Granularity and no emergence in biology

This time a post that bears some distant relation to my thesis topic: granularity. About 1.5 years ago I got concerned that emergence, emergent properties, and emergent behaviour would complicate developing a formal theory of granularity, so I read up on the topic. While writing along the overview and analyzing both the philosophical aspects and proposed examples of emergence in biology, I came to the realization that it doesn’t complicate granularity, but on the contrary: that granularity actually serves as a useful methodology to investigate (hypothesized) emergence, in particular because of the modeling advantages and prospects for structured in silico simulations.

This is very nice for my granularity, but 20 odd pages to support a useful application area of granularity even though it is not the focus-area of applications (wandering off too far from the narrative), and thus taking up too much space in the thesis. So, I’m phasing it out. Problem is, that I don’t know of any outlet where a cocktail of bio, IT, and philosophy would be publishable, because specialists of each discipline wouldn’t be too happy reading too much about the other two fields and can smack it because it is not necessarily detailed enough for their own field, despite that the idea of combining granularity & (hypothesized) emergence may have some novelty to it. Interdisciplinarity has its drawbacks.

Things being as they are, I’m putting the pdf online after the printed paragraph was getting dust for some 1.5 years – for there might just be an interested reader out there. Comments are welcome of course!

Topics that pass the revue in the manuscript are:
1 Introduction
2 Renewed claims of emergence in biology
3 Emergence from a philosophical perspective
3.1 Epistemological emergence
3.2 Ontological emergence
3.3 Strong emergence
3.4 Weak emergence
3.4.1 Simulations
3.5 Examples
3.5.1 Example 1: pseudoplasmodium formation by cellular slime moulds
3.5.2 Example 2: horizontal gene transfer with metagenomics
4 Emergence and levels of granularity
4.1 Preliminaries of granularity
4.2 The irreducibility argument
4.3 Non-predictability and non-derivability
4.4 Characterisation of granular level from the viewpoint of emergence
5 Concluding remarks

The abstract of “Granularity as a modelling approach to investigate hypothesized emergence in biology” is as follows.

Abstract. Informal usage of emergence in biological discourse tends towards being of the epistemic type, but not ontological emergence, primarily due to our lack of knowledge about nature and limitations to how to model it. Philosophy adds clarification to better characterise the fuzzy notion of emergence in biology, but paradoxically it is the methodology of conducting scientific experiments that can give decisive answers. A renewed interest in whole-ism in (molecular) biology and simulations of complex systems does not imply emergent properties exist, but illustrates the realisation that things a more difficult and complex than initially anticipated. Usage of (weak- and epistemological) emergence in bioscience is a shorthand for `we have a gap in our knowledge about the precise relation(s) between the whole and its parts and possibly missing something about the parts themselves as well’, which amounts to absence of emergence in the philosophical sense. Given that the existence of emergent properties is not undisputed, we need better methodologies to investigate such claims. Granularity serves as one of these approaches to investigate postulated emergent properties. Specification of levels of granularity and their contents can provide a methodological modelling framework to enable structured examination of emergence from both a formal ontological modelling approach and the computational angle, and helps elucidating the required level of granularity to explain away emergence. I discuss some modelling considerations for a granularity framework and its relevance for the testability of emergence in computational implementations such as simulations.

More on sudokus

Not that I’m into doing sudokus, but it is a fun area for computer science to show that theory isn’t that far off from harmless applications in daily life.

About a year ago I wrote about solving sudokus with constraint programming, which some readers still found a bit too cumbersome. Santos-Garcia and Palomino had a go with it by rewriting rules to solve sudokus [1]. Note that even if you are number-averse, then the puzzle works equally fine with letters (sometimes called godoku or scramblets), colours, figurines and whatnot. Either way, solving the puzzle computationally is known to be NP-complete, and even with additional regional constraints the number of valid sudoku solution 9 x 9 grids is 6,670,903,752,021,072,963,960. So, niftier strategies to automatically solve a sudoku are welcome.

Santos-Garcia and Palomino used rewriting logic, which is a logic of concurrent change that can deal with states and highly nondeterministic concurrent computations. Then, the approach is to, first, represent sudokus as a set of objects where each object corresponds to a cell, and, second, use 8 local transition rules in a possibly concurrent system that can be applied concurrently to different fragments of this set of objects (see article for the formal specification).

Now, all this is specified and implemented in Maude [2], with implementation details in sections 4.1 and 4.2 of the article. With the Maude files for the specification to solve sudoku monsters (order 4), along with the complete specification of the sudoku solver, you can play with it yourself.

But, alas, it is a research article to see if it could be done with rewriting logic –which it can – and is not the fastest online software, as the authors note themselves, who mention [3] [4] and [5] that can do it faster. On the other hand, if you have time to solve sudokus, then you probably also have time to wait slightly longer for the solution if you haven’t found it already.

[1] Santos-Garcia, G. and Palomino, M. Solving Sudoku Puzzles with Rewriting Rules. Electronic Notes in Theoretical Computer Science, 2007, 176:79-93.
[2] Clavel, M., Duran, F.J., Eker, S., Lincoln, P., Marti-Oliet, N., Meseguer, J., and Talcott, C. Maude Manual (version 2.2). 2006.
[3] SuDoku Solver by Logic v1.4.
[4] Sudokulist. (step by step solver, with hints at each step)
[5] A Su Doku solver. (on sourceforge)