The Hierarchy of the Sciences

There is an intuitive sense among scientists that an hierarchy exists in the sciences. It looks roughly like this:

The hierarchy is fuzzier than drawn, especially among the “soft” sciences. I'm not going to bother perfecting the diagram; just keep in mind it’s not perfect.

This hierarchy pops up in a lot of different ways. This xkcd, for example, expresses the hierarchy in terms of “purity”. In practice, there’s a lot more to it than just aesthetics - the hierarchy of the sciences has both historical causes and real social consequences.

Social Status

I once heard a biologist give a tangential parable about physicists in a talk. Physicists, he said, are like cowboys. Every now and then, a gang of physicists rides into your field, whooping and hollering, shoots holes in all your theories, and then rides off into the sunset.

Practitioners sometimes joke about the hierarchy of sciences the way xkcd does. What we usually avoid talking about directly is the social side - though most are loathe to admit it, the hierarchy of the sciences reflects a real status hierarchy among scientists. Physicists do not tell parables about biologists shooting holes in their theories. Or chemists. Or economists. But mathematicians… mathematicians have been known to shoot holes in the work of physicists.

In general, fields frequently contribute results to fields below theirs on the hierarchy. Mathematicians contribute useful results to all of the scientific fields, but other scientists contribute new math much less often. Physicists have established subfields within lower sciences - think biophysics or econophysics - but you don’t hear much about biologists or psychologists contributing new results to physics. This pattern mostly holds up further down the hierarchy.

Occasionally, people will contribute to a field immediately above theirs - physicists discover new theorems, chemists break ground in physics - but one rarely hears about people contributing to fields two levels or more above their own. Indeed, I recall one instance where a biologist rediscovered a major theorem of statistics, a biology journal published it as a new tool, and then everyone was soundly mocked by mathematicians for not knowing statistics 101.

(Note: Philosophers do not have any real status in the sciences. They are drawn at the top of the hierarchy in much the same way you’d tell a four-year-old that they get to be ship captain for a day, then let them stand on the bridge and give “orders”.)

“Real Science”

There’s a sense in which some sciences have matured into “real science”, an intuitive dividing line. On one side are fields like chemistry or physics,  where the existing theory is mathematically precise and experimentally powerful and generalizable and will always be useful even as new theory evolves. On the other side are fields like psychology and economics, where theories lack mathematical precision and/or experimental validity and don’t generalize and have limited utility. Some people use the terms “hard” and “soft” sciences to describe these.

Historically, everything started out “soft”. The line dividing “real sciences” has shifted over time, as chemistry evolved from phlogiston to the periodic table, and biology evolved from elan vital to today’s state of affairs. As far as I can tell, the “real science” dividing line today looks something like this:

As the dotted line suggests, I’ve heard a general sentiment among many people (including myself) that biology today is the frontier of real science; biology is currently midway through a transformation from ad-hoc theory to an experimentally robust, mathematically precise field. I recall the first session in MIT’s intro biology course, in which the lecturer spent about half the class saying “look, you probably don’t think biology is a real science, and the biology you learned in high school isn’t… but a lot of that stuff is out of date, and you’re going to find that the field has come a long way.” It’s an exciting time to be in biology.

(If you’re still not sure whether the scientific hierarchy actually reflects social status, then try telling both a physicist and a biologist that their fields are not “real science”, and see how they react. Better yet, don’t try this.)

Engineering and Applied Disciplines

One good way to recognize which fields have matured into “real science” is to look for corresponding engineering disciplines. Once a scientific field has reached maturity, its theory is robust and useful enough that engineers start to adopt it, and new engineering fields are born. This creates an hierarchy of engineering, in parallel to the scientific hierarchy:

Again, it’s an exciting time to be in biology, as biology’s first real engineering field is just starting off.

One of the things which surprised me in college was the social status hierarchy in engineering, which to some degree reflects the hierarchy in the sciences. Anecdotally, the salaries of my classmates in computer science/EE/ME/Materials/Chem E seem to follow the hierarchy.

The Engineering Frontier

The absence of any engineering fields corresponding to the fields lower on the hierarchy is one of the main ways to tell they’re still below the “real science” dividing line. The soft sciences have not yet matured enough to support robust engineering. However, we can speculate on which fields will likely become engineering-type fields once the corresponding sciences mature enough to support them. This results in a “real science and engineering” frontier:

This diagram has all sorts of interesting space for speculation. It’s generally assumed that, as biology becomes a real science, medicine will become a real, robust engineering field. More interesting possibilities exist in finance and marketing (and other areas) - imagine what these fields will look like once sufficiently robust scientific theories are available to underpin them! And then there’s sociology… at this point, it’s hard to even imagine what the engineering applications of robust sociological theory might actually look like, but it would involve engineering of society and culture. Perhaps the memetic equivalent of genetic engineering? Memetic engineering?

Then there’s AI. AI is squarely on the “real science and engineering” boundary right now. As an engineering field, it corresponds to the more philosophically rich areas of mathematics, ripe with issues like self-reference, logical completeness, and the deceptively difficult mathematical/ethical question of how to formulate an AI’s objective.