17.

Another way of looking at the fraction 413/17 is as the division problem 413 ÷ 17 which has the answer of 24 with a remainder of 5 or 5/17.

To convert a mixed fraction into a proper fraction, multiply the integer part by the denominator of the fractional part and add the fractional part to the result. For example:

3 5/6 ? 3/1 + 5/6

= (3*6)/(1*6) + 5/6

= 18/6 + 5/6

= 23/6

Next we will learn how to add and subtract fractions.

Addition and Subtraction of Fractions

Procedure:

  1. Change any mixed fraction into its equivalent proper fraction (example express 1 1/4 as 5/4).
  2. Find a common denominator for all fractions:
    1. For two fractions, multiply the denominators together to get a common denominator.
    2. For more than two fractions, multiply the first two denominators together
  3. Express each fraction as an equivalent fraction with the common denominator.
  4. Add and subtract the numerators to give a single number that will be the numerator of the result with the common denominator as the denominator of the result.

Example:

Multiplication and Division of Fractions

Ratios and Percentages

Flash Point: The False Flag for WWIII

World War III will be fought with the US and NATO on one side against an axis of Russia, China, and Iran on the other. None of these countries are particularly aggressive at this point, being interested in maintaining the current detente on their borders while perusing their outstanding territorial claims.

The US on the other hand views them as emerging regional hegemonic powers and a threat to the American Empire. The US is ready to use its superiority in weapons and naval strength to beat the threat back, using NATO as a pawn in the game.

Preamble for Instructors and Self-Learners

 

  • Before we start, we wish to make a couple of points about mathematicians:
    1. All mathematicians are lazy. They don’t like to write a lot so they invent symbols to represent most of what they do. Our study f numbers and arithmetic will emphasize this point.
    2. All mathematicians are playful. Every game has two things: a set of rules and a set of players or pieces or objects that are played with according to the rules. Every branch of mathematics can be reduced to a set of symbols and a set of rules governing how the symbols may be used. It’s all a game.
    3. For us, numbers will be the pieces in the game of arithmetic and the arithmetic operations of addition (+), subtraction (-), multiplication(x or • or *), and division (÷ or /). We will use “*” for multiplication partly it is the symbol used in computer programming languages and students may be exposed to it sooner or later. Also, we will eventually want to use the letter “x” for other purposes and that would be confusing. We will use the “/” for division for the simple convenience of having it on most keyboards.

 

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