More is different

For the previous post on causality, I went through lots of articles to gather information about how the concept of causal inference is interpreted, and particularly how it is tested by experiment. Although the epistemology of experiment is another discussion by its own, and although I believe that most of the experiments are designed in a biased way such that they are more likely to produce the initial results that were expected even before the experiment is conducted, I think there are some basic observations which cannot be ignored for the sake of verification and validation of a theory.

Let me be more specific. Assume that there is a mug standing next to your keyboard, and you are bored enough to push it to the edge of your desk and accidentally drop it to the floor to cause a perturbation in your lab. If I asked you what caused this mug to break into pieces, you wouldn’t think of the discussion between Hume and Kant on causality, nor you wouldn’t calculate the correlation between the event of pushing the mug and the event of it falling down. You wouldn’t think of any quantum mechanical experiment to support or invalidate your argument. You just simply think that pushing the mug caused it to fall down and break. 

Even though this is a very raw example, it is worth to think about. We have an intention to believe that laws of physics must be adequate enough to explain any phenomena, independent of its time, its space, and its scale. I believe that as humans, we passionately want to find a set of rules that we can apply to all systems, independent of the number or the scale of the agents constituting that system. We want to explain an atom by explaining the rules governing the subatomic particles, we want to explain a molecule by explaining the rules governing an atom, and we want to explain a living cell by explaining the rules governing a molecule; which is nothing more but a fallacy of composition [1]. I think as humans, we sincerely want this because it somewhat feels epic and complete, and it fulfils our expectations towards nature. That’s why when a theory is proposed, such as “causal inferences exist in nature”, we immediately look for the black swan to prove it wrong. It doesn’t matter If we find it in subatomic or astronomical scale, because we blindly accept that nature must be complete, elegant and beautiful enough to be explained by a set of simple rules, like it’s an axiom. But here is the real deal : Physical properties of the collection of particles (lets call it a system) are not mirrored by the individual properties of each particle (or each agent in the system) [2]. This phenomena is called emergence [3]. So if you conduct an experiment with the atoms that your mug is composed of, you can observe retrocausal [4] behaviour of electrons, and similarly, if you conduct an experiment with multiple people with multiple mugs in a lab, you can calculate the correlations between the broken mugs and bored researchers, but never be sure which boredom caused which mug to fall into pieces. 

Emergence manifests itself the most in living organisms. As a matter of fact, life itself is an emergent property. For instance, a single celled bacterium is alive, but if you chop it into pieces, you will observe macromolecules, which definitely are not alive1. It doesn’t matter if you know the thermodynamical laws determining how the proteins will fold in that bacterium, or if you know how an enzyme catalyzes a chemical reaction. The collective behaviour of all those dead macromolecules constitutes the living organism.
"All organised bodies are composed of parts, similar to those composing inorganic nature, and which have even themselves existed in an inorganic state; but the phenomena of life, which result from the juxtaposition of those parts in a certain manner, bear no analogy to any of the effects which would be produced by the action of the component substances considered as mere physical agents. To whatever degree we might imagine our knowledge of the properties of the several ingredients of a living body to be extended and perfected, it is certain that no mere summing up of the separate actions of those elements will ever amount to the action of the living body itself.” - J.S. Mill (A System of Logic, Bk.III, Ch.6, §1)
Emergence applies for all complex systems, such as the human brain containing billions of neurons, an ant colony containing of thousands of ants, or the world wide web containing of billions of users. All these systems are examples of emergent property. What is fascinating about these systems is that they can succeed lots of tasks which their agents are not capable of doing individually. One neuron is just an electrical switch, whereas our brain raises consciousness. A lonely ant means a dumb ant, but an ant colony performs numerous of complicated tasks such as cleaning the nest, brood care, and foraging. Furthermore, both ants and neurons accomplish to allocate and optimize their tasks without any central control mechanism. No ant tells the other ant what to do2.  

Long story short, neither the bottom-up, nor the top-down approach is fully capable of predicting the whole via its parts, or vice versa. The question now arises, how many parts are sufficient to constitute the whole? At least how many ants can behave like a colony, or how many neurons are sufficient to form a ganglion? If we know that the collision of two atoms has nothing to do with the entropy, how many atoms must behave collectively to diffuse due to the second law of thermodynamics? Is there a distinct number of particles that separates the emergent from non-emergent, or is emergent behaviour/complexity a continuous function of the number of particles constituting the system? In other words, where does the coarse grained differentiates from the fine-grained?
"We seek reality, but what is reality? The physiologists tell us that organisms are formed of cells; the chemists add that cells themselves are formed of atoms. Does this mean that these atoms or these cells constitute reality, or rather the sole reality? The way in which these cells are arranged and from which results the unity of the individual, is not it also a reality much more interesting than that of the isolated elements, and should a naturalist who had never studied the elephant except by means of the microscope think himself sufficiently acquainted with that animal?” - Poincare


1. To check what is alive or not according to the cell theory, visit http://en.wikibooks.org/wiki/Cell_Biology/Introduction/What_is_living.

2. Simulating the emergent behaviour of ant colonies is another matter of discussion. In the previous post named “Simulating Life”, I provided some information about the concept of cellular automaton and Langton’s ants. You can also check Conway’s Game of life for further research. 

Suggestions for further research




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