Reasoning About
Complex Systems
Equations
General Statements
General statements are used in many
contexts.
One might be a law of physics:
Energy can be neither created nor
destroyed.
Or, one might be an assertion in a logical
argument:
All men are mortal.
Equations = Relationships
An Equation is a general statement
An Equation expresses a relationship.
relates one thing to one or more others
invention is one part inspiration and 99 parts
perspiration - Thomas Edison
Example 1
invention is one part inspiration and 99
parts perspiration
Invention = 1 * inspiration + 99 *
Perspiration
I = N + 99 * P
Constructing Equations
Identify the components of the equation
the value of x depends on the values of y and z
x = f(y,z)
Identify the form of the equation
x = 24 + 2*y + 7*z
i = n + 99 * p
Example 2
The amount you save is equal to your
income minus the amount you spend
Savings = income – expenses
s=i-e
Equations
What variables will be used to compute
“Births”?
What variables will be used to compute
“Deaths”?
More Equations
Identify the equations in the following
diagram.
Endogenous and Exogenous
What are the endogenous and exogenous
variables?
Endogenous and Exogenous II
Stocks, Flows, Converters, Auxiliary,
Constants
Example System
Equation for a Flow
Equation for Stock
Expressing Equations
In computer languages:
“+” specifies addition
“-” specifies subtraction
“*” specifies multiplication
“/” specifies division
These symbols must be used explicitly
2(x + y) will not work
2*(x + y) is required
Expressing Equations II
Parentheses are used to assure an equation
is processed appropriately
Without parentheses multiplications and
divisions will be executed left to right and
then additions and subtractions will be
executed left to right
Example 1:
.9 - .2 * P / 3000
.2 * P
(.2 * P) / 3000
.9 – ( (.2 * P) / 3000)
Expressing Equations III
Example 2:
cs – cb * sv * af
cb * sv
(cb * sv) * af
cs – ( (cb * sv) * af)
Expressing Equations IV
Example 3:
(cs – cb) * sv * af
cs – cb
(cs – cb) * sv
( (cs – cb) * sv) * af
End