On example of bioinformatics are CpG-island. They are basically parts of DNA with a lot of C and G and those parts don't contain genes.
At the beginning people tried to identify them with standards such as when X% of a Y base pair long strain are C and G and that strain is a CpG-island. People argued about what numbers for X and Y would provide for a more real way of identifying CpG-islands.
Over time people decided against that approach. It better to have an expert identify a bunch of CpG-islands by hand by whatever standards he likes and then training a hidden-markov model to identify CpG-islands based on the trainings data.
Part of the idea is that CpG-islands are not supposed to contain genes. Should a hidden-markov model identify some genes in CpG-islands one then tries to change the training data for the hidden-markov model.
Over time that gives you a concept of CpG-islands that's useful because you put in training data to make it useful. The hidden markov model might still identify some strains of DNA as CpG-island that don't have the characteristics we expected CpG-island to have, but no model is perfect.
As long as we can learn something useful from the model it doesn't need to be perfect. There some distrust in bioinformatics against people who pretend that their model describes reality as is, because most models don't work in every case.
That also something to keep in mind when looking at projects such as the Blue Brain project. The goal isn't to model a full human brain as it really is but to test a simplified model of the human brain. When everything goes well that model is good enough to learn something interesting about the human brain.
To use the words of Alfred Korbyzski who wasn't a bioinformatician, the map isn't the territory. Good maps describes reality well enough that they are useful for navigating reality and making further discoveries.
It might be equivalent to physicists who don't focus on whether or not the Many World hypothesis is real but who focus on the math and whether equations provide good predictions via "shut up and calculate".
For shut up and calculate you need data. If you find a new way to efficiently gather reliable biological data then you can shut up and calculate instead of worrying whether your number are "real" or "hard" (whatever you mean with hard).
If you believe that science is about describing things mathematically, you can fall into a strange sort of trap where you come up with some numerical quantity, discover interesting facts about it, use it to analyze real-world situations - but never actually get around to measuring it. I call such things "theoretical quantities" or "fake numbers", as opposed to "measurable quantities" or "true numbers".
An example of a "true number" is mass. We can measure the mass of a person or a car, and we use these values in engineering all the time. An example of a "fake number" is utility. I've never seen a concrete utility value used anywhere, though I always hear about nice mathematical laws that it must obey.
The difference is not just about units of measurement. In economics you can see fake numbers happily coexisting with true numbers using the same units. Price is a true number measured in dollars, and you see concrete values and graphs everywhere. "Consumer surplus" is also measured in dollars, but good luck calculating the consumer surplus of a single cheeseburger, never mind drawing a graph of aggregate consumer surplus for the US! If you ask five economists to calculate it, you'll get five different indirect estimates, and it's not obvious that there's a true number to be measured in the first place.
Another example of a fake number is "complexity" or "maintainability" in software engineering. Sure, people have proposed different methods of measuring it. But if they were measuring a true number, I'd expect them to agree to the 3rd decimal place, which they don't :-) The existence of multiple measuring methods that give the same result is one of the differences between a true number and a fake one. Another sign is what happens when two of these methods disagree: do people say that they're both equally valid, or do they insist that one must be wrong and try to find the error?
It's certainly possible to improve something without measuring it. You can learn to play the piano pretty well without quantifying your progress. But we should probably try harder to find measurable components of "intelligence", "rationality", "productivity" and other such things, because we'd be better at improving them if we had true numbers in our hands.