Approximating spatial structure with the Ohtsuki-Nowak transform

Artem is the mathematical brains behind a project where he, Jacob Scott and myself have worked to come with a simple (a first order approximation) game theoretical model of the effect of edges on growing tumours. To do so we have used the Ohtsuki-Nowak transform. Here Artem explains the philosophy of our approach.

Theory, Evolution, and Games Group

Can we describe reality? As a general philosophical question, I could spend all day discussing it and never arrive at a reasonable answer. However, if we restrict to the sort of models used in theoretical biology, especially to the heuristic models that dominate the field, then I think it is relatively reasonable to conclude that no, we cannot describe reality. We have to admit our current limits and rely on thinking of our errors in the dual notions of assumptions or approximations. I usually prefer the former and try to describe models in terms of the assumptions that if met would make them perfect (or at least good) descriptions. This view has seemed clearer and more elegant than vague talk of approximations. It is the language I used to describe the Ohtsuki-Nowak (2006) transform over a year ago. In the months since, however, I’ve started to realize that the assumptions-view…

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On interdisciplinary research

Great minds think alike and, often, their ideas appear approximately about the same time. In this case I am taking about the following articles:

Stuck in the middle by Oxford’s Linus Schumacher, a colleague of my friend and fellow Moffitt researcher Jacob Scott.

Interdisciplinary research: why is is seen as a risky route by Sarah Byrne, a PhD student from Imperial College London

The role of mathematical oncology by my colleague and friend at Moffitt Philip Gerlee.

Byrne’s article highlights some of the challenges that young interdisciplinary researchers have to face in terms of career options. By becoming competent at many things it becomes very difficult to compete with people that are the masters of one field. Although places like Moffitt are happy to host scientists that are good at say, experimental research and mathematical modelling, most academic departments in many universities seem unwilling or uninterested in accomodating interdisciplinary scientists.

As Schumacher writes, this is not the only challenge for interdisciplinary researchers. A big problem, especially for us modellers, is getting recognition for our work and, as he says:

Sometimes I feel like the most valuable contribution by a mathematician to a collaborative research effort can be the different way of thinking they bring to the table, and the conceptual insights that result from the cross-disciplinary discussion.

That feeling seems to be mirrored in Gerlee’s post:

This is not to say that mathematical modelling does not contribute to our understanding of cancer, but rather that the insights gained from it arrive in smaller chunks and are absorbed by the experimental and clinical community. These insights and novel concepts then shapes their thinking and inspires them to perform new experiments or look at existing data in new ways.

This is not always the rule as he points out in an edit referring to a key piece of mathematical work that helped the field of CML research. Mathematical and computational models provide a number of benefits. One of the key advantages of bringing mathematical modelling to biology is that we can help distinguish the hypotheses worth exploring experimentally from those whose logic is faulty. It’s easy for people to forget the importance of weeding out the wrong hypotheses from those meriting further experimental work but that does not make it any less important.

Change, progress, and philosophy in science

Completely agree with Artem’s post. Philosophy of science does not usually serve scientists directly in a measurable way. But having the right intellectual infrastructure is key if we are going to do proper science… otherwise we will keep doing the scientific equivalent of stamp collecting (badly paraphrasing Lord Kelvin).

Theory, Evolution, and Games Group

Bertrand_Russell “Philosophy of science is about as useful to scientists as ornithology is to birds” is a quote usually attributed to Feynman that embodies a sentiment that seems all too common among scientists. If I wish to be as free as a bird to go about my daily rituals of crafting science in the cage that I build for myself during my scientific apprenticeship then I agee that philosophy is of little use to me. Much like a politician can hold office without a knowledge of history, a scientist can practice his craft without philosophy. However, like an ignorance of history, an ignorance of philosophy tends to make one myopic. For theorists, especially, such a restricted view of intellectual tradition can be very stifling and make scientific work seem like a trade instead of an art. So, to keep my work a joy instead of chore, I tend to structure myself…

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