THOUGHT: Part 3 led to a surprising conclusion, namely that the ultimate constituents of physical reality must be absolutely random. If their behaviour still possessed vestiges of pattern, they would cry out for further scientific explanation. If so, they would not count as the “ultimate constituents” of physical reality. There is no way round this important conclusion.
But it immediately poses the question: how can the intricately structured reality and immensity of the universe come about? There is only one possible answer: by the action of a mind somewhere imposing structure onto this absolute randomness.
So could a mind do this? The only minds any human being have ever encountered during more than a million years have been their own minds and those of other humans. So everything pivots on the question whether we humans can impose structure —by using our imagination and willpower— onto absolute randomness.
But first… “What is absolute randomness?”. Isn’t this a pretty woolly idea? Can we rigorously conceptualise absolute randomness? If not, there is a problem. Reasoning in physics is currently stuck in a horrendous mathematic traffic jam. Reasoning needs to show its mettle. Unless reasoning can make sense of the traffic jam, its credibility will remain dangerously poor. The situation is so bad that physicists have started to indulge in metaphysics (=fantasy thinking). They were repeatedly shown that they must resist this by earlier physics-minded reasoners like Popper, Wittgenstein, Ramsey, Schlick, Ayer. Metaphysics is a subform of reasoning which has consciously stopped conforming to the conditions necessary for genuine meaning.
Well, let’s start with the observation that randomness cannot be anything static, because static entities are predictable —in the simple sense that they are predictably still there after a lapse of time. Random Number Tables are a contradiction in terms. You can successfully predict the 15th number on page 17 by using the photocopy of page 17 you made yesterday. So Random Number Tables don’t begin to define randomess. Nor can mathematics define randomness. As the French mathematician Joseph Bertrand (1822-1900) pronounced “Randomness is the absence of all law”. If a mathematical definition of the nth random number existed, we could simply substitute n in the definition to predict the number: so it wouldn’t be unpredictable (=lawless) after all. What we need is a way of conceiving absolute unpredictability. This means, when rigorously conceptualised, ever-changing entities which can never be predicted, even in principle.
Let’s start with rigorous conceptualisation. Mathematics began about 7,000 years ago when people started using bundles of tallies (marks, scratches) like ///, ////////, ////////// to represent situations such as a catch of fish, a stack of clay bricks, or some amphorae in a storeroom. Each of these tallies is a minimally representational symbol.
Now consider a sequence of (say) four different tallies like |, \, _ and / coming into existence actively one after the other. One can envisage these tallies popping into existence in a random way. The result might be something like this:
The three dots indicate that there were earlier random tallies not recorded, while the >> denotes the “growing end” of the sequence. One has to imagine this sequence “popping” randomly indefinitely: so what you see is a never-ending sequence of new and past random tallies.
This is not, however, wholly free from vestiges of pattern, because where there are repeated tallies —as in the segment of six \ tallies (starting 12 places back from >>)—so there has to be an implied “clock” operating, punctuating this segment into six parts. To get round this difficulty, we need to specify that the sequence is a jumping sequence, where each tally is of a different type from that which preceded it. So the sequence above can be compressed down to the following shorter jumping random sequence:
Such a jumping random sequence can be treated as if it started an indefinite numbers of jumps earlier, and will go on for an indefinite number of jumps into the future. But our brains are finite, and if we are to impose structure onto such sequences, we need to recognise that we can only cope with a limited number of past jumps. Alan Turing coined the term ‘Ban’ for the smallest item of information to which the human brain can respond. So a realistic approach will involve going back to the point where absorbing the final tally is equivalent responding to a Bann.
Opinions differ about how slight the Ban is, but if we go back to 201 previous jumps, the information carried by the earliest jump may be somewhere near the Ban. If so, the total number of such “comprehensible” sequences —all different— is 4 x 3200about 1,062,455,955,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Something this big may be called a ‘Cosmic Number’.
We know the basic entities on the last rung of the deconstruction ladder of science need to be present in mind-numbing quantities such as this. Here, then, are the kind of fundamental building blocks required. They operate “over time” in the sense that one jump comes before another, but they are not “located in time”. They are certainly not located “in space”. This means that the concept is entirely relativistic. They are also wholly unpredictable, so we are not taking any content for granted, if we assume that such sequences exist. These sequences can therefore take on the role of the “basic bits” or “basic objects” of our universe.
The $64 question now becomes much more specific. Can we really impose structure onto a field which simply consists in a Cosmic Number of jumping absolutely random sequences?
The answer —it has always been assumed— is No. But a startling discovery has recently been made: we can impose structure onto this, and in innumerable different ways. By imposing a metric (a formula which produces a number associated with two different sequences when we compare their tallies) we can club them together into a three dimensional space. It may be observed that two distinct sequences are fairly close together if their last six jumps (say) consist of identical tallies. But they can’t move closer together at a rate faster than having the same kind of tally each time they jump. So in such a model proto-universe the basic objects can’t approach each other faster than a certain speed.
Compound objects may be formed in two different ways, by defining patterns of movement across the field, or by defining basic object bundles with precise properties. These recall the mass particles and massless particles of physics. There is every reason to believe that such a system could eventually model our world. In which case it would include the minds necessary to ensure it existed!
This is startling. Here is a self-justifying model universe!
An important discovery is the recognition that each basic object has what may be called “stochastic spin” when the tallies are momentarily going round bits of a cycle like | / _ \: this can be computed in six different ways, because there are six possible different cycles. The average amount of time when a basic object is “spinning” is 33.33%. But if we compute all six of the possible spins for a given object the largest spin tends to be roughly 4.5% above this average. This may be called the object’s ‘topspin’. Every object has a topspin. It may sound unimpressive, but when you multiply it by the Cosmic Number, it becomes an astronomically vast reserve of abstract energy —which can come into existence if there is an active mind somewhere in the system.
There are even large numbers of basic objects with synchronous topspin, where the patchy moments of spin coincide with what would occur if the spin was 100%. These may turn out to be specially significant.
The study of such systems amounts to a new abstract discipline (‘Actimatics’). It is based, like mathematics, on precise definitions, but using as its fundamental building blocks jumping random sequences which cannot be defined mathematically instead of static tallies.
Here, then, is the blueprint for a new digital kind of ‘Ultimate Physics’, based —unlike today’s physics— on an epistemologically sound foundation. Its very possibility can re-invigorate reason. It is extremely probable that the human race will eventually model our universe with it, though it may take 100 years or 200 years to sort it out. A world is now portrayed in which mindplays a crucial role, so what is revealed is a world with something like the warmth of religion, rather than the icy abstractions of today’s conflicted mathematical science.