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Models and Monsters

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The exception "proves" the rule. Using monsters to prove and improve models

This document describes techniques for the proving and improving of models, based on exception test cases, which (following Lakatos) we call monsters.
Lakatos Proofs and Refutations
Derrida Monsters and Change
art or science?

the model

the model





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Proofs and refutations

veryard projects > modelling > models and monsters > proofs and refuations

One of the simple ideas about science that has filtered into general knowledge is the idea of refutation. Something is scientific if it can be disproved. The best-known exponent of this idea is Karl Popper, who used it as a reason for rejecting several fields of endeavour as non-scientific, including Freudian psychology and Marxism.

Before his untimely death, Imre Lakatos wrote a brilliant book called Proofs and Refutations. Among other things, this book identifies several different ways of proving and improving mathematical models, and of preserving models against apparent refutation. With appropriate interpretation, these patterns can be used for any models, not just mathematical ones.

It is a natural tendency for modellers to justify and preserve their models, even when confronted with apparent exceptions. Meanwhile, other people question and challenge the model, for three reasons.

It is the exception that "proves" the rule. This statement has several meanings – some absurd and some quite useful. Among other things, it means that a robust model is one that stands up to repeated attempts to disprove by exception.
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Improving the Model

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Is modelling an art or a science?

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Art Science

Recognisable procedure for training artists

Recognisable procedure for creating art

Fierce disagreement about the quality of art

Fierce disagreement about what counts as Art at all.

Trial and error

No systematic procedure for creating models

Rigorous procedure for evaluating and rejecting models

Disagreement between scientists is common

  • but we can usually pinpoint the disagreement fairly precisely
  • and they rarely disagree about the nature of science itself

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Saving the Model

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How do we save our models?


Let’s start with a simple example. A training company runs courses at locations. Each instructor can run several courses – but only one at a time.
MODEL: instructor teaches course held at location


We now discover a case that doesn’t fit into the model – a monster. Thanks to the wonders of modern technology, Joe teaches a course simultaneously in New York and Los Angeles.
MONSTER: joe teaches course in NY and LA

The monster represents a challenge to the model. There are several possible responses.
Surrender Throw the model away and start again.
Reject the exception as invalid, a "monster". This usually involves refining the definition of one or more constructs, to explicitly exclude the exception as a monster.

For example, we could say that teaching two courses simultaneously, one in New York and one in London, doesn’t count as proper teaching.

Reframe the exception, so that it fits within the model. This usually involves refining the definition of one or more constructs, so that the monster is "tamed", converted or decomposed into something that can be accommodated by the model after all.

There are several reframing tricks that could be used in out example. Perhaps if the instructor is teaching in New York and London simultaneously, we define this, not as two courses, but as a single course with multiple locations. Or perhaps we have two occurrences of instructor: one real and one virtual. Or perhaps there is a single occurrence of location: the video link rather than the city.

Reformulate the rule, to incorporate the exception into the condition.

for any Instructor, except those capable of teaching remotely, and for any date you can think of, the number of the instructor’s outages on that date is never more than 1


Do you recognize these ways of preserving models?
Can you think of any examples from your own work?

What are the possible drawbacks or dangers of these ways of preserving models?

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Improving the Model

veryard projects > modelling > models and monsters > improving the model

In the context of evolutionary change, monsters can be of particular interest. Lakatos refers to the concept of "hopeful monsters". In biology, this means mutations that could start a new evolutionary line if fitting into an empty environmental niche.


Do you think the concept of "hopeful monster" is relevant to business modelling?
How might you use it?

Sometimes the goal of modelling is to represent and implement the existing structures and processes as accurately as possible. Sometimes the goal is to improve the structures and processes, to make them more robust.

Where do the monsters come from?
Some people are particularly good at inventing adhoc freaks, which can be seen as exceptions to a given structure. These freaks are usually handled adhoc, and result in complications to the model.
Some monsters may originate in errors or misunderstandings of various kinds.
Starting from the underlying concepts, we can broaden and generalize a given rule. This can sometimes result in simplifications to the model.

Kevin Kelly tells us to honour our errors.

A trick will only work for a while, until everyone else is doing it. To advance from the ordinary requires a new game, or a new territory. But the process of going outside the conventional method, game or territory is indistinguishable from error. Even the most brilliant act of human genius, in the final analysis, is an act of trial and error. "To be an Error and to be Cast out is a part of God’s Design," wrote the visionary poet William Blake. Error, whether random or deliberate, must become an integral part of any process of creation. Evolution can be thought of as systematic error management. [Kelly, p 470]

Sometimes a monster can become a brilliant innovation.

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Understanding monsters and monster-tricks

veryard projects > modelling > models and monsters > understanding monsters

Why would I want to play such semantic tricks? If I want to use an existing artefact or service I must. But surely these tricks are not appropriate when I’m building a new artefact or service? Indeed they are – because when used wisely they reduce the volatility of the model, and help avoid changing the model for trivial counter-examples.

Monsters are also used when testing an artefact – and if the modellers have used techniques such as monster barring or monster adjustment, there should be test cases based on the monsters to verify that the techniques have been properly implemented.
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Derrida on Monsters

veryard projects > modelling > models and monsters > derrida

'Monsters cannot be announced. One cannot say "Here are our monsters", without immediately turning the monsters into pets.' in "Some Statements, etc", 1990
'A future that would not be monstrous would not be a future; it would already be a predictable, calculable, and programmable tomorrow. All experience open to the future is prepared or prepares itself to welcome the monstrous.' in "Passages from traumatism to promise", 1995
both quotes found in Westwood & Linstead, p 329
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Sources and Resources - References and Links

veryard projects > modelling > models and monsters > sources and resources

Jacques Derrida, "Some statements, etc" in D. Carroll (ed), The States of Theory. Stanford University Press, 1990.
Jacques Derrida. "Passages - from traumatism to promise", in E. Weber (ed) Points - Interviews 1974-1994.  Stanford University Press, 1995.

Kevin Kelly, Out of Control: The New Biology of Machines. UK edition, Fourth Estate, 1994. See also

Imre Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery. Edited by John Worrall & Elie Zahar. Cambridge University Press, 1976.

Richard Veryard. Information Modelling: Practical Guidance. Prentice-Hall, 1992.

Robert Westwood & Stephen Linstead (eds), The Language of Organization. Sage 2001.

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Last update November 10th, 2003
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