STOP PRESS The coronavirus has changed personal perceptions dramatically. Nothing looks the same today as it did three months ago. It has made almost everyone aware of the inherent fragility of the present World Order… in health terms, in employment terms, in economic terms and, for those most dangerously affected, survival terms. We have glimpsed the potential scale of the threat lurking in one unexpected version of one of the seven potentially terminal crises. The coronavirus crisis may be the tragic nudge we needed to resume reason.
A sophisticated, inter-connected World Economy, operating on small margins and a “just on time” basis, is clearly not the kind of thing which reason would recommend. Its fragility is, in the last analysis, a consequence of the short horizons which have become the taken-for-granted norm (on Wall Street, the City, Frankfurt, etc.). They arise from an aversion to reason, because it is only reason which can tell us that we should be thinking and planning widely and securely for the future.
What can we do? It is abundantly clear that the precarious “hand-to-mouth” nature of much of today’s world economy is a tacit continuation of ancient streetwisdom, rather than any kind of expression of powerful modern thinking. So, perhaps the present crisis can serve as a wake-up call, provoking us to begin to apply the best modern reasoning to our situation. But we are in an ironical position. Namely, that today’s “just on time” methodology actually does already depend —to an unobvious extent— on high speed computing, the internet, sophisticated algorithms, deepfreezing and air freight. It has, of course, already been consciously or subconsciously configured like this —to minimise the expenses and to maximise the profits— within short time-horizons. So the change urgently needed is not merely to embrace the latest “technical” knowhow: it is a much more profound, difficult, cultural, personal change, from short sighted myopia, to long sighted vision.
Unfortunately, though, we know that long sight “cannot hold” —as W. B. Yeats’ “centre” of things could not in 1919— in an ever more frenzied, manic business culture.
We urgently need two things, (I) a resilient, secure, forward-looking economy, operating on a basis of confident systems, feasibility-studies, planning, research and development. (II) a hopeful, purposive vision of the future or “light at the end of the tunnel”. The former is very unlikely to happen without the latter. This is why we have been concentrating in this Blog, first on trying to dispel the dense fog created by two dismal (1920) defeats of reason, and second on the overall (anthropic) direction in which our scientific worldview urgently needs to move.
In the first five PARTS a revolutionary narrative has been revealed. It amounts to “Total Epistemology” —‘Epistemology’ because it is all about how we can consistently imagine (logically conceptualise) the furthest limits of science and mathematics. ‘Total’ because it completes the circle by explaining in a Kantian fashion how the universe comes about. It can be a powerful light at the end of the tunnel. It makes it clear that the physical universe is our universe —that it is much more closely integrated to us as conscious intelligences than formerly thought. This vision is the basis we need for a more mature, considered, reasoned, compassionate, enjoyable quality of life, work and leisure. But,because it is revolutionary, it will not be welcomed lightly by those vested interests which have long since taken its absence for granted.
Total Epistemology can become the basis for a more mature, considered, reasoned, compassionate, enjoyable, quality of life, work and social solidarity. Battles will be needed, though, to establish this. Everyone has been, in effect, deeply socialised into the common scientific assumption that the laws discovered by science are set in stone —by some awesomely mysterious agency we can never know. But why have they been wished-into this “set in stone” status by the scientists in the first place? The answer is because science is a piece-by-piece process and, as Peter Medawar memorably said, science is “the art of the soluble”. There is an infinity of things any particular scientist could, in principle, focus on. Scientific progress will only happen, though, if scientists are able to use their nous and intuition to seek out the ones which are closest to being solved. These are the best current “solubility bets”: the ones most likely to be solved. So scientists do need firmly to adopt temporary “givens” —if they are to be able concentrate with the intensity required onto these “best solubility bets”. However this is in-house wisdom. Popper’s caveat against assuming that an established scientific theory tells us the final truth (about its subject matter) applies in full force here. None of the laws discovered by experiment and observation are, or ever can be, genuinely “set in stone”. Whatever apparent empirical felicity they can boast, it cannot (logically cannot) underwrite this level of finality.
In the remainder of this PART we look more closely at the main principle on which the new vision rests. It is to be expected that it will be attacked in no uncertain fashion, by those who feel threatened by it. The aim here is to identify, clarify and consolidate the secure reasoning on which this principle rests:
Mathematics is a humanly constructed abstract discipline. Newton discovered that it could be used to find lucid explanations of natural events, e.g. the rainbow. The classical Greeks were amazed when they discovered simple mathematical patterns in the sphericity of the Earth, the motions of the planets, musical harmonies, etc. The apparent perfection of these patterns was striking. It seemed to say that they “came from God”. It seemed to be a sign that mathematics “must have been the language used by God when he created the universe”. This in turn seemed to imply that mathematics must be “a timeless, eternal discipline created by God”. Plato elevated the meaning of X itself —into a reference to the ideal behind the X. So it should be no surprise that the maths Elite of the 5th century BCE —and 24 future centuries— seized delightedly onto this account. They would, wouldn’t they? It gave them, as the mathematical experts, a superior, almost godlike social status.
Today we are much more aware that the feeling, that these simple, perceived forms are ‘perfection’ is predicated on assuming that they are final. But they are not. They are only first approximations to much more complex realities. So Platonism —which is still holy writ for many in the mathematical Elite— is a massive illusion: judged against modern knowledge, a howler.
The humble origins of mathematics. We know that mathematics (in the widest sense of that term) began with tallies like //, ///, ////////. Such tally bundles probably began to emerge about 7,000 years ago. They offered a simple, easy, self-evident way to represent a catch of fish, a stack of bricks, a group of soldiers… With much beneficial use in trading, building, making, military planning, etc. they became so familiar that their users started to adopt special symbols as names for particular bundles. For example, in the Roman World ‘V’ became the name of /////, ‘X’ became the name of //////////, ‘C’ became the name of ////////////////////////////////////////////////////////////////////////////////////////////////////…etc. The abacus was invented and beads on different levels could be used to represent units, tens (Xs), hundreds (Cs), etc. In trading it was often necessary to consider a bundle of bundles like V Xs or ////////// ////////// ////////// ////////// //////////. So the process of multiplication was introduced. Sometimes, in distribution situations, the reverse process was needed, so division was defined. In this way mathematics grew and grew —by the simple process that new definitions were constantly being adopted. For example, many numbers were multiples of smaller numbers. But there were a few which were not: they were the exceptions, soon tagged (defined as) ‘prime numbers’. As the field of defined objects increased, discoveries came to be made within this field. For example, the product of two adjacent odd numbers was always, apparently, one less than the square of the even number in-between them. Today the total archive of mathematical objects (i.e. elaborations built on further elaborations of tally bundles plus processes thus defined) and discoveries, contains billions of items. It’s most interesting public use is in modelling humanly important hypotheses —to tease out their observable implications. The totality of definitions and discoveries is, taken as a whole, a human-made ‘abstract built environment’ or ABE. Is this obvious? Yes! However… many people in the maths elite still can’t get this. They are deeply committed to the Platonic quasi-religious account of mathematics they swallowed in their youth. This Platonism was still a holy grail in the 1990s, though it is visibly wilting today.
From an early stage a cadre of people emerged who were especially good at handling this ABE. They were those who were able comfortably to set aside the colour, flavour, sound, etc. of immediate experience, and focus with their full attention onto the details of these defined abstract constructions. They were undoubtedly exceptionally able individuals, unworldly, and, often, reserved in temperament. They soon formed a socially fully recognised Elite —probably mainly because Kings, Princes, Generals, etc. relied on them when planning their military campaigns.
The triumph of Newtonian Gravity and Mechanics turned mathematicians into superstars. It came to be widely appreciated that mathematics could be used to model —and hence illuminate— the natural world. But… actually operating the mathematical models thus devised often led to technical roadblocks: baffling, apparently insoluble, equations. The problem how to predict the outcome when three mutually attracting bodies were moving around (‘The Three Body Problem’) was an example. To try to get answers, the best experts at handling the relevant pure mathematics were needed (but even they were stymied 99 times out of 100). This severe scarcity meant that quite tiny breakthroughs resulting from pure maths were treated as priceless. Pure mathematicians were highly rated by the public.
Around 1960 this era came to an end. The digital computer took over. In effect, mathematical modelling suddenly became viable —on an approximate basis, which was all that was really needed — across the board, sometimes in unlikely circumstances. Gradually the mathematics community is waking up to this change, turning to the kind of maths which amplifies computer power. The arrival of the new quasi-mathematical discipline, Actimatics, is likely to cement this change.
The individuals composing this elite-within-the-elite have dominated opinion inside mathematics ever since. They claim to be the only people who know what mathematics really is: they brook no opposition, on the basis that they, alone, are clever enough to know what is at stake. So let’s look at the position of mathematics as they expound it. They treat it as Olympian, high-level (but useless) wisdom which is privileged because it is timelessly true, and because it is at the unique pinnacle of human knowledge. They have failed to absorb the message of the modern era that mere timelessness is wooden, and valorising it is a kind of denial of the essential transience of our lives: also that useless disciplines are in-house conceits. The Elite unwisely stopped treating maths as ‘The Queen of the Sciences’ around 1900. Thus they effectively gave up their claim to be at the “pinnacle” of human knowledge. They will feel the discovery of a second, more realistic, more anthropic, ABE as a painful, unexpected, unwanted culture shock. But, being able, they will soon realise that their talents are vitally needed in the new ABE.