Saturday, 3 January 2015

How The Universe May Fool Us Then Enlighten Us


I remember reading an interesting paper a few years ago on the theory of a pixelated universe. Gerard ‘t Hooft and Leonard Susskind proposed 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’. All these years later it seems physicists at the Fermi National Accelerator Laboratory are going to put this to the test with what's being coined as The Holometer Experiment.

It'll be interesting to see how the experiment plays out, because 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. 

The newspaper illustration is a good one. 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 - 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.

Whether we are talking about information in Shannon terms, or even as a more generalised concept, information can't reasonably be treated merely as some kind of intrinsic property embedded in the system itself - it is necessary that information should be seen as an extrinsic property of a system too. 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 burned onto a disk is information only inasmuch as it consists of patterns that can be used by that computer as instructions. 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.

If we wish to call the patterns in nature 'information' in an intrinsic sense, then that's ok, but we must always bear in mind that expending resources on information through interpretation and analysis requires a second descriptive sense, because it is "information" intrinsically and yet also "information + mind" extrinsically. That's why whenever 'information' is talked about as pattern, those patterns are 'information' only when related to minds that have the capacity to correctly interpret the patterns.

Given that the informational property of the universe's patterns exists extrinsically by virtue of its relation to agents of perception and conception, there is good indication that nature only reveals the topographical secrets that we ask it to. But what does that mean in any sense that might be epistemologically useful?

To my mind, when it comes to human perception of reality, it means there is a logical discontinuity between the actual and the theoretical, which I'll try to explain.  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?

Here's my best guess. You've no doubt heard of pi - it's the irrational number 3.14159. Not only is it the ratio of a circle's circumference to its diameter, it's a pattern that appears regularly throughout nature in many other ways. Nature has various physical constants (speed of light, gravitational constant, Boltzmann constant, etc) that are mathematically consistent. Pi also runs right through physics in the form of constants: it appears in masses of elementary particles, in the molecular quantity in a volume of a gas, and 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. 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 probably because the physical aspect of reality is only a tiny fraction of the far broader and complex mathematical reality.

We've 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 probably is 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.

A bit more speculative, this, but given that mathematics and rules of numbers seem to be contingent on sentience perceiving them, and that the universe consists of patterns with evident mathematical constraints imposed on the system (see my Blog post here for more on this), we humans may well be perceiving patterns generated by a Cosmic Mind capable of orchestrating those highly unrepresentative constraints……a Mind that may well be justifiably referred to as…*drumroll*…..God.

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