# The Deluge of Spurious Correlations in Big Data

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## Abstract

Very large databases are a major opportunity for science and data analytics is a remarkable new field of investigation in computer science. The effectiveness of these tools is used to support a “philosophy” against the scientific method as developed throughout history. According to this view, computer-discovered correlations should replace understanding and guide prediction and action. Consequently, there will be no need to give scientific meaning to phenomena, by proposing, say, causal relations, since regularities in very large databases are enough: “with enough data, the numbers speak for themselves”. The “end of science” is proclaimed. Using classical results from ergodic theory, Ramsey theory and algorithmic information theory, we show that this “philosophy” is wrong. For example, we prove that very large databases have to contain arbitrary correlations. These correlations appear only due to the size, not the nature, of data. They can be found in “randomly” generated, large enough databases, which—as we will prove—implies that *most correlations are spurious.* Too much information tends to behave like very little information. The scientific method can be enriched by computer mining in immense databases, but not replaced by it.

## Keywords

Big data Ergodic theory Ramsey theory Algorithmic information theory Correlation## Notes

### Acknowledgments

The authors have been supported in part by Marie Curie FP7-PEOPLE-2010-IRSES Grant. Longo’s work is also part of the project “Lois des dieux, des hommes et de la nature”, Institut d’Etudes Avancées, Nantes, France. We thank A. Vulpiani for suggesting the use of Kac’s lemma, G. Tee for providing historical data and A. Abbott, F. Kroon, H. Maurer, J. P. Lewis, C. Mamali, R. Nicolescu, G. Smith, G. Tee, A. Vulpiani and the anonymous referees for useful comments and suggestions.

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