ESA/NASA Hubble Space Telescope image
Mathematicians Chase Moonshine’s Shadow <-- link here: once again, mathematics turns out to show the way to solving the universe! I've pretty much forgotten everything about the classification of the finite groups. This was a logical proof; one so large, it takes up four thick volumes. But, in the process of proving it(no, I didn't know those four volumes; I just read various articles including notices at the American mathematical society), they found these monster groups. Abstract algebraic structures that, geometrically, define symmetry. One could say quickly, aRb, bRc, and aRc, can kind of constitute a group, where R means some relation like +, or some other binary relation. Mathematicians proved a classification of all possible finite simple groups. Simple groups can be likened to prime groups. There's subgroups, and hence factor groups, and so you can kind of see from there an algebra of abstact objects/groups. Monster groups are abundant element groups. Like astronomically large finite groups. They found them through a kind of taking a slice of them process. So, finding each one(26 total) was a major accomplishment in itself!
I suppose I could mention something about how mathematicians were able to classify every possible finite simple group. Mathematicians back around late 1800s found that a single lie group can stand for an infinity of finite groups! They tried classifying lie groups as well. Likewise, they found a finite list of groups. They proved most through the 20th century, but one - E8. The classification of finite groups was, more or less, proved in the 1980s. E8 was proven a few years ago - by computer. It took a computer program to make up the deductive structure. So, here, with the classification of finite groups and the solving of E8, we have mathematical proofs beyond the general comprehension of a single human. Then, there's the monster groups, which if you read the article, may hold the clue to quantum gravity, not to mention number theory!
- Science/Archaeology goodie/extra,
Some English art(Roman times) depicting wolf being chased by a hair(a rabbit)!
No comments:
Post a Comment