Let us first bear in mind that science is one way of looking at the world: precision is not the same as truth. I want to put those caveats at the beginning, because I want to share with you that it just occurred to me that quite a lot of what I do isn’t actually mathematics or science. I suppose it is engineering; I take the caveats to imply that I don’t think this is any less worthwhile than mathematics and science.
For example, I’m interested in how lung tumors move when the patient breathes in and out. I’m modelling this motion with a really simple arrangement of springs and dashpots. Here’s a sketch:
This almost certainly isn’t mathematics, even if it is quite mathematical, because I do not start from axioms and theorems and deduce new theorems. Moreover, the hidden “scientific” hypothesis is that lung tumor motion can be modelled this way. The “problem”, from the point of view of declaring this to be science, is that it is not falsifiable. There is no way I can prove or establish in any way that a particular tumor trajectory cannot be so modelled. Even if I search a huge chunk of parameter space, and even if I try all sorts of configurations of springs and dashpots, the “solution” could be lurking nearby, simply a parameter set and arrangement I haven’t considered.
Filed under: mathematics, science | Tagged: dashpot, engineering, falsifiability, lung, lung tumor, math, mathematics, maxwell, maxwell model, popper, science, spring, tumor
