Parsimony

Parsimony is the use of the simplest or most frugal route of explanation available. The word derives from Middle English parcimony, from Latin parsimonia, from parsus, past participle of parcere: to spare. It is a general principle that has applications from science to philosophy and all related fields.

Science
In science, parsimony is preference for the least complex explanation for an observation. This is generally regarded as good when judging hypotheses. Occam's razor also states the "principle of parsimony"; however, some argue that parsimony should not be elevated to the status of a general principle.

In systematics, maximum parsimony is a cladistic "optimality criterion" based on the principle of parsimony. Under maximum parsimony, the preferred phylogenetic tree is the tree that requires the smallest number of evolutionary changes.

In biogeography, parsimony is used to infer ancient migrations of species or populations by observing the geographic distribution and relationships of existing organisms. Given the phylogenetic tree, ancestral migrations are inferred to be those that require the minimum amount of total movement.

Parsimony is also a factor in statistics: in general, mathematical models with the smallest number of parameters are preferred as each parameter introduced into the model adds some uncertainty to it. Excessively complex models suffer from overfitting and have poor predictive power (a problem known as the bias-variance trade-off). In general terms, it may be said that applied statisticians (such as process control engineers) value parsimony quite highly.

Lee and others provide cases where a parsimonious approach does not guarantee a correct conclusion and, if based on incorrect working hypotheses or interpretations of incomplete data, may even strongly support a false conclusion: When parsimony ceases to be a guideline and is instead elevated to an ex cathedra pronouncement, parsimony analysis ceases to be science. Oddly, in English literature, Parsimony refers to a sexual disfunction. For example, if a husband were not able to get erect during intercourse, this is a parsimonic device. This definition of the word comes from a separate etymology.

The scientific method
In science, parsimony is used as a heuristic (rule of thumb) to guide scientists in the development of theoretical models rather than as an arbiter between published models. In physics, parsimony was an important heuristic in the formulation of special relativity by Albert Einstein, the development and application of the principle of least action by  Pierre Louis Maupertuis  and Leonhard Euler, and the development of quantum mechanics by Louis de Broglie, Richard Feynman, and Julian Schwinger. In chemistry, Occam’s razor is often an important heuristic when developing a model of a reaction mechanism. However, while it is useful as a heuristic in developing models of reaction mechanisms, it has been shown to fail as a criterion for selecting among published models.

In the scientific method, parsimony is an epistemological, metaphysical, or heuristic preference, not an irrefutable principle of logic, and certainly not a scientific result. As a logical principle, Occam's razor would demand that scientists accept the simplest possible theoretical explanation for existing data. However, science has shown repeatedly that future data often supports more complex theories than existing data. Science tends to prefer the simplest explanation that is consistent with the data available at a given time, but history shows that these simplest explanations often yield to complexities as new data becomes available.

When scientists use the idea of parsimony, it only has meaning in a very specific context of inquiry. A number of background assumptions are required for parsimony to connect with plausibility in a particular research problem. The reasonableness of parsimony in one research context may have nothing to do with its reasonableness in another. It is a mistake to think that there is a single global principle that spans diverse subject matter.

As a methodological principle, the demand for simplicity suggested by parsimony cannot be generally sustained. Parsimony cannot help toward a rational decision between competing explanations of the same empirical facts. One problem in formulating an explicit general principle is that complexity and simplicity are perspective notions whose meaning depends on the context of application and the user’s prior understanding. In the absence of an objective criterion for simplicity and complexity, parsimony itself does not support an objective epistemology.

The problem of deciding between competing explanations for empirical facts cannot be solved by formal tools. Simplicity principles can be useful heuristics in formulating hypotheses, but they do not make a contribution to the selection of theories. A theory that is compatible with one person’s world view will be considered simple, clear, logical, and evident, whereas what is contrary to that world view will quickly be rejected as an overly complex explanation with senseless additional hypotheses. Parsimony, in this way, becomes a “mirror of prejudice.”

It has been suggested that parsimony is a widely accepted example of extra-evidential consideration, even though it is entirely a metaphysical assumption. There is little empirical evidence that the world is actually simple or that simple accounts are more likely than complex ones to be true.

Most of the time, parsimony is a conservative tool, cutting out crazy, complicated constructions and assuring that hypotheses are grounded in the science of the day, thus yielding ‘normal’ science: models of explanation and prediction. There are, however, notable exceptions where Occam’s razor turns a conservative scientist into a reluctant revolutionary. For example, Max Planck interpolated between the Wein and Jeans radiation laws used parsimony to formulate the quantum hypothesis, and even resisting that hypothesis as it became more obvious that it was correct.

However, on many occasions parsimony has stifled or delayed scientific progress. For example, appeals to simplicity were used to deny the phenomena of meteorites, ball lightning, continental drift, and reverse transcriptase. It originally rejected DNA as the carrier of genetic information in favor of proteins, since proteins provided the simpler explanation. Likewise, at one time Occam's razor rejected the sun-centered model of the solar system in favor of the geocentric model, and it would have certainly viewed Newton's laws as unreasonably complicated had they been offered in Galileo's time. Theories that reach far beyond the available data are rare, but General Relativity provides one example.

In hindsight, one can argue that it is simpler to consider DNA as the carrier of genetic information, because it uses a smaller number of building blocks (four nitrogenous bases). However, during the time that proteins were the favored genetic medium, it seemed like a more complex hypothesis to confer genetic information in DNA rather than proteins.

One can also argue (also in hindsight) for atomic building blocks for matter, because it provides a simpler explanation for the observed reversibility of both mixing and chemical reactions as simple separation and re-arrangements of the atomic building blocks. However, at the time, the atomic theory was considered more complex because it inferred the existence of invisible particles which had not been directly detected. The stronger form of Occam’s razor favored by Ernst Mach gives rise to logical positivism which rejects the atomic theory of John Dalton for over 100 years until the reality of atoms was more evident in Brownian motion, as explained by Albert Einstein.

In the same way, hindsight argues that postulating the aether is more complex than transmission of light through a vacuum. However, at the time, all known waves propagated through a physical medium, and it seemed simpler to postulate the existence of a medium rather than theorize about wave propagation without a medium. (Quantum electrodynamics eventually showed that the vacuum is not complete nothingness, but it is something of a medium with which light and fundamental particles interact.) Likewise, Newton's idea of light particles seemed simpler than Young's idea of waves, so many clung to it.

Three axioms presupposed by the scientific method are realism (the existence of objective reality), the existence of observable natural laws, and the constancy of observable natural law. Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified. Occam’s razor and parsimony support, but do not prove these general axioms of science. The general principle of science is that theories (or models) of natural law must be consistent with repeatable experimental observations. This ultimate arbiter (selection criterion) rests upon the axioms mentioned above.

There are many examples where Occam’s razor would have picked the wrong theory given the available data. Simplicity principles are useful philosophical preferences for choosing a more likely theory from among several possibilities that are each consistent with available data. However, anyone invoking Occam’s razor to support a model should be aware that additional data may well falsify the model currently favored by Occam’s razor. One accurate observation of a white crow falsifies the theory that “all crows are black.” Likewise, a single instance of Occam’s razor picking a wrong theory falsifies the razor as a general principle.

If multiple models of natural law make exactly the same testable predictions, they are equivalent and there is no need for parsimony to choose one that is preferred. For example, Newtonian, Hamiltonian, and Lagrangian classical mechanics are equivalent. Physicists have no interest in using Occam’s razor to say the other two are wrong. Likewise, there is no demand for simplicity principles arbitrate between wave and matrix formulations of quantum mechanics. Science often does not demand arbitration or selection criteria between models which make the same testable predictions.

Penal ethics
In penal theory and the philosophy of punishment, parsimony refers specifically to taking care in the distribution of punishment in order to avoid excessive punishment. In the utilitarian approach to the philosophy of punishment, Jeremy Bentham's "parsimony principle" states that any punishment greater than is required to achieve its end is unjust. The concept is related but not identical to the legal concept of proportionality. Parsimony is a key consideration of the modern restorative justice, and is a component of utilitarian approaches to punishment, as well as the prison abolition movement. Bentham believed that true parsimony would require punishment to be individualised to take account of the sensibility of the individual – an individual more sensitive to punishment should be given a proportionately lesser one, since otherwise needless pain would be inflicted. Later utilitarian writers have tended to abandon this idea, in large part due to the impracticality of determining each alleged criminal's relative sensitivity to specific punishments.