There is a common tendency for computerists to over-estimate the applicability of mathematical modelling to mysterious entities like the universe and the human brain*

We know that tally-bundling must have been the natural precursor to arithmetic, and that it (tally bundling) may have been in use for many millennia before confidence in using and trusting arithmetic gradually reached the level where it could be the main methodology used in building pyramids. (The largest pyramid needed 20,000 workers devoted to the task of building it —over a period of twenty years. This shows that that a huge confidence existed, both in the geometric design and the arithmetic logistics.)

This level of confidence showed itself, too, in Babylon where much arithmetic must have been used successfully to build and to operate the irrigation of the hanging gardens. We know that the Babylonians organised special  Arithmetic Schools to train the abacus-operators who were needed to plan their projects and enable their economy. 

Later the Roman Empire became a showcase for the efficacy of arithmetic and geometric modelling —in designing handsome buildings, efficient aqueducts and well-aligned roads.

But it wasn’t until the 17^th century that mathematical modellers showed —using Descartes’ geometry and Newton’s calculus— how much more their modelling could achieve.  The idea behind calculus was that maths could be used to model change-over-time such as velocity, orbiting movement, centrifugal behaviour.

*Part 3 of the Four-Colour inquiry will appear hopefully early  in 2024.

The earlier experience of modelling with static arithmetic/geometric configurations had looked like the best maths could do. (Its forte at the time was impressive building and civil engineering projects: an asset to society, of course, but with strict limitations.) Suddenly, unexpectedly, it transformed itself into a new modelling agent… one geared to exploring the possibilities of changing reality —tides, slides, topples, collapses, growth, movements. A new feeling of vitality had entered science. Also a promising economic vista beckoned: the study of possible, useful machines!

However did this transformation happen?  How did Descartes convert an equation (a kind of statement) into a description for curves? How did Newton re-conceptualise algebra as a way of describing motion?

The answer is that these pioneering modellers were applying imagination to their models. The time variable was a symbol, t seconds, or t days, (counting from some established moment) and the modeller could envisage an expression involving t changing all the time… in this way mimicking a dynamic process.

This kind of 17^th century modelling was naturally incorporated into the kind of post-renaissance scientific practice which limited the scope of modelling to piecemeal theorising.

So now there were two logical conventions which made mathematic modelling unsuited to attempts to model the universe, treated as a whole. It could never deliver a comprehensive a ‘model of everything’, because the imagination needed to activate the model was not itself “in” the model. Also the mathematical convention used in piecemeal scientific modelling depended on utilising axioms which were known to be reliable, substantial, truths which had been established prior to the new explanatory model. This was not a methodology which could be applied to the total universe, because these axioms, too, needed to be explained.

Similar factors apply to the human brain, because we take it for granted that the brain is the source of mind, and the entire discourse relating to the universe happens inside the human mind.

Do we need a scientific model of the universe? Well, it depends on what our expectations are. Modern science has, we know, conprehensively upstaged religion, because its concepts and methodology are clearly superior to the antiquated, uncertain texts on which religion rests. But this change has come about with a huge cost. The loss of religion’s former overwhelming credibility has thrown all forms of trustworthy human inter-action and co-operation into danger. Secular ethics exists, but it is in the last analysis only a life-style choice. It has no compelling force like religion.

For the reasons summarised above there can be no final mathematic model of the human brain or the universe. But we need a 100% credible picture of the universe, if our ethics is to recapture the compelling quality of religion.

Fortunately anti-maths has been discovered, a 100% abstract logos founded on tallies, but now ever changing, chaotic jumping tally sequences. The two obstacles —which prevented any mathematical configuration, however complex, however sophisticated, from being the last word— don’t apply to anti-maths modelling. No axioms are needed here, because if a cybernetic agent with freewill (=us) is  possible, it can underwrite its own axioms. Nor is imagination needed as an outside agent (necessary to activate the whole), because the basic chaotic tally sequences come along with their own intrinsic random energy.  So a new era beckons —always assuming that we are smart enough to recognise it, see its implications, and make it happen.

CHRISTOPHER ORMELL 4^th DECEMBER 2023
If you would like an online copy of the P E R Narrative Maths Manifesto, send an email to per4group@gmail.com