I don't know about this...I would think that complexity comes with order.
That's a reasonable approximation in this context. What happens when complex systems emerge is that they reduce entropy
locally at the expense of increasing entropy much more elsewhere (outside those systems). This is why the 2nd Law of Thermodynamics talks about entropy never decreasing in
closed systems; but it can decrease in open systems, where there is an external source of low entropy providing a gradient down which the system can export its entropy.
You could also think of it in terms of energy - when energy is evenly distributed, entropy is high. When energy is unevenly distributed in 'clumps' (e.g. like stars) entropy is lower. Systems can generate complexity and order by dissipating the available energy.
The best analogy I can think of is the flow of water when a dam is opened. The initial rush of water is far too energetic for order or structured complexity, but as the turbulence reduces and the flow becomes smoother, you can start to find eddies and vortices - relatively complex, ordered structures that persist for some time. While they tend to be carried along in the general flow, their rotation means that some parts of the eddy structure are moving counter to the main flow, the equivalent of a local reduction of entropy, at the expense of a greater reduction in the overall energy of the water flow than would otherwise occur; i.e. vortices and eddies are dissipative structures. When the flow reduces below a threshold velocity, the vortices and eddies will themselves dissipate, and when the flow stops altogether, all disturbances will die away.
Life, planets, stars, and galaxies are complex, relatively ordered, dissipative structures. The stars and galaxies formed as concentrations of low entropy/high energy in the early universe, and now they're 'unwinding', distributing their energy and acting as sources of low entropy for secondary and tertiary systems, such as living things, to generate their own complexity and order from. Complex systems self-assemble as dissipative structures when suitable materials are available and in suitable energy/entropy gradients.
What was this called before the idea of "entropy" arose?
What, thermodynamics? or do you mean what happens to living things, i.e. aging, senescence, & death?
Entropy is an explanatory concept of statistical mechanics - it explains why there is an arrow of time even though the underlying fundamental physical particle interactions are time-symmetric and 100% reversible. It's an emergent effect of probability at work.
Would there even be age without entropy?
That's not really a coherent question; entropy is a descriptive property of collections of particles, of
stuff. Entropy increases simply because there are many more ways for a system to be disordered than ordered, so if it starts out with some level of order, any random change is likely to make it less ordered.
Sounds poetic...but, also, it sounds like all this sciencey speak is the dogmatization of what some genius has imagined...
In other words...it's just a bunch of words...
Sure; the idea was to contrast a familiar poetic description when backed by the solid mathematics of statistical mechanics, with the same words as usually backed by supernatural handwaving