Moral support
At one point while I was at my dad's for Christmas, I made the mistake of trying to get an intelligent response out of my sister before she'd had tea in the morning. She refused to reply to my question until she got her tea –
I giggled gently at this at the time, but the same thing just happened to me: faced with a strange problem to investigate at work, I decided I couldn't face doing it without a cup of coffee to hand –

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Another explanation is that it's like reserves. If her plane is gliding just above the treetops, and you say "can you do a barrel roll", she'll just not, but if you fill her tank up first, she can safely, even if it doesn't actually use any more fuel than she had before. That is, you don't want to get embroiled, but once you *have* tea, then you're safe, so you can start to wake up without fear of having to think without caffeine :)
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Whereas I think your brain wanted more time to think quietly about the problem in the background, but wasn't willing to admit as such.
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I mean, I do enjoy the smell of tea, and will make myself a
Thing. Sorry. Babbling. Excuse me while I rush off to a lesson...
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That leads to stalling when the first item on the list is "Obtain Tea/Coffee". Your sister of course realised that tea was incoming without any effort on her part. However, "Update internal To Do: list" was second on the list, and so she couldn't break free until the tea actually arrived.
Once you've had the first tea of the day, you can parallelise as necessary, and thus circumvent similar stalls for the rest of the day.
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I find in the mornings I have very few functional brain cycles. If I know I need tea then devoting any of those brain cycles to anything more complicated than acquiring tea risks forgetting that I haven't had tea yet until it's Too Late. Once you're holding the tea you're not going to forget it's there (er, usually), which releases those brain cycles for reallocation towards intelligent responding. It sounds like she had enough brainspace to come up with intelligent answers, but not enough to commit to them publicly, until she had the tea. I can relate to that.
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Actually, I'm just exactly in the process of doing that now, give or take the odd spoonful of rum-soaked raisins. Perhaps I shall stop spodding and find some lunch.
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Right now, I'm finishing up looking at my morning webpages before I go and get a cup of tea or coffee (I haven't decided yet) and actually start working.
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