Self-reference, once again, once again

Another comment, this time from the biologist Richard Dawkins, that shows that importance of self-reference:

"Perhaps consciousness arises when the brain's simulation of the world becomes so complete that it must include a model of itself."

Richard Dawkins, The Selfish Gene, Chapter 4, The gene machine.

See this post and this one on self-reference. See also the last line of G. Chaitin quoted in this post.

Humble models

David Orrell got his PhD from the University of Oxford on the modelling of nonlinear systems. Although he got it only in 2000, he earned some authority and describes us in his book, The future of everything, his point of view of the failure of present models to predict correctly anything, from the weather to the economy.

His main argument is composed of two points. First, he notices that natural systems are like some theoretical systems that are called automata systems: they are systems based on a set of local interacting rules. Among the three classes of automata systems, one is composed of uncomputable systems: there is no way to speed up the calculation and the only way to know the future of the systems is to run the model.

The problem, which is his second point, is that we are not and may never use the right set of rules. All known models have some kind of parameterization of the processes that are not modelled -because we do not model from the atom to a society. The additional difficulty is that models of natural systems are like natural systems, full of feedbacks, which make them highly sensitive to any parameterization. They don't even have to be chaotic to be completely wrong:

"By varying a handful of parameters within apparently reasonable bounds, we can get a single climate model to give radically different answers"

David Orrell, The future of everything, Chapter 8.

And thus, we might never be able to predict the future as Laplace dreamed of:

"Lack of predictability is a deep property of life. Any organism that is too predictable in its behaviour will die. And in an unpredictable environment, the ability to act creatively, while maintaining a kind of dynamic internal order, is a prerequisite. The balance of positive and negative feedback loops, when combined with the computational irreducibility of life processes, makes the behaviour of complex life forms impossible to accurately model. The problem is not that such organisms are erratic, but that they combine creativity with control. House plants are quite stable (they tend to stay in their pots and don't suddenly walk off to join the forest), but it would still be impossible to predict the exact effect of moving a single plant from a shaded spot to a warm greenhouse, based only on a detailed understanding of its biochemistry. If we can't do it for a plant, we can't do it for a planet. Life, it seems, evolves toward rich, complex structures, which defy simplistic analysis."

David Orrell, The future of everything, Chapter 8.

Thus, should we even bother to try to predict? The answer is yes because although the models are wrong, they are one way to try to predict the future. What the authors try to put a term is on the confidence, and at times arrogance, of modellers. They should be the first to recognize that their models are not perfect and, on top of it, are not that objective at all -the models are full of assumptions that are, after careful look, just a set of subjective views of the world hidden behind technical terms. Thus, the author would like some kind of balance: between the objective ways to predict the future and the subjective ones:

"Objectivity and subjectivity must be in balance, and inform each other, just like the positive and negative feedbacks loops that characterize living systems. We will choose to protect nature only if we value it -and not just as an object, but because it is alive. The only way we will respect it is if we understand that we cannot control it.
In non-linear, complex systems, change often happens abruptly, like water turning to ice. Extreme change is normal. This makes prediction difficult, but it also holds out tremendous hope, because it means that a sudden change in course can be expected. Such change often comes from the bottom up, rather than the top down [...]. Unlike deterministic mechanical systems, we have a choice; we can determine our own destiny. We are not slaves to the initial condition, our genes, or the efficient market. We are unpredictable, and that's not a bad thing.
The science of complexity will not build a better GCM [General Circulation Model], and neither Gaia theory or earth system science. Their stories are more of humility than of human ingenuity. But if we as a species are standing at a precipice, it is better that we see the world feelingly than be completely blinded by our mental models; that we know what we do not know. Creativity often emerges from a state of uncertainty. Grasping for illusory knowledge by over-modelling our environment is therefore part of the problem.
[...]
Mathematical models will always be indispensable. Like language, they are a way to understand the world, and organize and communicate our thoughts. They help us perform hypothetical experiments, explore possible scenarios, and expose fragilities. Most of all, they help us comprehend what is happening now."

David Orrell, The future of everything, Chapter 8, italics are mine.

Thus, modellers, keep doing the good work. But please, drop the certainty and try to be more humble.

The structure of science

Ian Stewart, in his book Does God Play Dice?, describes how science is structured. The explanations and theories provided by science are hierarchic; they start from the theories of fundamental particles and atoms, follow through theories of fluid dynamics, ecosystem, etc and finish with theories of sociology and art. Each explanation is constructed on top of the theories that are at a lowest level but in the same time, it does not care of the detail of these lower-level theories: the equations of fluid dynamics are constructed for a small water parcel, typically several moles of water, but it does not care about the individual atoms, nor about the fact that gravity has yet to be explained by the physics of particles. This important view of science is also shared by Edward O. Wilson in his book Consilience. Here is Ian Stewart's quote:

"Current science possesses no truly fundamental theories - not in the sense that they describe what nature actually does. They are all approximations, valid within some reasonably well-defined domain. Quantum mechanics work well at the submicroscopic level. General relativity is great for describing entire universes [...]. Science is a patchwork of models, each of which has been enormously refined within its own domain. The models habitually disagree when those patches overlap. Some disagreements are relatively harmless: atomic theory and continuum fluid mechanics disagree on the fine structure of water, holding it to be respectively to be discrete and infinitely divisible, but on macroscopic scales continuity and discreteness effectively approximate each other. Others are fatal: for example, as I write, the best current theory of astrophysics and the best current theory of cosmology compel us to accept stars older than the universe that contains them. Today's science is a pluralist patchwork of locally valid models, not a global monolith. Indeed it succeeds because it is a pluralist pacthwork of locally valid models.
Our concept of explanation is also a patchwork. A philosophical model that fits it well is what Richard Dawkins calls 'hierarchical reductionism', which sees scientific theories as a hierarchical structure, with some on different levels from others, corresponding to different levels of description of phenomena. (The hierarchy is not rigid and the levels need not be like layers of bricks in a wall.) For example, the complexities of ecosystems are explained by referring them back to those of organisms; organisms are explained by the growth of spatially organized proteins and other macromolecules; the complex organization of organisms is referred back to the linear complexity of their DNA code; the complexity of DNA is referred back to combinations of simpler atoms - and so on, right back to the Theory of Everything.
As Dawkins rightly remarks, it is not necessary to trace every phenomenon right back down this chain of reductions in order to understand it. Chemistry can be considered as 'given' for the purposes of understanding DNA; DNA can be taken as 'given' for the purpose of understanding protein manufacture in organisms, and so on.
[...]
What we tend to forget, when told a story with this structure, is that it could have had many different beginnings. Anything that lets us start from the molecular level would have done just as well. A totally different subatomic theory would be an equally valid starting-point for the story, provided it led to the same general feature of a replicable molecule. [...] It has to be or else we would never be able to keep a goat [within a wooden fence] without first doing a Ph.D. in subatomic physics."

Ian Stewart, Does God Play Dice?, Farewell, Deep Thought.

Advantages and disadvantages of modelling

Ludwig von Bertalanffy writes about any attempt to model Nature and its constituents:

"Conceptual models which, in simplified and therefore comprehensible form, try to represent certain aspects of reality, are basic in any attempt at theory; whether we apply the Newtonian model in mechanics, the model of corpuscle or wave in atomic physics, use simplified models to describe the growth of a population, or the model of a game to describe political decisions. The advantages and dangers of models are well known. The advantage is in the fact that this is the way to create a theory -i.e. the model permits deductions from premises, explanation and prediction, with often unexpected results. The danger is oversimplification: to make it conceptually controllable we have to reduce reality to a conceptual skeleton- the question remaining whether, in doing so, we have not cut out vital parts of the anatomy. The danger of oversimplification is the greater the more multifarious and complex the phenomenon is. This applies not only to «grand theories» of culture and history but to models we find in any psychological or sociological journal.

Ludwig von Bertalanffy, General system theory, Chapter 8

A debate between theory and observations?

It seems that there is in academia some debate opposing the theoreticians on one side and the observers on the other, between the creator of ideas and the gatherer of empirical data. And the debate questions which ones are the most useful to science, which ones do not spend his time and people's money on futile work.

I am afraid that such debate is nothing less than another victim of human's favorite game to create divisions where there is none. For instance, Ludwig von Bertalanffy amuses himself in noting how much theory there is actually behind any observations:

"According to widespread opinion, there is a fundamental distinction between «observed facts» on the one hand-which are the unquestionable rock bottom of science and should be collected in the greatest possible number and printed in scientific journals-and «mere theory» on the other hand, which is the product of speculation and more or less suspect. I think the first point I should emphasize is that such antithesis does not exist. As a matter of fact, when you take supposedly simple data in our field [...,] it would take hours to unravel the enormous amount of theoretical presuppositions which are necessary to form these concepts [...].
Thus even supposedly unadulterated facts of observation already are interfused with all sorts of conceptual pictures, model concepts, theories or whatever expression you choose. The choice is not whether to remain in the field of data or to theorize; the choice is only between models that are more or less abstract, generalized, near or more remote from direct observation, more or less suitable to represent observed phenomena.
On the other hand, one should not take scientific models too seriously. [...] I believe a certain amount of intellectual humility, lack of dogmatism, and good humor may go a long way to facilitate otherwise embittered debates about scientific theories and models."

Ludwig von Bertalanffy, General system theory, Chapter 7.