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Science In Context:
The Evolution of a World View

‘The Rise of the West' - that distinguishing feature of world history in the last five hundred years - is synonymous with another ascent, that of ‘modern science‘. Our understanding of bodies, human and animal, the physical world and natural phenomena has been transformed by the application of a scientific method which proceeds by observation, measurement, experimentation, intuition about what might become known, and a self-critical method which is prepared to ask “Is what I think I know actually - true? Intellectual advance in these areas has improved the human condition by eradicating some infectious diseases and halting the spread of others through vaccination and improved public hygiene. Technology’s application of science means that lives that are longer-lived may also be enriched materially. Scientific inventiveness made industrialisation possible and the amenities of a commercial society displaced the drudgery of a labour-intensive, agrarian, economy.

Viewed retrospectively from the vantage point of the early 21st century this ‘rise of modern science' can seem almost inevitable - a long overdue victory for the forces of reason as modernity marched forward carrying all in its way having jettisoned its tutelage to obscurantism and superstition. This is in fact the way a good deal of ‘the history of science’ was written in the twentieth century. Reason in full pursuit was, apparently, rather like the Royal Canadian Mounted Police. It ‘always got its man’. Having seized one truth- and consigned all adversaries to perdition - it could then march on to the next, pre-ordained, conquest. Copernicus and Galileo were presented as precursors to Bacon, Newton and Boyle who could then pass on the torch to the next generation of luminaries waiting impatiently in the wings - Watt, Faraday and Darwin- before finally petering out in the early twentieth century, Heisenberg’s uncertainty principle and Einstein on relativity being perhaps awkward companions on a journey devised by and for the single-minded.

A more realistic view of the history of science emerges if we look at the historical context which made some discoveries possible. At each stage of enquiry there were many possible lines of future investigation. Some were followed and others abandoned. Chance, exhaustion, boredom, a patron’s interest, a sudden hunch : these were among the many signposts indicating one direction of travel and the consequent abandonment of another. Choices had to be made and the ‘History of Science’, like any other kind of history, is not a one way journey to an ‘inevitable’ conclusion. 

This research programme will start in autumn 2021

Areas of study include: The history of statistics and the mathematization of science



Domination by numbers : the history, and transmission, of an idea


This first section of the research programme will consist of an audit of four major statistical surveys conducted in recent and contemporary history and whose argued conclusions, implemented at a governmental level, have affected the conduct of daily life.


Statistical science - the collation and interpretation of data most often expressed numerically and in percentage terms - lies at the heart of contemporary government. Legislation is informed by debate about the significance of  ‘the stats’ and what they might, or might not, reveal about human impulses, ambition, likes and dislikes, hopes and fears ,along with our propensity to react in certain ways -behaviour being adjusted and beliefs modified when a law is enacted and enforced. ‘What the numbers say’ is the preoccupation not just of parliaments, assemblies,  senates and governments. Measurement of ‘the inputs’, ‘outcomes’, statistical averages (and deviations from the norm) are basic to management theory, opinion polling, ‘targeted’ political campaigning,  psychological testing (including attempts at influencing ‘behaviour’), advertising (especially through social media platforms) and to all the means open to organisations who wish to observe, and to influence, human conduct.

‘Statistics’, a term coined to describe the gathering of information by the pre-modern state. was once a humdrum and clerical pursuit, modest in its aims and devoid of pretention. Statistical tools, by holding a mirror to nature, enlarged the understanding through the identification of relevant, but previously obscured, detail. That was an age of innocence in the history of statistics, a period when the numbers and percentages, written in the ledgers and collated in files, could be presented as an almost self -explanatory, and neutral, description of reality. Subsequent developments, over the past century and a half, have combined to complicate the statistical enterprise.


Governmental objectives and responsibilities expanded consistently from the late nineteenth century onwards and officialdom became increasingly reliant on statistical data. The science itself became more ambitious. Its interpretation of facts and figures garnered from an ever wider area of human activity came to include speculation (through extrapolation) about possible future trends rather than just offering a commentary on the present. A seemingly limitless increase in the sources of information available on the web has been grist to the statistician’s mill. Private companies and businesses as well as governmental agencies now need battalions of statisticians to guide them through the density of the informational jungle. Reassuring noises about the sophistication of theory, commitment to the accuracy of 'modelling' ,  self confident dexterity in the presentation of conclusions: all have contributed to the contemporary dominion and authority of statistical science.  

This ascent, however dizzying its effects, has not succeeded in stilling some sceptical voices. Matter of fact-ness about what the data ‘really mean’ seems out of place when two (or more) statisticians, looking at the same material, arrive at differing conclusions. One expert might of course be sharper, less tired,  or more observant, on the day,  than the other. But the differences of interpretation, especially if they persist, may serve as a necessary reminder of the evaluative nature of statistics. Surrounded by high seas of multitudinous data the statistician needs to decide (oblivion by drowning being an undesirable alternative) that some are relevant to the task in hand. The decision is a choice, informed by knowledge of context – the likely accuracy of the source of reportage for instance and its explanatory potential. It is at that point, and having been chosen, that a piece of data can be baptised a ‘statistic’. And even then, when all are gathered in, there will be room for expert debate about how best to interpret the statistics and their relative significance in a pattern of cause and effect observed over different periods of time. Individual cast of mind and intellectual interests shape the dialogue and become even more apparent in the case of a statistical exercise involving in depth research.



Why The Numbers Came To Matter and How Math Took Over Science


This section of the research programme ‘Dominion by Numbers’ traces the origins, and consequences, of a major development in the history of natural science: its mathematization in the course of the seventeenth century. An emphasis on the experimental method proceeding by observation, comparison and classification is a well known feature of that age of genius. Mathematics experienced its own contemporaneous revival and the consequences in the realm of the natural sciences repay a closer scrutiny. In order to do so we need to take more than a few steps back in time-to Ionia and southern Italy in the sixth and fifth centuries BC: the milieu of the ‘ pre-Socratic’ philosophers.

Thinkers such as Heraclitus of Ephesus, Parmenides of Elea, Pythagoras of Samos,  and Thales of Miletus merged the ‘philosophical' with the ‘scientific' when investigating the nature of the world, its relation to the universe beyond, and the means by which truth can be established. Individual Pre-Socratics had different intellectual interests but common to all of them was the belief that the world was a kosmos – a term which signified its possession of a certain order. The world in some sense hung together and knowledge of this One world - in order to be accurate- had to be correspondingly structured. It was this line of enquiry, with its interest in the mathematical representation of symmetry, proportions and ratios, which made possible , for the first time in the history of the West, a scientific study of the world as an interconnected entity. Pythagoras (despite his famous theorem) seems to have done very few mathematical experiments. His development of number however into a concept that could explain cosmogony and musical sounds along with his ascription of abstract properties to certain numbers (four, for instance, representing justice) was highly original and the basis of an authoritative influence exercised both in his own time and posthumously. The least cultic of these followers were the ‘mathematikoi’. Although inspired by Pythagoras,  their mathematical experiments were more rigorous  and wide ranging than their founder’s own, more speculative, insights. The mathematikoi survived as  a distinctive school of thought until the early fourth century BC. Two world historical forces ensured their subsequent relegation to the sidelines and a two thousand year history of obscurity: neo-Platonism and Aristotle. The former, loyal to what they took to be their master’s legacy, suppressed the experimental method while Aristotle, although interested in almost everything that moved, was unremittingly hostile to the neo-Pythagorean position that numbers could be identified with sensible substances. He may well have been influenced by a personal dislike of the Pythagorean groupies whom he met and whose views are summarised in his lecture notes. It remains a striking fact that Aristotle never wrote (so far as we know) a tract devoted specifically to the philosophy of mathematics.

Aristotle is one thing and the Aristotelians – quite another. The philosopher’s subtleties find few echoes in the labours of his commentators – those ‘schoolmen’ of the twelfth to fourteenth centuries who fashioned a rigid syllabus out of his notes and writings. Aristotle became his followers, a melancholic fate of transmitted, half-understood influence and bowdlerised apercus. In one respect though the maligned scholastics were loyal to a fault. Their tomes could find no room for a mathematical philosophy. And so when ‘Aristotelianism’ became unfashionable the scene was set for a most surprising recall to the centre stage of intellectual endeavour. Pythagoras and those who acclaimed his influence (especially the mathematikoi) were resurrected to become highly influential seventeenth century figures. Their particular kind of mathematics gave the age of Kepler, Leibniz, Descartes and Newton exactly what it needed: the assurance, and theoretical underpinning, of an internally consistent intellectual system. This mathematical revival demonstrated that bodies were composed of numbers and how as a consequence their properties and causes might also be expressed numerically.


Number was everywhere and everything, therefore, hung together in the interlocking system revealed in the pages of Principia Mathematica. No Pythagoras; no Newton. Physics, along with all the other natural sciences, had become a branch of applied mathematics. This was not just a case of ‘ the mathematization of science’. if one wanted to be seen as a serious person in almost any area of intellectual exploration it was necessary to have a system- all the differing bits of knowledge at one’s command being linked up with each other.

The ‘Newtonian’ paradigm of a systematic basis of true knowledge - mathematical in its expression of the universal grammar of number - retained its appeal, so far as the West is concerned, until the early twentieth century. Einsteinian relativity chipped away at the mighty Newtonian edifice - a world in which objects existed at a specific time in a specific place. Quantum mechanics was even more unsettling since it enveloped objects in a haze of probability: matter could behave like a wave and as a result objects which had a certain chance of being at point A had another chance of being at point B (and so on infinitesimally). The natural sciences were transformed by this radical, if dislocating, account of the world and of the conceptual revisionism required, epistemologically. It is quite possible that statistics - like the social sciences more generally - remains largely Newtonian in its quasi-mathematical assumptions, unwilling to confront the need for a procedural update.


That seventeenth century insistence on a systematic approach - capacious in its embrace of an inter-locking body of knowledge - was a highly persuasive kind of orthodoxy. Resistance to this rush of the new required a degree of self-confidence, and originality, as the career of Robert Boyle (1627-91) demonstrates. He is now remembered as the founder of modern chemistry. It is though the sheer variety of his intellectual interests, and his unwillingness to create a system that might as it were smooth out the different ways of understanding the world that holds our attention in this second part of the research project. Boyle learnt a lot about the experimental method from Francis Bacon but he was too much his own man ever to be labelled a Baconian. The national organisation of inductive science in the service of useful knowledge, advocated by Bacon in Instauratio Magna (1620), one of the great mad books of the age, held few attractions for Boyle. Bacon was systems man par excellence. But for Boyle the whole point of the experimental procedure- evident his writings on subjects as diverse as chemistry, hygiene, medicine, religion, agriculture, philosophy - was that it preserved the particular character of each mode of understanding. There could be no Boylean system. He resisted the ‘spirit of the age’ and it is for that reason that he deserves a closer examination.



13. Francis Bacon, Paul van Somer I, 161
14. Instauratio Magna, Novum organum sci

Francis Bacon (b-d), Paul van Somer I, 1617 and Instauratio Magna, Novum organum scientiarum, 1645 edition

Part of Charles Booth's poverty map, 188

Scholars at an Abbasid library. Maqamat of al-Hariri, Yahyá al-Wasiti, 1237. Translation into Arabic and Persian of the Greek classical texts preserved knowledge of ancient Greek science while also transmitting its influence to European scholars from the twelfth century AD onwards

0.1 The %22Torun portrait%22 of Nicolaus

The "Torun portrait" of Nicolaus Copernicus  1473-1543, anon (c. 1580)


Adolphe Quételet, Joseph-Arnold Demannez, c.1870

Bruce Aylard, WHO epidemiologist, Bejing

Bruce Aylard, WHO epidemiologist, Beijing 2020

3. future-of-marketing-Main-Development-

Future Trends Cartoon

Plan of the Panopticon, Jeremy Bentham,

Plan of the Panopticon - or the perfect, most efficient jail - designed by the utilitarian philosopher Jeremy Bentham, 1791

Map of Ionia

6. Bust of Pythagoras of Samos.jpg

Bust of Pythagoras of Samos

7. Bust of Aristotle. Marble, Roman copy

Aristotle. Marble, original by Lysippos from 330 BC

8. Portrait of Johannes Kepler, anon, 16

Portrait of Johannes Kepler, anon, 1610

10. Isaac Newton, Sir Godfrey Kneller, 1
9. 'Principia Mathematica', first editio

Sir Isaac Newton (1642-1726) by Godrey Kneller (1689) and 'Principia Mathematica', first edition (1687)

11. Einstein.jpg

Albert Einstein writing his famous formula

The Shannon Portrait of the Hon. Robert

The Shannon Portrait of the Hon. Robert Boyle F. R. S., Johann Kerseboom, 1689

12. Quantum measurememnt problems, Getty

Quantum measurement problems

Part of Charles Booth's poverty map, 1889
Black - Lowest class. Vicious,
Red - Middle class. Well-to-do.
Gold - Upper-middle and upper
classes. Wealthy.

A 1950s advertisement for a Formica kitc

Mr Harold Macmillan (left), Minister of Housing, discovers a ‘lounge’ at the Ideal Home Exhibition in 1953’

A 1950s advertisement for a Formica kitchen

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