"Happy times together we've been spending
I wish that every kiss was never-ending
Wouldn't it be nice?"
My daughter Emma, upon hearing those lines, asked, "But Dad, if every kiss was never-ending, wouldn't that mean there could only be one kiss?"
"Hey, that's right," I responded.
To which my son Eamon replied, "No, there'd be zero kisses."
"Well, he'd never finish a kiss. And what's more, he'd never even really get any fraction of the way into a kiss."
(His point here being, by the way, different than the Zeno paradox -- he wasn't saying you could never cover any finite time of kissing, but that no finite amount is ever more than 0% of an infinite kiss. Similar problem: Throwing a dart at the real number line from 0 to 1, what is the probability you'll hit 2/3? Answer: 0!)
Discussing this with Wabulon, he noted that there are (theoretical) super-Turing machines that can do x amount of processing in time t, then x more in time t/2, then x more in t/4, and so on, thus completing and infinite amount of time.
"Good point," I said, "but given that Brian Wilson couldn't even get out of bed for around 20 years, I don't think he is an instantiation of one of those machines.
But, thinking it over a bit more, we figured out a way that Wilson could make his kiss never-ending for the rest of us, while it would end for him.
What did we come up with?
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