How to Quantify Failure

The following is an article from The Annals of Improbable Research.

By Martin J. Murphy
Faultline University
Center for tile Kinetics of Unreliable Processes
Palo Alto, CA

It has long been dear to the author (if to no one else) that science lacks a convention for measuring failure. While the discovery of many other basic laws of nature has led to an eponymous unit that describes a measurable quantity in the law -to wit, Newton's Law and the force unit of ‘newton’, Ampere's Law and the ‘ampere', etc.- there does not yet exist a qualitative physical expression of Murphy's Law. I propose to remedy the situation by defining a set of units that quantify failure, and then casting Murphy's Law in a mathematical form based on these units. As part of this undertaking, I attempt, and fail, to identify the physical principles that underlie this most basic of scientific truths.

I recognize that there already exists a colorful but imprecise English system of units- e.g., the 'goof', the 'screwup', the 'royal screwup', and onwards into the realm of profanity. Though highly descriptive and rich with history, these units are basically qualitative. True failures deserve to be measured.

The Basic Unit of Failure
The basic unit, which I modestly propose to call the ‘murphy', represents the magnitude of a standardized thing that can go wrong. To be meaningful and useful, this unit must be referenced to a universal standard of failure, the value of which is maintained by a public institution. Almost any local. national, or international agency would be an appropriate custodian of the standard.

Calibrating the Murphy Scale
A metric approach to failure needs a scale on which any failure can be rated. Failure can exist anywhere  along an enormous range of magnitudes. Therefore, let us use a logarithmic scale. Thus, a minor failure would be on the order of a ’millimurphy’ (spilling coffee on a blue dress). A major failure would be more on the order of a ‘megamurphy' (spilling the president's coffee on a blue dress). The scale can be extended on either end, when and as needed.

The system naturally produces composite units, such as ’murphys per second' as a rate of fouling up, and ‘murphys per square meter' as a concentration of incompetence.

More on Murphy Math
Now that we have a unit of measurement, it is possible to develop a mathematical expression of Murphy's Law. I model it on a quantum mechanical formulation, in which the degree to which something goes wrong is the expectation value of the wrongness operator, which is known as a Wrongskian. This defines a failure wave function whose integral over time is identically one, since according to Murphy's Law the probability of something going wrong sometime is unity everywhere.

Clearly the wave function is normalized, since it is normal to screw up. The entire formalism is renormalizable, in the sense of allowing us to turn failures into successes, successes into failures, and bad science into good public relations.

Empirically, there is a conjugate relationship between the impact of a failure and its likelihood. This can be expressed as the Murphy Certainty Principle:

The more you have to worry about failure, the more inevitable it becomes.

This principle allows a single unit- the ‘murphy' -to describe both the magnitude and the probability of a failure.

When we couple this with both the Heisenberg Uncertainty Principle and the original, basic formulation of Murphy's Law, a useful corollary results:

When you have measured failure, you can never know for sure what it is that you have measured.

The murphy is valuable in evaluating statistically the results of experiments. In common usage it is expressed as an inverse unit of confidence, the murphy-1, the so-called "minus murphy." The minus murphy is the probability that the result is correct. Also useful is the murphy-2, the so-called "double minus murphy." The double-minus murphy is the probability that your result is both correct and useful.

Advanced, Abstruse Murphy Theory
Our physical understanding of a natural law is not complete until the underlying mechanism has
been revealed. For all those who feel that their own personal failures have been caused by some malevolent cosmic agency, there is now compelling evidence that disasters are in fact mediated by a massless, charmless, and pointless particle called the murphion. This particle, previously misclassified as a weakly amusing bozotron, travels backward in time (thus allowing it to retroactively spoil apparent successes). After interacting with its victim, the murphion transfers whatever spin the project management chooses to put on it. The murphion is, however, extremely difficult to observe, since it has the anti-quantum mechanical property of instantly confounding the state of any detector that it interacts with. Consequently, its existence and properties have been inferred by assuming that all science experiments must make an equal amount of sense and then assigning to the murphion all of the missing sense in any actual observation.

Interactions of the murphion with normal matter are described by Murphy-Kojak statistics. In this picture, the murphion preferentially fills states of excess arrogance (beginning with the states of Texas and New York) until the Murphy surface-the level of maximum ineptitude-is reached. At this point, the particle begins to fill states of reduced arrogance, such as North Carolina and Iceland, until ultimately every state, province, and principality in the world is saturated with murphion. At the moment of saturation, nothing works and all the physicists get jobs pricing bond derivatives. (The consequences of that will be analyzed in another article as soon as the stock market stops bouncing like a wad of flubber.)

Thoughts on the Future
Apart from its obvious role in science and engineering, this formalism can also be applied to
such diverse fields as economics, management, and politics. In economic applications it might be argued that the murphy measures the same thing as the dollar (based on the observation that the probability of failure goes up with its cost), but clearly the murphy is the more fundamental unit. Most important, this formalism provides a means of evaluating the useful outcome of experiments and projects beforehand. It's use should spare us the trouble of starting any more expensive exercises in futility such as the Superconducting Supercollider.

_____________________

This article is republished with permission from the January-February 2000 issue of the Annals of Improbable Research.

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