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A Brief Introduction to Set Theory

This post is a very brief introduction to some of the basic concepts of set theory. Set theory is a branch of mathematical-logic, that has wide applications across disciplines. Its not just used in the obvious way of studying the foundations of mathematics by mathematicians but also in physics, social science, and even by philosophers as a theory of semantics for predicate logic (although you can do propositional logic without set theory).

A set is a collection of elements, or members; the notation for a set is specified by listing its components. So the set of even numbers can be represented a
$E: \left \{ 2,4,6,8 ... \right \}$$E: \left \{ x: x > 0 \wedge  even\right \}$ Either of these notations is valid. Further, elements of a set can only be in that set, once. So   $E: \left \{ 2,2,2,4,4,6,8 ... \right \} = E: \left \{ 2,4,6,8 ... \right \}$ The notation used to indicate that something is an element of a set, is using the Greek symbol "epsilon". That is: $4 \epsilon S$…
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Consistent Histories and the PBR theorem

Several years ago now a much discussed theorem in the foundations of physics was discovered by three physicists, Matthew F. Pusey, Jonathan Barrett andTerry Rudolph. I had meant to discuss their paper some time ago, and realized I couldn't find anywhere, where anyone was talking about the theorem in the context of the Consistent Histories approach. So I've decided now to correct that.

The theorem states that under certain conditions a model which affirms both that (a) there are underlying ontological states of a system and (b) the wave function is given an epistemic interpretation, cannot be consistent with quantum theory, and so must be discarded. 

Right off the bat, we know the Consistent Histories approach affirms (b), so the most straight forward response could be to reject (a) and some Consistent Historians are perfectly willing to do that, e.g. Lubos Motl and Roland Omnes. As for (b) in the CH approach, the wave function is treated as "pre-probability" in the sen…

Theresa May is No Liberal but She's Still Better than Jeremy Corbyn

It's a lonely time to be a classical liberal; none of the main parties are offering a truly liberal-Brexit.

All the main parties in Britain support regulations on pay, fixing prices (typically on energy or alcohol), telling businesses who they can place on corporate boards, all are supporting increased spending and further borrowing, (most noticeably on projects like HS2, foreign aid, pensions, winter fuel, defense or health care). All have industrial strategies.

Theresa May has at least some redeeming qualities, her one-in-two-out rule on regulation, her promise for flatter, simpler taxes and her commitment to free trade, to name a few. Jeremy Corbyn is far worse, proposing a dramatic change in how we accept goods and services, erecting barriers to trade and commerce around the world, he's offering full socialism. Nationalisation, tax hikes, sequestration of assets and a currency collapse that could lead to exchange controls.

Classical liberalism has never been cultivated in…

Trump's Corporate Tax Cuts

In a recent podcast Dana Loesch radio opened with the question "what is a Conservative?" The question was responded to by people, largely struggling to article the essential core of Conservatism.

A Conservative, as I see it, is someone who believes in each individuals inalienable right to life, liberty and the pursuit of happiness. In terms of policy that translates to upholding variety and freedom of choice, the provision of fair incentive and reward for skill and hard work, the maintenance of effective barriers against excessive powers of the state and a belief in the wide spread distribution of individual private property.

Think about that "excessive powers of the state". Soon to circulate in congress is a budget plan to reduce the higher end bracket of corporate taxes from 35 per cent to 20 per cent. That won't just boost the American economy, its productivity, investment and growth but raise commerce and trade to the benefit of every American citizen.

Whe…

A Thirty-Year Search for just Two Numbers

Allan Sandage "the Father of Modern Astronomy" at the Carnegie Institution of Science, 2010

In 1926 the astronomer Victor Slipher measured the spectra of light from distant galaxies, in his soon-to-be, revolutionizing work he found that they were almost all shifted to longer wavelength by some amount, $\lambda$. What Slipher had in fact discovered would send tremors across the scientific community, what he noticed was the red shift of galaxies $\Delta \lambda /\lambda =v/c$ but he didn't appreciate yet, what this meant.

Eighteen years earlier, the Harvard astronomer Henrietta Swan Leavitt discovered a relationship between the period of Cephid variable stars and their luminosity which allowed astronomers (like Hubble) to calculate their distance from earth, provided one first knew what period of their evolution they were in.

Edwin Hubble was able to use the relation discovered by Leavitt to calculate the distances of various spiral nebulae (galaxies) which contained Cephi…

Book Review: A Universe From Nothing

A couple of days ago I was lent a copy of Lawrence Krauss' book "A Universe From Nothing" and having been previously very critical of Krauss, I've decided I couldn't resist writing a review of my immediate thoughts on the book.

Already I'm taken aback by the somewhat ridiculous afterword written by Richard Dawkins when he says that "If On the Origin of Species was biology's deadliest blow to supernaturalism, we may come to see AUniverse From Nothing as the equivalent from cosmology."

Are we really going to compare what was arguably the most crucial publication in the advancement of biology ever in its history, with a book that doesn't propose anything original or new and that dabbles in speculative and untested (possibly untestable) physics? Well I guess we are.

Chapters 2-7

This is the best part of the book, it both recants much of the history of cosmology–from the viewpoint of what Krauss was working on–and some quantum mechanics. This muc…

Yes, the Problem is Socialism!

Almost every socialist regime has its admirers in the Labour party, Cuba, Nicaragua, Yugoslavia, Romania, even the USSR, at least up until their collapse and then the line is always the same "it wasn't real socialism". Venezuela is hardly an exception; now its reached a point of Armageddon.

It was praised and held up as an alternative to "austerity and cuts" by Jeremy Corbyn, Ken Livingstone, Diane Abbott, John McDonnell, Owen Jones and others. Now poverty has reached over 80 per cent, infant mortality has surged by ten thousand per cent, the minimum wage has fallen by three quarters, the homicide rate is over ten times the global average, inflation is over 900 per cent and the political class is reacting by reverting itself into a dictatorship, yet its the same excuse being trotted out.

"Hitler wasn't a real Christian", "Venezuela isn't real socialism" in the end its the same argument.

Its almost hard to imagine that while sitting …