Starting from the cornerstone of probability theory, this chapter elucidates essential concepts such as quantiles, expected values, and moments of distribution. It lays the groundwork for understanding both univariate and multivariate probabilities, which are fundamental for probabilistic modeling endeavors.

This chapter explores the pivotal role of modeling as a conduit between diverse data representations and applications in real, complex systems. The emphasis is on portraying modeling in terms of multivariate probabilities, laying the foundation for the probabilistic data-driven modeling framework.

Just as I thought to write these lines, a one-line programming error has frozen many airlines, banks, hospitals, video-streaming services, point-of-sales terminals and websites. The CrowdStrike code expected 21 values in an array, but received 20. Only 8.5 million computers were affected on 19 July 2024, but they were cloud/data centre-based servers running the Microsoft platforms for enterprise-critical services. The event has been termed the largest IT fail ever. The Microsoft Corporation blames the CrowdStrike event on the European Union and its anti-monopoly regulations.

Much of this book was written with a large language model constantly nudging me to accept line completions (GitHub 2023). I redacted almost all content suggestions as uninteresting. For instance, it suggests right now, having observed what I wrote in the paragraph above, that ‘the Crowdstrike event was a “wake-up call” for the world. It wasn’t. It was a one-line programming error. It was a wake-up call for the people who wrote the code’. The model making this suggestion, however, was itself trained to more or less write code for people, so that wake-up call might be hard to respond to. Who or what is being called by whom or what is not clear.

When readers meet passages of code in the book, they should be awake to the writing of the code. I have often supplicated generative AI platforms to write code (e.g. write Python code to demonstrate the basic operation of an endpoint detection response system such as CrowdStrike. Please provide comments.). Their facility in writing it attests to the sometimes startling predictability of coding.

There is a doorway on the southern wall of a large church in Venice, the basilica known as the Frari. The complex geometry of the Baroque-style doorway commemorates Giovanni Pesaro, 103th Doge of Venice (1658– 1659). Much disliked, Pesaro died suddenly in his first year as Doge. In 2024, the main resonance of the word ‘Doge’ is probably Dogecoin, a cryptocurrency first started with satirical intent but persistently traded on exchanges alongside the Bitcoin, Ethereum, Luckycoin and Litecoin in almost ten years of speculation.

The heavily ornate doorway (see Figure II.1) has the Doge seated on one of several platforms under a gold-tasselled canopy, flanked by a variety of martial, judicial, scholarly and artistic figures, as well as some quasi-mythical animals and angels. Above the Doge, close to the ceiling of the building, two small angels hover, holding an unfurled scroll, presumably inscribed with either the laws of Venice or the Doge's achievements. Pesaro and various attendants occupy niches separated by black marble columns. Two mythical creatures sit at his feet. The niches and columns stand on a thick plinth borne, along with heavy sacks of grain, on the shoulders of four black-marble figures clothed in torn fabric, slaves brought from Venice's colonies, themselves standing on four pedestals. A door to the piazza outside stands in the centre. At the base, and almost at the floor level where visitors and tourists go in and out in droves, skeletal corpse-like naked figures hold gold-lettered eulogies.

Platform edges are hard to locate. Power-laden like a city-state, vertiginous like a ten-metre diving platform, lifted-up like a concert stage, replete with technicalities like a geometrical proof, and as niche-rich as coastal rocks, platform edges run between inside and outside, core and periphery, on and off.

It may be that platform edges run along tangled lines of code and devices, through interfaces, networks, sensors, chips and screens. Inhabited in practice yet difficult to perceive or untangle, people step into these entanglements every time they open and close documents across different devices and platforms. Sometimes not knowing where the document is stored, they pause to ask: ‘Where is that file?’ They negotiate uncertain boundaries and thresholds between what belongs to them and what belongs to others, what is part of their work and what is not, or where their work takes place given the complete mixing of platforms into work, education, home life and government. Their work, their time with family and friends, their finances, health, education and leisure, increasingly run into platform edges guarded by requests for user names and authentication or ‘use Google/Facebook/Apple to login’ requests. They encounter limits in storage on their devices or in cloud data stores and wonder whether to copy everything somewhere else, or buy more space. They lose or find themselves using apps chosen from tens of thousands on offer in app stores such as GooglePlay and Apple Corporation's App Store.

This book anticipates re-grounded worlds in which platforms have become less consolidated as speaking positions, less encroaching along their edges and more seamful in their composition. In their gathering and alignments of devices, numberings, sensings, and closures or captures, platforms pre-figure what they are but cannot affirm: ensembles and their vibratory sensings.

There is something at once deeply theoretically and empirically disconcerting about re-working platforms as ensembles.

On the one hand, the ensemble concept developed in this book can draw on some fairly strong philosophical support. A high-level support comes from Gilles Deleuze's account of Ideas in Difference and Repetition (Deleuze 2001). Ideas are ensembles. Ensembles gather ‘differential relations and singular points’, they ‘begin with the inessential’, and their ‘essences’ are constructed ‘in the form of centres of envelopment around singularities’ (Deleuze 2001, 264). Ideas in this sense gather presentiments of divergences, approximations, and movements of ground and earth found in ensembles. Some instances of singularities or inessential points found in the platform world are terminals, chips, hashing, instruction sets, plugs, and floating point arithmetic. As starting points, they promise little, but much unfolds from them.

On the other hand, anticipating something by doing experimental ontology, and experimenting with such inessential and localized points of departure, seems to avoid central problems and controversies that affect all of us, and that many people suffer from greatly.

At base, Euclidean space has little concern with coordinates and numbers but much concern with figures and containers. In Euclid's Elements, the primary geometry textbook for engineering sciences, the definition of a figure makes no mention of dimensions or the coordinates that Descartes instrumented as Euclidean space. Euclid defines a figure as ‘that which is contained by any boundary or boundaries’ (Euclid 2012, 1). A figure could be a circle, a square, a triangle, and so on, but not a line or a surface extended indefinitely, since those have no endpoints or extremities. This definition relies on preceding ones, many of which rely on even more elementary propositions and line-drawing; for example, ‘Definition 2: A surface is that which has length and breadth only’ (Euclid 2012, 1).

Figures in Euclid's Elements are, broadly speaking, containers to be mixed together to construct new containers. The propositions of the Elements are, in practice, instructions on how to use the definitions, postulates and previous propositions in combination to make figures (such as Figure III.1): ‘Proposition 1: On a given finite straight line to construct an equilateral triangle’ (Euclid 2012, 3). The propositions are figurative in Euclid's sense of the figure in that they are constructed using a compass and ruler to draw figures. The propositions, even those concerning number rather than geometry, are figured out using lines as boundaries. For Euclid, figures contain other figures or containers.

What does experimental ontology do with devices? Implicitly posed in many places. It's a comfortable hotel, warm and well-lit, in the Lake District, north-west England, February 2016. The fields, hedges and woodland outside are snow-covered, sloping down towards the slate-grey waters of the lake. The meeting room is muted. Soft carpets, plush drapes, ergonomic seats and a continuous flow of fresh baked goods and locally sourced hot drinks cushion the participants. In the meeting room, computer scientists, a scattering of health and environmental scientists, statisticians, health and educational researchers chat around the table, waiting for the opening talk.

We wait to hear about the micro:bit, a BBC-sponsored device whose purpose in life is to usher youth and geeks in the UK and elsewhere into the world of embedded devices, and the more networky version known as the Internet of Things (IoT). The main speaker, a designer from the BBC, is passionate about the history of microcomputers and the BBC, narrating the story of a microcomputer, the BBC Micro, that transformed UK popular culture in the 1980s because of the amateur tinkering and hacking it facilitated. The micro:bit, a £10 piece of hardware, aims to re-capture and update some of the glowing meaningfulness of those days. The update for the internet-enabled post-platform economy is neatly symbolized by ‘:’. The BBC and the Micro:bit Foundation is just about to deliver hundreds of thousands of the devices to UK schools. Every 11-year-old will have one.

A guide to the coastal ecology of New South Wales from the 1940s praises the many rock platforms found along the shorelines of eastern Australia:

The coastlines in question intersperse beaches and rock platforms. These platforms biogeochemically mix sediment, the remains of hard-shelled creatures, microbes and minerals, and the veins and dykes of igneous rock such as quartz intruding from beneath the crust. The rock platforms unfold complicated edges of varying shape and thickness. Actually, not just on rock platforms, but along edges of many different kinds – between shadow and sunlight, between air and soil, between hard and soft, hot and cold or moist and dry – lives diversify.

The coastal rock platforms are edge-thickening events. Along their many edges, gradients of nutrient, water, air, sunlight, and heat shift with tides, seasons, sea levels and climate. They create the possibility of many niches in the same places. Edges are sites of pluralization and, because of that, are sometimes densely populated. The liveliness of coastal rock platforms owes much to tides, to weathering and sea levels, to processes of weathering and the relative durability or solidity of rock to waves, sand and sun.

The aim of the Dis-Positions book series is to bring together recent work in the emerging intersections of such disciplines as sociology, anthropology, history, geography, design and philosophy, not least as they bear on the broad field of science and technology studies (STS). Conversely, if STS is undergoing major shifts in how it engages with ‘the social’ and the question of ‘societies’, it raises vital matters of concern for these various disciplines and their inter-connections. Dis-Positions thus provides a platform on which varieties of generative mutualities across these areas of scholarship can be presented.

In this respect, Dis-Positions is undergirded by a desire to promote novel fields of enquiry, adventurous theoretical and empirical projects, and inventive methodological practices. It seeks to encourage authors to address live debates while drawing on and interrogating developments across academic areas, in the process disturbing and repatterning STS. In pursuing this ethos Dis-Positions comprises consolidated, rigorous and proactive space through which new creative and critical perspectives in STS and beyond can find a voice. Under this rubric fall discussions of the post-human, post-colonial, affective and aesthetic; methodological inventions that incorporate speculative, engaged, entangled and socio-material practices; empirical novelty that ranges from emergent technoscientific innovations to reformulations of the ordinary; and conceptually creative and critical developments that capture processual and pluralistic thought, extensions of assemblage and practice theories, and the turns to affect and post-performativity.