### Simulation Argument

Sometimes when ideas are trending in the scientific press, it's well deserved, a lot of the time however it's not. I imagine by now most people have probably heard of the Simulation Argument, it comes from a 2003 paper by the philosopher Nick Bostrom. It's essentially a statistical argument to the effect, that we're very likely living in a simulated universe rather than a real one. The argument goes something like this:

1. It's possible to simulate a universe like ours, with the kinds of experience we have in this world.

2. Perhaps far in the future, the technology to do so will exist and become sufficiently widespread.

3. Future beings will be interested in running ancestor-simulations of their past.

4. If 1-3 are true, then in the entire history of the universe simulated worlds will vastly outnumber real ones.

We should assume we’re typical observers and so, therefore, we are likely living in a simulated world rather than a real one. A lot of people like the idea that the universe is a simulation, they may think it speaks to their mental flexibility but actually, it portrays a fairly weak grasp of physics. The argument was covered on Sean Carroll's blog and he has a pretty good objection to it.

One way to understand this picture of the world is in terms of "digital physics" that all of reality, the laws of nature, spacetime, matter, energy are at bottom made up of grid nodes of bits, and encoded on an algorithm; looking at it top-down, one might say that since gravity is the curvature of spacetime, a quantum theory of gravity must entail that spacetime is made up of discretely quantized parts.

That's a very naive approach to quantum gravity, and today we know a lot better. If we try to build up spacetime from 'atomic-like chunks' then our theory wont be Lorentz invariant–that's fancy-sounding science jargon for "in conflict with known physics" namely special relativity–if with respect to one reference frame I cannot talk about time separations smaller than a certain duration, then I can have a second frame of reference moving very fast with respect to first where those separations become enormously large. Where violations in the principle of relativity will be observed.

Second, if spacetime is built up from Planck sized units of volume, I should be able to do a very rudimentary calculation to infer the total number of bits of information I need to specify for a complete picture of that given region of spacetime. It should be:

$S = \frac{V}{P_{v}}$

The problem here is that that's false. We have a better way to calculate the information encoded in a region of space, using the Holographic Principle. The degrees of freedom are limited by the area of the boundary of a given region of spacetime, so S is proportional to the area, not the volume of that region.

Certain features of our world–spacetime, potentially consciousness and in my view, God–cannot be simulated on a computer, that already makes the Simulation Hypothesis impossible to accept.

I wish science popularizes (or the science media) would stop promoting the simulation hypothesis as though it were serious science, it's not even close to being half of a scientific idea. Digital physics hasn't derived General Relativity or the Standard Model of Particle physics, and there are seriously questionable philosophical assumptions fed into the argument as well.

It neglects for example that the physical substrate for consciousness is a biological organ, not an algorithmic code. Bostrom assumes "substrate independence" but the fact that I can simulate something looking very similar to rain on a computer doesn't mean that the computer program is itself wet, inside. Even if you could simulate a conscious being neuron-by-neuron, it would be at least as complex as the brain itself. Each person can't be "copied and pasted" but is an individual, which makes it incredulous at best, to imagine that simulated people will hugely outnumber real people.

The simulation argument isn't something that keeps me up at night, most people who read about these ideas in the scientific press are probably going to conclude that these "science" authors are full of shit and I don't blame them.

### 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: $4 \epsilon S$…

### William Lane Craig and the Hartle-Hawking No Boundary Proposal

Classical 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 and exist in 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&#…

### 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 then 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 Hubble paramet…