Dimensional Reduction in Complex Living Systems: Where, Why, and How.

The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. But understanding these avalanches of high-dimensional data -- by distilling underlying principles of more general nature -- necessitates dimensional reduction. We will explain how some geometric insights by mathematicians allow one to identify genuine hallmarks of biological systems and distinguish them from universal properties of generic data sets. In particular, life involves many layers of information processing and internal representations that give rise to extreme dimensional reduction. We illustrate these general principles in a concrete example of a model of protein evolution.