an essay in the series science perspectives

April 5, 2020 leave a comment

The sciences traditionally follow a reductionist approach. They ultimately ask for a minimal set of entities and laws that can describe all observed phenomena, that predict new phenomena, which are then also observed, and that are consistent with each other. It is the quest for the building blocks of our world, for the “Lego set” out of which everything is built and for its function.

As looking deeper reveals, the quest is actually not for the “real thing”, and cannot be. It is rather for a set of elementary pieces out of which we can construct our representation of reality, our model world. In the following, however, the focus is not on such philosophical fine print but on recognizing what can and cannot be done with elementary building blocks.

elementary bases

The reductionist approach is farthest developed in physics. It ascertains that everything we observe today is built from a set of 17 elementary particles, all indivisible and perfectly identical within their group. A real “Lego set”. These particles come with an order: 3 generations of 2 quarks and 2 leptons, 4 exchange bosons, and the Higgs boson. From these, actually just from the first generation, all atoms are formed and from them all normal matter. There are strong indications from astrophysics, however, that all we can observe so far only accounts for an estimated 5% of the universe’s total matter-energy, that 95% is dark matter and dark energy of unknown composition. Still, for describing everything in our non-living environment and all of life, those 17 elementary particles suffice. Incidentally, a more prudent statement would be that nothing we did study so far, and for which the path down to elementary particles could be followed, did bring up anything different from the set of 17. For the time being, however, this is again philosophical fine print.

The full way down to the 17 elementary particles is hardly ever useful, not even in physics. More common bases are the about 100 different atoms that are based on them, or the already innumerable molecules that are based on atoms, or yet larger constructs like the components of life’s biomolecular machinery based on molecules.

Indeed, starting out from our directly observed world and actually going down the reductionist way – down towards the elementary base and establishing the different hierarchical levels on the way – is exceedingly difficult and kept science busy for a few centuries. On that way, science discovered that the non-living world at its base follows simple laws (Newton,…) and so does the living world (Darwin,…).

Simple laws. This is true even though a fundamental explanation of any one seemingly trivial phenomenon usually turns out to be quite demanding. The difficulties are invariably with the first steps of abstraction. An example in case is the formation of rings from the drying of spilled drops of coffee, or any other phenomenon in your kitchen for that matter.

down at the elementary base, now what?

Over the past few decades, science also learned that knowing the elementary building blocks does not tell us a lot about the world at large. Indeed, imagine the set of about 100 different atoms and look at the world right in front of your eyes: do you see the connection? If you happen to be an adept of natural sciences, you can certainly “see” your environment as it is composed of atoms. But the other way round? Would you predict what you see, from just knowing the set of atoms? Never ever! Not in its general structure, and certainly not in its specific detail. Just as a starter: How would you predict that there is oxygen in the atmosphere?

There is no predictive connection from the elementary building blocks to the macroscopic world around us.

There is a connection between the elementary base and the macroscopic world, but it is a contorted long path that contains a practical infinity of bifurcations. All of these could have been taken, almost none actually has been. It is this path that links from the elementary to what is realized here and now, and it traverses the eons, billions of years.

Of course, we knew that all along: Giving a large Lego set to a playful child we have no idea what she is going to build. The set determines only what can be built, and even that just to a very limited degree. What are the differences to our world? Its Lego pieces are real small and there are many of them. And there is no playful child. The pieces arrange themselves under a gentle flow of energy. The essence of it all?

Our world is built from simple pieces and follows simple laws. This does not imply simple phenomena, however.

not the Grail, still empowering

Apparently, the anticipation that understanding the building blocks together with their governing laws would suffice to understand our world is fundamentally wrong. The reductionist approach does not lead to the Grail. It is still enabling and empowering our culture, though.

Understanding elementary building blocks and laws does allow humankind to create like no other species, revolutionizing its life and reshaping the world. So far, this culminated in the tremendous advance of our technological culture that we witnessed over the past few decades, and can learn from history for the past few centuries. Instances include, among countless others, dense global networks for transferring energy, information, goods, and people, exceedingly complicated tools like iPhones, genetically modified life forms with hierarchical processing chains for our nutrition, energy demand, and health, or global knowledge bases and processing layers with emerging artificial intelligence.

on the way up, the limits of predictability

Prediction, looking into the future, is a key capability of cognitive beings. It allows to choose current actions such that they lead to desired result somewhere in the future. The depth of this look, together with the power to do the identified actions, determines the capabilities of an individual, of a species, of a larger system. This is true at all levels of cognitive life, from the level of microorganisms to that of humankind.

Prediction is more general than forecasting in time. It is the transfer of understanding from one setting to another.

Again, there is some philosophical fine print. What is predictable at all, or formulated more technically, what aspects of our world are fundamentally deterministic? What is a desired result? How is it judged? On what set of values and how are they weighted against each other? How deep into time, or into another setting, is the projection required to decide on its desirability? Obviously, such questions are eminently important operationally. However, the focus in the following will be much shorter, just on the extent of predictability, foregoing the deeper issues.

The raison d’être of the reductionist approach is that given a fundamental understanding in terms of elementary building blocks and governing laws allows prediction. There is unanimous agreement, certainly within the natural sciences, that the reductionist view of the world is correct. After all, we came to understand that the observable world indeed consists of elementary particles and of nothing else, admittedly of very very many of them. Given that this is the case and that we know the particles and their governing laws, which we do, how far can we then predict, how far can we move the way up to larger scales of time and of space, eventually to “me, here and now” hopefully even to “they, there and then”?

As highlighted above, there is no predictive connection between the elementary building blocks and the macroscopic world around us. Hence, the “how far” questions will all have a finite answer. Of course, nature does integrate the elementary base to the world at large – it actually knows nothing of all these humanly concepts – and it just takes this or that turn at any bifurcation that comes up. Imagine a rock rolling down a mountain slope, hitting another rock. It just continues rolling left or right, or it gets stuck, or it disintegrates in one of many ways, or the other one does. We know nothing of all those zillions of turns that eventually led to here and now.

Many aspects of our life are of course reliably predictable, from the functioning of my body and mind to that of the coffee machine. Where the “of course” is just to a point, we know, and the base is not the elementary.

Understanding the world obviously demands more than understanding its elementary base.

Indeed, the thrust of current fundamental research is about to shift its direction, from further details of elementary building blocks towards principles that drive and guide the unfolding of our world. We are still far from a comprehensive appreciation, let alone an operational understanding. Nevertheless, some main roads have emerged from the fog in recent decades: deterministic chaos, complexity, and evolution.

Deterministic chaos – finite time horizon

An apparent contradiction in terms, deterministic chaos just links the two regimes in time found in all macroscopic processes: predictable (deterministic) over short times, unpredictable (chaotic) over long times. This introduces a fundamental limit for how far we can see into the future, the finite deterministic time horizon. That horizon differs largely for different processes – some 0.00000001 seconds for the path of a molecule in water at room temperature, some 100’000’000 years for the path of planets in our Solar system –, but it is finite for all macroscopic processes, that means larger than 0 and smaller than infinity.

While the concept of deterministic chaos has a long history in mathematics and theoretical physics, reaching back to around 1890 to works by Poincaré and Hadamard, it became only popularized in physics by the work of E. N. Lorenz in 1963, and in the larger public after 1970. Lorenz nicely defined the concept as deterministic chaos is when the present determines the future, but the approximate present does not approximately determine the future.

Complexity – more is different

Very large ensembles of weakly interacting particles are found to self-organize into characteristic structures that are largely independent of the individual particles’ properties. These structures in turn gives rise to qualitatively new and unexpected so-called emergent behavior. Such systems are called complex.

An archetypical example of a complex system is a heap of dry sand with its slip-faces. Such faces with their constant slopes are observed in a wide variety, from heaps of rice to sand dunes and mountain slopes. The angle of these so-called critical slopes is self-organized and an emergent property that cannot be predicted from knowing the properties of the particles.

Critical slopes are not the only manifestation of self-organization, however. A second class are patterns, from the stripes of a tiger to the vegetation in dry landscapes and cracks in dry soils.

Also, “particles” can be very complicated. Very large groups of humans for instance behave as sets of particles, as becomes manifest in the formation of waves in intensifying freeway traffic or, sadly, in occasional large panic events with people dying in the emerging shock fronts.

The diverse examples of complex behavior already hints at a widespread phenomenon. Indeed, all sufficiently large ensembles exhibit self-organization and emergence, from elementary particles to the structure of our universe. To cite from the remarkable paper “More is Different” published back in 1972 by physics Nobel laureate P. W. Anderson, “at each level of complexity entirely new properties appear“.

Evolution – unfolding new spheres of realities

Complexity leads to the self-organization of a large number of pieces into some large-scale structure that exhibits new properties. A heap of sand or some crack patterns are just the first step, however. Self-organization can and does progress so far that something completely new is recognized to emerge and continues to unfold. We call this unfolding evolution.

One line of evolution, the deepest one we are aware of, started with the condensation and physico-chemical differentiation of planet Earth some 4 billion years ago, through the origin of life, all the long way to the emergence of Homo sapiens some 2 million years ago, and of its culture some 100’000 years ago. While “evolution” is mostly associated with the unfolding of biological life, and often restricted to it, it is in fact much more general. Indeed, life originally emerged from just simple minerals and small molecules that were subject to some weak flow of external energy. Also at the other end, the cultural evolution of humankind, it apparently leaves the realm of biology.

How does evolution work? The agents are self-replicating entities in some environment from which they extract their required resources like energy and building blocks. These entities exhibit variation in appearance, the so-called phenotype, that influences their replication rate in their environment. The final requirement is heredity, that aspects of the phenotype that influence the replication rate are transmitted to the next generation. Whenever such a situation arises, evolution sets in, must set in, and creates layers upon layers of unforeseeable novelty, until one of the conditions fails.

Entities in the evolutionary arena can be biological beings, naturally, but these may also be chemical reaction systems, as it is presumed for the era before life emerged. These may also be more abstract structures like groups, that actually bear some analogy to chemical networks. Finally, in the context of cultural evolution, evolving entities include immaterial aspects like languages, ideas and concepts, eventually also understanding.

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