Fundamental Inequalities

Equality is a cornerstone of the law, but it's not at all a feature of natural law.

Consider Heisenberg's famous Uncertainty Principle (but not in any deeper sense than the nature of the symbols):

 

On the left, Δχ and Δρ (position and momentum) are physical variables; on the right is a fixed value—i.e., half of ħ, the imponderable Planck constant.

Equations are like sentences with the equal sign being like the verb "to be;" they represent either equality or the more subtle notion of equivalency. Inequalities are also familiar from algebra but an inequality also expresses—more or less—an important direction of inequality. In this case, the observables are greater than or equal to the constants.

Bell's Theorem has been called "the most profound [theorem] in science" and it too reduces to an inequality. There's another: the Clausius Inequality, which embodies the Second Law of Thermodynamics, and which expresses changes in entropy against a value of zero. Comparing all three—without even understanding them—it strikes me that they all specifically pit observables against abstract constants. Is this general?

Wealth Redistribution and the Global Warming Agenda

There can be no doubt that the stop global warming and wealth redistribution agenda are linked. Look at this gem from the preface to Global Warming A Very Short Introduction:

So to deal with global warming, we must deal with developing countries, and thus we must for the first time in humanity's history tackle the unequal distribution of global wealth. Hence global warming is making us face the forgotten billions of people on the planet, and we must make the world a fairer place. In the 21st century we must deal with both global poverty and global warming. link

This is profoundly misguided logic. First of all, this is not the first time "we" have dealt with developing countries; nor is it the first time "we" have addressed the unequal distribution of global wealth.

I thought the way to deal with global warming was to stop emitting carbon dioxide? This means shutting down a goodly section of American and Western standards of livings.  Why mince words?  What does pumping up Africa have to do with global warming?  Surely the author of this polemic cannot seriously be thinking of improving the lot of Africa's poor.

A profound sense of humanity occurs when something is given to the poor.  A profound sense of propriety is violated when something is taken from someone and given to someone else. Mandated charity is charity destroyed.

I also object to the top-down driven "we" collectivism implicit in the author's grammar and syntax. The author implies that developing countries are unable to help themselves--they need a patriarchal benefactor--a global leveler.

Hence global warming is making us face the forgotten billions of people on the planet, and we must make the world a fairer place.

Imperatives aside, the author of sentence needs a refresher course on economics.  Need we reach back all the way to the Sumerians to show that poverty has always been with us?  Income disparity is a natural phenomenon. This was the implicit "message" of The Parable Of The Gas.

Inequality drives chemical reactivity--for example--electromotive force. Perfect equality is a depressing notion because it implies stasis: there is no potential or driving force for change.  There is no reason to invent because there is no reason to become different.

Parable Of The Gas Explained

A while back I wrote The Parable Of The Gas without explanation:

Consider a spherical, sealed glass container of gas. Further suppose that the gas inside is all the same -like helium in a balloon. Room temperature and stable. Everything equal inside...but it's not. The individual gas atoms in the container have unequal energies because there's a range--a statistical distribution--of energies present: Some atoms move more slowly than others, some more quickly, some much more quickly.

How can we make things fair? How can we make it such that each individual (atom) has the same energy as its next nearest neighbor? We cannot. The only way to approach that state is to remove energy from the entire system. Cool the economy. Everything slows. Eventually, approaching zero Kelvin, all motion stops. Of course catastrophic things like condensation (downsizing from gas to liquid) and solidification (loss of liquidity) occur along the way. But the goal is achieved: every atom is finally the same (or nearly the same) energy wise.

Here is what I was picturing:

Original

The figure shows how at higher temperatures the average speed increases but so does the spread (inequality). The range narrows at lower temperatures which is what some policymakers seem to want. But what they want is also unnatural and contrived. An Austrian physicist named Ludwig Boltzmann first came up with the mathematical model behind all this in 1877. He based his derivation on entropy--arguing that a situation where all members of a group have identically the same velocity is highly improbable--as improbable as all the gas molecules being located on just one side of the vessel. It's much more probable (favorable) to allow each member of the group to experience a range of velocities and not to constrain them into one single energy or spatial configuration.

Another physicist named Max Planck extended Boltzmann's ideas and also changed the world by extending statistical mechanics to heat and light thus introducing quantum mechanics.  Einstein ran even further with Planck's ideas.  Both men would have their doubts--"God doesn't roll dice" and all that--but neither man denied reality.

Added:  When I liken the economics of wealth and poverty to a gas, it's important to remember that "rich" and "poor" may interconvert: link