It Wasn't Big, and it Didn't Bang

This post will be the first in a series of posts dealing with what our best models of the pre-Planck cosmos are, what evidence supports them, what might falsify them, and what steps are being taken to make some progress. It was originally motivated by a forum post in which somebody reasonably scientifically literate asserted categorically that there was no way we could ever know what happened before the Big Bang and that all our models were unfalsifiable. While it's certainly true that such knowledge presents some extremely difficult challenges, our pre-Planck hypotheses, as with all hypotheses, have essential features that have predictable, testable consequences that we should in principle be able to observe. For example, you'll remember all the hoo-ha a couple of years ago about the BICEP2 results (I'll cover this in some detail later, in case anybody isn't familiar with it). Had they withstood scrutiny, they would have comprehensively falsified one of our best pre-Planck models, namely the Ekpyrotic, or 'brane-worlds' model. 

As it is, if this B-Mode polarisation in the CMBR is observed and we can rule out sources other than those arising from an inflationary period in the first Planck second, then brane-worlds will be dead in the water. Further, and given some other details, it's possible that eternal inflation can gain some traction, and that will definitively rule out the idea that the BB that marks the past-boundary of our local cosmic expanse constitutes the beginning, although there are still problems to be faced, such as those arising from the BGV theorem so beloved of  Craig and other apologists who don't understand it.

But I'm getting ahead of myself. I'll cover much of this later, including BGV theorem, but I should lay a little ground work.

Before that, I wish to make a linguistic distinction so that I can plough on without a probable derail. I use the term 'universe' to deal with the whole shebang, and the term 'cosmos' to deal with our local cosmic expanse. Definitionally, they're identical, and this is merely my own convention for dealing with the distinction, because it makes matters clearer. Indeed, I might as well firm up this distinction for later clarity.

There is a long-standing problem with the multiple ways the word 'universe' is employed, and it requires a little history:

For most of history, the word 'universe' simply meant 'that which is', and referred to what we can observe in the night sky. It wasn't actually thought to be that large, in universal terms (pardon the pun). Sure, it was always going to be huge, but it was thought that the entire universe was contained within just what we think of as our own galaxy. Indeed, almost all of what can be seen with the naked eye is contained within the Milky Way. Hubble, of course, changed all that in the 1930s, when he demonstrated that some of the things that had been historically observed were too far away to be part of our galaxy, and that it was all rushing away from us. Did the meaning of the word 'universe' change at that point? Of course not! It still meant 'that which is', but it now encompassed a good deal more in our perception, because our understanding of what is had expanded.

So now, we understand that our local cosmic expansion may not be the entirety of 'that which is'. Does that change the definition of the word 'universe'? of course not! The word still means 'that which is', but now it encompasses whatever (if anything) preceded or lies outside of our local cosmic expansion.

In short, there is, and can be, only one universe, because the universe is 'that which is' and encompasses all of existence. 

Now, I can hear the objections already, namely that physicists and cosmologists talk about 'other universes' and 'multiverse' all the time, so I should spend a moment addressing that. 

The first thing to note is that cosmologists and physicists, unlike evolutionary biologists, are not used to having their words dishonestly equivocated by propagandists.

The second is to note that when cosmologists and physicists write, they tend to write for other cosmologists and physicists and, as such, their language is a) geared toward an audience that understands what they mean when they use the word, based on context and b) often lazy. For an example of the latter, one need only look at how popular science authors treat the concept of entropy as disorder, with very little qualification of what they mean. More on that particular topic in a near-future post .   

Since even in the most basic definition of the word 'universe', one finds 'the entirety of time and space', and since it's far from clear that time began at the big bang, then the most that can be said is that our local cosmic expansion arose from the big bang, not the universe. Indeed, the standard big bang model doesn't even deal with the beginning of our local cosmic expansion, for reasons I shall be dealing with shortly.   

What all of the above should make clear is that our language is often insufficient to deal with the deep principles of what constitutes the universe, and how careful we have to be. This is not a failure of understanding, but a failure of language. It is precisely for this reason that I am such a pedantic twat, and why semantics, oft-maligned and dismissed as irrelevant, is so important. Semantics is the heart of communication and, in my opinion, any dismissal of an argument based on the idea that 'it's just semantics', is not just fallacious, but indicative of a failure to think critically. It is, to use a favourite football analogy, the equivalent of diving in the box.  
This is why I employ the distinction I do. I refer to that which arose from the big bang as the cosmos, and the universe as a whole as the universe, while recognising that this may be a distinction without a difference.

Author's note 28/09/2017: I've become aware of a terminological convention that's exactly the opposite of my usage, employing 'cosmos' to refer to the broader conception and 'universe' to refer to our local expanse. I've been writing about these topics since a fair bit before multiverse ideas were really taken serious, so I make no apologies for that. By the time the book is published, I will reverse my usage to reflect the accepted convention.

So, a little history of cosmology:

Let's start with the Big Bang itself, because it was very much a conjecture, albeit one that was rooted in good science. In fact, we weren't absolutely certain it WAS good science at the time, because it was rooted in General Relativity, which was a new theory then.

The Big Bang is, in a nutshell, the name we have for the fact that the cosmos is expanding. It isn't the beginning of anything in any more than the most theoretical sense. There also isn't a single Big Bang theory, despite popular contrivances to that effect. As a famous physicist once commented, when asked by an apologist 'were you there at the big bang', the correct response is 'yes, I am', because all extant theories have a Big Bang in them..

It stemmed from the work of Georges Lemaitre, who first proposed that the cosmos was expanding based on Einstein's General Theory of Relativity from 1915. This was also independently proposed by Alexander Friedmann. Einstein had actually noted that GR implied that the cosmos couldn't be static if the fundamental equations of GR were taken at face value, and he didn't like this implication, so he introduced a fudge factor into the equations, the so-called Lambda term, or cosmological constant. A lot has been said about this over the years by people who want to romanticise, but Einstein was correct in calling it a blunder, despite the fact that modern cosmology has reintroduced the term. We'll come to that again shortly. Suffice it to say that Einstein's motivation for introducing it was entirely unjustified, because it was only because he believed the universe to be static (often, and not to be, confused with 'steady state', another term I'll come back to) and eternal. Lemaitre, a Belgian cleric, followed the equations, and posited first an expanding cosmos, and then the idea that it had a beginning in the so-called 'cosmic egg' hypothesis. Lemaitre was also the first to derive what later became known as Hubble's Law, which tells us in essence that the further away something is, the more quickly it's receding from us.

All of this was prior to Hubble actually making his famous observations, first that there were galaxies outside our own (it had been thought that extra-galactic sources were actually dust clouds or nebulae inside our own galaxy; Hubble didn't just show that the cosmos is expanding, he showed that there was far more of it than we'd thought, as detailed above), then that they were all receding from us.

So, now we have our expanding universe, and the classic Big Bang theory, but we've got some problems:

First, there's the horizon problem, a very specific problem with the classic Big Bang, namely that, as we look around the cosmos, we measure the temperature to be pretty much the same in every direction (isotropic). You'll have seen the images from COBE (Cosmic Background Exporer) and WMAP (Wilkinson Microwave Anisotropy Probe), no doubt, and the more recent Planck images of the CMBR:

Beautiful hi-res image here

You'll see that there are differences in that image, between the blue and the red bits. As you'd expect, the blue bits are the coldest bits and the red bits are the hottest bits (note that this image doesn't deal with the temperature of space, because space can't really be said to have a temperature; this is the temperature of the radiation pervading space, a measure of how quickly particles are moving; a bit of an aside, but it may become important later). Anyhoo, it looks like the temperature varies a fair bit, until you realise what those differences represent. The actual temperature is about 3 Kelvin, or -270 degrees Celsius, 3 degrees from absolute zero, and those differences are tiny, representing no more than a few 10,000ths of a degree. This is minuscule, and the standard Big Bang can't account for it. The problem is that at no point during a standard expansion have the furthest reaches of the cosmos been sufficiently close together for them to have reached thermal equilibrium, because they were always so far apart that even light couldn't have traversed the distance in the time the cosmos had been around. This was known as the 'horizon problem', and was one of those embarrassing things that arises now and then that the relevant scientists don't talk about. More on this shortly.

Then there's the flatness problem, which is a problem concerning why we measure the cosmos to be flat (Euclidean) on large scales.

The universe can basically take three 'shapes' on large scales (possibility of equivocation here, as I'll be using the term 'shape' to describe the actual topology of the cosmos shortly, so be aware); Flat, open and closed. 

The easiest way to think of this is in terms of either triangles or parallel lines. If the universe has positive curvature (Ω>1), triangles will have internal angles adding up to greater than 180 degrees and parallel lines will converge (i.e. Euclid's fifth postulate does not hold). This is like a sphere (a torus is a possibility). In the jargon, this is known as a de Sitter space.

If it has negative curvature (Ω<1), triangles will have internal angles adding up to less than 180 degrees and parallel lines will diverge (i.e. Euclid's fifth postulate does not hold). This is like a saddle, or a Pringles potato chip. In the jargon, this is an anti-de Sitter space.

If the curvature is zero (Ω=1), the internal angles of a triangle add up to 180 degrees and parallel lines will remain parallel (i.e. Euclid's fifth postulate holds). This is like a flat thing. In the jargon, this is known as a Minkowski space. 

Note that this is a 2D representation (both text and image) of a higher-dimensional principle.

So why is this a problem? Well, it's a fine-tuning problem to do with the energy-density of the cosmos. Note that fine-tuning here isn't open to apologetic manipulation, i.e. we're not talking about something that had to be fine-tuned by somebody twiddling knobs, it refers to specific parameters having to fall within a narrow range of values if the model in question is correct. In this instance, it means that the energy density of the cosmos has to be almost perfectly within a certain narrow range in order for the cosmos to be flat on large scales. In the above text, the energy density is the Omega term in the brackets. It's worth noting that, in the case of the universe being flat, the possibility is there for the cosmos to be infinite in extent.

Before I move on, a small clarification of what is meant by the terms 'expansion' and 'inflation', because they're not the same thing:

Expansion is simply the observed fact that everywhere we look, galaxies are receding from us, and the further away they are, the quicker they're receding (indeed, beyond a certain distance away, they're actually receding at greater than light speed, which we might naïvely think impossible, but it doesn't violate special relativity, because nothing's actually travelling through space at greater than c; I'll come back to this).

Inflation is a very specific idea, often confused with expansion. Inflation is a bolt-on, a fudge, if you like, designed to explain the 'horizon problem' dealt with above.It refers specifically to a period of very rapid inflation in the earliest moments of the cosmos, which is required to smooth everything out so that we see the degree of isotropy (sameness) that we observe.

So, we have our standard Big Bang model, which is rooted in observing that the cosmos is expanding. Wind it backwards, and it soon becomes clear that, at some point in the past, everything in the cosmos was much closer together. Then, in 1970, Hawking and Penrose presented a paper called The Singularities of Gravitational Collapse and Cosmology, which showed that, if General Relativity holds under the appropriate conditions, any cosmos that is spatially closed, or constitutes an object undergoing relativistic gravitational collapse, must end in a spacetime singularity. It's worth noting here what's actually meant by that term, because it's the source of much confusion, not least because the second word of it has two distinct definitions. The first is the popular conception, namely an area of infinite density and infinite curvature, physical in nature, while the second is a set of conditions that our physical theories are unable to describe. The condition described in Hawking and Penrose's paper is of the former type, and this is the idea that most people have of how the cosmos began, namely an expansion from this physical singularity. It's interesting to note that neither Hawking nor Penrose think that this describes our universe, not least because this type of singularity is actually an asymptote according to Quantum Mechanics, which means essentially that it's prohibited. Indeed, Hawking had this to say as far back as 1988:

"The final result was a joint paper by Penrose and myself in 1970, which at last proved that there must have been a big bang singularity provided only that general relativity is correct and the universe contains as much matter as we observe. There was a lot of opposition to our work, partly from the Russians because of their Marxist belief in scientific determinism, and partly from people who felt that the whole idea of singularities was repugnant and spoiled the beauty of Einstein’s theory. However, one cannot really argue with a mathematical theorem. So in the end our work became generally accepted and nowadays nearly everyone assumes that the universe started with a big bang singularity. It is perhaps ironic that, having changed my mind, I am now trying to convince other physicists that there was in fact no singularity at the beginning of the universe – as we shall see later, it can disappear once quantum effects are taken into account."

Now, this has some interesting implications, the first of which is what largely motivates the idea that time began at the Big Bang. It's an idea that stems again from relativity, and it's about the deep relationship between space and time and the equivalence principle (the idea that being immersed in a gravitational field and being accelerated are the same thing). It boils down to the fact that, at a singularity, because of the acceleration, time stops. I've mentioned before that this doesn't actually mean that time didn't exist before the singularity, only that the singularity didn't experience it (in much the same way that photons don't experience time, yet time still exists).

So, now that's out of the way, we can summarise the standard Big Bang model as the idea that spacetime arose from a physical singularity some 13.72 billion years ago. We're aware that there are some problems with it; the horizon and flatness problems discussed previously, and a couple of other issues, such as the coincidence problem, which is that the vacuum and matter densities appear to be roughly equal, and the smallness problem, which is that the Lambda term from General Relativity (the cosmological constant) is so small.

Then, in the 1980s, Alan Guth had an interesting idea, namely what if the cosmos had undergone a period of hyper-rapid inflation very early on? That would mean that the furthest constituents in the cosmos could have been sufficiently close together to equalise. This also solves a couple of other problems concerning the shape of space and the energy density of the cosmos. This inflation would have massively inflated space from a singular density, exponentially expanding to about the size of an atom or so (yeah, that huge! lol).

So what's inflation?

Inflation is simply the idea that, very early in the history of the cosmos, there was a period of extremely rapid expansion. During this period, quantum fluctuations occurred as normal but, because the cosmos was expanding at a ridiculous rate, these fluctuations were stretched out. It is this stretching of those fluctuations that we see as the tiny inhomogeneities we observe in the CMBR. Moreover, the details of the theory tell us that those inhomogeneities would have generated gravitational waves, and that those gravitational waves would a) fall within a certain range of the energy spectrum and b) polarise the photons in the CMBR in a certain mode, the so-called B-Mode polarisation that the BICEP2 experiment was thought to have identified.

Here's an image of the patch of the CMBR they were looking at with the polarisation indicated:

You can see the 'twisting' in a spiral formation around the hot spots. This was what they were looking at, as the photons were polarised (if you looked at them through a polarising filter, you'd have to tilt the filter to that angle in order to be able to see the photons) by the angles shown by the black lines. Unfortunately, the polarisation was discovered to be a result of dust, and once corrected, showed no sign of polarisation from primordial gravitational waves.

Here's Pulsar explaining:

"Here's the killer plot:

The black dots with error bars show the original BICEP/Keck results, the purple dots with error bars show the corrected results after subtracting the dust contribution found by Planck. The red line is the B-mode polarization that’s expected from gravitational lensing alone (so without primordial gravitational waves). Clearly, the new results show no hint of primordial gravitational waves, except for a slight (not statistically significant) excess signal around multipoles of order 200.

So for now, the champagne can be put back in the fridge. It's important to emphasize though that the BICEP experiment only looked at a small patch of the sky and at one particular frequency. We'll have to wait and see what the other ongoing experiments will reveal

One of the interesting things about inflationary theory, beyond the problems it solves, is that there is a broader theory dealing with how inflation occurs, and this broader theory has an implicit multiverse built in. The idea is that the fabric of the universe is constantly expanding, but different parts of the universe slow their expansion at different times, and this slowing causes little bubble universes to pinch off. That inflationary energy has to go somewhere, so it converts to the radiation that filled the early cosmos and became the seeds of later structure. This is well beyond the scope of current observation, though, and possibly inherently untestable, but the BICEP results, had they been confirmed, would have been taken by many to be strongly suggestive of a multiverse.

I should point out, regarding William Lane Craig's citation of BGV theorem as allegedly supporting his formulation of the Kalam, that Guth, for whom the G stands, does not think that, for example, time began at the Big Bang.

Here he is, comparing inflationary theory to the brane-worlds model, which will be up next:

"So far, it's been made to sound, I think for the purposes of simplifying things, that until the cyclic model, all scientists had believed that the big bang was the origin of time itself. That idea is certainly part of the classic theory of the big bang, but it's an idea which I think most cosmologists have not taken seriously in quite a while. That is, the idea that there's something that happened before what we call the big bang has been around for quite a number of years... In what I would regard as the conventional version of the inflationary theory, the Big Bang was also not in that theory the origin of everything but rather one had a very long period of this exponential expansion of the universe, which is what inflation means, and, at different points, different pieces of this inflating universe had stopped inflating and become what I sometimes call pocket universes."

He goes on to say:

"What we call the Big Bang was almost certainly not the actual origin of time in either of the theories that we’re talking about. … The main difference I think [between the inflationary theory and Neil and Paul's theory] is the answer to the question of what is it that made the universe large and smooth everything out. … The inflationary version of cosmology is not cyclic. … It goes on literally forever with new universes being created in other places. The inflationary prediction is that our region of the universe would become ultimately empty and void but meanwhile other universes would sprout out in other places in this multiverse."

Source, a radio interview with Guth and Neil Turok. 

Moreover, the theorem itself doesn't imply what Craig says it does. Here's the meat of the issue:

It stems from the work of Arvind Borde, Alan Guth and Alexander Vilenkin, and we can take a look at the abstract of the paper:

"Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime."

Inflationary spacetimes are not past-complete - Borde, Guth & Vilenkin - Arxiv 2001

Note the bold bit. They don't say that the universe requires a beginning, or even anything remotely like it. They are saying that inflationary cosmology alone cannot explain some of the issues with the boundary conditions of the cosmos.

 That seems a good place to leave this post, because I'm going to move on to branes next, and that requires an awful lot of groundwork, including a potted history of SR, GR and the standard model of particle physics.

In The Beginning

What does it actually mean for something to begin?

This is a question that has troubled philosophers for millennia and, contrary to the wibblings of some apologists, it's still a problematic question if not treated with some care.

When, for example, did this post begin? Did it begin when I hit the save button for the first time? How about when I first made an account to blogspot? Or maybe the wholesale demolition of a vibrant community, the event that drove me to seek out a new platform in the first place? Or maybe it was my birth in Croydon, or my parents' births, in Nenagh and Turloughmore respectively? There are many points I could describe it as beginning, and all would be entirely arbitrary.

Now for the care, which will require the unpacking of some terms. The first of these terms is ex nihilo, which means 'from nothing'. Some religious types will tell you that for something to begin from nothing is not possible, and they even have a kinky Latin phrase to make it sound like they've given the matter more than a cursory glance; ex nihilo nihil fit - from nothing, nothing comes - attributed to Parmenides sometime around the turn of the 5th century BCE. Of course, what they can't do is to show this in any robust fashion, they merely assert it, and will often point to the thoughts of past philosophers as their only justification. This attempt at justification has problems deeper than those with the assertion itself, for reasons I hope to elucidate shortly. In brief, we can point to phenomena that arise quite literally from nothing, but in a very special sense.

The second term is ex materia which, as the astute reader will no doubt spot, means 'from material'. This seems to gel well with our understanding of the universe, and especially the laws of thermodynamics, but even this is laden with issues when we try to apply it to the universe as a whole. More on that later. All of the 'beginnings' we've ever encountered have been of this type (with some qualification, which appears below).

The third term is ex deo, or 'from god', which I hope requires no further explanation. 

Often, this discussion is couched in terms of 'cause', which relies on concepts handed down to us from Aristotle. Aristotle, student of Plato and tutor to Alexander the Great, is considered by many to be the first true scientist. As I said in my introductory post, there's a good reason we pay attention to what Aristotle said, and that reason isn't that he was right. Indeed, he was often wrong, and sometimes 'not even wrong'. To highlight this concretely, he concluded, through reason alone, that women have fewer teeth than men. He reasoned this based on nothing more than conjecture, and wouldn't be swayed from it. He could have sorted it all out, of course, by the simple expedient of having some passing bint open her gob and counting. The problem was that Aristotle was so impressed with himself that he thought he didn't need to. Besides, observation and measurement were the work of artisans, and entirely beneath him. In many ways, Aristotle was an idiot, or at least, we'd recognise him as such today. If you look at those of his ilk around today, such as William Lane Craig, we quite rightly ridicule them (of course, it's more probable that, were Aristotle alive today, he'd be in the peanut gallery along with us). We've come a long way from thinking that the umbilicus was a source of information about anything other than the colour of the lint therein (or some of us have, at least).

That's not to say that Aristotle was wrong about everything, of course, it only represents a caveat to putting stock in such authorities. Aristotle is largely talked about today because he earned his place in the history of ideas, but we shouldn't be talking about Aristotle at all when we're talking about modern physics, for example, because he has nothing remotely of interest to say on the topic, any more than we should listen to him on the topic of feminine dental hygiene. He wasn't privy to several thousand years of gathered evidence and, as a result, much of what he said, particularly about 'cause', is total bollocks. This caveat can be expressed in the term argumentum ad verecundiam, meaning 'argument from authority', a crystal clear logical fallacy. There'll be more about fallacies later (one of the coming posts will be specifically about logical fallacies), and I'll link to some helpful resources on the topic at the bottom of this post.

This brings me to another important point concerning how philosophy is taught. As Alfred North Whitehead noted, Western philosophy is a series of footnotes to Plato. This is largely correct, but there's a danger here; it's all too easy to think, especially for one who's studied philosophy in a formal setting, that doing philosophy consists of nothing more than learning by rote what others have said. In my introductory post, I implicitly warned against this in the statement concerning the collection of ISBN numbers. Far too many of those who've studied formally have missed the point of philosophy, which I shall encapsulate as follows:

1. Ideas are disposable entities.

2. Bad ideas exist only to be disposed of.

3. Philosophy is the art of disposing of bad ideas.

Now, this all looks fairly straightforward, doesn't it? Of course, it gets a bit more complicated where the pick meets the coal-face, but not intractably so. The first two statements are fairly uncontroversial, although the first of them might seem on the face to be a problem, because it is, in itself, an idea, and should thus be considered disposable. However, when we start looking at the means by which we dispose of bad ideas (and indeed of assessing whether or not an idea is a bad one), it should become clear that there is no issue.

So, how do we go about disposing of bad ideas? Well, we begin by assessing an idea for whether it's bad. And how do we do that? Simple; we learn to ask the right kind of question about it. This is what's at the heart of philosophy; learning to ask the right kind of question.

There's a famous quotation by Nobel laureate Richard Feynman dealing with how we go about discovering a new physical law. You can find it in the Feynman Lectures on Physics, and in the book The Character of Physical Law, both of which I recommend highly. Here's a clip from the former with that quotation:

Note the latter part of that quotation:

"If it disagrees with experiment, it’s WRONG. In that simple statement is the key to science. It doesn’t make any difference how beautiful your guess is, it doesn’t matter how smart you are who made the guess, or what his name is… If it disagrees with experiment, it’s wrong. That’s all there is to it."

So, what Feynman is expressing here encapsulates nicely how we go about testing ideas in science. The important part of it is, of course, formulating the right kind of question. In this instance, the question is 'what would this idea imply about what we should observe?' Feynman expressed it succinctly as 'compute the consequences'. Once we have that question in place, we can start to devise an experiment that should manifest those consequences. If those consequences do not manifest, we should modify the idea to reflect this circumstance or, where that effect is critical to the correctness of the hypothesis, we should discard it. 

If my guess is correct, I should observe this consequence in my experiment designed to look specifically for that effect. I didn't observe that effect, so my guess is not correct.

Some effects will be critical to the idea, while others are corollary effects, the non-observance of may not fatally undermine the hypothesis, but will require the modification of the hypothesis at the very least, and the devising of new experiments to test whatever consequences are implied by this new hypothesis. You can think of a hypothesis as a machine for generating predictions, because that's what it is.

I should also note that, in the sciences, there's another, related principle employed for testing ideas, namely the null hypothesis. In a nutshell, it's a reversal of what's been expressed above, and it takes the form of a prediction regarding something that will definitely not be observed if the hypothesis is correct.

If my guess is correct, I will definitely not observe X effect. I observed X effect, so my guess is not correct. 

These two principles can be expressed neatly in propositional form, and they form the basis of what Karl Popper called 'falsification'. They take the form of the modus tollens, which will be familiar to those who've studied any philosophy or logic. Formally:

P => Q, ¬Q

(Proposition P implies Q, not Q, therefore not P)

And the negative form, or null hypothesis:

P=>¬Q, Q

(P implies not Q, Q, therefore not P)

As an aside, you may hear it said that proof does not apply to science. This isn't actually true, as the above should readily demonstrate. Properly defined, proof is a formal procedure, applicable only to axiomatically grounded systems of deductive logic, in which a route is taken from true premises (axioms) via valid rules of inference (reasoning) to a conclusion that is necessarily true. Axiomatically grounded simply means that all our axioms, or premises, are definitely true. Mathematics is an axiomatically grounded system, so it's certainly true that proof applies, but a sound syllogism (such as the modus tollens above), for example, is also axiomatically grounded (I'll have more to say on syllogisms shortly). Because the majority of scientific epistemology is inductive, we can only say that we have a degree of confidence that a conclusion is probably true. You'll hear it said that the difference between deduction and induction is that deduction reasons from the general to the specific while induction reasons from the specific to the general. This is also untrue, although it does serve as a vaguely useful first approximation. The real difference is that deduction leads to conclusions that are definitely true, while induction leads to conclusions that are probably true. So, we observe an event that falls in line with our conjecture, and each new supporting observation increases the confidence (probability) that our hypothesis is correct. This expresses David Hume's famous 'problem of induction', namely that, while confirming observations increase our confidence in the truth of a conclusion, they can never actually demonstrate its truth, because that would require that all possible observations have been made and that no falsifying observation is possible. This would, of course, require omniscience, which is self-refuting (I treat the three famous omnis here).

So, we test ideas. In science, this is usually reasonably straightforward (although not always, as some areas are horrendously difficult to test properly), but it's not always possible to test ideas this categorically, not least because not all ideas have consequences that manifest physically, or in testable ways, so we have to look at other kinds of question (I'll be revisiting this shortly). We might, for example, look at the premises employed in arriving at a conclusion and asking ourselves if there's axiomatic groundedness, i.e. whether the premises are actually true. In any case where a premise is not shown to be true, we can reasonably be suspicious of any conclusion drawn therefrom. This is the core of skepticism (there are those that insist that skepticism is the rejection of all claims, but this is little more than an attempt at poisoning the well; it's not skepticism to reject claims that have good support, only to be wary of claims that do not).

We can also look at the route from premises to conclusion to see if proper rules of inference have been applied in arriving at the conclusion and, where any route is suspect or the conclusion doesn't follow from the premises, we are again enjoined to be suspicious of the conclusion. That doesn't mean that we should reject the conclusion outright, even where an argument has been shown to be entirely invalid, but we have good reason not to accept the conclusion on the basis of that argument. 

Note that any problem with the soundness of an argument is grounds for not accepting the argument. It doesn't matter whether the issue lies in the form of the argument, in the route from premises to conclusion or in the veracity of the premises, any failure of reasoning is grounds to be skeptical of the conclusion. 

I should also note that any argument that contains anything inherently untestable or unfalsifiable fails on those grounds alone, and no further attention need be given to it.

So, now the groundwork is out of the way, let's get back to talking about beginnings:

There's a famous, ancient argument for the existence of god. It stems from Islamic theology, specifically the Ilm al-Kalam, or 'science of discourse'. Today, we know it simply as the Kalam Cosmological Argument, and its main modern proponent is William Lane 'Kalamity' Craig, whom we met earlier.

Craig has gone to book length in laying out this argument and justifying his premises and has, despite having had it eviscerated from every conceivable angle, continued to give voice to it in public debate. Here, in this post about beginnings and having laid out the beginnings of what it means to be a scientific skeptic, I wish to use it as an example of how not to do philosophy. One might think that I, as a non-philosopher, attacking an argument formulated at great length by somebody with a double doctorate in the discipline, am overstepping the mark, but what I'm really demonstrating is that collecting ISBN numbers is not doing philosophy. Some professional philosophers have described Craig's formulation of the Kalam as one of the most sophisticated theological arguments of the modern era. I describe it simply as sophistic.

So, here it is:

P1. Everything that begins to exist has a cause for its existence.
P2. The universe began to exist.
C. The universe had a cause.

Seems fairly intuitive, doesn't it? So what's the problem?

To get to that, we need to unpack the argument properly. Craig does this at book length but, luckily, in public debate, being the extremely talented Gish Galloper he is, we're lucky that he's condensed it to key hit-points. Let's go one step at a time.

P1. Everything that begins to exist has a cause for its existence.

Craig even defends this premise as being 'intuitively true'. That's problematic for a start. It's intuitively true that time runs the same for every observer except, of course, that if it were actually true, your satnav system would be a pipe dream. It's intuitively true that something cannot be in two places at once except, of course, that if it were actually true, the technology I'm employing to share my thoughts with you today wouldn't even rise to the level of fantasy. It's intuitively true that I can't walk through a wall (I've never managed it yet) except, of course, that if it were actually true we couldn't exist, because fusion in stars wouldn't occur, thus elements heavier than the beryllium (in trace amounts, along with hydrogen, helium and a small amount of lithium) that theories predict was synthesised in the Big Bang would be impossible. This fallacy is the 'appeal to intuition'. Some, notably David Chalmers, have attempted to defend this as not a fallacy, but it's an irrelevant appeal and can be dismissed on that basis alone. Intuition is helpful in formulating hypotheses but, as support for an argument, it's arse-gravy.

How about the claim itself? Well, two of the examples of things that are intuitively true given above raise some problems for its factual correctness, not least because we can point to no cause with regard to quantum tunnelling, which is responsible for both fusion in stars and the device I'm holding forth on to deliver this little missive, the implication of which is that it's perfectly possible for me to walk through a wall, though I'm quite a large fella, so it's unlikely to happen in the life of the universe, but it's also purely a matter of scale. The laws that govern these processes also imply something else. The underlying principle here is Heisenberg's Uncertainty Principle. In a near-future post, I'll be doing some cosmology stuff, and I'll cover this at some length but, suffice it to say for the moment that a consequence of that principle is something known in the jargon as 'pair production' which, in a nutshell, involves pairs of particles (properly a particle and an anti-particle), which borrow a little energy from spacetime, pop into existence, move apart, and then come back together and annihilate (because their energies cancel out, or 'sum to zero'). This effect has been measured by virtue of a very clever thought experiment, the physical experiment for which was realised some years ago, and the behaviour matched the predictions with ridiculous precision (this has been compared with being asked how far you were from the moon and the response being 'from the top of my head or my chin?'). We can point to no physical cause for this behaviour (the question of whether it can be described as ex nihilo is a separate question, but it doesn't favour the argument; I'll cover this in the next post). Now, while we can't categorically state that those events have no cause, they give us some pause. In short, the premise commits, at best, the fallacy of bare assertion and, at worst, is counterfactual.

What about the second premise?

P2. The universe began to exist.

Here Craig brings in arguments from all sorts of places, not least Big Bang cosmology and mathematics. He asserts that 'an actual infinity is impossible', with no justification whatsoever. I'm no mathematician, so I won't attempt to address the mathematical claim itself, but there's a beautiful analysis of this by Wes Morriston of CU Boulder, so I'll simply link to it (pdf).

How about the cosmology? I'm going to be treating this extensively in the next post, which will deal with specifically where our current understanding is, what our best options for future progress are, and precisely why the claim simply doesn't stack up.

Craig is relying on an extremely rudimentary understanding of Big Bang cosmology. He asserts that Big Bang cosmology involves the universe having a beginning. To properly treat this assertion, we need to clarify precisely what we mean by 'universe'. More precisely, we need first to differentiate between the observable universe and the universe at large (many use the term 'multiverse' to deal with all such concepts, including those concepts that deal with only our cosmic expanse, but I'm not fond of the term). What Big Bang cosmology deals with is our local cosmic expanse only and, in fact, it doesn't even deal with the beginning of that in any robust fashion. I want to leave the majority of the meat of this topic to my next post, as it will address it far more completely and deserves to be treated separately. For the time being, we only need note that, without defining the term 'universe', and only citing broad areas of cosmology as purportedly supporting the claim that the universe at large began to exist, we can reasonably reject this claim as unsupported. 

I should also add that, while Craig's argument relies on the impossibility of an actual infinite, the singularity theorem, upon which his assertion that time began at the Big Bang is predicted, constitutes an actual infinite, which is sufficient to defeat that support on its own terms.

Craig also cites Alex Vilenkin, Arvin Borde and Alan Guth, and their paper Inflationary Spacetimes are not past-complete from 2001 as allegedly asserting that the universe must have had a past boundary, but this assertion is simply counterfactual. BVG theorem deals specifically with inflationary cosmologies, and only states that new physics is required to explain inflation. You'll note that this is a very different claim. Again, this will be treated in more detail in my next post, but the take-away here is that a) BVG theorem does NOT state that the universe must have had a beginning and b) not all cosmologies are inflationary.

Suffice it to say that, once the alleged support for this second premise is analysed in any detail, it's shown to commit yet another fallacy of blind assertion. It's reasonable to be skeptical of the conclusion on this basis.

So, now that the premises have been treated, what about the route from conclusion to premises?* Is it even valid?

Sadly, no, there isn't even any consolation for Craig here. He's identified a principle that appears to prevail within the cosmos, then applied it to the cosmos itself. This commits the informal fallacy known as the 'fallacy of composition', which is committed in any argument reliant on the idea that a property of the parts is a property of the whole. This is easily exposed by telling you that the second Interview With Matter album Remotion (produced by yours truly, incidentally; album three, as yet untitled, is running on rails at the moment, and should be released shortly, time permitting), is composed of tracks that are all less than ten minutes long, yet the album itself is just a smidge over an hour long. This is because the property 'length of time' is not expansive. Whether the apposite principles that apply within the universe are expansive is not known but, given the current state of cosmology, there's good reason not to rule out the idea that they may not be.

There's another fallacy in there between the first two premises in the term 'begin/began to exist'. Here, Craig is relying on two very distinct definitions of beginning to exist, namely ex materia, and ex nihilo. Thus he commits a fallacy of equivocation.

Recall that any error in reasoning, formal (having to do with the structure of the argument) or informal (having to do whether proper rules of inference have been applied other than in the structure, which mostly involves ascertaining whether or not the premises are true (is it really the case that P=>Q?)), is sufficient to cast doubt on the truth of the conclusion. In other words, we can consider the argument 'unproven'. As a system of deductive logic, this argument is not axiomatically grounded. In fact, it's only the fallacies holding it together.

Watch out for a reasonably comprehensive treatment of cosmology in the next few days, including a potted history of physics and brief material on relativity and quantum mechanics.

Thanks for reading.

A Taxonomy of Logical Fallacies

* Edit: This was a typo, and should have read 'the route from premises to conclusion. I thought about editing it out, but then I realised that the typo is perfectly apposite, because Craig's entire argument is one whose circumference is related to its radius by a multiple of π. Indeed, his entire career is not only circular but, given the breadth of his influence on the credulous, he might be described by Swiss astronomer Fritz Zwicky as 'spherical'.


Welcome back!

Here I just want to lay out what can be expected of this blog. What follows began as the germ of an idea on the Richard Dawkins forum some years ago, prior to its ignominious demise. It was eventually to be a book, compiled from the posts of the members of the forum, and dealing with how we think about things, what we think of as knowledge, and why we think that. The idea was to lay out, in easily accessible terms, how to go about assessing truth-claims, what tools were necessary and how to acquire them.

Now, for those coming to these pages for the first time without any prior experience of my output from all the places on the internet in which I've been writing for the past decade, I should probably declare my prejudice - or, more accurately, post-judice - up front: I'm an atheist. This doesn't mean, for me, that I actively believe that nothing that could reasonably be described as a deity exists, only that I don't actively believe that any such entity does. But that's a topic for another post.

In each post, I'm going to try, as comprehensively as I can, to tackle a specific area, or a specific claim. Some of the posts will be addressing common arguments for such claims such as deities, aliens (and the probability that we might have been visited by them and/or anally probed), expanding Earth, creationism (and ID, a.k.a creationism in a stolen lab-coat), perpetual motion machines, claims concerning evolution, superluminal travel, quantum teleportation (and what we actually mean by that), and a whole host of other things.

When I joined the Richard Dawkins forum, it was somewhere I'd just chanced upon, while looking for some scientific information pertaining to a particular claim. I'm an autodidact, and a didact. I love to learn, and I love to teach. In the forum, I found somewhere that I could do both, the former by engaging with tenured professional scientists in their fields of study and testing my understanding against that of the professionals, and the latter by delivering that learning to others. I've always enjoyed finding really good analogies that firm up my understanding of a subject area, and I found I had a knack for formulating and delivering them. Oh, and swearing. A lot. Here's a nice précis of why this is desirable and, some would argue, even necessary (though not in the technical definition of 'necessary').

There was such a wealth of knowledge and understanding there, and plenty of instances of those with claims they wanted to lay at the door of the heathen skeptics to see if they stacked up (they fairly uniformly didn't). It occurred to me that it would be wonderful to put all of that knowledge and understanding in one place that one could pluck off one's bookshelf at will and peruse. Then the forum went tits-up.

We moved ourselves, and set up a new forum at Ratskep, and the idea went on the back-burner. I toyed around with it for a while, and it internally morphed into a book just about what I'd learned about thinking, about science, and about how to assess truth-claims.

What will unfold here is basically that idea, though it will be all my own writing.

With all of the above in mind, I wish to acknowledge the help I've had from many and diverse people over the years, far too numerous to recall completely. This set is composed of all the people I've ever interacted with during discussion of these topics including, and in some cases especially, those with whom I've shared disagreements. I would like to name a few, though. I'll use their forum names, as I don't even know quite a few of their real names. They can mostly be found at the above address, or in some other places which I'll link to.

First, I want to thank LIFE, for providing us with a lifeboat after the night of the long knives. Calilasseia, famous blue flutterby, entomologist and mathematician, whose broad knowledge of diverse topics, including an almost autistic knowledge of Linnaean Taxonomy have, at various whiles, kept me astounded and entertained in equal measure. Goldenmane, because he's a cunt. DarwinsBulldog, for his steady stream of new material from the primary literature, especially in evolutionary theory, and for his challenges to my own thoughts. I especially want to thank Twistor59 and Campermon, physicist and physics teacher respectively, for their invaluable input in firming up my understanding of relativity and quantum mechanics.Pulsar, for the  brilliant knowledge of physics, the beautiful sums, and the fantastic LaTeX tutorial (shame it isn't working...), Vazscep and Thommo, mathematicians and logicians, for not laughing too hard when I talked crap about mathematics, and for helping me to find things to say about it that weren't crap, as well as for being among the only people I know of who can talk about consciousness without talking through an orifice most readily associated with a more solid form of waste, to borrow a phrase from the aforementioned blue butterfly. Vazscep also warrants a special mention for helping me out with Gödel's incompleteness theorems. susu.exp, for his encyclopaedic knowledge of the minutiae of the modern quantitative synthesis of evolutionary theory, probability, chaos, Bell's theorem and its implications, and many other areas. Darkchilde, for her helps with various areas of physics and mathematics. Evolving, for hers. Fallible, for her incisiveness and her humour. Cito di Pense, for his wonderful sarcasm and often labyrinthine prose, which I always liken to Edmund Blackadder on steroids, and for his laser-like precision in identifying the guff. Speaking of lasers, Occam'sLaser, for his pragmatic analysis. ADParker, for the same reason. surreptitious57, for that trick so beloved of three-year-olds (but why..?) which, while sometimes frustrating, always has me grasping for better ways to explain things, and keeps me looking closely at what I think I know. Starr, for her patience and for her impromptu songs about forum members. Pappa and Rachel, for just being fabulous friends. Rumraket, for his exceptional knowledge of evolutionary pathways and the chemical foundations thereof. Genes4Life, research oncologist, who may one day change the world, for his dedication to real knowledge, his height and his ability to dodge raindrops (seriously, if you want to see string theory in action, he's yer man!) Shrunk, headshrinker, for his takedowns. Sciwoman, whose coming-out tale still puts a lump in my throat. Paul Almond, philosopher, for his analytical skill and humour. Sendraks, ScholasticSpastic (quoted as saying that you've got to be a real asshole to quote yourself), and many others. Spinoza'sGalt, for my lovely avatar, and for his incisiveness. Also AndromedasWake, AronRa, Lawrence Krauss, Gawdzilla, JustATheory, Cdesignproponensists, RoaringAtheist, Opiedid, Concordance, Potholer54, my old friend DPR Jones, CDK007, Ozmoroid , philhellenes and, indeed, all the rest of the rationalist crowd at Youtube.

I could keep this up at some length, and I'll necessarily miss some off that I would have wanted to include, so I'll simply say thanks to all the members of RDF, Ratskep, Rationalia, The League of Reason (these latter two especially for opening their doors to us after the demise of RDF), the Atheist Foundation of Australia, TalkRational and all the other forums and social media groups I've contributed to and learned from over the years.

I'll add the usual clause here about how anything I get right is due to all those people I listed above, while anything I get wrong is my own fault. I'm more than happy to accept serious corrections, though it isn't my intention to make this a debate platform. 

So, are we sitting comfortably? Then let's begin. And where should we begin..?

Edit: Just for info, where you see blue text, it's a link. Where you see yellow text, it's a footnote in a mouse-over pop-up.

Giving Something Back

Well, folks, it's been a while.

I've made several aborted attempts to resurrect this blog since my first foray into my public meanderings, but problems logging in, distractions elsewhere on the internet and in real-life have meant that this has been somewhat hapless. 

After much mucking about on forums and social media platforms of various stripe, I've now pretty much extricated myself from the web and, having failed to make any serious headway on the book I promised my readers almost a decade ago, I feel like it's time to knuckle down and do some serious writing.

This is an introduction to what I hope will be a concerted effort to finally make sense of things, as well as a place to distil the things I've been thinking about for the past several years into a single, coherent entity.

Under the rubric of this blog, it's my intention to post on various subjects, mostly geared toward the book, which means that much of the content will be about reason, logic, learning, and the importance and utility thereof, politics, science and philosophy (with due caveats regarding the separation of the latter two), but I'll also be including some interesting stuff about music and music production and various other topics .

Warning: There will be equations. I hope to keep them reasonably simple and straightforward, and I'll certainly be explaining everything as I go, including how equations and mathematical notation work, how to work out what numbers should be plugged in and what said equations mean.

Ultimately, the aim of this blog is to give something back, especially to all those people who've contributed so generously to my education over the years. Wherever possible, I'll name them and link to the writings by them that opened windows into reality for me, so that others may benefit from their knowledge and wisdom.

Most of all, I want to talk about logic and philosophy, what their remit is, how they're used, and how most of what people think of as being philosophy isn't philosophy, and what most people think of as being logic isn't logic. 

These latter might cause some consternation, not least because I'm really not a philosopher, at least in the classical sense. I think, though, that it's time somebody really drilled down what philosophy is about, not least because it's massively misunderstood, especially in the academic world, in which philosophy comprises having a ready list of ISBN numbers. Such work isn't philosophy, it's book-keeping. There's a reason that we teach philosophy the way we do, and it isn't because Aristotle was right.

Properly, this is going to be a blog about what we think we know and why we think it constitutes knowledge. The most important term in there is 'think', for various reasons: 1st, whatever we think we know, we can only ever think we know it. It MUST be held provisionally (there will be some clarification later, because there are things we can know with absolute certainty, but we have to be extremely careful in distinguishing them, for all sorts of reasons that I hope will become clear). 2nd, this is first and foremost about thinking, and in fact thinking about thinking, or metathinking.

Here's hoping that somebody's still watching this, and that it finds you well.