Tuesday, September 9, 2014

Blog Post: Why Use Models at All?

By Ben Brown-Steiner

I intend on touching on many topics related to the broad expanse that is climate science, but for a first post I’m going to tackle a question that comes up every once in awhile and probably should come up more often: Why use models at all?

At its purest science is about careful experimentation and observation. We take measurements. We come up with theories. We test those theories. And science gets done. Why bother with complicated models at all?

Well, there are a lot of reasons. The first is that experimentation and observations can be expensive. Or extremely difficult. Or even impossible. We can’t create a second Earth and start tweaking with the climate. No one is advocating that neuroscientists start methodical lobotomies to learn about the brain. And it’s no longer computationally prohibitive to run a meteorological model a dozen times and look at the possible weather patterns in order to make informed decisions about tomorrow’s weather.

Second, as any tinkerer, engineer, mechanic, or chef will tell you, the best way to learn about how something works is to take it apart, look at the individual pieces and how they interact, and put it all back together. Modeling of any type, from simple toy models to expansive climate models, hold at their core this basic mentality.

To introduce the beauty and power of models of all sizes, I’m going to explore a particularly practical type of model: a model intended to help us cook a perfect steak. Apologies if you’re not a meat eater. Just pretend the rest of this post is talking about tofu or seitan.

Before we start, it’s always a good idea to define our terms. For our purposes, a simple and workable definition of a model is: a model is a representation of some aspect of the real world. I like this definition for its simplicity and its brevity. It has three main parts, each of which is important. First, “representation.” A representation is not the real thing, it doesn’t strive to be the real thing. But it does strive to approach the real thing. Any model is going to be a simplification. Second, “some aspect.” A model doesn’t try to represent the entirety of the world around us. A model represents a part of the whole, and often for a particular purpose. Third, “real world.” A model tries to represent some part of the actual real world that we all live in. A model strives to claim some aspect of “reality” and “truth.” These are big, philosophical concepts, but concepts that are at the core of any modeler or programmer’s vision for their model.

So let’s explore various types of models used to cook our perfect steak.

Perfect Steak Model #0:

To really start at the beginning, we should imagine how we would try and cook our perfect steak without any models informing our procedure. We could, perhaps, buy a thousand steaks and randomly toss them on the grill, flip them on occasion, and hope to discern the secret to steak. It’s extremely unlikely that you’ll learn much through this method. Alternatively, we could skip the whole idea of trying to cook steak ourselves and follow a procedure instead.

Perfect Steak Model #1:

So this first model is less of a model and more of a procedure. This procedure goes: go to your favorite restaurant (or friend’s house) and have them make the perfect steak for you. Alternatively, we could describe this procedure more generally: go to an expert and rely upon the expert’s knowledge to produce a perfect steak for you.

Really, this is a great model for the perfect steak. Chefs are culinary experts trained in the alchemical combination of physics, chemistry, thermodynamics, and practical realm of food science. They know how to make a great steak. For our current purposes, however, this is cheating.

Perfect Steak Model #2:

If you happen to enjoy cooking, you probably consider yourself an amateur steak-cooker (or perhaps an expert steak-cooker), and thus have your own procedure for cooking a perfect steak. This procedure, almost certainly, is based off other experts’ procedures which have been simplified for your purposes. For instance, there are many cookbooks with cooking times per side for a perfect steak that probably look something like this (taken from http://www.raysmarketonthecommon.com/):

This table is a simple procedure distilled from some expert model (i.e. representation of a real-world steak cooking procedure) prepared for the at-home cook’s needs. This simple table can be further simplified  by the following recipe: “Heat a grill to 350 degrees F. Cook the steak on one side for 3 minutes plus one minute for every quarter inch of thickness over one-half inch. Then flip the steak over and cook the other side for two minutes plus one minute for each quarter inch thickness of the steak greater than one-half inch.” It’s not a graceful recipe. It ignores some of the complexity, but it gets the job done.

The following graph is a more insightful representation of this our Perfect Steak Model #2:

Note that the blue line (for the first side) is quite simple. A straight line like this is called a linear trend. The red line (for the second side), however, is not so simple. It’s not linear, and this non-linearity implies that there is some underlying steak science that has been simplified in this method. 

Perfect Steak #3:

If you are a particularly dedicated at-home cook and was determined to produce the perfect steak, you might create on your own (or stumble upon, like me) this website https://groups.csail.mit.edu/uid/science-of-cooking/home-screen.html, which turns up the complexity to the maximum. This site includes many parameters (which we’ll talk about in a later post) including: thickness, time per side, meat type, starting temperature, and number of sides (i.e. number of times you flip the steak). If you fill out the individual parameters and click on the “cook” button, you’ll get a figure, similar to this one which represents a particular slice of meat and the amount of “doneness” throughout:

Quite quickly you’ll notice the complexity captured by this method:
  • note that the meat keeps cooking for over five minutes after you remove it from the heat.
  • note the percentage of meat that’s “done” for each category: raw, rare, medium rare, medium, well done, browned, and charred) and how complicated the interior of the steak looks.
  • note an option to view the final temperature of each portion of the meat.
  • if you visit the link, you’ll find caveats and sources and alternative methods to compare.
This particular model, developed by the people at MIT for an online class on the science of cooking, has taken into account aspects of physics, chemistry, and food science to develop, parameterize, tune, and code this model. It’s informative, a little absurd, and a great analogy for the complexity possible for any type of system, for any type of model. If you follow this procedure, you can have high confidence that you’ll get your perfect steak.

So now we need to address the question: Which model is the best model?

All three methods above rely on assumptions and simplifications of the complex task of cooking a steak. Models help us understand a complex part of our world by simplifying the complexity into something that’s palatable (pun intended). Determining which model is the best model depends on you and your goals and various constraints. Do you want a quick-and-dirty method? Then methods #1 and #2 are probably the best for you. Do you like the challenge of an involved and detailed recipe? Then play with method #3 and tweak the model until you get exactly what you’re looking for.
I’ve stretched this analogy too far already, so I’ll leave this post here for now. I’ll touch on many other aspects of climate and climate modeling in upcoming posts.

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