Let’s talk about information, mind and reality at a
deep level. Consider pi - the irrational number 3.14159… and so on. Not only is
pi the ratio of a circle's circumference to its diameter, it's a pattern that
appears regularly throughout nature in many other ways; for example, in the
equations governing the wave function in quantum mechanics, in the time period
of a pendulum's swing, and in Heisenberg's uncertainty principle, to name but
three. Nature has various physical constants (the speed of light, gravitational
constant, Boltzmann constant, etc) that are mathematically consistent, and pi
also runs right through physics in the form of constants, such as the forces
that knit matter together, like the strength of the electromagnetic force that
governs the behaviour between electrons and photons.
So, pi appears in nature in the physical substrate, but it also appears as a number with an infinite series. That is to say, if you tracked the decimal digits of pi beyond the sequence 3.14159, you'd find the number series would carry on infinitely. Humans currently have the computational ability to calculate pi to over 13 trillion decimal places - which is impressive - but that is only a minuscule number compared with the actual n sequence in its entirety. What this points to is that when it comes to human perception of reality, there is a logical discontinuity between the actual and the theoretical. In mathematics, we have a clear conception of infinity. We can conceive countable sets, which are sets with the same cardinality (number of elements) as some subset of the set of natural numbers where every element of a set will eventually be associated with a natural number. We can also conceive uncountable sets, which are sets that contain too many elements to be counted.
Once we step back and have a reality check, we are entitled to find infinite sets a bit peculiar. What does it mean for finite physical human minds locked into a finite physical nature to be able to deal with infinities? Consider a simple illustration to show what's particularly strange here; if you were able to step outside the universe and drop in a grain of sand for every digit in pi, you would run out of space in the universe long before you ran out of sand. That's an astounding thing to grapple with, and leads to other interesting questions, like what does the ability to abstractly conceive an infinite pi representation mean, and what does it mean that a computer can calculate to 13 trillion decimal places? It appears to mean that theoretically if the computer kept on calculating, then the computation can map to a size greater than every particle in the universe and still be far short of the whole pattern. In other words, as far as human perception goes, we are contemplating the logical discontinuity between the actual and the theoretical, and finding that that is most likely because the physical aspect of reality is only a tiny fraction of the far broader and complex mathematical reality.
Physicists Gerard ‘t Hooft and Leonard Susskind once proposed a theory of a pixelated universe: a theoretical model of the universe as being comparable to how a newspaper dissolves into tiny dots as one zooms in on the fine detail, as if nature is ‘pixelated’. We know in our attempts to resolve general relativity with quantum mechanics that the more we dig down granularly the harder things are to measure or even detect, and the less like macroscopic reality things apear.
A few years ago, I wrote some material of my own on how the pixelated universe idea is a good illustration for how we humans deal with information theory, and how the universe itself is a mathematical object that is ultimately reducible to lots of single bits of information. The logical corollary of ‘t Hooft and Susskind’s pixelated universe model is that the universe is a physical 2 dimensional set of patterns that are brought to 3 dimensions when light bounces off them (much like what happens with the holograms on credit cards). In terms of the universe, we are thought to be experiencing holographic projects (our 3D world), that without minds would be a 2D series of pattern storage. Actually, the newspaper illustration is a particularly good one with a deeper meaning. Technically a newspaper can be expressed as millions of single bits of information that come together as an aggregate whole in the form of words and pictures that then take on newly invested meaning. Both the newspaper and the universe have something important in common here - there is a necessary relationship between information and sentience. A newspaper is merely paper and ink without a mind able to expend its resources on interpretation of the content of the paper and ink.
Or take something like DNA, which clearly contains a lot of information. As we increase our knowledge of the human genome, the surprises it contains become fewer. Now of course we can be quirky and conflate observer and observed - the ribosomes that construct proteins do not know the system informationally like we do, but they receive messages from the nucleus where DNA resides. So, if you were a ribosome, you'd contend that the quota of information in DNA is always complete.
To expand the model from DNA to the universe, as far as we are concerned, when we conflate observer and observed, we find we are in a universe that in theory can be informationally complete with full knowledge of the physical system. But once we start to think in terms of measurement and possibility, we find that the information content goes into infinite realms again. So if the nexus between the physical and the theoretical is "information", then the physical is dwarfed by the theoretical, making information more like a canvas and the physical more like a painting that the canvas hosts. But then we go round again, because information is the observed only relative to an observer.
Or think of thermal energy and how in the form of heat it always flows spontaneously from regions of higher temperature to regions of lower temperature. This heat flow reduces the state of order of the initial systems, and this process is an expression of increased disorder. Here’s an analogy to express how information flow has commensurability with what we’ve been discussing. Although the universe is one interconnected whole, our abilities for computation are reduced to regional capacities (known as horizons). We are causally attached to a horizon because light emitted from our vicinity of the cosmos at the point of the big bang has only reached a distant surface in space, so as far as our endeavours for computation apply, information flow limited to that region has a correlative computation system with the same limitations.
This is also commensurate with our modelling disorder in the cosmos. If you imagine the horizon expanding with time as light moves outward into space, you’ll infer the fairly obvious corollary that that region would have had less capacity for computational resources in the past. This is because each horizon contains a finite number of particles, and quite naturally the computational capabilities reflect this, where fewer particles equals more parsimonious computation. If one thinks of the horizon at the point of Planck time just after the big bang, then the computational scope would have been essentially non-existent, because increase in computability increases with increase in disorder. Using the stretched rubber band model – which is that, as the rubber band expands, the distance between any two points on its surface increases - we actually find that the universe is already reflecting this model in how the distance between galaxies in the universe increases as space itself expands.
At a fundamental level, the universe is a mathematical object of information - and this can give us profound insight into the deeper nature of reality, because whether we are talking about information in Shannon terms, or even as a more generalised concept, information can't reasonably be treated as some kind of vitalistic property lurking in the system itself. It's essential that information is seen as an extrinsic property of a system. That is to say, a system contains information by virtue of its relation to another agent or system capable of perceiving, interpreting and responding to that information. For example, a computer program, a set of songs, or a bunch of holiday snaps shared on social media is information only inasmuch as it consists of patterns that can be used by that computer as instructions to be perceived by sentient minds. Likewise, a universe only contains information by virtue of its relation to minds that have the capacity to correctly interpret the patterns though cognitive instructions. Ostensibly we have a universe of patterns awaiting their informational content when interpreted by minds.
So, to recap; it's best to talk of what we habitually call 'information' as pattern, and those patterns as being 'information' only when related to minds that have the capacity to correctly interpret the patterns. And the informational property of the universe's patterns is not intrinsic to the pattern itself; it exists extrinsically by virtue of its relation to agents of perception and conception.
We've also seen that nature probably is pixelated, and that every part of physical reality is amenable to be described in informational terms, where its constituent parts can be broken down to n single bits of information, where n is as large as its informational content goes. But given that the n of the informational content of even the whole physical universe is dwarfed by the informational content of just the pi sequence, the only reasonable conclusion, I think, is that mathematics belongs to a reality far broader and more complex than the physical reality we physical beings inhabit. It’s almost certainly the case, then, that the conceptual and the physical aren't at odds with one another - the conceptual infinites are examples of our interfacing with the fact that mathematical realty is much more primary and grander than physical reality, and that mind is even more primary than mathematical reality.
All this is to say, at a deep and profound level, there is good indication that nature only reveals the topographical secrets with which we are created to interface. I believe it might be like T.S Eliot conveys in his Burnt Norton, especially:
Are both perhaps present in time future,
And time future contained in time past.
If all time is eternally present
All time is unredeemable.
What might have been is an abstraction
Remaining a perpetual possibility.
And.....
The unheard music hidden in the shrubbery,
And the unseen eyebeam crossed, for the roses
Had the look of flowers that are looked at.
And given that mathematics and rules of numbers seem to be contingent on sentience perceiving them, combined with the fact that the universe consists of patterns with evident mathematical constraints imposed on the system (see here for a far more detailed analysis of that observation), I think we can fairly safely conclude that we are perceiving patterns generated by a Cosmic Mind capable of orchestrating highly unrepresentative constraints, to which the attribution of God’s genius is wholly appropriate.
This seems to be one of the ways where human minds and God's mind meet - in engaging with the patterns and mathematical raw material, and bringing them to life, a bit like how an artistic genius might exhibit his craft to a nascent audience. And that we can view those patterns through so many lenses (mathematical, poetical, imaginative, artistic, scientific, psychological, philosophical, theological, etc) highlights that even the entirety of physics is simply one lens of reality among many. Hence, it makes sense that if God is the Creator and observer of this information, we would expect the fundamental asymmetry between the physical and the theoretical, because mind is more expansive than its physical properties (as even a human mind shows).
