Jan 1, 2016
JANUARY 1, 2016 ANNOUNCEMENT
Happy new year! 2016 has just begun, and so it's worth doing another announcement for this site. Even though I dropped the monthly announcements a while back, a little while ago I thought of a change of plans for how I'll post content to this site, and given that a new year just started now's a good time to share those plans.
First off, if you've noticed, I haven't been producing as much content as I promised I would exactly a year ago. I think that's not only because I've been doing a lot of other goofing off, but also because some of the content that I planned to cover isn't all that fun to write about. I created this website because I found large numbers an enjoyable topic to write about, and I have often dropped other projects of mine when they became boring; given how much progress I've made, and the positive reviews I've gotten, it would be a shame if that were to happen to this website.
Now which topics do I think would be boring to cover? I think the main one here is all the recursive large number notations: Extensible-E, Bowers' arrays, the fast-growing hierarchy, and all the less-known ones people have come up with. Recursive notations like this are a popular thing for starter googologists to make. Every so often on Googology Wiki a user will come up with some recursive notation and share it on the wiki. Those don't really interest me that much anymore. While the first few notations you'll find out about can be really invigorating, eventually, when you scour through all the notations people have made, they start to get repetitive. Some of those notations are very poorly designed, which can be frustrating because occasionally users will get their notation posted on the wiki as an article with a vibe of professionality when it's so clearly thrown together that I don't even know what to say.
Instead of focusing on all these recursive notations, I want to try and focus more on other aspects of googology. I planned a while back to start a subsection on fast-growing sequences, but I still haven't even started that. Those sequences are a part of googology that many people acquainted with the subject don't know much about, even though those are actually the aspect of googology that's relevant to "professional" mathematics. I promised I would give some coverage of those sequences, like Kirby-Paris hydras or Harvey Friedman's sequences, but that hasn't happened.
So what have I gotten done in 2015? In the first few months of the year I released my last few section 2 articles in fairly rapid succession. Then I released a page on Bowers' arrays up to 4 entries, then part of a page on Sbiis Saibian's childhood googology, and for the last few months I gradually switched gears to my number list followed by reformatting all the pages of my site in general, mostly small tweaks to make it better. The number list is easily the most popular part of my site, so after I finish reformatting I hope to work on the list pretty intensively. After I feel I've made all the improvements I need, I'll start writing articles about large number sequences.
Come to think of it, maybe I should just cut to the chase and give an explanation of, let's say, the deal with TREE(3), something which I've seen described as pretty simple but doesn't really have laymen explanations on the Internet. I really think that at least at some point I should make an article on that. If I followed through with how I originally planned this website to go, only amidst dozens of articles where I exhaustingly come up with fanciful definitions of higher BEAF and explain the gimmicks of the clusterfuck that is all the variant ordinal notations and figure out how Hollom's hyperfactorials work and whether they're actually as powerful as he says they are and cover a whole bunch of miscellaneous notations would I get around to covering TREE(3). But I seriously think I could at least give an explanation as to how the sequence works even if I'm not quite ready to explain its size using whatever ordinal notation in the fast-growing hierarchy I end up using. Same goes for Kirby-Paris hydras and whatever else.
I think I'll still cover stuff like Bowers' array notation, it just won't be as high of a priority because it's been covered by so many other people. I can't make any promises as to when those articles will be released, just that they won't be as high of a priority.
Long story short: Over this year, expect overhauls to section L of this site followed by progress on section 3.3 which will cover fast-growing sequences that lead to large numbers. Recursive notations like Bowers' arrays are less of a priority.