paranoia, again (also: i love walks)

i'm getting prone to paranoia.

last saturday i was writing up some of the technical parts of a manuscript, and at some point i stopped and rubbed my eyes.

then i looked at the top of the page, one more time.

i don't see it.
why should that weak-star limit exist?
..
..
.. this looks like nonsense ..

.. and then the paranoia kicked in.

for most of the day i was completely torn: while trying my best to work out a counter-example, i was simultaneously hoping that it wouldn't work [1]. it got to the point where, having promised to meet friends for a symphony, i paid the ticket and couldn't appreciate the performance.

forget brahms! he means nothing to me:
what about banach-alaοglu?

after the second part, i ditched my friends, went home, thought through thoughts that didn't work .. went to sleep fitfully ..

.. woke up on sunday, averted my eyes from the pages on my dinner table .. decided to go on a walk instead ..

.. and while sitting on a park bench, watching dogs and humans, waiting for rain .. wondering how it is convenient for the human to leash the dog and restrict its movement. as long as the leash is long enough, the dog is not unhappy.

suddenly, it hit me: leash .. not too short, not too long ..?
didn't i have this one other hypothesis? ..

.. so i bolted home and leafed through the pages of my notes:

sure enough, at the bottom of the last page before my paranoia:
based on this context, without loss of generality .. [2]

and then i sighed a great sigh, powered on my laptop, typed furiously for a few hours, and then called up a postdoc friend to have a beer.

epilogue: on monday i realised that the proof is even simpler. once one makes use of this hypothesis, you can argue essentially without weak-star limits ..

[sighs]

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that said, if you're like me, then: never think and mark up LaTeχ at the same time.
also, get enough sleep and take an occasional walk.

on a related note: my students have term papers due tomorrow .. and rewrites are due in two more weeks' time ..

.. and i was really hoping to finish this manuscript before that.

[sighs]
plans change, i guess.

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[1] i've heard of the word Schadenfreude before, so this could be a strange case of .. Selbstschadenfreude! this may be a personal contradiction, but not a mathematical one! q-:

[2] while typing later, i couldn't help but think about the usual twist endings to the show house, m.d.