The universe around us is extraordinarily complex. It contains galaxies, stars and planetary systems, but also living cells, organisms and eventually beings capable of thinking about the universe itself. Yet none of this complexity was present at the beginning. The early universe was much simpler: a hot and nearly uniform mixture of elementary particles and radiation.
We have already followed much of this history. As the universe expanded and cooled, the original particle soup gave way to protons and neutrons, then nuclei and eventually neutral atoms. Small departures from the otherwise nearly uniform distribution of matter grew under gravity, producing galaxies and stars. Nuclear processes inside stars produced heavier elements, which were released into space and became available for later generations of stars and planetary systems.
Our Solar System emerged from material that had already passed through this history. On the early Earth, the availability of many different elements allowed increasingly complicated molecules and chemical structures to form. At some point this chemistry gave rise to systems capable of maintaining and reproducing themselves, although the detailed path connecting nonliving chemistry to the first life remains an open problem. Once replication appeared, evolution and natural selection provided another mechanism through which increasingly elaborate structures could develop.
Throughout this progression, the fundamental ingredients and the laws governing them did not have to change. The same laws determine how particles interact and how the state of a physical system evolves. Under the right conditions, these dynamics reorganize matter into structures that were absent from the initial state. Complexity is therefore not something added on top of the fundamental laws; it emerges from the evolution governed by them.
What does change with increasing complexity is the most useful way of describing the system. The subatomic physics governing elementary particles is ultimately the same physics governing a chair, even though describing the motion of a chair tossed through the air in terms of its elementary particles would be spectacularly impractical.
In principle, the microscopic description contains the underlying dynamics. In practice, following every microscopic degree of freedom quickly becomes impossible and, more importantly, unnecessary. We instead blur over details that have little relevance to the behavior of interest and retain the quantities that matter at the scale under consideration. This is an effective description.
A gas provides a simple example. Rather than following the position and momentum of every molecule, we describe it using quantities such as temperature, pressure and density. These variables discard enormous amounts of microscopic information while retaining what matters for the macroscopic dynamics. Similarly, chemistry is naturally described in terms of atoms and molecules rather than quarks and gluons. As complexity increases, the fundamental description remains valid underneath but becomes increasingly impractical and can eventually make the problem computationally inaccessible.
This is an important aspect of emergence of complexity. New concepts become useful not because new fundamental laws appear, but because the organization of the system changes and different collective variables become relevant. The effective description is less microscopic and less detailed, but often much more useful precisely because it ignores information that has little bearing on the dynamics of interest.
At higher levels of complexity, these effective variables increasingly depend on the particular state and history of the system and therefore have to be determined by observation. Knowing the laws of particle physics does not tell us the temperature of a particular room, the structure of a particular cell, or the present state of a brain.
Living organisms take this hierarchy considerably further. They interact with their surroundings, retain information about previous states and alter their behavior in response to both. At this level, microscopic physics is no longer a useful language for describing the behavior we are interested in. We instead speak about stimuli, memory, goals, choices and decisions, just as for a gas we speak about temperature and pressure rather than individual molecular trajectories.
This does not place decision making outside fundamental physics. It means that matter has become organized into a system for which a very different effective description is useful. The history of the universe can therefore be viewed both as the emergence of increasingly complex structures and of new levels at which those structures are best described.
The underlying laws need not have changed at any point. What changed was the state of the system, its organization and, with increasing complexity, the language required to describe its behavior. Complexity does not supersede fundamental physics; it makes effective descriptions unavoidable.