You can practice regulating exhale rate in a pool or bath by blowing bubbles. I find it helps with freediving exercises where you fix the number of breaths in between reps.
In quantum mechanics, what you can measure experimentally (observables) are given by integrals. You can do the integrals computationally, but then you only have an empirical understanding of how the observables behave when you change some parameter of your experiment.
In our experiments, we need to know how the frequency of an electromagnetic resonator will change when we couple it to a quantum system. We calculate these frequency shifts with integrals. Being able to calculate these integrals analytically for some limiting cases helps us understand the dependence on the parameters. And usually you can patch the limiting cases together and not even have to compute the integrals numerically.
Random thoughts from physics researcher:
- Too much imitation delays innovation.
- For all the emphasis on high risk research, the system doesn't reward it.
- Creativity isn't valued as much as it should be.
- negative results and failed experiments hold back careers but are signs of attempts at innovation
- the VC world may understand that only 1/100 projects will be novel and perhaps successful, but funding agencies don't
In our physics research lab we use some COTS components down to 10 mK. Many passive components no longer work and we have to use C0G capacitors and NiCr resistors. Only some discrete SiGe and HEMT transistors will continue to work. But then our thermal budget is 50 uW so design is difficult even if the components remain operational.