This is the last instalment this year of the blog which looks at the role mathematics could play in helping to renew reason —something we urgently need if education and civilisation itself are not to become extinct. The soundbite this year has been that we need to achieve 20-20 vision in mathematics. This does not mean an exceptionally acute kind of vision, rather just a robust, reliable working vision.

Two important truths:

1  the threat of mental extinction is the main danger facing humankind at this time. If mental decay continues to spread at its current rate, it will presently begin to assume  catastrophic proportions.

2 Getting the public to see mathematics as it actually is, plainly, clearly, realistically, can play a major part in fighting this problem. The first step is to recognise how far we are from this condition at the moment.

A top priority is to clarify the relationship between mathematics and computing.  This was compromised in the 1960s when salesmen trying to sell the new machines started reassurring the public that <<Computers have nothing to do with mathematics>>.  This mantra has since become a thoroughly taken-for-granted principle by the masses, in spite of the fact that it is one of the largest, most brazen, most misleading, lies in history.  Anyone who knows anything about the origin of computers knows that they were first conceived by Charles Babbage, Alan Turing and John von Neumann, three outstanding mathematicians. They know, too, that numbers and mathematical logic underpin the software coding on which the machines rely (and which generates the magic).

If we stand back and look at computers from a distance, it is plain that computers are simply electronic devices which use a list of instructions (a program) to automate operations which have been skillfully converted into mathematical operations, store the results and, if necessary, use them to modify the program. The results of such a program can be presented in the form of graphics or sounds.

This is not just mathematics, it is, or can be, on-going mathematical process plus presentation.  The claim that these machines “have nothing to do with mathematics” is not an over-simplification, or a half-truth: it is a blatant denial of the heart of the matter.

So why do the public by-and-large believe this blatant, self-serving denial of the truth which has been put out tendentiously by the computer industry for more than half a century?

The answer is that, when this audacious lie was first devised (to sell computers to people who were nervous about maths) it was what the gurus, who formed the leadership of the subject at that time, wanted to believe. So they didn’t indignantly deny it, pour scorn on it, etc.  —something they could easily have done in the early 1960s. The mathematical profession lacks the financial clout of the computer industry, but even after all the glitches of the 20^th century it still carries enough academic authority to lodge a vehement protest: which would have prevented the mantra from becoming an unquestioned tenet among the masses.

The leadership of mathematics at the time did not lodge the slightest protest. They simply rolled over and let it stand.

They turned a blind eye towards a huge mathematisation  of every kind of human activity which occurred as a result of applications of computers. This is another glitch not listed in the set of six offered in instalment 6.  It follows the same pattern as the extra glitch mentioned in instalment 7, namely that it resulted from the same leadership style which is based on the principle <<If in doubt, do nothing>>.

Does this public misapprehension matter?

Yes, it matters a lot, and for all sorts of reasons:

>> It misleads children from a very young age about the source of the magic within the gadgets they love so much.

>> It misleads children about the role of mathematics in today’s society. They don’t register that mathematical brainpower is behind what they think is electronic brainpower.

>>The same misapprehension affects the media and the corridors of power.

>>It even affects the higher intelligentsia who have acquired an exaggerated anxiety about the threat to civilisation posed by the new AI-powered computers.

>>The fact that today’s machines can sometimes exhibit fragments of what looks like ‘intelligence’ has been used by the computer industry blandly to brag that their machines  display ‘artificial intelligence’. The public and the higher intelligentsia have swallowed this: something they might not have done… if they had realised that you have to take self-serving mantras put out by the computer industry with a pinch of salt.

There is however a more positive side to this misapprehension. It has led to a vast growth of mathematical modelling in feasibility studies, innovation, technology, administration, logistics, etc.  It is unlikely that this would have taken place if the leadership of higher maths had been promoted to being the leadership of ‘Greater Maths’ (a term which may be used to cover the totality of higher maths and automated maths). The gurus would have applied their minimalist do-nothing leadership style to many of the promising opportunities which presented themselves during the last sixty years to do mathematical modelling.

The initial result has been: that the modelling actually happened.  It produced brilliant results, which have transformed the human race.

The significant result: it is now patently obvious to the average intelligent person (if they have rumbled that computers are a form of Greater Maths) that the meaning and purpose of mathematics arises from its modelling uses.

Compared with the relatively flimsy academic arguments wheeled out in support of the various standard interpretations of the meaning of maths (Platonic, Formalist, Intuitionist, etc.), this unmistakable triumph of the neo-Peircean modelling interpretation is conclusive.  The question can now be regarded as finally settled. The main source of the meaning we attach to maths comes from its modelling uses.

All of which might look rather banal and utilitarian, if it were not for the fact that having a firm account of the source of the meaning of maths allows us at last to tackle and settle the various contradictions which have disfigured the modern subject.

CHRISTOPHER ORMELL December 2020