Due to emergence, reality is stratified. This is reflected in the existence of semi-autonomous scientific disciplines and subdisciplines. A major goal is to understand the relationship between different strata. For example, how is chemistry related to physics? How is genetics related to cell biology?
Before describing two alternative approaches —top-down and bottom-up —I need to point out that in different fields, these terms are used in opposite senses. That can be confusing!
In the latest version of my review article on emergence, I employ the same terminology traditionally used in condensed matter physics, chemistry, and biology. It is also consistent with the use of the term “downward causation” in philosophy.
Top-down means going from long-distance scales to short-distance scales, i.e., going down in the diagrams shown in the figure above. In contrast, in the quantum field theory of elementary particles and fields (high-energy physics), “top-down” means the opposite, i.e., going from short to long distance length scales. This is because practitioners in that field tend to draw diagrams with high energies at the top and low energies at the bottom.
Bottom-up approaches aim to answer the question: how do properties observed at the macroscale emerge from the microscopic properties of the system?
History suggests that this question may often be best addressed by identifying the relevant mesoscale at which modularity is observed and connecting the micro- to the meso- and connecting the meso- to the macro. For example, high-energy degrees of freedom can be "integrated out" to give an effective theory for the low-energy degrees of freedom.
Top-down approaches try to surmise something about the microscopic from the macroscopic. This has a long and fruitful history, albeit probably with many false starts that we may not hear about, unless we live through them or read history books. Kepler's snowflakes are an early example. Before people were completely convinced of the existence of atoms, the study of crystal facets and of Brownian motion provided hints of the atomic structure of matter. Planck deduced the existence of the quantum from the thermodynamics of black-body radiation, i.e. from macroscopic properties. Arguably, the first definitive determination of Avogadro's number was from Perrin's experiments on Brownian motion, which involved mesoscopic measurements. Comparing classical statistical mechanics to bulk thermodynamic properties gave hints of an underlying quantum structure to reality. The Sackur-Tetrode equation for the entropy of an ideal gas hinted at the quantisation of phase space. The Gibbs paradox hinted that fundamental particles are indistinguishable. The third law of thermodynamics hints at quantum degeneracy. Pauling’s proposal for the structure of ice was based on macroscopic measurements of its residual entropy. Pasteur deduced the chirality of molecules from observations of the facets in crystals of tartaric acid. Sometimes a “top-down” approach means one that focuses on the meso-scale and ignores microscopic details.
The top-down and bottom-up approaches should not be seen as exclusive or competitive, but rather complementary. Their relative priority or feasibility depends on the system of interest and the amount of information and techniques available to an investigator. Coleman has discussed the interplay of emergence and reductionism in condensed matter. In biology, Mayr advocated a “dual level of analysis” for organisms. In social science, Schelling discussed the interplay of the behaviour of individuals and the properties of social aggregates. In a classic study of complex organisations in business, understanding this interplay was termed differentiation and integration.
I thank Jeremy Schmit for requesting clarification of this terminology.
Judea Pearl-type 'Causal Modeling' to a large extent only cares whether 'intervention' for one collection of measurements has statistically detectable effects for another collection of measurements, which I think accords well with the relatively less scale-focused sentiments in your final paragraph.
ReplyDeleteIf we can try again with different instrument settings and that has measurably different consequences, then 'we' caused those consequences.
I think of this as:
In the (inevitable) absence of complete information about small scales (unknown electrochemical potentials at all points in my head, say), information about much larger scales (about how my hands changed instrument settings, say, or about how a committee agreed to fund a given experiment) can be the best available causal explanation of what happened or might happen in the future.