Interesting! Quite by accident, I became aware that I was thinking more clearly and with a sharper focus after a period of modest fasting - this in the few months before I was diagnosed.
(cue image of scantily-clad eastern mystic on mountaintop living on one lentil per day...)
I've not performed any robusts tests, but I'd say that I am at my sharpest, mentally, between 4.0 and 4.8 - even when I happen to have tested a bit lower, down to 3.8, I'm mentally still sharp although a little physical tiredness creeps in.
When I was on Met, I did hit 3.5 and 3.6 on a couple of occasions; then I did feel a bit odd, but I was in the midst of a serious low-carbing weightloss regime. I'm still reasonably lowcarb, but backed-up by a few mins of exercise half a dozen times per day, plus a longer period of reasonably brisk walking.
Hit 5.0 or above and I'd say I've slowed back to normal and in the days when I used to hit 6 or above I'd really notice it; that feeling just like after a big lunch and a couple of pints.
Obviously, this is all anecdotal and it is difficult to self-analyse with any great accuracy, but when I occasionally look back from end-of-day perspective at the complex mental tasks I've sometimes achieved in an afternoon when I've skipped lunch, I'm pretty sure it is a real effect.
I don't know how much glucose you'd burn off with 6 hours of intensive Sudoku, but the scalp is well supplied with blood for the very good reason that the brain does generate a lot of heat that needs to be carried away; that certainly indicates that it consumes a fair amount of fuel too.
Conversely, watching too much reality TV or soap operas probably shuts the brain down, causing BG to rise...
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