The Mass Media is the system that dominates the modern world, having taken over from politics, which took over from religion.
Clearly, the Mass Media - by which I mean newspapers, magazine, TV, radio and the internet and social media; all put together - is huge - far bigger than any other social system there ever has been.
Huge - but is it complex?
No it isn't.
A complex system is subdivided hierarchically, by specialised function - and such subdivisions are sustained and reproduced over time. By contrast, the modern Mass Media is almost formless.
Compare the Medieval State in England - which was a truly complex system and which persisted for several hundred years.
There was a hierarchy of information processing starting with the strategic and unifying person of The King, and descending through Princes, Earls, Lords, Knights, Gentlemen and Commoners (this was also the military hierarchy, since fighting was the main role of the aristocracy).
There was another closely related functional hierarchy of the Church with the Pope, Archbishops, Bishops, Priests Deacons and many minor clergy - and the laity. The aristocracy and the Church perfomed different aspects of the ruling function - coercive force and cohesion/ motivation.
There was an economic hierarchy too - including most people. Within common people there were apprenticed craftsmen in Guilds, lower level craftsmen, and some rich merchants as a middle class; among the 'peasants' there were many levels from freemen, via cottars and villeins and the like, down to landless serfs (I can't recall the precise order).
The whole society was strcutured, inter-related and held together by many laws, rules, and traditional practises.
My point is that Medieval Europe is what a complex social system looks like. Compare the modern Mass Media - it simply is not organised, it is a maelstrom.
The fundamental simplicity of the modern Mass Media can be seen in its uniformity. On any particular day, the whole vast sea of communications is massively dominated by relatively few 'stories', and these stories are found 'everywhere'.
Quantitatively, the mass media includes very few things, and deals with them very simply - and these few things are found 'everywhere' in the system and almost instantly.
All this is the exact opposite of a truly complex system in which information is processed by specialized individuals, working in specialised divisions and subdivisions, and through multiple hierarchical levels leading up to a specific person who ensures purpose and direction.
That is because a truly complex system has coherence and purpose - indeed the coherence is in-service-of its purpose.
The modern Mass Media has no teleology, it is not going anywhere, it is not trying to achieve anything positive - it is, indeed, a system of parasitic destruction: a simple system which feeds-off more complex systems (until, eventually the Mass Media kills its host - or is defeated first).
Thus, modern life may be informationally overwhelming, in terms of the sheer mass of 'stuff' being deluged over us - but this multiplicity is not complexity, any more than a polluted river containing millions of different and varying toxic chemicals is a complex ecosystem.
The Modern Mass media is just a massively-multi-component mixture - in formal terms of information processing, it is not a complex system.