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M.Sc student in Maths. B.Sc in Maths and Physics. Classical Liberal. Anglophile. Optimist.

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There's No One Left To Lie To

on May 12, 2018

Communism corruption coup Grace Gucci Grace Mnangagwa Mugabe Rhodesia Robert Mugabe Zanu-PF Zimbabwe

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Are We Living In A Simulation?

on May 03, 2018

are we living in a simulation? Bostrom simulation Simulation argument simulation hypothesis

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Inaction in Syria is Unconscionable

on April 14, 2018

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Pop Goes the Universe

on April 02, 2018

cosmology inflation Leob Ljjas Multiverse Planck Pop goes the universe Steinhardt Turok

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Is Quantum Cosmology Serious Science?

on March 28, 2018

CDT Cosmic Inflation cosmology Hartle-Hawking Hawking inflation Isham Quantum cosmology singularity singularity theorem Stephen Hawking Vilenkin wave function

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AronRa Please Stop Talking Nonsense About Physics!

on March 25, 2018

AronRa Big Bang Cosmic Inflation cosmology physics

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Andrei Linde and Inflation

on March 22, 2018

Big Bang Cosmic Inflation cosmology flatness problem Guth horizon problem inflation Linde monopole problem Planck singularity singularity theorem

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Penrose-Hawking Singularity Theorems

on March 16, 2018

closed timelike curve Friedman FRW George Ellis metric Penrose-Hawking Roger Penrose singularity singularity theorem Stephen Hawking

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No Deal is Better than a Bad Deal

on February 11, 2018

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Brexit Transition Worries

on February 08, 2018

Brexit EU European Union no deal transition period

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Set Theory

on January 20, 2018

Logic Maths Platonism Set theory Sets

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Andrew Wells

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Popular Posts

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 in philosophey. I'm only going to cover in this post what's needed for predicate logic (although you can do propositional logic without set theory) but it has for many other applications. 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 as $E: \left \{ 2,4,6,8 ... \right \}$ $E: \left \{ x: x > 0 \wedge even\right \}$ Either of these notations is valid. Further, elements of a set can only be in that set once. $E: \left \{ 2,2,2,4,4,6,8 ... \right \} = E: \left \{ 2,4,6,8 ... \right \}$ The notation used to indicate that somethin...

William Lane Craig and the Hartle-Hawking No Boundary Proposal

Standard hot Big Bang cosmology represents the universe as beginning from a singular dense point, with no prior description or explanation of classical spacetime. Quantum cosmology is different in that it replaces the initial singularity with a description in accord with some law the "quantum mechanical wave function of the universe", different approaches to quantum cosmology differ in their appeal either to describe the origin of the material content of the universe e.g., Tyron 1973, Linde 1983a, Krauss 2012 or the origin of spacetime itself e.g., Vilenkin 1982, Linde 1983b, Hartle-Hawking 1983, Vilenkin 1984. These last few proposals by Vilenkin, Hartle-Hawking and others are solutions to the Wheeler-DeWitt equation come under a category of proposals called "quantum gravity cosmologies" which make cosmic applications of an approach to quantum gravity called "closed dynamic triangulation" or CDT (also known as Euclidean quantum gravity). I've n...

Can inflation be eternal into the past?

Back in 2003 a paper appeared on the arXiv titled " Inflationary spacetimes are not past complete " that was published by Arvind Borde, Alan Guth and Alexander Vilenkin which has had considerable amounts of attention online. The theorem is rather uninteresting but simple and doesn't require a very complicated understanding of math. So I thought I'd explain the result here. It's purpose is to demonstrate that inflationary models are geodesically incomplete into the past which they take as "synonymous to a beginning" but Vilenkin stresses that the theorem can be extended to non inflationary models so long as the condition of the theorem that the average rate of expansion is never below zero is met. These models too are incomplete into the past. Consider the metric for an FRW universe with an exponential expansion Where the scale factor is Since the eternal inflation model is a "steady state cosmology" the mass density and the Hub...

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