Why complexity?
We admire simplicity but are awed by complexity which achieves some particular purpose. In our universe we are surrounded by complexity. However, for any required level of complexity, we give great value to being as simple as possible. When two hydrogen atoms refuse to remain simply single, but pair to give a hydrogen molecule we have complexity. The apparent purpose is stability – a balance. Helium atoms, of course, are confirmed, stable bachelors. Complexity – it seems – always has purpose. Without a purpose complexity is pointless. Could it be that purpose is necessary for complexity? Can there be purpose without consciousness? Do the laws of nature have purpose? Whose purpose then?
Does the universe even care?
It is not a law of nature but the principle of parsimony (also called Ockham’s or Occam’s Razor) holds that of many possible explanations, the simplest, least energy-intensive explanation having the fewest assumptions, is most likely the correct one. William of Ockham (c. 1287–1347) advocated that when presented with competing hypotheses about the same prediction, one should select the solution with the fewest assumptions. The term razor refers to distinguishing between two hypotheses by successively “shaving away” unnecessary assumptions. Isaac Newton wrote, “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances”. But the parsimony principle had been expressed even in antiquity. Long before Newton, Ptolemy (c. AD 90 – c. 168) stated, “We consider it a good principle to explain the phenomena by the simplest hypothesis possible.” In short, parsimony is about only what is necessary and no more than is sufficient.
Parsimony and simplicity and an absence of superfluity is given much value in many fields. Parsimony lies at the heart of minimalism in all fields. I associate parsimony with simplicity and simplicity with elegance. In language, I perceive elegance to lie in using as few words as are necessary and sufficient to convey a precise meaning. In philosophy and science, elegance lies in having as few assumptions as possible. Elegance in engineering constructs lies in using as few components as possible, consuming as little energy as possible, and in expending as little effort as feasible, to achieve a given function. As an engineering student, I learned to appreciate simplicity in complexity. My maths professor instilled in me the elegance associated with simplicity. With the study of machines and constructions I was fascinated by how creativity and purpose converted simple things to complex things. Elegance in engineering arose from having the greatest simplicity for any required complexity. It is not surprising therefore that I tend to see simplicity not only as a ground state of existence but also as the source of elegance.
(A word about entropy. From my thermodynamics professor I was introduced to entropy as the measure of that enthalpy that could not usefully produce work – the 2nd Law – and came to understand it as a quantification of the distance from equilibrium of an isolated system. The closer to equilibrium the less the work that can be extracted and the greater the entropy. Higher temperatures are thus further removed from equilibrium than lower temperatures. The heat death of the universe as an isolated system then represents that final equilibrium when nothing more can change and entropy will be at the highest level possible for our universe. I always felt it would have been easier to teach entropy from the end-state of final equilibrium as having the lowest negentropy. Any increase in complexity moves any system further away from the final equilibrium and is generally an indicator of lower, local entropy. However, my logic seems to become circular when attempting to relate simplicity and complexity in terms of entropy and I leave that for some later post).
Complexity is the attribute of a whole thing made up of interacting parts. The parts must be interacting for an assembly of parts to gain complexity. Any part of a whole, by definition, is a simpler thing than the whole thing, but may itself be complex and exhibit complexity in its own right. Whereas simple has many meanings (innocent, modest, humble, stupid, naive, fundamental, uncomplicated, ..), simplicity, in this context as opposed to complexity, is the quality of things having as few interacting parts as are necessary and sufficient. The simplest things of all have no component parts and are indivisible. In the material world, the ancients considered the simplest, fundamental elements, making up all matter, to be indivisible (earth, fire, water, air, aether). The Greeks developed this into the notion of fundamental atoms of matter. Nowadays we have the Standard Model where all matter is composed of 17 elementary particles. But most of these elementary particles cannot exist in isolation. Many, it is thought, only existed in the first few seconds after the Big Bang. For some reason or other (let us call it purpose) they assemble and interact in complex ways to create the matter and energy we more readily perceive.
There are two types of fundamental particles: matter particles, some of which combine to produce the world about us, and force particles – one of which, the photon, is responsible for electromagnetic radiation. These are classified in the standard model of particle physics, which theorises how the basic building blocks of matter interact, governed by fundamental forces. Matter particles are fermions while force particles are bosons.
Matter particles are split into two groups: quarks and leptons – there are six of these, each with a corresponding partner. Leptons are divided into three pairs. Each pair has an elementary particle with a charge and one with no charge – one that is much lighter and extremely difficult to detect. The lightest of these pairs is the electron and electron-neutrino. The other two neutrino pairs (called muon and muon neutrino, tau and tau neutrino) appear to be just heavier versions of the electron. The six quarks are also split into three pairs with whimsical names: “up” with “down”, “charm” with “strange”, and “top” with “bottom” (previously called “truth” and “beauty” though regrettably changed). The up and down quarks stick together to form the protons and neutrons which lie at the heart of every atom. Again only the lightest pair of quarks are found in normal matter, the charm/strange and top/bottom pairs seem to play no role in the universe as it now exists, but, like the heavier leptons, played a role in the early moments of the universe and helped to create one that is amenable to our existence. .. There are six force particles in the standard model, which create the interactions between matter particles. …. The Higgs boson is the final particle which completes the roll call of particles in what is referred as the standard model of particle physics so far described.
We look for the simplest possible explanations even though the physical universe around us is far from simple. But why does the universe create complexity from simple things? Physics tells us that we cannot find smaller, more elementary particles than those in the Standard Model. (I have some reservations about how elementary particles which have no independent existence can be taken as being elementary – but that is another story). But physics also tells us that most of these elementary particles only exist together with other particles, where the coming together always resolves some apparent imbalance in force or energy or charge. If the fundamental particles were truly fundamental, it should surely be simpler for them to remain as fundamental particles rather than combine in complex ways to create matter. Why do atoms combine to produce elemental molecules if not forced to? Why would simple molecules choose to create complex molecules? If nothing else, seeking a balance of some kind appears to be the purpose. But why should the universe abhor imbalance and have the achieving of balance as a purpose? What were the imbalances which led to the complexity exhibited by organic molecules? And why would complex, inanimate molecules get together in just the right, but highly unlikely, configurations to create life? And what was the purpose for simple life to increase in complexity when it would have been so much easier to remain simple?
We observe complexity not only in the world of matter and energy, but also in the immaterial, abstract world. Simple thoughts become complex thoughts and simple emotions become complex ones. Simple ideas accumulate and interact with others creating vastly complex ideas. But here, we have no practical, quantitative way of distinguishing the complex from the simple and resort to language to express qualitative differences. (We cannot say, for example, that an atom of anger and two of jealousy give a molecule of rage). Our reason tells us that complex things are built up from simple things. Always. Our reason does not allow us to consider that complexity is created first and is then followed by the breakdown into simpler parts.
I observe that in all things, complexity is always more effort-intensive than simplicity. Complexity always requires more energy, or more thought, or more planning, or more coordination, or more creativity, or more skill. Take any collection of simple things and complexity does not, in my experience, spontaneously emerge. It requires the input of some external driver such as energy or thought or planning or whatever. It takes further effort to maintain a state of complexity. Complex things often break down into simpler things because some motive agent which sustains the complexity disappears. I cannot conclude for certain that purpose is always resident in the external impulse which drives from the simple to the complex, but wherever humans create complex things from simple things, purpose is always evident. For us, complexity takes effort and to expend effort needs purpose.
The universe around us is not parsimonious. In fact, that the universe exists at all is not the simplest state that can be imagined for all that the universe contains.
- Simplicity gives elegance
- Simplicity is more parsimonious than complexity.
- Biochemistry is more complex than chemistry.
- Nothing is always more parsimonious than something.
- Complexity needs purpose
- But whose purpose?
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