Caporegime
- Joined
- 9 Nov 2009
- Posts
- 25,773
- Location
- Planet Earth
There is a difference between being mathematically inept and lacking advanced mathematical training. Often biologists do not satisfy the second condition. Even where you find biologists who have a good grasp of difficult topics like ordinary differential equations, they are very unlikely to know far more abstract topics like, say, ring cohomology. This does not mean there are no biologists who have that background. There are many biologists with first degrees in mathematics, for example. Or ones who took advanced courses in more liberal education systems (e.g. in the US system). But these are not in the majority. Unless one were to define mathematical biology as biology rather than mathematics.
Anyway, as far as simplifying models go, this is a property of the scientific method more than anything else. The scientific method is all about approximating the laws of nature such that it is possible to make useful predictions. (A shining example of this is the Born-Oppenheimer approximation in quantum chemistry.)
The more quantitive these models, the more accurately and precisely these predictions can be made.
I'm not saying biologists lack knowledge. Let's not make this a personal war between biologists and mathematical scientists. Biology is certainly a field relying extensively on the volume of knowledge. Even fields as far apart as anatomy and molecular biology are based on extensive bodies of well-researched knowledge with little or no intersection. However biologists, historically and as a rule, tend to have far less developed background in mathematics, as opposed to engineers, physicists and theoretical computer scientists (in order of increasing reliance on pure mathematics). As such, errors in this area are not unheard of. Perhaps the biologists of your experience have a good grasp of the fact that bacterial growth is not exponential.
But my research often crosses the borders of biology and as such I often have interactions with them. And I've heard some claims that stem from a lack of background in mathematics. For example, I've read papers positing that Maynard-Smith's "Theory of Evolution as an Optimization Process" are wrong on the basis that evolution does not always lead to more optimal forms (being the gist of the argument). The entire paper only demonstrates a lack of mathematical background. These views are not uncommon in biology. Mathematically, it is easy to see why the optimization process called evolution leads to less optimal forms and why it appears to be difficult to discover an objective function. It is because of profound theoretical limitations such as the P vs NP problem (which fundamentally implies that a perfectly evolved state is not computable) and consequently, the need for stochastic techniques (meta-heuristics) to solve such problems because the search space grows exponentially (and this time it really is exponential). As such requiring approximation techniques that AS A REQUIREMENT lead to less optimal states in order to avoid the local maxima problem. Such things are lost on many biologists -- though I certainly agree, not all. For John Maynard-Smith himself was a evolutionary biologist, albeit one whose initial training was as an aerospace engineer, and therefore a particularly mathematically-capable one. And not every biologist disagrees with him. In fact, I would think that man don't.
Similarly, I've worked with molecular biologists who insisted that bacterial growth is exponential, though, to their credit, they certainly deferred to my correction. His extension to the Nash equilibrium by introducing the Evolutionary Stable Strategy, for one, is, I think, generally accepted by biologists.
Anyway this is widely off-topic and unrelated to graphics cards. I'd be happy to discuss this further elsewhere.
This is the whole problem. You seem to make a "one size fits all" judgement on entire fields and TBH it is rather irritating and condesending at times..! Unfortunately it is not the first time or the last time a scientist will do it.
The fact is that there are enough non-biologists who don't have an effective knowledge of the biology themselves, who make the same mistakes you accuse biologists of doing due to lack of understanding. You need to understand it from both sides,honestly.
It is no different in any field TBH.
Last edited:
