So brain waves are the net measure of the highest electrical activity of those many millions of neurons that can be detected outside the cranium: it is not the activity of all neurons, but since it is scientific fact that the cortex and especially the frontal lobes are involved in intelligent thought, social interaction, learning and personality then the measure of brain waves is quite likely a proxy of the most important activity in the brain. Pretty lucky that it can be measured without drilling through the skull!
Why does the brain have wave like rhythms and combinations of longer wave Hz with short burst type activity such as in beta waves ? Why do conversely the dominant wave form detectable in sleep and relaxed thought have a higher amplitude ie signal strength while slower Hz ? What also does the Gamma relatively high Hz wave pattern tell us when it can be seen as associated to enlightenment experiences and “deep wisdom” ?
Fundamentally then the brain can be seen to work in a non chaotic way: there is both an underlying pattern in the main amplitude long waves, with a periodicity parameter, and then the shorter waves which appear more random but are still "Up and down" and change when the major wave changes amplitude and frequency.
Why does the “measurable and important brain” create waves and why do we actually need wave patterns?
Well as a mol biologist, it is known that neurons require time to carry out various “recharging” functions and also biochemical summations at their synapses, followed by a degree of clearing out receptors by breaking down molecules so that new signals or summations can be made at the synapses.
Even silicon wafers have their physical limits of how many circuits per micron and how many of opening-closing each logic gate can facilitate per millisecond. Chips also get hot the denser the circuits are packed and the more calculations required per second.
So there is quite another fundamental issue arises quite a lot more fundamental than recharging complex biochemical pathways: heat - the brain is dense and uses and fluid heat exchange system to dissipate heat: These are not an ideal combination within a solid spherical enclosure! A common way in nature that biological systems cool themselves is by cycling the activity. This applies to many things, from bombardier beetles boiling defence spray to the way lizards move in the dessert.
However I feel from my first delve into this whole topic for over 25 years, that these two bio-physiological requirements are not the be-all-and-end-all of brain waves: they are not the reason for higher thought being associated to brain waves: rather the whole wave activity is likely to have evolved into a meta system from this basal need to dissipate heat and regenerate biochemical entities.
In other words these two characteristics of multicellular neuron systems, brains and spinal cords, actually became a meta operating system in its own right : it became a system above the biochemical processes that then actually began to feedback and influence the biochemistry in order to perform higher and higher neural functions ie mental activities such as motor, reasoning, feeling, considering, summating, calculating, evaluating risk, and interacting socially.
In a way brain waves may be the like the winding of the earliest computers: these calculation engines are wound by hand- this is a good analogy- there is a good deal of set up of the system by adjusting wheels or pins and then the system calculates at a higher hertz, or rather literally RPM! Without the set up and the fast running the two cannot function on their own. On the one side we would be locked into a pondering coma like status, always loading up for the reasoning but never releasing the number crunching mechanisms to come to a resolution in time. Or alternatively, the whole high hertz system running without any pre-programming, just chaotically, producing nothing of any sense or repeating eternally a single programme.
Well being can be in fact defined by the reasonable ability or habituation to changing gears, especially out of the demanding Beta ( and perhaps for some, the loading from the theta wave periods in day dreaming, loose reasoning and REM associated sleep). We need to shift gears in order to have well being. We cannot be happy or relaxed with two much beta and we cannot be motivated and fulfilled without these periods of intense medium high frequency beta waves.
Another analogy is to look again at the modern computer: it has in fact several layers of operating system- the hard cored logic on the chip, like the physical, biochemical and neurological structures in the brain, then the binary commands recognised by these hard circutis and operating them in to different parameters and tasks, on top of this again, then the machine code software feeding into this and then the assembly language or higher programmer language being compiled to the lower level software, and on top of this then the operating system like Windows tm. That is what you just need to turn on and be able to start to think about carrying out a meaningful function.
Unlike the brain though, computers have a maximum Hz for logic gate calculations while all activities relating to functioning can be considered directly related to demand if not actually linear in relation to programmes running. Unlike the brain then, computers dont need to work in waves above the required or available hertz capacity. The limiting factor is also heat. Perhaps computers would benefit from working in more controlled -ccyclic ways, and perhaps they do now!
Finally to bring in another set of ideas based on the computer " onion skins" of layers of operating systems for actually getting stuff donw: In the brain wave system we have by in large only measured EEG from outside the brain and this tends not to detect deeper sources of signals or the gamma wave activity when it is sublimated from recordings by the higher amplitude waves from the cortex. Perhaps there is another meta system which uses gamma waves to disseminate learning experiences for example ? Or do the low amplitude, yet intense gamma wave activity stimulate higher activities, awaking them or signaling the need for gear shift from sleep to beta ? Perhaps the longer waves carry more fundamental calculations or summations rather than serving merely a heat and biochemistry care-taker function, and wash forward the summations of the more hectic activity through different neural pathways or by being a meta signal within the current pathways, thus exploiting more from the system being carried like an FM signal ?