Wednesday, 17 October 2012

The Mathematical Bias Theory: Why There Probably ‘IS’ a God – in 20 Steps

This was written a couple of years ago, but as the subject is always cropping up, I thought I’d present it as a Blog post.  Look around and you and you’ll see a plethora of junk theology and pseudo-science centred on Creationist ideas and Intelligent Design movements.  I reject Creationism and Intelligent Design as being fabrications of the truth.  What’s often missed, though, is that real, authentic science gives (I think) some kind of exhibition to the Divine Cosmic Mathematician behind the law and disorder of the cosmos.  So here are a few ‘back of the envelope’ style jottings on why I think there almost certainly is a God.  I’ve decided to call it The Mathematical Bias Theory: Why There Almost Certainly ‘IS’ a God – in 20 Steps

God: The Cosmic Mathematician?

In science we don’t start by assuming we have all the answers on a plate ready for easy consumption – we spend our time bringing together information and ideas on how to assess variable and diverse protocols, and we work hard to bring them into exquisite theoretical descriptions.  To this end, and through a particular lens, science is descriptive inasmuch as it is about deciphering mathematical patterns that are imposed upon the substance of the cosmic order.  There are many facets to this deciphering that remain too complex or too multi-dimensional for a full cognitive purchase, particularly when we talk of the deeper scientific questions.  Even the complex patterns generated through our observations in, say, quantum mechanics are so complex that they only permit statistical descriptions.  So, naturally, statistical descriptions are human constructions that approximate a reality ‘out there’ – and they can only be considered accurate to the extent that we can formally conjecture about them and create models and labels to communicate them. 

Various proposals have been put forward by physicists about descriptions of nature; there are speculations about string theory, M theory and other conjectures about multi-dimensionality; conjectures that at sub-Planckian levels the universe has no dimensions at all and is just an arrow line.  We’ve had different conjectures about what spacetime is, the nature of gravity, non-linearity effects in spacetime, a geometric duality that reverses linear dimensions and undermines spacetime, theories about the true nature of particles and waves, or differing kinds of energy and mass relative to differing speeds – the list goes on.  All those examinations have one thing in common – they won’t tell us if there a Divine Cosmic Mathematician underpinning it all, because they are heuristics that deal only with the descriptive aspects of nature’s law and disorder.  As the last few thousand years of science has shown, our heuristics are almost always subject to augmentation with further knowledge and technology.  Most importantly, though, descriptive science cannot eliminate the burden of contingency related to the ‘Why is there Something?’ question. 

I’ve said all of the above for one good reason; grand theories that explain reality will not take the form of descriptive physics – they will take the form of a conflation of mathematics and philosophy, because both those subjects bootstrap our physical descriptions - and physical descriptions of reality are not complete, as they only simulate possibility.

What I’m going to say isn’t one bullet-pointed proof of God – it is a picture of a worldview that suggests to me that the cosmos is designed by a Cosmic Mathematician.

1) If mathematics is the language to describe the signature of God as some sort of Cosmic Mathematician, then nature can be modelled by some sort of mathematical template or blueprint that deals purely with constitution in numbers.  This is because when seen through the mind of omniscience, nature as we know it and engage with must be amenable to statistical description if concepts like laws, patterns and information are to mean anything. For this reason, given that at a simple human level mathematics is the language we use to embed conceptual reality into patterns of description, I can conceive that a complete and totalising description of reality in the mind of omniscience will be (at least in one form) a complete set of information that consists of mathematical pattern storage.

2) Given that nature is reducible to bits of information, then to an omniscient mind (with no gaps in knowledge) the whole cosmic spectrum of law and disorder is computable - so even though omniscience has other forms of complex conception that we cannot grasp, we know of at least one way to describe nature in that way – a description of pure pattern storage.

3) Given the foregoing, a fairly obvious corollary follows.  Nature provides us with a form that is descriptively compressible.  But descriptive science can only compress so far - we reach a point at which our road to compression hits a conceptual brick wall.  Further, even compression doesn't tell the full story because each physical compression requires an algorithm, so the ultimate compression of our cosmos must involve algorithmic precursors to enable compression, so whichever way we look at it, we seem to be faced with a reality that ‘just is’ – and that seems like a miracle. 

Note: Mathematical compression is not to be confused with the reducible complexity found in the material substrate.

4) Given that information is measured using probability, and probability doesn’t have a negative value, the formal structures of data compressing equations and algorithms must always return ‘something’ not ‘nothing’ – so we can’t reach the point of reducing or compressing the universe out of existence or ‘to nothing’ anymore than we could compress one of Hooke’s springs to zero. 

Note: Most complex forms can only be converged upon algorithmically if either the algorithm is executed for a period of time far beyond the capacity of any human or computational machine or if we had access to the initial precursory conditions.  There’s no way of escaping it - given what we know of our universe, those precursory algorithms would have to be alarmingly complex if they underwrite our cosmos, because we know how alarmingly complex our cosmos is, even in its most elemental statistical descriptions.

5) When it comes to ultimate explanations, complexity only comes from precursors that are also at the upper end of the complexity spectrum.  That's not to say, in the simple physics of our universe, that with a long execution time simplicity cannot produce complexity, because it can - but that's not a satisfactory 'ultimate' explanation, because it fails to eliminate the burden of contingency, and it doesn’t leave us with a plausible ‘just is’ closure – it only relates to mathematical patterns ‘within’ physics.  An algorithm posited as an ultimate explanation must be scrutinised to provide a reason why it exploits a principle that is algorithmically ordered at all - and so, we are left with a multiple regression of 'why?'

6) At the heart of “something” the mathematical configurations must be complex, because at every instance we are always left with complex brute fact algorithms.  At the very least we know that any bootstrapping algorithms must have complex blueprints because we know for a fact that this universe has an incredibly complex blueprint.  In fact, if the cosmos is genuinely open ended (stress, ‘open-ended’, not infinite) and randomly generated in its output, which it seems to be (stress, ‘randomly generated’ is not to be confused with the ‘random configurations’ in the spectrum of order-disorder) then the algorithm that underwrites the cosmos may well be as long as the cosmic data itself, and that won’t just pop up out of nothing.

Note: Considering the patterning view of randomness - it is a dynamic that produces a sequence, and this could be anything from a book of random numbers, through to a computer printout, to the heads/tails sequence of coin tossing.  Hence if we have, say, a coin that we continue to toss, as far as the patterning notion of randomness is concerned, the eventual sequence of heads and tails stretches out producing a pattern notion that has a denumerable (in other words, ‘countable’) set of possibilities available to it, and so we know that the sequence generated by the coin tossing will assume one value taken from a countable set of possibilities, it’s just that we don’t know which one!  The patterning view of randomness sees that the ‘to-be actualised’ possibility is simply an unknown pattern stretching out into the future before us!  This is configurational randomness; it is a rigorous mathematical description of what our intuition tells us are ‘untidy’ and complex sequences of 1s and 0s.  So, a configurationally random sequence is a particular class of pattern.

7) Given the foregoing, the universe and all its laws are bootstrapped by complex algorithms, and as complex algorithms of that order will not just pop up, nor are they intelligible at all unless they are reified on an up and running sentience, there seems to be a senselessness without a mind to reify them, because patterns are meaningless without a mind to interface with them.  What this hints at is that the universe is endowed with a network of computation that is itself only intelligible if 'mind' is at the core of that intelligibility.  It appears very plausible that complex sentience bootstraps the kind of universe we find ourselves in, and in an extraordinary way, our minds make everything intelligible by reifying those concepts.  To that end, the relationship between mind and mathematics can be regarded as being extraordinarily ‘hand in glove’.

8) In our universe of compact and neat physical laws we can conceive of a type of data compression, because it is the ordered patterns that make it amenable to compression.  However, like all data compression, there comes a point when no further compression can take place, so we are left with this problem of what I call an ‘is-ness’ that just won’t go away and cannot be removed from the burden of contingency.  That is to say, I’ve said that those compact and neat physical laws in our universe cannot be compressed to a mathematical zero, but what of the patterns that provide the compression for those laws? 

9) In the morass of disorder those highly compressed compact and neat physical laws would be highly unrepresentative patterns in that configurational system.  Pictured mathematically, what we have is a mathematical generating system that generated mathematical configurations which tended towards maximum disorder, yet embedded a constraint on itself to produce the order of stars, planet, life, and minds that would go on to understand concepts (including those of God) with high level self-awareness.  This wouldn’t be unreasonably construed to be giving exhibition to conscious sentience creating and sustaining the cosmos in its vast mind.

Note: In trivial and simplistic form, most of these algorithms are counting operations which involve systematically sifting through a search space of all possible permutations of characters.  Whichever way we look at it, whether from a theistic or naturalistic perspective, knowledge of the entire cosmos would bring with it a system with a permutation of characters that effectively holds the data describing our cosmos – and this will consist of a finite map of information, with a scale of order and disorder, and this what we are looking at here.

10) Logical incompressibility has to do with equations and algorithms used for data compression.  Although in mathematical terms it is true that physics effectively defines a set of stable structures in morphospace (where morphospace = the richly ordered mathematical configurations that facilitate biochemical life) - with the random walk of morphospace and physics, combinatorial space has a huge class of possible configurations which simulate many other alternative possibilities embedded in the mathematical potential. 

Note:  Combinatorial space is the level at which something is computationally complex – and hereby refers to the space of possibilities that are unconstrained by an evident set of mathematical laws and constants.  

11) Clearly amongst the class of every cosmic possibility the overwhelming number of configurations in the cosmos tends to more disorder than order.  Inside that class, the complex ordered configurations of life has a representation as very very very negligible (1 in 10 to the power of many many many trillions).

12) Even if we are the only life in the entire cosmos (that is doubtful), and our history does appear somewhat cosmically fortuitous, this outcome (when compared to the vast number of possible configurations that tend towards disorder) is a vast over-representation of an otherwise very unrepresentative class of configuration in probability terms. So instead of wondering why the universe seems so life-unfriendly, the question is rather; why does the cosmos have this extraordinary mathematical bias that allows it to facilitate any kind of order at all?

13) We know that the universe is expanding.  Expansion is part of a universal principle from the maximum order of the big bang (zero entropy) to greater and greater disorder as expansion increases.  Maximum entropy is everything we should expect from an expanding universe, yet against all odds we have living things with low entropy.  And the astonishing thing is this; the only time in the history of the universe that we should expect to see the sort of low entropy we see in systems like life, or even planets and stars, is at the point of the big bang.  After the initial expansion every instance of spacetime should be more and more disordered, but it isn’t – we are here to testify that it isn’t, because despite an increased acceleration towards disorder, there are huge mathematical constraints on the universe.

Note: I must bring to attention one common misconception about how nature behaves with regard to thermodynamics.  The second law of thermodynamics says that in a closed system disorder increases with time, but some people would likely disregard the possibility of the huge mathematical constraints I am talking about by pointing out that amongst the tend towards disorder when one bit of the system becomes quite ordered, there will be an exhaust of disorder elsewhere to offset the decrease in entropy, and that the overall effect still produces higher disorder.  This is akin to saying that because thermodynamics is very complex low-mass and low-speed Newtonian contingency barrier on general relativity, and that because there is an overall increase in disorder to compensate for the pockets of order, that this somehow relegates the postulation of a mathematical bias down to the realms of pure speculation.  In a moment we will see why this isn’t true.

14) Why do we have a universe with laws that ought to tend heavily towards maximum disorder (and do in most cases)?  The reason for this is fairly straightforward; at an atomic level thermal energy has a diffusion that arranges mass in random motions causing an increase in disorder.  But that doesn’t mean that increasing entropy necessarily corresponds to increased complexity due to the random arrangements of mass and energy – in fact, it is a mistake to equate simplicity with disorder because there is a vast degree of complexity in highly disordered random systems because their complexity is such that they contain vast numbers of cases in which they are not amenable to a simple mathematical system. 

Note: When it comes to means and frequencies in mathematics, even a highly disordered system is configurationally complex in that it contains a lot of complex data. Even in the evolution of life, in the mathematical sense phenotypical organisms are configurationally not maximally ordered or disordered, and this means that high order doesn’t necessarily entail high complexity. 

15) We have a universe with laws that ought to tend heavily towards maximum disorder but that also contains an astonishing mathematical skew in its emergent order towards the facilitating of genetic algorithms, conservation of sequence and function in biology, and maximisation of fitness of those organisms.  This alone tells us that there is such a constraint provided by the physical regime of laws.

Note: Obviously the distribution of energy in the universe doesn’t tend towards maximum disorder – if it did there would be no thermal energy and chemical energy to produce stars, planets and life.  Once we get to the stage of the emergence of biochemical life and the point at which organisms begin to evolve and eventually pass on their genetic material we can say that the active information in the laws of physics has leaped over a significant hurdle, because bit by bit evolution achieves progression through the system of cumulative ratchet probabilities

16) We can see that in less localised terms the laws of physics impose order on the universe in that the physical model has many possible states, but regulating laws limit those possibilities.  In actual fact, the question of why we have any order at all in the universe is a very worthwhile one, so the fact that we have an order of the magnitude that produces stars and planets is quite astounding.  The problem is that most people think of stellar explosions and the seemingly happenstance occurrence of the formation of the planets in our solar system and see a pretty chaotic and disordered mess, thanking their lucky stars (literally) that we ever got here at all.  On one level this is acceptable, but in truth the sort of mathematical skew I am talking about makes even that seemingly fluky activity incredible.  Here’s why.  Given that the universe should be heavily tending towards maximum disorder, even something like the emergence of stars requires an extraordinary restriction on the laws to facilitate the cosmic bottle neck to eliminate every other possible state to see that such a facilitation occurs.  This cosmic frontloading should under no circumstances be such that this kind of order should ever occur, because a universe without a mathematical bias would run down to maximum disorder very freely. 

Note: As I’ve said once we get to the earth’s biochemistry the appearance of another bottleneck is easier to reconcile because with biochemistry the severe constraint on the space of possibilities has already limited the possibilities and produced an increased ratchet probability where the statistical weighting favours the probability of life and not maximum disorder. 

17) As an illustration concerning combinatorial space, consider that quantum mechanics is all about measuring probabilities.  In quantum mechanics the wavefunction is a single-valued function of position and time, and it is a model we use to support a value of probability of finding a particle at a particular position and time.  Even concerning one particle we have a complex conjugate because specifying the real physical probability of finding the particle in a particular state involves a fairly broad search space.  Search space is best seen as a metaphor for our representing the probability amplitude for finding a particle at a given point in space at a given time.  Now imagine the complex permutational variables in a cosmos that has been expanding for nigh-on 14 billion years.  That is a lot of information and an incredibly vast search space of possibilities.  For the conditions of any order to be met, the laws of nature must preclude so many degrees of permutation (trillions of trillions) that far from physical probability being even diffused throughout nature, it must heavily constrain the laws in favour of non-maximal disorder (let alone biochemical life) to the following extent; that whether one believes in a personal God or not, the fact that the cosmos looks blueprinted for life is impossible to deny. 

18) As a second illustration; consider in biology one of those tiny gradual steps up evolution’s mount improbable.  Yes, it’s an accumulation of bit by bit selection, but that doesn’t tell the whole story - for even one very simple beneficial mutation which is just one small step in a long evolutionary history is itself woven into a huge fabric of other possibilities, and is just one tiny part of an incredible bias that drives the laws of physics towards life – a bias already embedded in nature and that is required to severely reduce the size of the cosmological search space by providing what seem to all intents and purposes carefully blueprinted generating algorithms that produced an information-rich universe set up for life.

Note: What the second law of thermodynamics does is produce a random walk across all possible states, and settles on the state that the statistical weight skews it towards.  In other words, the second law facilitates a migration based on huge statistical weighting whereby the skew directs a system towards its most probable state.  As a simple illustration, if I turn on a gas flame, the statistical weighting does not tend towards heat all staying in the same region, it tends towards diffusion into colder regions away from the flame’s output.  The reason being is that the colder regions provide far more microstates (that is, possible combinatorial search spaces) for the diffusion to arrange itself in than the hottest regions, so the heat tends towards regions with the greatest possible search space. 

19) On a greater scale, what we are seeing is thermodynamically optimum diffusions, but under the constraints of the laws of physics, and as a mathematical pattern we are seeing this right through nature’s blueprint.  Many make the mistake and say ‘Well in a universe the size and age of ours we are bound to have the occasional cosmic fluke that then goes on to produce stars and (if we’re ‘really’ lucky) planets and life’.  But such a claim shows that the person has a misjudged understanding of the subject at hand, because the very very tiny number of ways of locking in to order are not do with serendipitous moments of cosmic fortuity that just happen to throw up the odd fluke, they are to do with the enormous unlikelihood of having laws that constrain a system enough to produce anything other than maximum disorder - that is what is so remarkable. 

20) I fancy that a universe without a designer would be nothing like the universe we see – it would be maximally disordered and we would not have ever been born to talk about it, because a physical regime where disorder is unconstrained by a mathematical bias wouldn’t produce any biological evolution at all.

That’s not intended as a seat of the pants formal presentation – just a few back of the envelope scribbles – and as long as we are aware that we are dealing with realms of speculation beyond the headlights of ordinary empiricism, opinions about this are fine.  I would contend that the mathematical bias in the universe, and the fact that with the ‘is-ness’ of reality we have a kind of cosmic free lunch (in that seems like it shouldn’t be here at all), we have genuinely convincing reasons to infer the handwriting of a Cosmic Mathematician.  


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