Bioinformatician here. All my formal training is in biology, but I've spent most of my research hours learning CS, statistics, etc, rather than biology.
> An astonishing amount of biology is rather mechanistic, systematic, and logical.
I disagree vehemently. Or, to be more precise, it is very likely that this is true in reality, but in terms of the dominant way it's viewed in both clinical and research practice, it's very much not.
The average paper's findings are qualitative, not quantitative, in nature. Of course, numbers, statistics, etc, will be used -- but they will be used to get p-values to support a qualitative conclusion, rather than to work towards a quantitative, systematic understanding of biology.
There are exceptions, of course -- a decent amount of biochemistry is quantitative enough -- but when you get to topics like cell signalling, "cell biology", etc, it is almost never quantitative.
I have a favorite question I like to use in seminars when someone is presenting findings along the lines of "protein A regulates protein B". The question is: "Among the various regulators of B, how important is A? Is A a key regulator of B, or simply one of many?". Or, even more simply, "What is the most important regulator of B?" I invariably get blank looks, as if this is an unreasonable or impossible question to answer. Of course it is, as long as your models are qualitative. The point of the question is to get the speaker to think about that, but so far, no luck.