## Critical thinking and philosophy

Regular readers of TheEGG might have noticed that I have a pretty positive disposition toward philosophy. I wound’t call myself a philosopher — at least not a professional one, since I don’t think I get paid to sit around loving wisdom — but I definitely greatly enjoy philosophy and think it is a worthwhile pursuit. As a mathematician or theoretical computer scientists, I am also a fan of rational argument. You could even say I am a proponent of critical thinking. At the very least, this blog offers a lot of — sometimes too much — criticism; although that isn’t what is really meant by ‘critical thinking’, but I’ll get back to that can of worms later. As such, you might expect that I would be supportive of Olly’s (of Philosophy Tube) recent episode on ‘Why We Need Philosophy’. I’ll let you watch:

I am in complete support of defending philosophy, but I am less keen on limiting or boxing philosophy into a simple category. I think the biggest issue with Olly’s defense is that he equates philosophy to critical thinking. I don’t think this is a justified identity and false in both directions. There is philosophy that doesn’t fall under critical thinking, and there is critical thinking that is not philosophy. As such, I wanted to unpack some of these concepts with a series of annotated links.

## Stem cells, branching processes and stochasticity in cancer

When you were born, you probably had 270 bones in your body. Unless you’ve experienced some very drastic traumas, and assuming that you are fully grown, then you probably have 206 bones now. Much like the number and types of internal organs, we can call this question of science solved. Unfortunately, it isn’t always helpful to think of you as made of bones and other organs. For medical purposes, it is often better to think of you as made of cells. It becomes natural to ask how many cells you are made of, and then maybe classify them into cell types. Of course, you wouldn’t expect this number to be as static as the number of bones or organs, as individual cells constantly die and are replaced, but you’d expect the approximate number to be relatively constant. Thus number is surprisingly difficult to measure, and our best current estimate is around $3.72 \times 10^{13}$ (Bianconi et al., 2013).

Both 206 and $3.72 \times 10^{13}$ are just numbers, but to a modeler they suggest a very important distinction over which tools we should use. Suppose that my bones and cells randomly popped in and out of existence without about equal probability (thus keeping the average number constant). In that case I wouldn’t expect to see exactly 206 bones, or exactly 37200000000000 cells; if I do a quick back-of-the-envelope calculation then I’d expect to see somewhere between 191 and 220 bones, and between 37199994000000 and 37200006000000. Unsurprisingly, the variance in the number of bones is only around 29 bones, while the number of cells varies by around 12 million. However, in terms of the percentage, I have 14% variance for the bones and only 0.00003% variance in the cell count. This means that in terms of dynamic models, I would be perfectly happy to model the cell population by their average, since the stochastic fluctuations are irrelevant, but — for the bones — a 14% fluctuation is noticeable so I would need to worry about the individual bones (and we do; we even give them names!) instead of approximating them by an average. The small numbers would be a case of when results can depend heavily on if one picks a discrete or continuous model.

In ecology, evolution, and cancer, we are often dealing with huge populations closer to the number of cells than the number of bones. In this case, it is common practice to keep track of the averages and not worry too much about the stochastic fluctuations. A standard example of this is replicator dynamics — a deterministic differential equation governing the dynamics of average population sizes. However, this is not always a reasonable assumption. Some special cell-types, like stem cells, are often found in very low quantities in any given tissue but are of central importance to cancer progression. When we are modeling such low quantities — just like in the cartoon example of disappearing bones — it becomes to explicitly track the stochastic effects — although we don’t have to necessarily name each stem cell. In these cases we switch to using modeling techniques like branching processes. I want to use this post to highlight the many great examples of branching processes based models that we saw at the MBI Workshop on the Ecology and Evolution of Cancer.

## Personification and pseudoscience

If you study the philosophy of science — and sometimes even if you just study science — then at some point you might get the urge to figure out what you mean when you say ‘science’. Can you distinguish the scientific from the non-scientific or the pseudoscientific? If you can then how? Does science have a defining method? If it does, then does following the steps of that method guarantee science, or are some cases just rhetorical performances? If you cannot distinguish science and pseudoscience then why do some fields seem clearly scientific and others clearly non-scientific? If you believe that these questions have simple answers then I would wager that you have not thought carefully enough about them.

Karl Popper did think very carefully about these questions, and in the process introduced the problem of demarcation:

The problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as ‘metaphysical’ systems on the the other

Popper believed that his falsification criterion solved (or was an important step toward solving) this problem. Unfortunately due to Popper’s discussion of Freud and Marx as examples of non-scientific, many now misread the demarcation problem as a quest to separate epistemologically justifiable science from the epistemologically non-justifiable pseudoscience. With a moral judgement of Good associated with the former and Bad with the latter. Toward this goal, I don’t think falsifiability makes much headway. In this (mis)reading, falsifiability excludes too many reasonable perspectives like mathematics or even non-mathematical beliefs like Gandy’s variant of the Church-Turing thesis, while including much of in-principle-testable pseudoscience. Hence — on this version of the demarcation problem — I would side with Feyerabend and argue that a clear seperation between science and pseudoscience is impossible.

However, this does not mean that I don’t find certain traditions of thought to be pseudoscientific. In fact, I think there is a lot to be learned from thinking about features of pseudoscience. A particular question that struck me as interesting was: What makes people easily subscribe to pseudoscientific theories? Why are some kinds of pseudoscience so much easier or more tempting to believe than science? I think that answering these questions can teach us something not only about culture and the human mind, but also about how to do good science. Here, I will repost (with some expansions) my answer to this question.

## Ecology of cancer: mimicry, eco-engineers, morphostats, and nutrition

One of my favorite parts of mathematical modeling is the opportunities it provides to carefully explore metaphors and analogies between disciplines. The connection most carefully explored at the MBI Workshop on the Ecology and Evolution of Cancer was, as you can guess from the name, between ecology and oncology. Looking at cancer from the perspective of evolutionary ecology can offer us several insights that the standard hallmarks of cancer approach (Hanahan & Weingerg, 2000) hides. I will start with some definitions for this view, discuss ecological concepts like mimicry and ecological engineers in the context of cancer, unify these concepts through the idea of morphostatic maintenance of tissue microarchitecture, and finish with the practical importance of diet to cancer.