9,931 Pages

LittlePeng9

aka Penguin!

My favorite wikis
• I live in Poland
• I was born on May 23
• My occupation is http://youtu.be/sDj72zqZakE
• I am your local penguin
• PSA - IRC

December 23, 2016 by LittlePeng9

Hello everyone. Today I am bringing you a public service announcement regarding our IRC channel.

Over a past few months we've had many new users join our wiki, and our IRC channel isn't really well-advertised anywhere. Because of that, I wanted to semi-officially invite all of you to join us there! You can find all the instructions written up here. Let me also remark that the chat at many times is rather inactive, but if you see me (Wojowu) online, feel free to highlight me so I know someone is around!

See you all there!

(btw, if you want to be noticed, I recommend staying there for more than 85 seconds (I am looking at you, Mush9))

• LeaF - Aleph-0

November 13, 2016 by LittlePeng9

Recently a BMS artist called LeaF has released a song called ℵ0 (Aleph-0). I thought some of you might be interested by this because of the cardinal number reference in the title.

You can check out the song at the composer's SoundCloud, or on Youtube, accompanied with the official video (which I personally very much like). You can also check out the BMS chart of this song, if you want.

• First order oodle theory - clarification

October 9, 2016 by LittlePeng9

I really should have made this blog post sooner than after two years, but oh well, at least I am making it now. In what follows I will refer to my old blog post.

TL;DR: When I have defined FOOT (and BIG FOOT) I have a somewhat bottom-up language to describe it, starting from the universe of sets and building up. Taking this too literally leads to many serious foundational issues. What I should've done is emphasize the top-down nature of my construction.

Long story short - I have described FOOT in terms of some unheard-of concept of oodles, only saying that they are analogous to sets, defining in it what I have called "sets", "ordinals", which were ought to resemble structures familiar to all of us, then iteratively extending the language to …

• A blog

September 12, 2016 by LittlePeng9

Hey guys, I have a blog on Wordpress now. It's not going to be written with googological purposes in mind, but I thought you might still be interested.

• Computing digits of mega

July 5, 2015 by LittlePeng9

Yesterday while talking to Sbiis on IRC he has mentioned the topic of computing more than 14 last digits of mega. Later I have decided to see what I can do. After about 5 minutes of thinking, I have figured out an iterative algorithm to find the digits of that number, and the day later (i.e. today) I have found simplification. I told vell about it, he said it should be possible to write this in Julia and then execute. He has found the following, short, code:

The idea of the algorithm is to simply iterate map $$x\mapsto x^x\mod 10^k$$ 256 times (in order to find k digits). However, it's not immediately clear why this algorithm works: after all it's not true in general that $$a^b\equiv a^{(b\mod m)}\mod m$$. Now I'll explain why it works anyw…