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A Brief History of Quantification in Science

Modeling Nature and Society

Writing was a gamechanger, especially recorded measurements, for humans could extend quantification beyond the immediate environment to seasons, celestial bodies, and the general passing of time, rendering a broader swath of reality cogent and predictable. Humanity moved away from notions of spirit as the essence of reality to a world of material substances evincing signs of spirit, more serried as technology became pervasive in civilized settings. Existence transitioned from numinous augury towards analytical prediction of inanimate particulars as inert, nonvitalistic objects of spiritual intentions. Mathematical mensuration and calculation blended with premonitional intuiting and practical problem-solving to produce astrology, symbolic architecture and all the hermetic arts. Causality fractured into the corporeal and incorporeal realms, a division of spirit into materiality and soul.

Pioneering thinkers tried to conceptualize humanity’s growing sense for the orderedness of environments, with observation and contemplation of the natural world becoming less superstitious and more systematic. An almost religious significance was attributed to mathematical abstraction’s power to harness material phenomena, notions developing parallel to math’s use for standardizing value with currency in economies of trade throughout the civilized world. Philosophical cults of mathematics such as the Pythagoreans of ancient Greece attempted to explain complementarity between tangible and mathematical form, seeking to fashion their ideas into principles for orderly and measured existence, mediating the material and immaterial. Plato’s conceptualizing of the forms climaxed these efforts to comprehend the relationship of number with nature and soul (‘nous’), alongside closely linked attempts at inferring conclusions about total, ‘metaphysical’ causality, human nature and optimal action.

Plato placed great emphasis on the concept of ‘logos’, a crystallization of the idea that intrinsic order is accessible as rational truth obtainable from reflection, musings abetted by language use, a means to validate, refute and refine opinions in the context of amicable argumentation. Conviction that viewpoints must be explicitly justifiable, probably brought to the foreground of Athenian philosophy by a democratic system of disputative, oration-based government in search of consensus, stimulated development of rhetoric, then an empirical analysis of ‘logic’, the nature of proof. In math, procedures that prove inferences technically came to prominence also, as antiquity’s philosophers deduced truths from basic axioms to systematize mathematical knowledge and practice, increasing the clarity with which math is thought about and applied.

Ancient Greeks did not yet have Arabic numerals, so even elementary computations such as multiplication were cumbersome, requiring considerable expertise. With these limitations, they relied on geometry to do algebra. Solving for unknowns was not accomplished with expressions, as language, but rather using interrelations of geometric objects manipulated according to the laws and principles of ideal shapes in order to balance quantities and obtain ratios and equivalences. Euclid’s Elements formulated a theoretical framework for the discipline of algebraic geometry, and together with additional works of early mathematicians, most of which have been lost to us, introduced the paradigm of quantitatively defined systems of shapes that would be so crucial to scientific modeling.

Geometry-based algebra and deduction never became scientific during antiquity, as the ancients did not manage to synthesize it with empiricism. Aristotle, Plato’s pupil and a devoted naturalist, was concerned to catalogue facts within numerous categories of academic knowledge he and his associates were striving to expand and diversify, as well as with making hypotheses for testing intuitions, a sort of qualitative protoscience. Plato’s vision of centering progress on the integration of ideas via defining them with mathematical form was never fully embraced and assimilated by the empirical schools of thought Aristotle inspired.

After the heyday of Platonic and Aristotelian analysis, when ancient Greek academies were on the cusp of a modernlike science organized around quantitative theorizing, qualitative thinking was the rule in Europe’s metaphysics and natural philosophy, influenced by an up and coming Christian religion with its emphasis on introspection, personal devotion, and submission to spiritual authority, put on full display by profound but more informal and unsystematic authorship such as St. Augustine’s Confessions. Advancement of academia stagnated, and philosophical schools closed when, despite centuries of tradition, the populace lost interest in nonreligious commitments that probably no longer seemed relevant. With decline and fall of the Roman empire, then the collapse of a Frankish empire that had initiated the 8th-9th century Carolingian Renaissance, a brief effulgence of study, only Arab scholarship and preservation of Greek accomplishments prevented Western empiricism and philosophical math from being lost to civilization.

Europe slogged through its 10th century dark age at an intellectual nadir, entering the Middle Ages with poor health, concentrating population, and a desperate need for medicine, but three centuries were required for the continent’s knowledge to again reach B.C.E. levels. In Western physiology, such as it was, explanations based on concepts like bodily humors predominated, the harmful technique of bleeding patients prevailed, also notions of medicinal benefit based on likenesses between superficially similar objects — cauliflower for the brain for instance. An interest in logical verification began to revive as Scholasticism, but this was at first concerned more with theology and metaphysics than advancing technology within the corporeal sphere.

Confusion about the material world was rampant in early Medieval thought, with it not being at all clear to Westerners which commonalities amongst phenomena were significant enough to be the basis of explanation, and which negligible or chimerical. Features of reality were conceived as microcosmic, symbolic, and objects understood as analogous to each other in ways Moderns easily debunked by more systematic analysis. European conceptualizings of the world were in turmoil as this continent had failed to preserve precedents from antiquity, with almost no application of mathematics to natural philosophy. Technological utilization of math was likewise underperforming, limited to construction of drafty castles, geometrically simple towns and the first cathedrals, forging of handmade weaponry, all esoteric crafts that were not even in the same ballpark as modernity’s standardized and scaled-up analyticity.

Meanwhile, Arabs had committed to a study of Aristotelian philosophy, incorporating some of these concepts into Islamic thought. They had adopted Hindu numerals, which increased ease of mathematical calculation, and also developed linear algebra, solving for unknown values using languagelike statements. These innovations simplified numerical problem-solving and made possible more intensive geometry when a coordinate system was later introduced to make spatial objects interchangeable with algebraic equations called ‘functions’, which are much simpler to work with, a synthesis that laid the foundation for quantitative modeling.

During the European Renaissance, interest in Greek and Roman civilizations gained steam, and artists rose to the challenge of their past’s masterpieces. Visual artistry soon sought to surpass ancient motifs of ideal form, including human form, becoming concerned with achieving greater realism, representing both humanity and nature in an accurate way, making lifelike impressions within all genres. This humanist aesthetic consisted in heightened regard for the details of sense-perceptual structure and its workings, delving into deeper technicality than mere concepts and stylings of piety, passion and the desired. Some such as Leonardo de Vinci were forward-thinking: he meticulously studied human anatomy, the anatomy of organic life, and natural form generally, complementing these pursuits with an interest in the architecture of technologies, making copious blueprints of engineering designs. In his work, we can see material and anatomical knowledge merging with the idea of machine, presaging modern science. As studied observation revivified and advanced, the structures and processes of corporeal and organismal bodies were increasingly viewed as composed of parts coordinating mechanistically.

Isaac Newton’s notion of gravitation was revolutionary, as it made quantitative the most constant phenomenon on Earth, the tendency of bodies to accelerate towards our planet’s surface, also accounting for synchronized behaviors of objects in outer space, the orbiting and wobbling both generated by mutual pull. Conceptualizing of gravity allowed positions and motions of any macroscopic object in the solar system to be analogized with any other in terms of size, speed and friction. However, applying this idea required better mathematical techniques, a powerful way of analyzing geometrical figures that would enhance capacity to precisely quantify properties of more complex shapes needed for modeling the dimensionality of matter in contemporaneous physics’ brave new world. These geometries of multiform and asymmetric curvature were intricate enough that their most specific values, particular points along their lengths, and their most general values, averagings of the space encompassed within their ranges, made traditional techniques that relied on direct measurement insufficient for defining mathematical structure.

Newton resolved difficulties presented by mathematical analysis of an expanding assortment of ‘physical’ phenomena — contents of the material world interpreted as subsisting in mechanistic systems — with calculus. It was a paradigm for assimilating more esoteric geometry into practical usage using ‘limits’, which are essentially solutions of procedures for making successively closer approximations to a figurate value and then estimating the actual value by extrapolation once negligible imprecision has been reached. Ancient Greeks had utilized the concept of a limit in engineering as rudimentary applications of the method of exhaustion, their incrementally closer approximations to values such as the area of a circle, the volume of a sphere or the weight of a column, but Newton generalized this into an algebra of limits, the laws, principles and methods of calculus by which any average or specific value can be easily obtained within a data set of any geometry by manipulations of the corresponding function. Figures of any kind could be fitted to phenomena and their functions calculatively processed with as much exactness as necessary, then the many functions of empirical investigations averaged or otherwise synthesized into modeling expressions called ‘formulas’. Formulized phenomena were integrated in the context of quantified gravitation operative on all, a framework potent enough to make the era’s whole cosmos of sense-perceptual scale describable as numerically defined mechanism. Giant leaps in prediction capability ensued from which were assembled what has come to be known as ‘classical physics’, the bedrock of structural engineering.

Around this same time, the Early Modern period of the 17th and beginning of the 18th centuries, uncertainty intrinsic to theoretical modeling began to preoccupy the minds of natural philosophers and mathematicians. A facet of criticality blossomed within systematic thinking that called into question many conventions, influenced by cosmos-shattering discoveries in astronomy, which tried to make sense of the conditionality of truth, its context dependency and tendency to obsolesce. It was becoming clear that order in the known universe is not strictly spiritual, material or mathematical in the mold of any previous tradition, but nonetheless patterned in intelligible ways, and this enigmatic logicality came under close scrutiny. A chasm opened up in the midst of human knowledge, cognizance of disjunction between logical parameters of the reflective mind and mechanistic laws of the natural universe, mediated by a theoretical empiricism that might trump every accepted intuition, assumption, belief and institution thus far garnering consent. The mechanistic universe would wax ever more deceptive, with systematic reality bizarrely engendering systematic fallacy and ultimately systematic doubt as a core mindset.

Critical empiricism became standard methodology, bolstered first by many unintuitive findings of early laboratory and naturalistic observation, then differentiating into disciplines of speculative hypothesis and generalizing theory, initial incarnations of chemistry, biology, politics and economics. Advances in optical instrumentation between the 16th and 18th centuries transformed worldviews by revealing the astronomically large and microscopically small, with mathematics employed to model this profusion of fact and knowledge as quantitative data analyzed by way of assistance from calculus for patterns of proportion, rate, and extrapolated or interpolated trending. Interpretations of fact into geometrical form made the contents yielded by analytical techniques much more analogizable in their structure, with theorizing in all academic fields growing more cohesive even as knowledge broadened in scope.

Alchemy had been amassing a large collection of precedents regarding what seemed like almost miraculous transformations in material substances. As measurement and controlled experimentation achieved exacting preciseness, systematic principles of the changes in matter became apprehensible. It was shown in every test that material is never created nor destroyed but only converted into a different form; entropy — the disorder in a system — inclines towards increase; and there are a finite though vast number of possible combinations and dissolutions of what transitioned in the human mind from hylic form with numinous animation to inanimate, physical matter conforming to mechanistic laws. The new science of experimental chemistry had major implications for comprehension of biological systems in which many of the same principles applied, cuing the field of organic chemistry.

Quantifying in physics and chemistry spilled into the arena of what can be classified as protoscientific ecology, with modeling of human populations for economic and political theorizing, then animal and plant populations for knowledge of nature, an effort to make cultural engineering of civilization in institutional settings more cogent and optimizable. The insight that diverse species evolve from common ancestors in a process of mutation, adapting to natural environments, then deeper understanding of inherited bioactivity as mechanism, were conjoined with quantitative modeling of matter and rates of replication, expansion and contraction on macroscopic and microscopic levels to unify chemistry, biology and genetics. Greater understanding of life’s biochemistry, physiology and evolution led to modernized medicine, advances such as anesthetics, antibiotics, prophylactics, better surgical procedures, synthetic manufacture of pharmaceuticals, a whole industry of improved health care.

On the inanimate side of knowledge, inorganic chemistry and mechanization of manufacturing fueled industrial revolutions, along with a reciprocating consumer culture of demand for mass produced and distributed products. Infrastructure technology increased the volume of world trade and the international influence of political institutions that regulate it. In the 20th century, wars became global events, as did economic cycles, population exploded as mortality declined, civilization was saturating the planet. As gaps between centers of population and commerce began to fill in, consciousness of the interrelatedness and joint future of all life dawned on humanity and the concept of ‘ecosystem’ was introduced. As technology impacted nature in escalating ways, it became clear that humans could diminish their own prospects by plundering of the Earth’s resources, and ecological thought with a view towards sustainability fitfully made its way into the public’s decision-making.

The pursuit of knowledge is maturing into science, our world revolving around research, innovation and efficiency. Human life fast becomes a mechanistic system, centered on theoretical models that shape the environment via technology and dispel many long-standing uncertainties, though the awesome power of nature still humbles us on a regular basis. While technical progress seems indomitable, ethical issues loom larger as the behavior of populations in one region or even small cadres of scientists can impact the whole globe. Managing amplification of both cultural rivalries and conflicting priorities as well as the more catastrophic potential of single errors is an ongoing challenge. The requisite that humans mobilize huge, optimized group actions for international need and the vulnerable interests of our descendants, logistically demanding for everyone, means that even average individuals must think seriously about remodeling outlooks on finance, their political lives, and assume greater responsibility for the future of civilization. Quantification is a blessing and a curse, powering advance, but also engendering and bringing to our attention phenomena at the intersection of nature and technology that in their unintuitive novelty are nearly incomprehensible to us. Society depends on a commitment to proceed rationally and moderately, reflecting on the nature of both the cosmos and culture as we travel together at an accelerating rate down the path of our inextricably linked human futures.

Chapters from the book Standards for Behavioral Commitments: Philosophy of Humanism, and more!