Well I'm okay, apart from a week's pretty horrible toothache. My work is kinda chill - I feel a bit underemployed at times. But it's partly because I'm doing stuff that generates work for others, and then I have to wait for them to do it before I can do my next bit. I definitely get more done when I'm at the end of a chain like that than in the middle. Out of work, I want to enter Grant Sanderson's Summer of Math Exposition competition this year, and I've co-opted Raak as maths consultant. Deadline for that is mid-late August so I've still got weeks to go. I think/hope the work is in the last 10% (the part that takes 90% of the time) but... we'll see.
[SM] Did you get my answer suggesting that the Collatz jelly has fallen off the wall again? :) I just noticed I sent it to the zen[randomnumbers] address instead of your readable email.
[Raak] I did receive it - the darn webmail form constantly auto-refills the zenxxxxx address every time I tweak the email (such as by adding an attachment), and it's easy to fail to catch it. My short answer to the jelly question is that I don't think it matters because even when the numbers rise, their 'rail number' still ticks down inexorably. Showing that numbers can rise as high as they like and yet it still doesn't help them escape is a key thing I'm trying to make clear. But you exposed an area where I'm not saying what I really wanted to - so I'll be fixing that and sending you a reply, probably at the weekend. I was also sidetracked into wondering whether numbers in the sequence have a provable 'high water mark'. If you could show that no number n can ever rise above, say, 2^n, that could be another clincher. 2^n ought to give sufficient headroom, right?
[nominative etymology] There's a place called Kenovay on the island of Tiree, which looks like a phonetic rendering of its Gaelic name Ceann a’ Bhàigh, which means "head of the bay", or Bayhead ("the parst of a bay most distant from the larger body of water with which it is confluent"). There are a couple more Ceann a’ Bhàighs and Bayheads in the Hebrides. So that could be the origin of the name.
[blame] Turned out the issue was that ā, entered directly from the keyboard, apparently upsets mc5 to the point where it can’t even. It works over at Dan’s place.
Does anyone know if ISIHAC ever played Just A Minim with Aretha's "Respect"? - I found myself giggling a little too much imagining the "sock it to me" and "just a little bit" parts in that game. For that matter, and plummeting to the opposite end of the musical quality spectrum, Gina G's "Ooh ah, just a little bit" might have been rich territory too.