## Friday, May 30, 2014

### Monsters in their Prime

Tons of stuff about monsters today on my blogger feed. I think there's a blog hop, maybe? I'll investigate this matter further. BUT, did you know there are mathematical monsters? Of course that's the first thing I thought of when I saw all these monsters. The Monster and Belphegor's Prime are the two monsters of math, named so because they're just so god-damned big.
1000000000000066600000000000001 is Belphegor's Prime. Belphegor is one of the seven princes of hell, a demon of inspiration who suggests ingenious inventions to make people rich. It's not all ideas he inspires though, just those ideas people come up with stoned and drunk then actually follow through with, later using the money and the fame to just party hard and sin like a demon. He inspires those ideas. The best ideas.
ANYWAYS, you might notice that it is an evil number, because the heart of the number is the sign of the devil, 666, surrounded on both sides by 13 zeros. It also cannot be divided by any numbers except one and itself. It falls under the class of Palindrome prime numbers, because it's the same backwards and forward. OH, oh, oh and the total number of digits? 31. Yup, 13 backwards. If math represents the structure of the universe, then this number is the basis for the evil in the world. Man, I really need to spend a week talking about primes. There are so many of them in tons of categories and are insanely fascinating.
The Monster Group is the second mathematical monster, a finite simple group in group theory. This is fairly tough to try and describe in a blog post, but here is my best attempt. A group is a mathematical system that obeys four axioms (rules)1:
1. CLOSURE: If a and b are in the group then a • b is also in the group.
2. ASSOCIATIVITY: If a, b and c are in the group then (a • b) • c = a • (b • c).
3. IDENTITY: There is an element e of the group such that for any element a of the group
a • e = e • a = a.
4. INVERSES: For any element a of the group there is an element a-1 such that
• a • a-1 = e
and
• a-1 • a = e
Any system that follows the rules is a group. The Monster is a group, and more importanly it is a simple group, which just means it cannot be broken into smaller groups. Finite simple groups are the prime numbers of Group theory2.  What you should know for the purpose of this blog is this:
The Monster is a really large finite simple group. It was first constructed by Robert Griess as a way to symmetrically rotate 196,883 dimensional space. And as much as I really, really want to get deep into both simple finite groups and prime numbers and their relation to each other, I need to keep this light for today. "Symmetry and the Monster" is an excellent book though, because he attempts to explain the Monster using history, geometry, basic algebra and simple addition. In fact, it's the only "pop math" book I know of that acknowledges people know math and enjoy geometry, algebra and simple addition.

#### 3 comments:

1. I've never heard of The Monster and Belphegor's Prime, but one of my CPs is a math professor so I'm sure he has. Thanks for the interesting post!

1. Prime numbers are strange, and I've been finding not a lot of mathematicians are aware of all of them. There are tons of classes of primes, and they can stretch to infinity. Glad you enjoyed learning something new though