Inequality and equality

Triangle_inequality (Photo credit: Wikipedia)

Usually, but not always, I have an idea in the back of my mind of the structure of a post before I write it. Well, I have an idea of a few key concepts and how they will fit together. Sometimes it goes much like my skeleton idea and sometimes it turns out completely different. However, today, I have no structure in mind.

Inequality. It’s an interesting concept. The things that are being compared can be practically anything, but have to be of the same sort, hence the saying “you can’t compare apples with oranges”. Like all adages, this saying has more depth than appears at first glance. Of course you can compare apples with oranges if, for example, you are comparing their Vitamin C content or their fibre content. What the saying conveys is that it is incorrect to mix categories when the attribute being comparing is obviously not found in one of the categories, or the attribute is expressed differently in the two categories.

Apples & Oranges - They Don't Compare
Apples & Oranges – They Don’t Compare (Photo credit: TheBusyBrain)

For example, it would be wrong in most cases to compare the tastes of apples and oranges since the tastes of apples and oranges are significantly different. Or one might compare the performance of a truck and sedan car, and someone might object that any comparison is like comparing apples and oranges – while both are vehicles, but they are by nature significantly different.

Apples and Oranges
Apples and Oranges (Photo credit: Automania)

An inequality yields a true or false verdict. In logic and mathematics this is often called a Boolean value after mathematician and philosopher George Boole. In computer languages a Boolean value is usually, but not invariably, given a value of 1 for true and 0 for false.

George Boole, mathematician, 1858-1908
George Boole, mathematician, 1858-1908 (Photo credit: Wikipedia)

When children learn arithmetic and mathematics the emphasis is usually on equality rather than inequality. They learn that 1 + 1 = 2 and often don’t get taught such formulations as 1 + 1 < 6. When learning algebra they may be taught that y = x² is the equation of a parabola, but they may only learn in passing that y > x² represents all the points in the plane inside the parabola, and that y ≥ x² also includes the points on the parabola.

This is a graph of an inequality.
This is a graph of an inequality. (Photo credit: Wikipedia)

Computer programmers are usually deft at dealing with inequalities. When programming a payroll for example, the programmer may be required to calculate the tax that an employee may have to pay. Say the first $10,000 is taxed at 5%, and anything between $10,000 and $50,000 is taxed at 7%, and anything over $50,000 is taxed at 10%.

Tax (Photo credit: 401(K) 2013)

The programmer has to check if the salary is less than or equal to $15,000 (≤) and if it is he or she taxes the pay at 5%. If the pay is greater than (>) $10,000 and less than or equal to (≤) $50,000 he or she subtracts $15,000 from the salary and calculates 7% of that. He or she then calculates 5% of $15,000 and adds the two numbers to make up the tax for that employee. And so on, for the CEO who obviously exceeds the $50,000 threshold.

"Pay Day! Pay Day!"
“Pay Day! Pay Day!” (Photo credit: JD Hancock)

The simple statement – “Is the pay ≤ $15,000?” hides a complexity that is not obvious. It can be rewritten as – “Is it true that the pay ≤ $15,000?”. Such a statement has a value of “true” or “false”. The sub-statement “the pay ≤ $15,000” has a value of “true” or “false “. If the pay is $9,000 then the sub-statement  has the value “true”. Putting that back in the original statement yields “Is it true that true”. A little ungrammatical maybe, but it can seen that the whole statement is in this case true. This sort of complexity can trip up the unwary.

True/False Film Festival
True/False Film Festival (Photo credit: Wikipedia)

Logicians and mathematicians aren’t content with simple “true” and “false”. They have contemplated a third value, neither true nor false. Some versions call it “unknown” but it could be called “fred” or something. It doesn’t make any difference. Of course, mathematicians would not be satisfied with that, so they have derived “many-valued” logic systems.

It’s probably worth mentioning that some computer language allow for a “null” value, which is essentially the value you have when you haven’t set a value. Using the old pigeon hole analogy, if a pigeon hole is called “A”, then when the pigeon hole is empty, its value is “null”. When it contains, say, the integer 3, it’s value can be said to be “the integer 3”, so the statement “A contains a value greater than 1?” can be “true”, “false” or “null” so multi-valued logics can be more than an intellectual exercise.

Graphic for "the present king of France&q...
Graphic for “the present king of France”, a philosophical quasi-paradox from Bertrand Russell’s work on “definite descriptions” (is the statement “The present King of France is bald” true or false if France is a republic?). (Photo credit: Wikipedia)

Another form of inequality relates to societal inequality. There are very poor people and astronomically rich people. Of course people will never be universally equal, but a society that doesn’t recognise the extreme inequalities will not be a good society by most people. We don’t have a working philosophy which can address this inequalities. We have Marxism economics which favours the workers, and the Smithian lassez-faire economics which favours market forces, and Keynesian which has supply and demand economics.

English: The invisible hand of the market. Fra...
English: The invisible hand of the market. Français : La main invisible du marché. (Photo credit: Wikipedia)

None of these philosophies (and there are many others to choose from) really deal with the gap between the rich and the poor. Marxists would destroy society to rebuild it, but there is no guarantee that it will be better, and a very large chance that society would easily recover from such a cataclysm. Smithian economics would not admit to there being a problem. Keynesian economics at least considers unemployment but doesn’t directly address poverty.

English: Differences in national income equali...
English: Differences in national income equality around the world as measured by the national Gini coefficient. The Gini coefficient is a number between 0 and 1, where 0 corresponds with perfect equality (where everyone has the same income) and 1 corresponds with perfect inequality (where one person has all the income, and everyone else has zero income). (Photo credit: Wikipedia)

There does not appear to be a working economic model that deals with poverty as such. Distributing public funds through the dole doesn’t result in a decrease in poverty and merely reduces the self-esteem of the poor. Likewise, reducing support through reduced “benefits” doesn’t drive the poor into employment and doesn’t reduce poverty by providing an incentive to the poor. This is largely because the few jobs available to the unskilled don’t provide a route out of poverty as they are not well paid.

English: Arkwright - Colliery wages office Sho...
English: Arkwright – Colliery wages office Shortly after the pit closed in 1988. (Photo credit: Wikipedia)

There is no doubt that poverty is relative. The poor in the developed countries are well off as compared to the poor in developing countries, but that’s not really a justification for the vast inequality that is seen between the very rich and the very poor, in any country.

Strike Solidarity
Strike Solidarity (Photo credit: Light Brigading)
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