Dictionary of the History of Ideas Studies of Selected Pivotal Ideas |

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9 |

2 | VI. |

V. |

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3 | I. |

VI. |

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3 | III. |

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1 | VI. |

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3 | I. |

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9 | I. |

1 | I. |

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1 | VI. |

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3 | V. |

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4 | III. |

I. |

7 | V. |

2 | V. |

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4 | I. |

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Dictionary of the History of Ideas | ||

####
*WHAT IS A MODEL?*

Biologists, like other scientists, use the notion of

model in a host of
ways. At one extreme they may

mean a scaled-up, three-dimensional wire and
plastic

representation of a cell. At the other, they may mean

an
abstract structure such as a “mathematical model”

of
evolution which may consist only of a set of differ-

ential equations. In what sense can the wire and
plastic

cell be said to be the same kind of structure as a set

of
differential equations? And in what sense are they

like a mouse, which is
said to be a “model organism”

for the study of
certain physiological or genetical

problems?

The similarities of these models can best be under-

stood by beginning with the most abstract. The basic

theory of
evolutionary genetics is well worked out,

based on a detailed knowledge of
the mechanics of

inheritance and certain empirical information about

the biology of reproduction and survival of a variety

of organisms. This
theoretical superstructure is suffi-

ciently complex that quantitative predictions of the

outcome of
evolutionary changes cannot be made by

inspection. In order to find out
what is entailed by the

theory in any particular case, a model is built.
First,

the theory is abstracted and is framed in terms of a

logical
flow diagram involving dummy variables and

logical relations among these
variables. Then this logi-

cal structure is
realized by a program for a computer,

or a set of matrices and matrix
operators, or a system

of difference or differential equations. All these
real-

izations are isomorphic with each
other and with the

original logical structure.

A second possibility is that a series of resistors, ca-

pacitors, and other electric and electronic devices is

used to make a physical model such that these electri-

cal elements produce a set of electrical
quantities

(current, voltages) that behave isomorphically with the

dummy variables of the abstract system. Alternatively,

a “model
organism” may be employed, like the fruit

fly, *Drosophila,* which is thought to be a specific real-

ization of the same general principles as are
expressed

in the abstract representation of the original theory.

In
fact, with a physical analogue as complex as a

“model
organism,” the explicit construction of the

abstract system that
served as the pattern for the

mathematical realizations may never be made.
Rather,

the model organism is assumed to embody the general

properties
of the system being modelled and, in fact,

the general theory of
evolutionary genetics supposes

that all organisms embody certain general relations

which are
the subject of investigation. A model orga-

nism can then be used, and often is, in the absence

of a well
worked-out theory of a biological process

on the assumption that general
biological similarities

between the systems will guarantee isomorphism
with

respect to the specific aspects under investigation.

The differences between the mathematical model,

the electronic model, and
the model organism as real-

izations of the
underlying abstractions, are of great

importance. The physical entities in
the latter two

kinds of models carry with them certain intrinsic prop-

erties that are different from those in
the original being

modelled. That is, these physical realizations are *
meta- phorical
* and their iconic elements can be a source of

serious difficulty. The physical realizations were chosen

because some set of their properties was isomorphic

with some set of properties of the original system or

theory. In the case of the electronic analogue, the

theory of capacitors, resistors, and vacuum tubes is so

well understood and the empirical properties of these

objects are so different from the system being modelled

that there is no danger of confusion from the meta-

phorical elements. That vacuum tubes glow, get hot,

break when jarred, make a tinkling sound when

knocked together, will in no way confound the biolo-

gist since he is unlikely to confuse these properties with

the properties of evolving organisms. In the case of

model organisms, however, the danger is very great,

because the metaphorical elements introduced by these

organisms are in some cases so subtly different from

the properties being modelled, that they cannot be

distinguished, yet they produce great distortions.

Moreover, since such metaphors are often introduced

without an explicit
laying out of the abstract system

of which the model should be a
realization, there is

no clear way of differentiating relevant from
irrelevant

from obfuscating properties of the model. For example,

*Drosophila* was used for a long time as the model for

the genetic mechanism of sex determination in man,

because of a general
similarity of genetic mechanisms

between flies and man. But this has turned
out to be

completely wrong, and the conclusions that arose from

this
model were erroneous. This danger does not arise

only from using complex
organisms as realizations. The

“digital computer”
model of the central nervous system

has been one of the most misleading and
possibly

harmful examples of allowing metaphorical properties

to
intrude. In this case such properties as redundancy

checks, topological
relationship between physical ele-

ments and
conceptual elements, and the bit structure

of information characteristic of
electronic digital com-

puters, although all
metaphorical, were taken to be

system, whereas they certainly are not. It is for this

reason that an explicit abstraction of the original sys-

tem, followed by a realization of that abstraction in

either an abstract or physical form is much preferable

to modelling by generalized and “felt” analogy.

There is some confusion in biology between “models

of”
and “models for.” The isomorphisms with particu-

lar biological systems are
“models of.” But models in

the sense of ideals or
patterns, like the “model of a

modern major general,”
are also found in the biological

literature. The essential difference is in
their epistemo-

logical status.
“Models of” are not intended, especially

when they
are abstract, as contingent. They are ana-

lytic isomorphs of some phenomenon or system. They

may be good or
bad models as they are perfect or

imperfectly isomorphic, but they cannot
be said to be

true or false. On the other hand, “models
for” like the

logistic model of population growth or the Lotka-

Volterra model of species
competition, or the gradient

model of development, are taken as statements
about

the real world, as contingent, and are in fact assertions

about
the way organisms really behave. Sometimes

such models (patterns) are
introduced as examples of

how nature *might* be, but
they very soon become reified

by biologists. Such
“models” are most common in those

branches of biology
where there is little or no theoret-

ical
basis. In these cases it is quite proper to speak

of “testing
the model” since it is not really a model

but a hypothesis.
Unfortunately, confusion between

these two senses of
“model” sometimes results in an

attempt to test a
“model of” which always results in

a vacuous
“confirmation” of the model. Since the

model is
analytic, it must be, and always is, confirmed.

Some such
“tests” of analytic models go on in popula-

tion biology, where a model organism is placed
under

extremely well controlled experimental conditions so

that it
realizes a mathematical structure that has been

solved. If the mathematics
has been done competently,

the model, which is a living computer, confirms
it. But,

of course, no “test” (except of the
competence of the

investigator) has been performed.

Dictionary of the History of Ideas | ||