Why does science work? Why is math so unreasonably effective at describing the physical world? For that matter, how can simple equations predict the behavior of really complicated things?
Seriously, think about it for a minute. Newton's laws (for example, force = mass x acceleration) mathematically describe the motion of objects like balls and rockets. But balls and rockets are made of billions upon billions of molecules. So if we want to understand how balls fall and rockets fly, shouldn't we have an equation for every individual atom? It seems crazy that Newtonian mechanics can ignore all those details, but still make absurdly accurate predictions! What's going on here? Why does it all "just" work out?
As it happens, there's a branch of statistical physics that asks these questions. Even better, it offers some concrete answers.
This week on Soft Matters, Katie sat down with Prof. Jim Sethna, whose work on "sloppy models" sheds light on why science works, and why physicists can safely ignore so many small details when asking questions about larger objects.
In essence, the idea boils down to this: Some variables matter more than others, especially when you have lots of them. Moreover, given an ultra-detailed microscopic picture, there's a method that lets you calculate which variables (or combination of variables) are important, and which don't matter at all. This lets you throw out all the extra useless information to end up at an extremely distilled theory that includes only the bare minimum in order to make accurate predictions.
Appearing in this week's issue of Science, Prof. Jim's group published some new results on the subject. Watch the video, and be sure to check below for a science-to-English dictionary.
High energy physics
A branch of physics that studies particle collisions at obscenely high energies. Heard of the Higgs Boson? That discovery falls under the umbrella of high energy physics.
Relativistic quantum mechanics
Basically, it's quantum mechanics on steroids. Or moving really fast anyway. Also, it predicts antimatter, which actually exists. (10 facts about antimatter set to overly dramatic music.)
There are four fundamental forces in the universe: Electromagnetic, gravity, weak, and strong. The strong force is the force that holds the nuclei of atoms together against the electromagnetic repulsion of all the positively charged protons.
A fundamental theory of the universe. It's still being developed, but has attracted a lot of interest from theoreticians trying to address challenges posed by quantum mechanics and gravity. Listen to a Bohemian Rhapsody a capella with fresh lyrics about string theory.
Hierarchy of physical theories
There's a sliding scale of physics theories where at one end we have the physics of the every-day macroscopic world, and at the other, theories of the subatomic:
The key idea here is that the more macro theories emerge from the more micro theories, and as a consequence, macro theories are approximations of the "real" world, which is at a more micro scale. But as Prof. Jim's work with sloppy models shows, we can get away with the more macro theories because the overwhelming majority of details as the micro scale don't significantly affect the macro scale.
Traditional approaches in biology are reductionist -- they focus on details for their explanatory power. In contrast, systems biology is a holistic approach that seeks to understand the network of connections that ties all the smaller details together. Explanations are drawn from mechanisms operating on this higher-level of organization. Uri Alon is one of the field's godfathers, and has an excellent series of videos on YouTube from a course he taught. (As a side note, I'd bet dollars to donuts Uri gets a Nobel prize in the next 25 years.)
Certain types of mathematical theories include lots and lots of variables, but make the same predictions even when the variables themselves are changed dramatically. This surprisingly common phenomenon is called "sloppiness," and offers useful insights on what actually matters in a mathematical model.
Reaction constants (Reaction rates)
Chemical reactions happen at a certain rate, which depends on the specific atoms/molecules involved. These rates are referred to as "reaction constants."
"Explanatory power of science is independent of details"
This is one of the most interesting comments made during Katie's chat with Prof. Jim. The core idea here is that science has a split-personality: It strives for generalities while obsessing over details. At the end of the day, any good scientific understanding emerges from specific examples that are generalized.
Read about sloppy models on Prof. Jim's site here.