>Power consumption grows with the square of frequency
You may be thinking of the power of a mechanical wave, which is composed of the kinetic energy of particles in e.g. a vibrating string. A CPU's power consumption is linear with regard to clock frequency, and I'd hazard a guess the brain is similar. If consumption were quadratic, you'd basically be able to get power-free computation by parallelizing to a large number of very slow processors.
> A CPU's power consumption is linear with regard to clock frequency.
That doesn't sound completely accurate. It's fairly well known that when overclocking processors, the "highest" achievable clocks can often take substantially more power than the frequency increase. eg 25% more power for (say) 8% frequency increase.
So, it might be a linear thing for most of the range, but it doesn't seem to be 100% linear in all cases.
I'm talking mainly about dynamic (switching) power. I'm not sure about overclocking, but I believe it tends to involve also increasing voltage (power does scale quadratically with voltage) and a higher internal temperature (this will also lead to increased power). The parent was looking at the lower end though and implying that there are big wins to be had if only we could do our computation at around 200Hz, which I don't think is justified.
You may be thinking of the power of a mechanical wave, which is composed of the kinetic energy of particles in e.g. a vibrating string. A CPU's power consumption is linear with regard to clock frequency, and I'd hazard a guess the brain is similar. If consumption were quadratic, you'd basically be able to get power-free computation by parallelizing to a large number of very slow processors.