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Oct 26, 2015

OCTOBER 26, 2015 ANNOUNCEMENT: PLANS FOR THE NUMBER LIST

Hey everyone! It's been a while since I last did an announcement for this site, hasn't it? Remember when I planned on doing announcements on the first day of each month? That clearly didn't last long. April 1st isn't the best day for announcements because it's April Fools Day, and I guess after that I didn't bother with the first-day-of-the-month plan and forgot about it. But now, I do have quite a lot to say, because I have some pretty big plans for the most popular part of my site, the Pointless Gigantic List of Numbers.

Before we start, I'd like to apologize for being so much slower in site progress than I promised. I hoped to be done with section 3 in fall 2015, but here I am smack dab in the middle of the fall and still far from finished with section 3.1. I'll be honest here: I haven't bothered working on my site all that much, doing a lot of other goofing off on the computer. It's not really because I'm flooded with homework either, because my horrendous time management skills cause me to unintentionally intertwine work time with goof-off time.

OK, now for the stuff about my number list. Lately I've been working on it quite a bit: I'm on a phase where I'm recoloring it so that only the names of the entries are colored while the descriptions are colored black, so that the bold names of the entries and the section headings stand out more - also I've been improving entries as I go. I've realized that the later parts of the list could use a bit of an overhaul. When you get to parts 5 and 6 of my list, a large portion of it is scrolling through descriptionless Saibianisms, instead of all these numbers with cool things about them, not to mention that I screwed with the names of some of them. To fix that, I plan on severely truncating those parts of the list. I think I'll make a goal to have every entry in my number list have some kind of description, or at least almost every entry. Maybe the later parts of the list will be trimmed down so much that I can combine them into one. Maybe those parts were already short enough to merge together to one page that falls within the Google Sites page length limit. Maybe I won't even have a separate part 7 of the list because it doesn't have enough entries worth including. I don't know. All I can guarantee is that the later parts of my number list will be shorter than they were, to allow them to be more interesting.

One thing I'm not yet sure about is how to deal with the Bowersisms above goppatothplex, which is arguably Jonathan Bowers' largest well-defined number. It's become more and more accepted in the googology community that Bowers' higher googolisms should not be presented in a way that gives us the impression that they're properly defined numbers. Maybe I should do something about that. I think I might replace his higher googolisms with likely approximations in the fast-growing hierarchy (like kungulus ~ fΓ0(100)); some people have qualms with even that, but I think it's not such a bad solution. As for the even higher numbers like the bukuwaha and whatnot, I'm not sure if I'll even include those since we kind of have no idea how big those likely are because they're so very ambiguous and all. I think I'll keep my entry for the meameamealokkapoowa oompa (his largest number) for famed numbers' sake. Maybe I won't include many other googolisms around that mysterious range either; for example, the higher hyperfactorial array notation numbers reportedly reach very far through the fast-growing hierarchy (past ordinals like the Takeuti-Feferman-Buchholz ordinal), but I honestly have no idea how most of that notation actually works, or how reliable those claims are. Maybe I'll stick in a few numbers as example values for numbers around that range and leave it at that. It might seem disappointing to do that, but if I'm being honest, maybe it's for the best, because the early parts of my list are in my opinion the most interesting.

After I finish up at least the recoloring project, I'll round out my infinite numbers list. I could potentially add entries that lead to a logical conclusion to the list without dwelling too much on the progression through super huge ordinals. Some people have been waiting for an update to that long-untouched list.

Long story short:
  • I plan on cutting down long stretches of random googolisms on the later parts of my list, in order to make the later parts as interesting as the early parts;
  • I will likely merge the later parts of my number list;
  • and after at least finishing the list recoloring project I'll finish up my infinite numbers list.

—Cookie Fonster
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