Many digital cameras offer two ways to store images: in large, highly detailed files, or smaller, compressed JPEGs. At a casual glance, you probably wouldn’t notice the fine details lost in the compressed image. It’s a pretty good approximation of the larger file. 

Models for complex systems, from economics to quantum physics, also blur some of the smallest scales to show the larger picture. Macroeconomics is “a summary of an incredibly complicated and messy world that people inhabit,” says Simon DeDeo, external professor, in the introduction to his new tutorial called “Introduction to Renormalization,” available on SFI’s Complexity Explorer.

Renormalization is the study of what happens when we toss out fine details to get a picture of a bigger system. DeDeo’s tutorial covers the basics of information theory and image processing, as well as foundational theories of complexity. 

Some of the most exciting advances in post-1950’s physics are related to renormalization, says DeDeo. “The Higgs boson was invented because electromagnetism had a renormalization problem; String Theory was created because gravity had one.” The tutorial offers a series of increasingly complex examples to explore how theories change as they move to include more or less detail.  

“Renormalization is usually something you learn in the second semester of a graduate level quantum field theory class,” says DeDeo. However, the majority of this tutorial should be accessible to people who have basic comfort using probabilities. The seven-part tutorial covers classic problems in physics and cutting-edge questions in machine learning and artificial intelligence and includes homework and quizzes to test both beginners and more advanced learners.

The Complexity Explorer's self-paced tutorials are free to watch at any time. Watch the new Introduction to Renormalization when it suits your schedule.