I have been meaning to write about this for quite some time. Really, I wanted to reply to Chad's article on science at Uncertain Principles, but you know how things go. So, here are my key and interesting points about science in random order.
Science is all about models (not ball bearings)
Science is about making models. What is a model? A model can be lots of things. It can be a mathematical relationship, a conceptual model, or even a physical model. One model I like to use is static friction. For many cases, the frictional force can be modeled as:
This model says the frictional force is proportional to the force that the two surfaces are pushed together with. A pretty good and useful model. However, friction is actually an extremely complicated thing. The atoms in one material are interacting with the atoms in the other material. So, there are some situations where this model doesn't work. This model says that the surface area doesn't have an impact on the friction force. However, look at drag racing cars. Why are their tires so wide? More friction.
So, that is a model for friction that is useful. It doesn't always work though. So, science would try to make a better model. However, a better model may be much more complicated. In this case it is still useful to keep the old model for some situations.
Here is the basic game plan for science:
- Collect evidence (experimental data)
- Create a model to explain evidence.
- Use model to predict other stuff.
- If the prediction doesn't work, change the model.
I like to use "model" instead of theory, law or whatever. It just seems nicer.
Science is not about the truth
I keep using this quote, but it fits here.
"If it's truth you are looking for, Dr. Tyree's philosophy class is down the hall" - Indiana Jones.
Science is all about models but we never really know if our models are the truth. We just know how well they agree with data. I hate saying this around people because there will always be someone that says "Ah HA! See. Evolution is not true." Ok, but then neither is gravity or electricity or any of the other fundamental models that you base your life on. Evolution and gravity are both supported by a lot of evidence.
What is a hypothesis?
I don't really like this word. Mostly because of how it is misused. I would like to propose a definition of hypothesis as the following:
Hypothesis: The predictions that a model makes about an experiment.
See, I used model again. I like that word. The problem is that all too often people use the definition of hypothesis as "educated guess". In a way, this is an ok definition. However I think people take it too literally . I am not sure what they think "educated means". It is funny going to the science fair or looking at elementary science activities. I always see "guess what will happen" and "our prediction was right (or wrong)". Really, it doesn't matter what YOU think will happen, it matter what your model "thinks".
Enough attacking hypothesis.
Numerical calculations are not experiments
I am surprised I see this so much. It usually comes around with someone talking about the three aspects of science: theory, experiment, and simulations. Yes, simulations LOOK like an experiment, but it is not an experiment. A simulation, or a numerical calculation is just like any calculation.
My favorite example of this is a mass on a spring. It is not too difficult to show that the equation of motion for such a situation is a trig function (like cosine). You could also model this with the following (very simple to do with python or a spreadsheet):
- Calculate the forces on the mass (in this case it is simply negative of the displacement times the spring constant)
- Calculate the new momentum: new momentum = old momentum + force * dt (dt is the small time interval)
- Calculate the new position: new position = old position + velocity (from before) *dt
- Update time
If you want more details on this recipe, here are my detailed instructions. Anyway, the point is that numerical and analytical solutions give the same thing. They are both theoretical calculations. Just because one doesn't use calculus does not mean it is something other than a calculation.
If you talk to computational scientists, sometimes this gets them upset. I think computational people are victims of a battle. They had to fight and struggle to be seen as legitimate. One of their arguments was that computational was a necessary 3rd component of science. Really, computational solutions are just another tool of science - same as vector calculus.
Scientists have to be creative
When I teach courses for non-science majors, it is interesting to see what stereotypes students have about scientists. One big misconception is that scientists just follow some procedures without any creativity. In fact, scientists have to be creative in coming up with new models to test and in creating experiments to test these models.
What is a science fact?
I don't know, but this term gets used quite often. Different people interpret 'fact' differently. I think the general public would interpret it as a piece of absolute truth. However, (see above) science doesn't really deal with truths. I think I would call a science fact a piece of data or evidence. Actually, I just don't use this term.
Science uses inductive logic
Inductive logic starts with evidence and tries to find one model that can explain this evidence. Deductive logic starts with some assumed truths and uses logic to figure out the details. There are three great examples of deductive logic:
- Sherlock Holmes: He was the king of deductive logic. Think of all the things he assumed to be true to deduce some other piece of evidence.
- Aristotle and the other Greeks: They started with assumed truths like heavy things fall faster than lighter things. From that they deduced ideas about motion. The problem here is that if your "assumed truths" are wrong, you are in big trouble. They did not actually test their assumed truths. If they did, they wouldn't be assumed.
- Monty Python and the Quest for the Holy Grail. See clip.
Some biologists may claim that science is both inductive and deductive. Maybe what they are calling deductive should be called "applying a model".
Why do we do science? Why do we study it in school?
I like Chad's answer:
"Science is what humans do"
That is it. That is why we do science, because we are human. The same is true for art. Why do we make pictures or music? I know it is difficult to compare art and science, but really they are quite similar. Why do we do art? Why is art taught at schools? This reminds me of a great essay about math education Lockhart's Lament (pdf).
It is all too easy to slip into the thinking that we do science because we get good stuff from it. We should promote science in schools because...hey look velcro! We got velcro from NASA and the space program. Really, that is just a bonus product from science. It is unfortunate that many grants have something in there about "how will this benefit people". The real answer should be "dunno, we will do it anyway".
Go back to art. Do we get things from art? Yes, there are benefits. However, that is not the point of art. Think about ancient man making paintings on the wall of a cave. Why did he (or she) do that?
Well, why then is science taught in schools? Why is art taught in schools? Here is a typical quote from a student:
"I don't know why I have to take science (art), I am never going to use this stuff in the real world."
This student might be correct. To really answer the student, you need to think about the purpose of school. Is education there as training for future careers? Some say yes. If you think so, then maybe the student shouldn't be taking physics if they are a business major.
I say that the role of education is to further develop as a human. So, you need to take art, literature, science, music, etc... All the things that make us human. Honestly, how many people are going to make free body diagrams after they graduate from college? Will a doctor? Even an engineer?
The Scientific Method - come on man!
Go into a 4th grade classroom and you will see it on the wall - THE SCIENTIFIC METHOD. For some reason, textbooks use this as though it were the gospel truth of science. If you do a science project you MUST follow the scientific method. There are a few variations, but most go something like this:
- Identify a problem.
- Research the problem.
- Develop a hypothesis.
- Test the hypothesis.
There are some nuggets of truth in this, but I think that it is all too often misunderstood. This sort of reminds me of a great post by The Lansey Brothers about their experiences in a classroom with science.
Finally, what do students think about science?
Here are some fun questions to ask your students (both before and after a science course):
- What is the purpose of experiments?
- What is a hypothesis?
- How does science prove a new theory?
I think this is a good place to end my rant.
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How does a car with 1"-wide tires and then with 18"-wide tires mounted have summed different friction where the rubber meets the road? The wider tire distributes the thermal load and interactions with road asperities. However, rub two flat blocks of Teflon TFE together. The greater the contact pressure the lower the friction, then it asymptotes with increasing pressure.
Does a single crystal solid sphere of right-handed quartz vacuum free fall identically to a macroscopically identical sphere of left-handed quartz? Physical theory allows both results - Newton (yes, Green's function), metric gravitation (yes, Equivalence Principle postulated), teleparallel gravitation (no, explicitly), quantized gravitations (no, Einstein-Hilbert action supplemented with a parity-violating Chern-Simons term).
(physical reality) - (empirical reality) = faith
Theory predicts what it is told to predict. Pulling on a cylindrical length of taffy makes it longer and thinner. Pulling on a cylindrical length of Gore-Tex valve packing makes it longer and thicker (large negative Poisson's ratio). All the fun is in the footnotes. Somebody should look (e.g., a parity Eotvos experiment for the quartz).
I had a great in-depth conversation with a racecar builder one day, and the subject of friction and wide tires came up. It turns out that what you get with wider tires is not friction in the sense that we teach it in high school, but instead it is an increase in normal (contact) force.
Our typical model of friction involves rigid materials in contact with one another. If you have the same weight over a smaller surface area, the decrease in area alone would lead to less friction, and the increase in weight per area would lead to more friction. Both of these effects are linear in nature, so the two cancel out, leading to our typical "surface area doesn't matter" conclusion.
With racing tires, however, as the soft, wide tires contact the road surface, they sink in a bit. This is the key. If you picture a car driving to the right, imagine the contact between the tire and a miniscule v-shaped depression in the road. The left side of the v provides a forward component of normal force when the tire pushes against it. It is the cumulative effect of this over the greater surface area that results in the benefits of wider tires.
NASCAR tires are intentionally soft so that they'll sink in more. Of course, this also leads them to have to be changed every pit stop or two as they wear out faster. NHRA tires are spun intentionally when the drivers get ready for their run, heating and softening the tires, again to increase the amount by which they'll sink in to the surface.
It's all about normal force.
Oh, and about models (which is what it's really all about)...
In my classroom, I use an example of a 1967 Mustang that my Dad used to own (not really, but it made for a good story.). That car no longer exists, but if I have a drawing of the car, I can learn some things about it. Better than that would be a matchbox car so that I can look at it and understand more about it in 3-dimensions. Of course, the trunk doesn't open and the car doesn't run. So I could even get to build a model out of today's parts that would much closer approximate my dad's car ... but it wouldn't have his fingerprints on it; the carbon-dating of the leather steering wheel wouldn't be the same, etc.
In each case, the prior model was useful, and the later model was more useful. But in NO case is any model actually "truth". Same as in science, as we proceed from Galileo to Newton to Einstein to ???, we're not speaking new truth and throwing out old truth, we're just making better, more useful models, none of which can ever be said to be "true".
And sometimes, it's stillt nice to look at the old picture...