In the ScienceDaily article:

This is the first result showing such a complicated self-arrangement of hard particles without help from attractive interactions such as chemical bonds

The authors go on to say that:

We knew that entropy on its own could produce order, but we didn't expect it to produce such intricate order. What else might be possible just due to entropy?

This is quite puzzling to me. How can intricate order be produced non-randomly, just through entropy? Is it just as you say, because of certain temperatures and pressure? So in that case are crystals simply the product of the right chemical elements being aggregated in an environment with certain temperature and pressure present?

As for the singularity, I think it makes sense to use the concept as the jumping point for the next "breakthrough" in the evolution of life, but as something more powerful than speciation.

I agree, although I have had my questions about whether the term singularity is useful. I think as long as we stick to a very clear definition of what we mean by singularity, we should continue using it... but it is still problematic and not a metaphorically consistent with a physical singularity. I see the technological singularity and the global brain as mutually consistent concepts that should develop in tandem for the next metasystem transition. I struggle to understand how one could happen without the other also happening.

The new order created by the meta-system transition (or phase transition) will result in (whether we know it or not) giving up some of our more primitive freedoms so that we may reach a higher level of order and complexity as a whole species, not unlike the development of the first multi-cellular organisms. Humanity went through a similar transition when we started to coalesce into cities. We suddenly became subject to a larger set of social laws which guided our behavior. This was essential for the new order and higher living standards we now benefit from.

I have yet think about the sacrifice of certain freedoms in such a context before, but I really think you're right. Great point. Whenever a higher-level of order is achieved, previous freedoms are sacrificed for the collective. It is interesting to see how they interact and perhaps some further insight could be achieved by researching the relationship between individual and collective freedoms over time in human civilization.