Is It Foolish To Model Nature’s Complexity With Equations? by Gabriel Popkin.

From the post:

Sometimes ecological data just don’t make sense. The sockeye salmon that spawn in British Columbia’s Fraser River offer a prime example. Scientists have tracked the fishery there since 1948, through numerous upswings and downswings. At first, population numbers seemed inversely correlated with ocean temperatures: The northern Pacific Ocean surface warms and then cools again every few decades, and in the early years of tracking, fish numbers seemed to rise when sea surface temperature fell. To biologists this seemed reasonable, since salmon thrive in cold waters. Represented as an equation, the population-temperature relationship also gave fishery managers a basis for setting catch limits so the salmon population did not crash.

But in the mid-1970s something strange happened: Ocean temperatures and fish numbers went out of sync. The tight correlation that scientists thought they had found between the two variables now seemed illusory, and the salmon population appeared to fluctuate randomly.

Trying to manage a major fishery with such a primitive understanding of its biology seems like folly to George Sugihara, an ecologist at the Scripps Institution of Oceanography in San Diego. But he and his colleagues now think they have solved the mystery of the Fraser River salmon. Their crucial insight? Throw out the equations.

Sugihara’s team has developed an approach based on chaos theory that they call “empirical dynamic modeling,” which makes no assumptions about salmon biology and uses only raw data as input. In designing it, the scientists found that sea surface temperature can in fact help predict population fluctuations, even though the two are not correlated in a simple way. Empirical dynamic modeling, Sugihara said, can reveal hidden causal relationships that lurk in the complex systems that abound in nature.

…Sugihara and others are now starting to apply his methods not just in ecology but in finance, neuroscience and even genetics. These fields all involve complex, constantly changing phenomena that are difficult or impossible to predict using the equation-based models that have dominated science for the past 300 years. For such systems, DeAngelis said, empirical dynamic modeling “may very well be the future.”

…

If you like success stories with threads of chaos, strange attractors, and fractals running through them, you will enjoy Gabriel’s account of **empirical dynamic modeling**.

I have been a fan of chaos and fractals since reading *Computer Recreations: A computer microscope zooms in for a look at the most complex object in mathematics* in 1985 (Scientific American). That article was reposted as part of: DIY Fractals: Exploring the Mandelbrot Set on a Personal Computer by A. K. Dewdney.

Despite that long association with and appreciation of chaos theory, I would answer the title question **with a firm maybe**.

The answer depends upon whether equations or **empirical dynamic modeling** provide the amount of precision needed for some articulated purpose.

Both methods ignore any number of dimensions of data, each of which are as chaotic as any of the others. Which ones are taken into account and which ones are ignored is a design question.

Recitation of the uncertainty of data and analysis would be boring as a preface to every publication, but those factors should be upper most in the minds of every editor or reviewer.

Our choice of data or equations or some combination of both to simplify the world for reporting to others shapes the view we report.

What is foolish is to confuse those views with the world. They are not the same.