Look at a Mercator map of the world. Note how the farther you get from the equator, the more distorted the sizes of the continents are. The Mercator projection is used for navigation, it is designed so that a straight line drawn between any two points on the earth will have an angle equal to the compass course a mariner would have to steer to travel between them. It also has straight, parallel and orthogonal latitude and longitude lines so that exact coordinates for any spot on the map can be quickly and easily determined without calculation, and rhumb line distances between locations accurately measured. The price you pay for this is that the latitude lines are not evenly spaced, and Greenland is bigger than Brazil.

But it is a good metaphor for a favorite point I’m trying to make here all the time. There is no “correct” map projection, just as there is no “correct” political or economic theory. You are entitled to pick and choose, or even devise your own tailored to your particular needs. If you want to plot a continuous compass course (rhumb line) between New York and Moscow, you use the Mercator projection. If you wish to plot the shortest possible (great circle) course between the two, you use a map based on the Gnomonic projection. Its not a question of which is right or wrong, but which is appropriate for your application.

The theories we use to interpret the world around us are just tools. We get to pick the ones that work best for our purposes; although not arbitrarily of course. But none of them is intrinsically correct. This is especially true in the behavioral and social sciences. This is why the strict ideological solution can get you into so much trouble if you insist on using it in every situation.

We need to constantly remind our Conservative friends of this, or they will surely sail right off the edge of the earth trying to pound history into an ideology that doesn’t quite fit.

When Hubble showed observationally through the measurement of the Red Shift that the universe was expanding, a modification to the PCP had to be proposed to save the theory from the universe’s eventual death by dilution, and its birth in a singularity. This would mean the universe was finite in space and time and was evolving into a different condition. It had a destiny and a history, which violated the PCP and every prejudice and intuition about the universe held by scientists. Creation, evolution, perhaps death, a finite age, perhaps even a finite size, no, it would just not do. It sounded too much like all that god nonsense.

To preserve the PCP, new matter had to be spontaneously created to maintain the mean density of matter constant as the universe expanded into vacuum. Spontaneous creation of matter from nothing isn’t really such a radical idea, after all, either it is being continuously created to maintain the PCP, or it was all created at once in the singularity. Take your pick. The necessary creation rate was calculated to be quite modest: 1 atom of hydrogen per cubic meter of space per century. This would provide enough new matter to maintain a constant density as the universe expanded forever into infinity, and it was safely protected from pesky challenge by observational astronomy and experimental physics. Such a rate of spontaneous creation could never be detected in the laboratory or observed at the telescope. It was just too tiny.

The major objection to this idea was “Where do the elements originate?” The earliest proponents of the Big Bang theories argued you needed a singularity to create a fireball massive enough to create the periodic table by hydrogen fusion. Fred Hoyle, a British astronomer who was a champion of the Big Bang’s rival theory, the Steady State Theory, came up with a solution, and it just happened to be true. He proposed the chemical elements were produced by thermonuclear reactions inside stars, and returned to the interstellar medium by supernovae and outgassing by dying stars. This eliminated the need for a fireball at the beginning of time to create them. The only creation you needed was this magical introduction of hydrogen from nowhere (1 atom/M^3/century). Everything could be explained with only one a priori (or is it ad hoc?) assumption.

Unfortunately, in the 60s incontrovertible observational evidence of the Big Bang was revealed, the cosmic microwave background radiation, and it no longer was possible to deny the Big Bang, there apparently was NO Perfect Cosmological Principle. Other evidence, concerning isotopic abundances, soon confirmed this. This debate was still going on when I started my undergraduate work in astronomy, a coincidence of truly cosmic proportions. I can rightly claim I was present at the birth of the universe as we know it.

Mainly I found it fascinating that such a bizzare concept was used (with some controversy) in cosmology to evaluate various cosmological models.

http://arxiv.org/abs/1505.02780

http://arxiv.org/pdf/1508.01017.pdf

https://www.newscientist.com/article/mg22229692-600-quantum-twist-could-kill-off-the-multiverse/

–Aleister Crowley

In the relativistic view Time and space cannot be talked about as separate distinct entities- there is only space-time. Our human perspective of a 3 dimensional world advancing through a separate thing called time works fine for us as long as we all share the same reference frame with each-other and all that we observe. But when we move (or we observe something moving) very vast relative to us our primate intuition breaks down. We see that there is only the 4 dimensional space-time, and our relative motion, and local curvature of space can rotate us relative to the 4 axes-in our 3-dimensional perception- lengths get contracted and time becomes dilated…

Were the curvature of space-time to be positive, then the universe would eventually stop expanding and collapse back in on itself in a ‘big crunch’… While that is a grim view of our fate it at least has the comforting familiarity of a beginning, middle, and end.

If space-time were flat then the expansion would stop- after an infinite amount of time…

And if the curvature is negative the universe will expand for eternity.

As for the actual curvature of space-time, it would seem that it is negative based on our observations- in fact Current observations suggest that our universe is not just expanding for eternity, but that the expansion is accelerating.

Eternal expansion, infinite time, infinite space- these are not just mind boggling concepts, they are concepts that cosmologists have found to lead to absolute madness. Madness that results from Rational, logical conclusions – but madness nonetheless.

We exist at a point in time where we can look around us and determine from observation that the universe came into being just over 13 billion years ago. Given an eternity, what are the chances that any randomly selected moment will be within 14 billion years of the start of it all? Or within 100 billion? The chances are zero. In fact, it’s infinitely more likely that you will pick a moment in time so far removed from the big bang that all traces of it have been erased- for all but an infinitely small fraction of the universe’s existence, it will be impossible to observationally determine that it even had a beginning. The acceleration of the expansion means there will be no perceivable cosmic background radiation, there will be no nearby galaxies to see receding from us… indeed there will be no solar systems or planets.

One can say ‘well, we could not possibly exist in the universe of the far future since it would be uninhabitable – there could be no one to ask these questions in the infinite future. In other words, while the universe may eventually encompass infinite time and space, sentient beings can only exist in this finite sliver of time near the beginning.

But this is where the madness starts…

We have all heard the thought experiment- If you have an infinite number of monkeys and an infinite number of typewriters and an infinite amount of time they will produce an infinite janitorial bill and infinite copies of every novel written by man (Except the novels by Dan Brown, because there are some things even monkeys won’t do).

An even more simple example: You put the parts of an unassembled watch in a box and shake it… at some point the parts will come together to assemble the watch in perfect working order. Given infinite time it is a certainty… in fact the watch will be assembled and disassembled worn down into its component atoms and those atoms recombined to reassemble the watch and infinite other watches an infinite number of times.

Life on Earth started after only a few hundred million years of ‘shaking’ and random collisions between molecules. That required no infinities at all…

Empty space is not really empty- particles are flitting in and out of existence constantly- given an infinite amount of time and an infinite volume of space, eventually a perfect copy of our galaxy will pop into existence. Of course it’s far more likely that something simpler like our solar system will arise spontaneously… popping into existence from random fluctuations in the vacuum.

And far more likely still is the creation of a single brain, pre-programmed with a lifetime of experience and memories… perhaps it even is created with the synapses firing to make it think it is typing silliness into a computer- or maybe to think it is reading silliness on a computer. In fact- given infinite time and space it is certain that both versions and infinite others will exist… There is a term for such random creations in cosmology-‘Boltzmann Brains’.

If you pick an observer at random in an infinite universe, the chances will be %100 that the observer you pick will be a Boltzmann Brain. The same odds apply to you as well. But that can’t be correct can it? We all ‘know’ we are real… right?

At this point you probably think that I have lost my mind – but I assure you this is a serious topic in cosmology- just google “The Boltzmann Brain Problem”… here are a few links for further reading:

http://www.nytimes.com/2008/01/15/science/15brain.html?pagewanted=all&_r=0

http://fqxi.org/data/essay-contest-files/Carroll_fqxitimecontest.pdf?phpMyAdmin=0c371ccdae9b5ff3071bae814fb4f9e9

https://plus.maths.org/content/dreaming-dream

http://blogs.discovermagazine.com/cosmicvariance/2008/12/29/richard-feynman-on-boltzmann-brains/#.Vm3AB3arRD9

http://www.preposterousuniverse.com/blog/2013/08/22/the-higgs-boson-vs-boltzmann-brains/

Just remember, once you realize the water is over your head, it really doesn’t matter how deep it is.

I started writing something about it probably being positive, given that many things in the physical world seem to drop back to a baseline after a disturbance, but then I remembered we can see the oldest galaxies by light that seems to travel forever, and it also occurred to me that a disturbance isn’t the same thing as changing a vector, which can definitely be irreversible, and I realized I was heading for the deep end of the pool. Think I’ll just stay here and paddle around.