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MODEL ABSTRAK = MODEL KONSEPTUL
An abstract model (or conceptual model) is a theoretical construct that
represents something, with a set of variables and a set of logical and
quantitative relationships between them. Models in this sense are constructed
to enable reasoning within an idealized logical framework about these
processes and are an important component of scientific theories. Idealized
here means that the model may make explicit assumptions that are known to
be false (or incomplete) in some detail. Such assumptions may be justified on
the grounds that they simplify the model while, at the same time, allowing the
production of acceptably accurate solutions, as is illustrated below.
Examples
Mathematical models
Model of a particle in a potential field. In this model we consider a
particle as being a point of mass m that describes a trajectory modelled by a
function x: R → R3 given its coordinates in space as a function of time. The
potential field is given by a function V:R3 → R and the trajectory is a solution of
the differential equation
Note this model assumes that the particle is a point mass, which is
certainly known to be false in many cases where we use the model, e.g. when
we use it as a model of planetary motion.
Model of rational behavior for a consumer. In this model we assume a
consumer faces a choice of n commodities labelled 1,2,...,n each with a market
price p1, p2,..., pn. The consumer is assumed to have a cardinal utility function
U (cardinal in the sense that it assigns numerical values to utilities), depending
on the amounts of commodities x1, x2,..., xn consumed. The model further
assumes that the consumer has a budget M which she uses to purchase a
vector x1, x2,..., xn in such a way as to maximize U(x1, x2,..., xn). The problem of
rational behavior in this model then becomes one of constrained maximization,
that is maximize
subject to
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This model has been used in models of general equilibrium theory,
particularly to show existence and Pareto optimality of economic equilibria.
However, the fact that this particular formulation assigns numerical values to
levels of satisfaction is a source of criticism. But this is not an essential
ingredient of the theory and again, the model is an idealization.
Other types of models
These two models are examples of mathematical models; following are
examples of models that are not mathematical (or at least not numerical).
Myers-Briggs personality type.
Myers-Briggs Type Indicator is a technique that claims to produce a
representation of a person's preferences, using four scales. These scales can
be combined in various ways to produce 16 personality types. Types are
typically denoted by four letters — for example, INTJ (introverted intuition with
extroverted thinking) — to represent a person's preferences. This model is
claimed by CPP (formerly known as Consulting Psychologists Press, Inc.) to
produce a good predictor of a person's career and marriage partner
preference. It should be pointed out, see [1], that there is considerable
disagreement among psychologists on whether this assessment technique
(and the implied idealized personality model) is of any value.
Model of political contagion.
Some versions of this model are sometimes referred to as the domino
theory. In the broadest possible terms, according to this model, political
movements that take hold in one country are likely to spread to geographically
neighboring ones. This model is surprisingly popular, although as it stands, it is
extremely impoverished conceptually, saying nothing about the type of political
movement, the degree of geographical proximity, the time scale at which these
events take place, etc.
Use of models
The purpose of a model is to provide an argumentative framework for
applying logic and mathematics that can be independently evaluated (for
example by testing) and that can be applied for reasoning in a range of
situations. Models are used throughout the natural and social sciences,
psychology and the philosophy of science. Some models are predominantly
statistical (for example portfolio models used in finance); others use calculus,
linear algebra or convexity, see mathematical model. Of particular political
significance are models used in economics, since they are used to justify
decisions regarding taxation and government spending. This often leads to
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hotly contested debates in the academic world as well as in the political arena;
see for instance supply side economics.
Abstract models are used primarily as a reusable tool for discovering
new facts, for providing systematic logical arguments as explicatory or
pedagogical aids, for evaluating hypotheses theoretically, and for devising
experimental procedures to test them. Reasoning within models is determined
by a set of logical principles, although rarely is the reasoning used completely
mathematical.
In some cases, abstract models can be used to implement computer
simulations that illustrate the behavior of a system over time. Simulations are
used everywhere in science, especially in economics, engineering, biology,
ecology etc., to discover the effects of changing a variable. The validity of
different simulation methodologies is a subject of debate in the philosophy and
methodology of science.
The automated use of modeling has been identified as a significant
issue in the creation of artificial intelligence. Some researchers argue a system
without a model cannot achieve understanding, while others argue that running
full, consistent models is too computationally costly for either machines or
animals, and that much intelligent behavior is reactive or instinctive.
Structure of models
A conceptual model is a representation of some phenomenon, data or
theory by logical and mathematical objects such as functions, relations, tables,
stochastic processes, formulas, axiom systems, rules of inference etc. A
conceptual model has an ontology, that is the set of expressions in the model
which are intended to denote some aspect of the modeled object. Here we are
deliberately vague as to how expressions are constructed in a model and
particularly what the logical structure of formulas in a model actually is. In fact,
we have made no assumption that models are encoded in any formal logical
system at all, although we briefly address this issue below. Moreover, the
definition given here is oblivious about whether two expressions really should
denote the same thing. Note that this notion of ontology is different from (and
weaker than) ontology as is sometimes understood in philosophy; in our sense
there is no claim that the expressions actually denote anything which exists
physically or spatio-temporally (to use W. Quine's formulation).
For example, a stochastic model of stock prices includes in its ontology
a sample space, random variables, the mean and variance of stock prices,
various regression coefficients etc. Models of quantum mechanics in which
pure states are represented as unit vectors in a Hilbert space include in their
ontologies observables, dynamics, measurement operators etc. It is possible
that observables and states of quantum mechanics are as physically real as
the electrons they model, but by adopting this purely formal notion of ontology
we avoid altogether this question.
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Modeling
Modeling, especially scientific modeling refers to the process of
generating a model as a conceptual representation of some phenomenon as
discussed above. Typically a model will refer only to some aspects of the
phenomenon in question, and two models of the same phenomenon may be
essentially different, that is in which the difference is more than just a simple
renaming. This may be due to differing requirements of the model's end users
or to conceptual or esthetic differences by the modellers and decisions made
during the modeling process. Esthetic considerations that may influence the
structure of a model might be the modeller's preference for a reduced ontology,
preferences regarding probabilistic models vis-a-vis deterministic ones,
discrete vs continuous time etc. For this reason users of a model need to
understand the model's original purpose and the assumptions of its validity.
Having found a model for some desired aspect of reality, it can serve as the
basis for simulation, the only way for non-invasive examination of physical
reality besides real-world experiments.
References
Briggs Myers, I. and P. Myers, 1993. Gifts Differing. Understanding Personality
Type, CPP Books.
Frigg, R. and S. Hartmann, Models in Science. Entry in the Stanford
Encyclopedia of Philosophy.
Lancaster, K. 1968. Mathematical Economics, Dover Publications.
Quine, W. 1961. From a Logical Point of View, Harper Torchbooks.