Science as making models


Humans have evolved the capacity to make sense of the world. By that we mean that humans do not just passively experience the world, they actively try to understand how it works. Science is an extension of this basic human desire to make sense of the world. That is,

Science is not just about figuring out how the world works. 
Science is about figuring out how we can think about how the world works.

In our science class, you will do more than just learn about scientific results -- you will also practice the strategies that are particularly valuable for making sense of observations.  In all sciences, and in particular physics, making sense of what we observe involves building theories, principles, and models.

Theories in Science

What makes science different from everyday sense-making is that scientists have developed systematic strategies for thinking about the world, and demonstrated that those strategies work well. Instead of just making a best guess about how something works, scientists articulate their ideas with concepts and principles, often using abstract representations, diagrams, and a precise technical vocabulary to create a powerful and coherent structure. In many areas of scientific research, these ideas developed into broad powerful structures that help us think about and make sense of a wide variety of phenomena.

 A scientific theory is a formalized set of ideas about how some aspect of the world works that specifies the relevant objects, agents, or constructs (the stuff) as well as the ways in which they influence, interact with, and relate to one another (relationships). It establishes the framework for scientific thinking and provides the structure and principles that guide how to model specific phenomena and examples.

In physics, an example that we will study this term is Newton's theory of motion. This theory sets out the concepts we need to understand how things move -- velocity, acceleration, force, energy, and so on. The principles of this theory, Newton's Laws, allow us to make sense of a huge range of physical phenomena, from the motion of planets to the meaning of temperature in a gas. 

In biology, an example of a very general and powerful theory is Darwin's theory of evolution. Darwin fleshed out the details of his ideas in his book, On the Origin of Species, but it can really be boiled down to a few simple principles.

Principle-Based Reasoning

One difference between introductory physics and introductory biology and chemistry is that physics has a tendency to focus more strongly on core principles. Physics, building on understanding the simplest possible physical systems, has developed powerful theoretic frameworks that contain principles that have been demonstrated to hold in wide ranges of situations and that give extraordinary power to control our environment.

A fundamental principle of physics is a statement (often a mathematical relationship) that is expected (or known) to hold over a very wide range of physical situations. For example, Newton's laws are know to hold for all objects larger than the size of an atom up to the size of a galaxy at all speeds up to a significant fraction of the speed of light. The quantum theory is known to hold for describing the structure of all atoms and building of molecules. (While there are some obscure exceptions, a f.p.o.p. is something you can almost always trust.)

The use of fundamental principles like Newton's laws of motion, the laws of thermodynamics, Maxwell's theory of electromagnetism, and the quantum theory have led to some of humanity's most dramatic engineering developments -- sending probes throughout the solar system, the industrial revolution and the power of steam, electrical devices and communication such as radio, TV, and wifi, and the building of chips that enabled lasers and the computer revolution.

In this class, we'll rely heavily on identifying and learning to use the fundamental principles of physics as powerful tools. But knowing the fundamental principles of physics doesn't solve all problems! As biologists (and chemists) know well, there are many highly complex situations where, even though the principles of physics apply, it isn't easy to figure out what they tell us. For this we need to build scientific models.

Scientific Modeling

When a scientist, doctor, or engineer tries to make sense of any specific observation, they have to select, organize, and pare down the broad general ideas of scientific theory. The real world is immensely complex and not everything is important for all specific observations. Which of the broad ideas of a scientific theory you have to consider to make sense of a particular situation depends on both the situation and the questions one is asking.

In science, a model is a decision about what parts of a phenomenon you have to consider in order to make sense of it. What are the objects you need to talk about? What properties of the object are relevant? What interactions are there among the objects? What physical principles have to be considered?

The model we choose depends on the questions we are asking. In a situation with a cat on the dining room table pushing against a plate that is teetering near the edge of the table, if our question is whether a cat can knock an plate off a table, we only need to think about the plate's mass, the friction of the table, and the force the cat can exert. If our question is whether the plate will break, then the material of the plate, plastic, glass or ceramic, will also be important. 

In medicine, the functioning of how the heart moves blood through the body can be most simply captured based on blood pressure and heart rate. In thinking about cancer we have to zoom in further and consider where the blood flows, as cancers tend to generate their own blood vessel system and foster leakage from these blood vessels. Other diseases require even more detail, such as sickle cell anemia, which is tied to the mechanical properties and cohesivity of the cells in the blood. The ideas in this model of the blood can easily be represented verbally, but other models might require quantification to get the specificity they require. 

An example from biology where quantification is required is the Lotka-Volterra model of predator-prey interactions. The ideas in the model are very simple: prey populations increase due to reproduction and decrease due to predation, and predator populations increase with amount of prey and decrease when prey die. However, making predictions with this model requires quantification as to how fast each population grows or shrinks. The quantitative model (usually a series of differential equations) works well to describe some aspects of the interaction of predators and prey that lead to non-intuitive changes in population size such as oscillations of the numbers of foxes and rabbits, for example. But this highly simplified predator-prey model ("toy model") ignores the fact that the prey has to live on something. In some situations this additional complexity requires we modify or add to our model. 

The value of modeling

Models serve a variety of purposes in science. Sometimes models just help us think through ideas; other times, models allow us to make precise quantitative predictions about the world; other times, models point out what we don't yet know.

How models are constructed, used, and evaluated in science depends upon the particular question, aim, or purpose that is relevant to the situation.

To clarify the distinctions among different types of models, let us consider three broad classes of models:

1. Descriptive models are used to formally describe some aspect of the world, some pattern or observed regularity. Such models arise from scientists’ attempts to observe and systematically record what they see. Watson and Crick's model of the structure of DNA is an example of a simple descriptive model. Galileo's description of the motion of objects by specifying the position, velocity, and acceleration of objects (whose size and structure are ignored in this model of motion) is a critical start to predict motion and to understand how and why things move and was perhaps the first real quantitative model in science.

Descriptive models often help scientists articulate what it is they want to understand and often pave the way for deeper investigations. Once we understand and can describe some of the regularities that exist in the world, the next step is making predictions and providing explanations.

2. Predictive models are used to make specific predictions about what might happen in the future given some range of starting conditions. Such models may or may not include a deep understanding of the underlying mechanisms. Even without deep understanding of mechanisms, observations of consistent empirical regularities or correlations often allows us to build predictive models. In medicine, many disease models are of this type: Though many details of the biology of a particular disease may not be known, predictive models of survival rates are often based on extensive empirical observations. Some empirically derived parameters (e.g., genetic indicators) can be very accurate in their predictive power even when a deep understanding of the underlying disease mechanisms is lacking. 

3. Explanatory models are constructed and used to explain how the world works. Explanatory models unpack the causal mechanisms that underlie what we observe in the world. They go deeper than descriptive models in their attempt to uncover the particular process or set of interactions that drive a phenomenon. Natural selection is an example of an explanatory model that allows us to explain patterns of change in populations over time in terms of the underlying causes. Explanatory models answer questions: What causes x? How does x happen? Why does x make sense? How can we explain x pattern?

Two examples:

  • A model of natural selection can be used to explain the observed frequency of a trait in a population.
  • A model based on Newton's laws relating the net force felt by an object to its acceleration can be used to explain its motion.

Note that explanatory models can be qualitative (e.g. predicting whether something speeds up or slows down) or quantitative (e.g. predicting the amount of speed-up).

In this introductory physics course, we will work toward explanatory models that focus on such sense making.  Our topics will include concepts that are key to making sense of living systems, such as Brownian motion or entropy.    

An example: The same reality can be described by many different models.  Let's consider a protein. But what is a protein really? Your answer to that question probably depends on who you are and what you want to learn about the protein. If you are a polymer scientist, a protein is an entangled polymer. If you are a molecular biologist, a protein is a sequence of amino acids folded up into a functional 3D structure. If you are a chemist, you may think about a protein as a sequence of hydrophobic and polar blobs (essentially simplifying the complexity of 26 amino acids down to two broad categories). If you are a pharmacologist, you may think about the protein as a two state system - either open or closed - giving an even simpler description of its characteristics.

Each of these ways of viewing the world is valid, of course, and each is a different model of the protein that allows us to tackle different questions about how proteins work. The chemist's model can highlight polar region and hydrophobic pockets of the protein that may be important for binding; the pharmacologist's view is needed to develop an understanding how this protein operates as part of an enzymatic reaction or signaling pathway.

Summary: The main ideas about models in science


  1. Modeling is a general practice that scientists use to describe, predict, and explain natural phenomena.     
  2. Models may be qualitative or quantitative.
  3. Ideally, models are tested against empirical data.
  4. Constructing models requires making decisions about how to bound the world into manageable chunks. It includes choosing and justifying assumptions, simplifications, and being upfront about what you are trying to describe, what you are including, and what your are ignoring -- and the resulting limitations of your model.
  5. All fields of scientific inquiry rely on model construction, use, and evaluation to move theory forward, to suggest areas in need of further investigation, and to interpret empirical data.
  6. Different fields and even different scientists within a field will use models in different ways depending on their interests and depending on question, aim, and purpose of an investigation.

Julia Svoboda Gouvea, Joe Redish, and Wolfgang Losert  7/19/17


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Last Modified: February 10, 2019