If you’re in a technical or hard-science field, chances are if you’ve not heard this joke in particular, you’ve heard several of its cousins. The engineer, the physicist, and the mathematician are as instrumental to science jokes as the priest, the rabbi, and the minister are to religious jokes. This is my favorite, and goes as follows (hat tip to the science jokes archive)….
An engineer, a mathematician, and a physicist went to the races one Saturday and laid their money down. Commiserating in the bar after the race, the engineer says,
“I don’t understand why I lost all my money. I measured all the horses and calculated their strength and mechanical advantage and figured out how fast they could run…”
The physicist interrupted him: “…but you didn’t take individual variations into account. I did a statistical analysis of their previous performances and bet on the horses with the highest
probability of winning…”
“…so if you’re so hot why are you broke?” asked the engineer. But before the argument can grow, the mathematician takes out his pipe and they get a glimpse of his well-fattened wallet. Obviously here was a man who knows something about horses. They both demanded to know his
“Well,” he says, between puffs on the pipe, “first I assumed all the horses were identical and spherical…”
We have a saying in our culture: “Numbers don’t lie.” While it is true that you can’t argue the results of two plus two into being six, or even “three and a bit”, math is merely an abstract logical structure- as long as you follow the rules, you will get the same result every time… depending on the inputs. If your inputs are incorrect, or if you left out a variable, you will get the same wrong answer every time. Programmers, who have to deal with this reality on a professional basis- feed a computer the wrong inputs and it will instantly cease to work- have a characteristic pithy acronym for this: GIGO. Garbage In, Garbage Out.
Computers, however, are a very limited and simplified branch of reality. Most of the time when we use math, it’s in an attempt to describe some highly complex phenomenon; to give a simple and obvious example, there’s an equation that biology students learn, the Hardy-Weinberg Equilibrium. It describes the frequency with which you may expect to find a given allele in a population, and it looks like this: (p+q)2 = p2 + 2pq + q2 The p variable is one allele, the q variable another; each squared term represents homozygotes, the 2pq the heterozygotes.
Of course, the catch is that in order for a population of creatures to be in Hardy-Weinberg equilibrium as described by the equation, there has to be no mutation, no natural selection, no genetic flow or drift, and totally random mating- in other words, there is actually no such thing as a population of real organisms in Hardy-Weinberg equilibrium. The equation is not useless- it’s a brief algebraic proof that genetic variability will be maintained with no selective pressures at all required, which was a big deal in the infancy of population genetics and still something students need to understand when they’re coming to grips with how evolution works. Hardy-Weinberg populations are spherical racehorses- abstract descriptors of a concept, simplified to make the math doable. If you tried to include all the variables that describe a real population, the math would rapidly become completely unworkable; even if you managed to put absolutely every single possible variable in your equation, the equation would become instantly useless the second something changed, which happens pretty much every second in a system as complex as a biological one. The more “macro” the biological system, the worse it gets, because all parts start to effect one another in major ways and become impossible to detangle.
Now, psychology comes into play. There’s a pernicious phenomenon in biology- and I suspect a lot of the other sciences perceived to be “softer”- called physics envy. Because so much of biology must be described and approximated, and cannot even remotely be represented with numbers and equations that elegantly predict with perfection, people have this way of thinking about it as though it were therefore less “real” than classical physics, in which, so long as you have all the required data (numbers), you can make completely confident predictions with ease. An astronomer can know exactly where Jupiter will be in a hundred years; an animal behaviorist can only predict what a blue jay is going to be doing ten minutes from now with about ninety percent accuracy. (Forget about an hour from now unless it’s the dead of night. Even then, complete surprises are possible.) Physics is the quest for definable variables in a system that can be agreeably reduced and expanded*; biology is the quest for patterns in apparent chaos, much of which simply can’t be reduced without destroying the system in the process. This is why you can take a clock apart and put it back together and still come up with a working clock, but you can’t do the same to a giraffe.
Still, though, numbers are comfortingly solid, and models unquestionably have their uses. Things like the Hardy-Weinberg model are transparently just abstract illustrations of concepts because it’s basically obvious that it assumes conditions that never exist, but it’s about the simplest example of a model I could come up with- most are much more complex, like optimal foraging models. The very best models identify the most influential variables in a given system, and can describe many different kinds of related systems- and the very best users of models recognize that the point at which the model is the most useful is when it fails, because then it becomes an effective way to discover previously unconsidered but highly influential factors.
This is where the psychology comes in: people get really, really attached to models, the same way they get attached to simple ideas that accurately describe most of their experiences. Models (or grand theories of society, if you like) are extremely useful and pleasant to deal with; they simplify phenomena that are simply too complex to think about, and present a clear range of options and optimal choices. Models are friendly and easy to work with; reality is messy and frequently comes with sharp edges. If the model was good or even halfway decent, then every experience that the model predicted and described accurately reinforces the model and rewards the individual using it. When the model fails in an unexpected fashion, it’s psychologically much easier to discard the data than it is to discard the model, or to go investigate intensively why it failed. The dog trainer who immediately assumes that any failure of his training methods has to do with “user error” (which, bear in mind, is in fact common- but if the model fails to take into account common patterns of user error, that’s still not a good model), the social theorist who explains every societal problem in terms of race or class or religion, the economist who ascribes all financial woes as either too much or too little regulation, or the psychologist who thinks all common marital problems amount to a misunderstanding of “male” or “female” nature… they are all victims of this kind of thinking.
Neo-neocon has a post up today explaining a specific aspect (hardly the only one) involved in our current economic problems- the question of just why people who deal with finances for a living, smart people with perfectly functional reasoning skills and access to history books, could possibly assume that they could continue to behave as though certain kinds of market values would rise indefinitely, and as though they could turn bad debt into good merely through “diversifying”. The answer boils down, once again, to models- computer-run mathematical models showing just that result, which were apparently irrefutable. The problem was that the models made a number of assumptions which were quite simply fatal to the model as a completely accurate descriptor of reality- for example, that all people have infinite market knowledge and always behave in a completely rational fashion**. The assumptions were built into the model to make the math doable, and the models worked amazingly well in that self-reinforcing fashion, until they quite simply didn’t.
The second reason this problem is so endemic, especially across fields in which the participants must trust numbers because there’s nothing else even remotely reliable TO trust, is that while numbers themselves may not lie, it’s really damn easy to manipulate them so that, in effect, that’s exactly what they will do, given the right audience. If the audience is not both suspicious and familiar enough with the kinds of number manipulations being performed, they can be firmly brought to a conclusion that is actually either completely unsupported by the data- or is actually OPPOSITE to the data. People are not basically inclined to question the numbers that “don’t lie”, and they don’t necessarily recognize a spherical racehorse when they see one- and therefore it is extremely easy for any motivated party to create a powerful persuasive tool out of a bad model and a bit of unfamiliar statistical manipulation.
If you have a strong interest or cause, you can probably bring up a dozen examples of how this is done on a regular basis. Maybe you’re an advocate for gun rights, and you know every deceptive, slimy study and report that’s ever done such things as including suicides in gun-violence statistics, or including all individuals up to the age of 21 in a study about gun deaths in “children”. Perhaps your crusade for individual liberties is against the nanny-state “for your health” agenda, and you know what was done with studies on second-hand smoke- in which the data (and the reporting) were essentially massaged until the desired conclusion was reached. I follow the creationist/”intelligent design” movement, and I can give you an earful of how blatantly they’ve exploited the faith in math- essentially creating a mathematical theorem that supposedly renders evolution impossible, but contains assumptions even its creator openly admits do not apply to life on Earth. Nonetheless, among the receptive, the notion that intelligent design has been proven mathematically (and is therefore now irrefutable) persists.
Keep these lessons firmly in mind whenever someone pushing something you’re NOT familiar with is making their case with models and statistics- they may not necessarily be wrong, but that doesn’t mean the horses really ARE spherical and identical, either.
*The historical (and in some quarters, ongoing) reaction of physicists to quantum mechanics has to give any “soft” scientist a warming glow of schadenfreude.
**Exercise for the reader: how many political theories also contain this assumption, tweaked a bit as appropriate?