2. System Fundamentals
Source: ebook ch. 3–4 (“Sets Vs. Systems”, “Systems Function”).
This chapter builds the minimal formal model of what a system is, as distinct from a mere collection of things, and introduces the concept of function that gives a system its identity.
Sets vs. Systems
Common definitions of “system” converge on three ingredients:
- Wikipedia: “A system is a set of interacting or interdependent components forming an integrated whole.”
- Oxford: “A set of things working together as parts of a mechanism or an interconnecting network.”
Unpacking these: a system is (1) a composite entity made of a number of parts, called elements; (2) these elements are interconnected and interdependent — there is a set of relationships between them; (3) through these relations the elements are arranged in a particular way to perform some collective function that defines the system as a whole.
A set, by contrast, is a group of objects that share no common function — they exist independently of one another. A group of cups on a table is a set of cups; a pile of bricks is a set; people waiting at a bus stop are a set. Because the elements of a set don’t work together, describing the properties of each element individually tells us everything we need to know — the set is simply the sum of its elements.
The difference between a set and a system is not the elements — it’s the relations. Take a pile of bricks (a set) and build a house out of them: the bricks haven’t changed, but by arranging them into a particular set of relations that let them function as an interdependent entirety, the pile has become a system (the house).
Set vs. system is a binary distinction, but once something is a system, “how much of a system”
it is turns out to be a matter of degree. Complexity can be treated as a graded property
along (at least) four dimensions: number of elements, their diversity, their degree of
interconnectivity, and their capacity to adapt. A system can be simple on all four (few, similar,
loosely connected, static parts) or complex on all four — most real systems sit somewhere between.
This graded view of complexity, and the distinctive dynamics that show up once a system scores
high on it, is picked up in 10-complex-adaptive-systems.md.
“So, what is a system? A system is a set of things — people, cells, molecules, or whatever — interconnected in such a way that they produce their own pattern of behavior over time.” — Donella H. Meadows
This is also where emergence first appears (treated fully in
04-relations-synergy-emergence.md): a system is not a
thing the way its elements are things (bricks, cars, people, planets). A system is what
emerges out of the interaction of things working together as an entirety. This makes systems
more abstract than their elements — we can touch a brick, but not “the house” as a system; we
can see a bus or walk on a road, but not the urban transportation system as a whole.
Because elements have much better-defined boundaries than the system as a whole, it is common — and sometimes justified — to fall back on analytical methods that simply describe a system by describing all of its parts, i.e. reducing it to a set. This is appropriate for low-interconnectivity systems, but breaks down for the highly interconnected, interdependent systems (social systems, ecosystems, information systems) that Systems Thinking, grounded in synthesis, is built to handle. Set theory (the foundation of contemporary mathematics) is the natural tool of the analytical paradigm; systems thinking is the natural tool wherever we are actually dealing with systems rather than sets.
Systems Function
A system is defined by the function it performs — to see the world from the systems perspective is to see not things but functions. A function is a very broad, highly abstract concept central to systems theory (and to mathematics and engineering generally): a process that transforms energy or resources from one state to another.
A function has three parts:
- Input — the capturing and assembling of elements that enter the system to be processed
(fuel into a car; water taken in by a plant’s roots). Any given system can only process a
specific range of inputs (a car processes only certain fuels) — what a system can and cannot
process is a defining feature of its boundary, which filters inputs (see
03-boundary-and-environment.md). - Process — a series of actions performed on the input to achieve a particular result, often understood as an algorithm or set of instructions (a recipe transforming raw ingredients into a cake). Processes are not necessarily linear: they may be cyclical, feed back on each other, be nested within larger processes, or run in parallel.
- Output — energy or resources produced by the process that travel across the system boundary back to the environment. A function can be understood simply as the difference between what goes into the system and what comes out.
Black boxes
A system whose internal functioning we do not know is called a black box: a device, system, or object viewed purely in terms of its inputs and outputs, without knowledge of its internal workings. This is valuable precisely because it lets us hide away internal complexity when it isn’t relevant to the question at hand.
Directionality
A function is often symbolically denoted as an arrow from one element (or set of elements) to another — in mathematical language, a mapping or transformation.
- A unidirectional function only maps input → output.
- A bidirectional function can also be inverted (output → input) via an inverse function.
Many processes are effectively unidirectional because inverting them would require vastly more (or infinitely more) energy than performing them cost in the first place — aging in the human body is a unidirectional process. Building a Lego house is, by contrast, easily inverted, so bidirectional.
Function requires collective purpose, not just membership
The model of a function cannot properly describe a set — because sets do not perform a common function. A group of nations at war can only be described by talking about their individual attributes and interactions, not by a shared function they perform together. The function model applies wherever components genuinely work together toward some common end — which is exactly the criterion that separates a system from a set.
“To enable a system to perform effectively we must understand it — we must be able to explain its behavior — and this requires being aware of its functions in the larger systems of which it is a part.” — Russell L. Ackoff