First, I’ll define Objective and Subjective questions.
If you ask a group of people a question and receive only one answer from all of them, that is an Objective question. For instance, people tend to agree that 2 + 2 = 4.
But people don’t always tend to agree on the answer to a question, especially if it’s a question that appeals to their a priori values. So when you ask a Subjective question, you won’t get consistent responses. For instance, people tend to fall into two camps on the abortion issue, with very few people in the middle. Note that very intelligent people can be found on either side, which illustrates that this is a Subjective question, rather than a complex question like whether roundabouts are more efficient than stoplights.
The trouble, of course, often lies in determining whether a question is Subjective or merely complex. Different sides of a heated, Subjective debate like abortion tend to believe their opponents are simply uninformed about a complex question. As a rule of thumb, a person with strong beliefs about a Subjective question tends to rely more on “many” personal definitions (often very bad definitions) than ratiocination from a few basic definitions. (But this is a rule of thumb, and must not be used as a metric because rules of thumb are easy to abuse.)
I’ll introduce two more factors with lazy definitions: intelligence and specialization. Intelligence correlates with wordsum pretty well (p = 0.7ish, if I’m remembering Jim Bowery correctly), and specialization correlates with hours spent doing X (I adhere to the 10,000-hour rule in most things).
Now I’ll to finish off the definition.
A science is Hard when the questions it addresses become more Objective as the selected group’s intelligence and (related) specialization increase.
In a pinch, you can substitute wordsum for intelligence and hours of practice for specialization. But there will be a few cases when this is inappropriate; e.g. the estimated IQ of an English or a classics major will probably be skewed on wordsum.
One quick warning:
If you both care about and understand this definition, you may feel an inclination to apply cardinal numbers where they don’t belong. For instance, after polling groups of 100 phD physicists, 100 phD evolutionary biologists, and a control group of 100 muggles you may be tempted to make the claim that physics is 15% more objective than evolutionary biology, or whatever. This would be an incorrect interpretation of the descriptive statistics, as 15% is itself not an objective metric. “Percent” means “per hundred” (cent means 100 as in century), so you have to be clear on your units. 15% is fifteen per hundred what?
Using the absurd case as an illustration, you can’t poll all of humanity on 2 + 2 and declare it 100% objective. Nothing is 100% objective, even though 2 + 2 lies on the far, far right end of the Objectivity distribution. Similarly, an even split doesn’t mean abortion is 0% Objective. It doesn’t make any sense until you define the units corresponding to %.
However, you can still compare questions and sciences to each other, in terms of Hardness. So it is perfectly logical to say that physics questions are Harder than evolutionary biology questions. It is only nonsense to quantify the absolute, numerical difference in Hardness.