# Understanding this metaphor involving e-mails, chaos and phase transitions [closed]

I asked this question on the English Stack Exchange and people advised to try get the answer here. I can’t get the idea of metaphor in the last sentence of the following quote:

Instead, email operates more like chaos theory: at some point the time/energy required crosses a critical threshold, an unpredictable, invisible boundary. It undergoes a phase transition, like ice changing to water and then to steam. The parameters change and the effects explode, cascading across the rest of your workflow with mounting consequences.

## closed as unclear what you're asking by Kyle Kanos, CuriousOne, Norbert Schuch, Gert, John RennieFeb 1 '16 at 6:41

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• There are at least three distinct metaphors there, and they are badly mixed, inconsistently used and not very well thought out from a physics point of view. It just means that at some point handling email dominates your time and you get no actual work done. In the end, however, I don't think this is a physics question at all. You were given poor advice. – dmckee Jan 31 '16 at 16:06

As somebody who works in the field of chaos theory (for whatever that’s worth), I confirm Dmckee’s assessment: There is no reasonable relation to any concepts from chaos theory. There is, however, an attempt in your quote to relate this to the phenomenon of criticality – which is not chaos theory, but like chaos theory is related to the field of complex systems.

Applied to e-mails, the concept of criticality can be summarised as follows:

• Let $φ$ be the average number of e-mails sent as a consequence of a given e-mail.

• If $φ<1$ and there is no mechanism (other than other e-mails) causing people to sent e-mails, e-mails will eventually die out.

• If $φ>1$, there is an exponentially growing cascade of e-mails and we will eventually drown in them.

• Therefore, there is a critical point at $φ=1$ separating the two phases described above and marking a phase transition.

However, I cannot see any reasonable connection of the above concept to your quote. The time a given person spends on e-mails does not affect $φ$ in general and thus there is no critical point to cross when increasing the time you spend on e-mails. Moreover, this is neither unpredictable nor invisible nor is there a cascade involving the rest of one’s workflow. Finally, I fail to see any other way to apply the concept of criticality to e-mails.

• Didn't know that. Done! – AlinaSaidova Feb 1 '16 at 10:16