as we have previously discussed systems
are essentially the global functionality
that emerges out of the inter
changement of a set of elements
thus systems are defined by the function
that they perform to see the world from
the system's perspective is to not see
things but to see their functions
so in this section we're going to talk
about these things called functions a
function is a very broad and fundamental
concept that is central to Systems
Theory it is also used in many different
domains being particularly important
within mathematics and engineering
put simply a function is a process that
transforms energy or resources from one
state to another so there are three key
things to note in this definition we
have a set of things that is the input
we have a process that changes these
things in some way and we have an output
firstly inputs involve the capturing and
assembling of elements that enter the
system to be processed putting fuel into
your car is an example of an input to a
mechanical system the water taken in by
the roots of a plant is an example of an
input to a biological system an
important thing to note is that any
given system can only process a specific
range of inputs our car can process a
certain type of fuel but not all fuels
as we will discuss in a later lecture
what a system can and can't process is a
defining feature to its boundary that
functions to filter inputs to the system
for example an electrical power socket
is designed in a particular shape to
ensure that only the right plug is
inputted to it
thus it is functioning as a boundary
filter to accessing the system
secondly resources that are successfully
inputted are processed within the system
a process is a series of actions
performed upon the input in order to
achieve a particular end result
processing is often understood in terms
of information that is an algorithm or
set of instructions that are performed
upon the input in order to produce the
output
so baking a cake is an example of a
process it takes a set of ingredients
such as eggs water flour etc the cook
then has a recipe to follow that
represents the set of instructions to be
performed upon these raw ingredients
such as chopping mixing baking and so on
if these stages in the process are
correctly performed the result should be
the desired output
this same process is true for the
internal working of a computer
biological cell or a financial
transaction processes are not
necessarily linear in nature they may be
cyclical feeding back on each other with
the output from one process being the
input for another they may also be
nested within larger processes or run
parallel to them
but ultimately there will be some energy
or resources produced by this process
that travels across the system's
boundary to be returned to its
environment and this is what is called
the system's
output
one way of understanding a function then
is simply as the difference between what
goes into the system and what comes out
we call a system whose internal
functioning we do not know a black box
in science computing and engineering a
black box is a device system or object
which can be viewed in terms of its
inputs and outputs without any knowledge
of its internal workings this can be of
great value to us as it helps to hide
away the complexity of the internal
workings to the system
a function is often symbolically denoted
as an arrow from one element or set of
elements to another and in the language
of mathematics may be called a mapping
or transformation functions may be
unidirectional meaning the function only
Maps an input to an output or the
function may be bi-directional meaning
it can also invert this process to
transform the output back to the input
through what is called an inverse
function
many processes are essentially
unidirectional requiring vastly or even
infinitely more energy to invert the
function than was required to perform it
in the first place aging within the
human body may be cited as a good
example of a unidirectional process
whereas the building of a Lego brick
house is an example of a function that
can be easily inverted and thus
bi-directional
we should note that the model of a
function cannot be properly used to
describe a set of things because sets do
not perform a common function so if we
take a group of Nations at war with each
other because they are not working
together to perform a function we can
only describe them by talking about
their attributes and interactions but
the model of a function can be
effectively used to describe any type of
system
the concept of a function will appear to
be very simple and intuitive to us this
is due to its high level of abstraction
which also makes it a powerful model in
very important tool in our systems
thinking toolbox