I see it as kind of analogous to when you starve a circuit/device of power - it behaves in unexpected ways, revealing implementation details.
Some examples that I remember: after a particularly long all nighter (I was a freshman in college and wanted to try it while I could still do it by choice and not necessity) I was editing an article I was writing for the school magazine. I was starting to fade and realized that I couldn't read and comprehend well-formed, meaningful sentences that I had just written.
I've noticed that when sleep deprived I notice different things and have a more diverse set of emergent thoughts/recall events. For example, today I noticed the plug for an electric oven at a restaurant I have not only been to at least 100 times, but have worked at for months. I randomly remembered the lyrics to China's five-year-plan song walking home from class. I will suddenly remember and think fragments in Spanish, despite not touching it for years.
Truly, it appears the nature of effective cognition is restricting all of the many responses to stimuli to those that are useful and relevant, and I think the parts of the brain that do that may have 'fallen asleep' in all those instances.
The weird thing is that after the migraine is over I can actually remember most of what happened during it, so somehow things are still finding their way into my long term memory - though it's mostly just conversations like "hey, I'm having a migraine, I'm going to lie down for a few minutes, because I'm having a migraine, it's affecting my memory, so I'm going to lie down, I think this migraine is affecting my memory" "ok dude, take a break" "woah, how did you know I need a break? I was just thinking that I should take a break, because I'm having a migraine, and it's probably affecting my memory. Did you know I get migraines that affect my memory? I should probably go lie down"...
Perhaps your migraines sometimes trigger a waking dream state, or something functionally equivalent, where you're still seeing the real world instead of one your mind has created, but parts of your brain that are used to interpret your sensory input have switched to dream-mode.
 Not formally diagnosed as migraines (migraines don't typically cause a single headache that never goes away for years, but just fluctuates in intensity), but my sister has been so I suspect there is a link.
Weirdly I can still code easily, even keeping in my head high level module interactions and abstractions, to low level implementation details, but I'll occasionally stop, stare at a word, convinced that it's spelt wrong, google it and see its correct, and go back and stare at it - because it just feels wrong.
When I've reached this point, I know it's time to break!
The longest its ever lasted was about 1.5 hours. Usually about the time the freight-train of pain arrives, everything goes back to normal. Of course then I'm in no mood to read anything anyway.
Focus and sleep are clearly related. When my sleep apnea goes untreated, I feel like I suffer from ADHD. In fact, I was certain I had it until I received treatment for SA. Its incredible what poor sleep can do to us. The list of things that go wrong with poor sleep is pretty long.
If you're getting this often, I would get checked for SA.
A relative of mine had tinnitus which was cured by hearing aids; the theory offered there was that tinnitus was effectively the brain turning the automatic gain control on hearing up too far.
Is the brain solely a computer? I don't know. But it certainly contains information processing aspects that we should study and understand, and as we understand them with these tools, we may find other frameworks to apply at different (perhaps higher) levels.
Doesn't that still hold true today with string theory and social sciences?
Now, it's potentially the case that string theory makes predictions for a given model that can't be practically tested. That's definitely an issue. Another issue is that we haven't yet pared down the possibilities in string theory to a parameter space that can be reasonably searched experimentally.
I don't know about the social sciences. That's painting with a pretty broad brush, IMHO.
Until then, it's just a child-AI, dependent on human brains to be designed and optimized.
And how long time do you give it? The human race haven't solved that problem in some 20k+ years. If we build an AI today, would you wait that long to decide if it is "true"?
But someone else being smarter doesn't mean the AI isn't intelligent.
Inteligence is inteligence regardless of origin.
Might as well call us AI Accidental Inteligence.
I kinda like Engineered Inteligence.
The brain is not just something you dump things on. It's not a big truck. It's a series of tubes. And if you don't understand, those tubes can be filled and if they are filled, when you put your thought in, it gets in line and it's going to be delayed by anyone that puts into that tube enormous amounts of material, enormous amounts of material.
Having spent enough time in extremely sleep-deprived states for projects recently, I've experienced firsthand a lot of funky stuff going on (e.g. falling asleep and waking up with a full page of class notes in front of me, or realizing that I've started 'dreaming' while editing a document, the dream being seeded by the words I was processing.)
If it was actual noise it would have absolute minimal statistical chance of having any coherent structure.
So "meaningful" output doesn't necessarily mean the input wasn't random.
Last nights had Donald Trump, my wife and Jennifer Love Hewitt. There were riots going on and people reading newspapers with moving video ink. There was an old book called "The Fall" that was filled with fascinating ink drawings of ritualistic acts (eg: a man sat cross legged on broken fragments of his own arms). Etc. That kind of stuff. Had a full story.
Noise on the line in Brain-space could still be the case, but if so we can learn something from that noise regarding the way brain structures work.
What I'm saying is if it is just noise, then the noise must be feeding into an entire projective area of creativity that amplifies that noise, not just locally but over time, and in ways that maintain consistency.
Really fascinates me
I've had some dreams like short sci-fi stories. Some with time travel/causality loop tangles as plot. Some with twists. Complex character and places.
Mangled data with structure are not noise -- at worse they contain some noise (like a dirty dataset).
This also only works well for scalar fields, not associations (pointers in the C program's case) and more finely grained items.
Also, where would that (the definition of the "struct") happen with the brain? Is there any literature showing anything similar, that we have memory fields that pre-correspond to specific objects through some mechanism?
Besides, dreams can have very clear structure and narrative, which takes them outside the realm of what can be achieved with noise, unless the "struct" has fields that correspond to things like emotions, faces, narrative changes, etc.
To take another example, a self-driving car might make a decision to switch the lane. If you randomize on that level, it will randomly switch, but the movement will still be smooth, because this is done one or more layers below.
We examine the circles not to learn about the data from which those circles are derived, but rather to learn about which structs and other properties are defined in the system. We might find circle struts, square structs, triangle structs, but never spheres, boxes, or pyramids. Or maybe some people (schizophrenics) have the metaphorical three dimensional structs and others do not.
E.g. noise in the brain might be an increased incidence of errant impulses/signals. There's evidence that sleep involves pruning meaningless connections - noise in this case might mean signals propagating farther than they ought.
Noise was meant in an abstract way, not statistically random noise you see in physical circuits.
I've seen very specific semblances in coffee spills, knot-holes, etc. The reason they're not movie-like is because they're still and static, and not connected directly to my brain.
Dreams have the advantage of being on the bare wires, whereas Rorschach tests and the like are air-gapped.
On the other hand, I'm currently sleep deprived due to insomnia (it's 1320 on Tuesday, and I've had less than an hour sleep since 0900 on Friday), and the effects have been much more gradual. It's a steady build-up of fatigue and general "brain slowness" for lack of a better word (e.g. I was playing Picross last night, and puzzles that normally would take me less than ten minutes took me more than half an hour), but I'm more or less fine - no visual effects, my thoughts are coherent, and it doesn't feel much different to how I'd be after a long day working (just significantly more severe).
The dissertation was partly very poor planning on my part, but I also stumbled on a doctoral thesis that more or less disproved the central tech. behind my dissertation less than a week before the final deadline, which gave me two options:
A) finish up what I'd done, knowing it was fundamentally flawed and that I'd never be able to defend it if called for a viva voce (unlikely, but a definite possibility)
B) rewrite pretty much the entire thing (~30k words) to take a different approach, re-implement the hardware (audio filtering; didn't help that the spec. sheet lied to me and said it had an FPU but actually just emulating floating-point in software which was unusable slow), and come up with a convincing conclusion explaining why a year-long project produced nothing particularly useful.
I went with B, hence the 100 hours of solid work, and it went OK (mark was a marginal pass, but a pass nonetheless), but I'd hate to do it again. It took me 3 or 4 days to start feeling normal and alert again, despite sleeping 18 hours after crashing once it was finished.
The current insomnia is really weird though. I saw my GP this morning, took a fairly hefty dose of sleeping aids (15mg diazepam on top of the 20mg tamazepam and 75mg promethazine I was already prescribed), yet somehow feel more awake than before taking those, despite the fact I'm only about three hours away from having had less than than an hour sleep total in the last six days. Honestly, I just feel bored more than anything at this point (hence this somewhat unnecessarily long post :p) - I don't have the physical energy to do a great deal, but mentally I feel more or less normal (though I suspect when I finally do get some sleep, it'll catch up with me and I'll have a rouge couple of days).
 FWIW, I've also got Zopiclone, but I saving that as a dug of last resort. The benzodiazepines cause me no side effects, but last time I used the Zopiclone it was rather unpleasant - it caused mild hallucinations (my room looked like it was bathed in a lemon-yellow light, despite it being the dead of night and no lights were on), and it had a strong amnesiac effect (my memory of the night pretty much goes "I'm in bed, why is everything yellow?", "I'm in the bathroom, how did I get here?", "I'm back in bed, but it's three hours later", and I have literally no idea what happened between each thought. It's just like a jump cut in a movie - there isn't even a hazy memory of I did something; it literally just goes from being in one room to being in other, despite there obviously being a chuck of time missing. It's pretty disconcerting).
I'm also looking into evidence that a blood sugar deficit may have been involved. Reportedly some of the techniques used to maintain alertness can result in increased glucose metabolism coupled with the unfortunate side effect of having zero appetite.
Partial sleep in the context of augmentation of brain function
Inability to solve complex problems or errors in decision making is often attributed to poor brain processing, and raises the issue of brain augmentation. Investigation of neuronal activity in the cerebral cortex in the sleep-wake cycle offers insights into the mechanisms underlying the reduction in mental abilities for complex problem solving. Some cortical areas may transit into a sleep state while an organism is still awake. Such local sleep would reduce behavioral ability in the tasks for which the sleeping areas are crucial. The studies of this phenomenon have indicated that local sleep develops in high order cortical areas. This is why complex problem solving is mostly affected by local sleep, and prevention of local sleep might be a potential way of augmentation of brain function. For this approach to brain augmentation not to entail negative consequences for the organism, it is necessary to understand the functional role of sleep. Our studies have given an unexpected answer to this question. It was shown that cortical areas that process signals from extero- and proprioreceptors during wakefulness, switch to the processing of interoceptive information during sleep. It became clear that during sleep all “computational power” of the brain is directed to the restoration of the vital functions of internal organs. These results explain the logic behind the initiation of total and local sleep. Indeed, a mismatch between the current parameters of any visceral system and the genetically determined normal range would provide the feeling of tiredness, or sleep pressure. If an environmental situation allows falling asleep, the organism would transit to a normal total sleep in all cortical areas. However, if it is impossible to go to sleep immediately, partial sleep may develop in some cortical areas in the still behaviorally awake organism. This local sleep may reduce both the “intellectual power” and the restorative function of sleep for visceral organs.
Fascinating stuff, imo. I've definitely felt the difference between partial sleep restedness and total sleep restedness, and the idea of sleep pressure seems to line up with my experience and with my idea of explorable, falsifiable models of phenomena. The idea that we dream while processing internal organ information is beautiful to me on multiple levels- maybe memory consolidation has a whole lot to do with pre-existing organ health! Maybe instead of the idea that we dream with only our heads, we dream with all of our organs- just imagine how differently Jung would interpret Pauli's dreams if he knew about this!
I wonder if it extends to reptiles, fish, etc.
For me it's in meetings or when someone's telling me a vital piece of information I must remember.
I am glad that functioning of the brain is understood much better. Also, this could be utilized if we could find ways to increase focus, maybe even artificially, well artificially until brain gets trained for full flow state for example.
Small price to pay if it gives you an edge in the valley!