[HPsquared]

Phase transitions are a really nice way to explain to someone how a complex system can appear to flip from one state to another. Especially the importance of looking at the right variable. If you look at water at 99°C or 101°C (at standard pressure) it appears like a sudden change. But if you consider energy balance, it's not like it just flips: it takes substantial energy input to boil water. If you measure energy input, you see a gradual change of phase (mass fraction slowly turning from liquid to vapour) as more energy is supplied. But then you can also have superheated water in the microwave and it's just waiting to (partially) boil... So many analogies.

[NitpickLawyer]

> it's not like it just flips.

Does this apply to that cool chem trick where a solution goes from black to transparent and back again a few times? I don't know enough to know if that's relevant or not, but I remember seeing that and be puzzled about how "sudden" the reaction appears.

[HPsquared]

That sounds like something sufficiently strong at absorbing light where it appears to be black at a fairly low concentration, so even if the concentration changes smoothly (maybe a sine wave) but to our eyes it looks more like a step change near the bottom.

[gnubison]

Maybe the Briggs-Rauscher reaction?

[energyscholar]

Exactly right. The phase transition analogy is powerful precisely because it's not just analogy — the same mathematical operators that describe water at criticality also describe markets approaching crashes, ecosystems approaching collapse, and cardiac rhythms approaching fibrillation.

What surprised us was how many fields derived this independently. The superheated water intuition you describe maps directly to what ecologists call "critical slowing down" and what financial engineers call "increased autocorrelation near instability." Same math, three different names, minimal cross-citation.

[kjshsh123]

3Blue1Brown has a good video on phase transitions.

https://youtu.be/itRV2jEtV8Q?si=qm51bvuo-ZIT_Pjk

Veritasium has a good video on how criticality applies to other things too,

https://youtu.be/HBluLfX2F_k?si=nK51yQVlNXz5bNSA