Determinism (and
hysteresis)
Copyright 2016 Graham Berrisford. One of about 300 papers at http://avancier.website. Last updated 14/07/2017 12:08
This paper contains thought related to determinism.
Contents
Determinism
in biology and business
Indeterministic/probabilistic
systems
Activity systems perform behaviors and change state.
State: the current values of an entity’s variable properties.
Process: one or more state changes over time, or the logic that determines which state changes lead to which other state changes.
Hysteresis: the process by which the system’s information state can be derived by replaying all events that have so far cross the system boundary.
Deterministic: the quality of a system that means its next state is predictable from its current state and input event.
Stochastic: the quality of a system that means its next or future state is not predictable, and appears random.
In this and related papers:
·
Orderly or deterministic <is contrasted
with> random or fuzzy, probabilistic or stochastic.
·
Linear change or outcome <is contrasted with>
non-linear or chaotic change or outcome.
·
Adapting (changing variable values) <is contrasted
with> evolving (changing variable types or rules).
This two-dimensional taxonomy of theories contrasts deterministic and probabilistic theories.
|
Theories of the universe |
Continuous |
Discrete (quantum leaps) |
|
Deterministic |
Relativity |
Digital
system modelling |
|
Probabilistic |
Social systems thinking? |
Quantum Mechanics |
Given a deterministic system you can predict how an actor or system will respond to a discrete event.
Providing that is, you know enough of its current state or memory and the rules it applies when responding to events.
An actor responds to a particular input event in:
· conventional determinism: by following rules that refer to its current state.
· hysteresis: by following rules that refer to past input events.
So, to predict an actor’s next output, you must know not only its rules, but also its current state or past event history.
Hoare Triples
A Hoare Triple specifies a deterministic process in a formal logic statement of the kind {P} S {Q}.
This means:
· IF the precondition (P) is true
· WHEN an event is detected and the process (S) terminates successfully,
· THEN the post condition (Q) will be true afterwards.
The precondition refers to the state of the system (or its memory of past events) when the new event is detected.
The post condition refers to the state of the system after the system has responded to the event.
Service-oriented (stimulus-response) specification of business systems is discussed in other papers.
It is important to note that architects need logical service contracts to be extended with measurable non-functional requirements.
Deterministic
machines
A deterministic machine is an entity that performs deterministic processes.
Honey bees, motor cars, human games and businesses can all be described as deterministic machines.
|
IF (Preconditions) |
WHEN (Event) |
AND (Process completes) |
THEN (Post conditions) |
|
A football is in play |
The ball crosses a side line |
A player takes a throw in |
The football is in play again |
|
A taxi journey is in progress |
The destination is reached |
The driver collects payment |
The taxi is available for hire. |
|
Your hair needs cutting And you have money |
You sit in the barber’s chair |
The barber washes and cuts your hair |
You have shorter hair Money has been transferred from you to barber The barber's scissors have worn down a little. |
|
An applicant is > 18 years old |
An application is made |
The application is approved |
Application state = accepted |
In “Design for a Brain” W Ross Ashby treated the brain as a deterministic machine.
The quotes
below are taken from chapter 2 and appendix 1.
Ashby “Our starting point is the idea,
much more than a century old, that a machine, in given conditions and at a
given internal state, always goes to a particular state.”
Ashby took
the view that the responses of the human brain to its senses are
state-determined.
Many business operations are similarly
state-determined.
When a payment
has reached its due date, the enterprise will invoice a customer for the amount
due.
Ashby: “We take as basic the
assumption that an organism is mechanistic in nature.”
Ashby
considered the human brain as deterministic system.
(This is a
theoretical position, since we cannot know the internal state or processes of a
human well enough to predict the choices it will make.)
Business
operations are often defined as deterministic systems.
Ashby: “From whatever position they
have initially, they go towards a state of equilibrium.”
A homeostatic
system reaches stability by maintaining variables within acceptable limits.
A business
does not strive to reach a state of equilibrium in the way a biological entity
does.
But it does
strive to avoid states in which it goes out of business or business rules are
broken.
And it
strives to meet measurable business objectives, which (being SMART) are
expressed as target variable values.
Ashby: “A variable is a measurable
quantity that has a value.”
To monitor or
direct a system’s behaviour, the observer must identify suitable variables.
Business
variables may include an employee’s salary, a customer’s credit balance, and a
supplier’s average delivery duration.
Ashby: “The state of the system is the
set of values that the variables have.”
A system’s
behaviour is determined by the state variables the system holds and updates.
A business
holds state variables values in databases of (e.g.) employees, products,
orders, customers and suppliers.
The enterprise
is seen as collection of control systems connected to business operations by
feedback loops.
The control
systems monitor and direct entities (employees, customers, suppliers) in the
performance of business operations.
They monitor
the state of those entities and activities by collecting information messages.
They direct
those external entities or activities (or try to) by sending them messages.
Ashby: “A system is any set of
variables which he [observer] selects from those available on the real machine.”
An observer’s
system description is, necessarily, a selective abstraction from the reality of business operations.
A system
description is abstract, it describes core processes
and variables, but cannot fully represent business operations.
An architecture
description is necessarily a selective abstraction from the reality of business operations.
To paraphrase Ashby: Enterprise
architects deal with all kinds of business process that are regular, or
determinate and reproducible.
Determinate
means the responses of a business (to events and service requests) are
determined by business rules applied to system state or memory.
To facilitate the transactions of government and commerce, EA formalises inter-actor communication and behaviour.
Not only is the representation of information in messages
and memories standardised using data types (defined in data models).
But also, the behaviour of actors is standardised using business rules (defined in data and/or process specifications).
EA frameworks assume business systems behave according to presumptions distilled in the UML 2.1 standard.
· “all behavior in a modeled system is ultimately caused by actions executed by so-called “active objects”
· “behavioral semantics only deal with event-driven, or discrete, behaviors”
Clearly, a business must respond to discrete events and service requests.
Many responses are determined by applying business rules to the current state of the business and/or its memory of past events.
And in formalising a social system, the memory must be independent of any individual human.
Service-oriented (stimulus-response) specification of business systems is discussed in other papers.
It is important to note that architects need logical service
contracts to be extended with measurable non-functional
requirements.
The opposite of determinism is the view that events are not caused deterministically by prior events.
It appears in quantum mechanics and in philosophical discussions of free will
The Copenhagen interpretation is an informal collection of attempts to express the mathematical formalism of quantum mechanics.
Presumption: the results of experiments must be reported in ordinary language (not in arcane terms, using names or clusters of mathematical symbols).
Postulate of the
quantum
Subatomic events are
only perceptible as indeterministic physically
discontinuous [discrete] transitions between discrete stationary states.
A transition is called a quantum leap.
No event is certain; the entire outcome of anything is unpredictable except as a probability.
Various consequences are inferred from this postulate.
Heisenberg's
uncertainty principle
Generally:
incompatible conjugate properties cannot be measured with arbitrary precision
at the same time.
Specifically: the more precisely the position of
some particle is determined, the less precisely its momentum can be known, and
vice versa
The Copenhagen interpretation also attempts to reconcile the apparent dualism of "wave" and "particle" in a fashion suitable to human understanding.
There are three broad positions on free will
The first two below are incompatibilist;
meaning that free will is incompatible with determinism
Metaphysical libertarianism
Metaphysical libertarians claim that
determinism is false and therefore free will is possible.
Hard determinism
Hard determinists claim that determinism is true and therefore free will is impossible.
A biologist may say attributing free will to a person is ego-centric or species-centric.
It is merely the way we interpret abilities and behaviours that have developed through biological evolution.
We are nothing but vehicles constructed by our genes to reproduce themselves.
Socio-cultural systems thinker Boulding wrote that humans act according to input messages and remembered mental images.
In other words, a person’s actions are deterministic, based on their internal state.
Are humans and social groups deterministic?
There seems to be no convincing way, no logic or test, to answer the question
Certainly, a human actor’s current state includes a memory of past events, and this influences its decisions.
But you cannot inspect or measure an actor’s current state or past history
Nor can you know the rules it applies to making decisions in response to events or conditions.
Note: a hard deterministic system can produce unpredictable or unexpected outcomes in the long term.
Also, all human societies and laws assume sane people make choices of their own free will.
It would be impossible to live in a human society without assuming the same.
And so, the only practical position seems to be compatiblism.
Compatibilism
Compatibilists conceives free will to be compatible with determinism.
They consider the debate between libertarians (free will) and hard determinists (determinism) to be a false dilemma.
Contemporary compatibilists identify free will as a psychological
capacity, such as to direct one's behavior in a way responsive to reason.
To paraphrase Ashby: Enterprise
architects deal with all kinds of business process that are regular, or
determinate and reproducible.
Determinate
means the responses of a system (to events and service requests) are determined
by rules applied to system state or memory.
If a process
cannot be described in this way, then it lies outside the scope of the
operational systems designed and governed by architects.
When applying system theory, Ashby and Boulding assumed people’s actions are deterministic, based on their internal state.
However, there is an anti-determinism streak in much socio-cultural systems thinking.
Socio-cultural systems thinkers often seek to differentiate human activity systems from deterministic systems.
They do this by characterising human systems as “complex”, “adaptive”, “non-linear”, “indeterminate” “chaotic” etc.
However, the use of these terms in opposition to deterministic is questionable.
The question about business systems that employ human actors is not whether humans behave deterministically or not.
Suppose for the sake of argument that humans are indeed deterministic machines; there are three questions
Q1) Is a human’s machine merely a subsystem of the business machine?
No! The former exists independently of the latter, it is more complex, and its rules may be different.
Q2) Can a deterministic human actor disregard the rules of the business system, or act outside them?
Yes! They often choose to follow their own rules.
Q3) Do business managers want to capitalise on the natural abilities of the human machines?
Often, yes. Human actors may be encouraged step outside the operational system
They may step up to a meta system in which they analyse and change the roles of the operational system.
This is a principle of “agile development” methods discussed in other papers.
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