25 January 2011

Workout notes With Lynn. Yoga, then 3 mile run (2.3 miles, conked out, then .7 miles more; 10:10, then 4 reps of 0-1-2 at 9:30, then 7 minutes more), 12 minutes elliptical, then 2 miles of walking at 25:40 walking on the treadmill (some hills).
Yoga was ragged, my knee doesn’t quite straighten all the way nor does it bend all of the way.

I am getting stronger but I have a long, long, long way to go.

What I am doing: my latest blog post on Lebesgue integration and measure theory.

Posts
Here is an advance in number theory (not my area, but interesting nevertheless):

For centuries, some of the greatest names in math have tried to make sense of partition numbers, the basis for adding and counting. Many mathematicians added major pieces to the puzzle, but all of them fell short of a full theory to explain partitions. Instead, their work raised more questions about this fundamental area of math.

Emory mathematician Ken Ono is unveiling new theories that answer these famous old questions.

Ono and his research team have discovered that partition numbers behave like fractals. They have unlocked the divisibility properties of partitions, and developed a mathematical theory for “seeing” their infinitely repeating superstructure. And they have devised the first finite formula to calculate the partitions of any number.

“Our work brings completely new ideas to the problems,” Ono says. “We prove that partition numbers are ‘fractal’ for every prime. These numbers, in a way we make precise, are self-similar in a shocking way. Our ‘zooming’ procedure resolves several open conjectures, and it will change how mathematicians study partitions.”[...]

On the surface, partition numbers seem like mathematical child’s play. A partition of a number is a sequence of positive integers that add up to that number. For example, 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1. So we say there are 5 partitions of the number 4.

It sounds simple, and yet the partition numbers grow at an incredible rate. The amount of partitions for the number 10 is 42. For the number 100, the partitions explode to more than 190,000,000.

“Partition numbers are a crazy sequence of integers which race rapidly off to infinity,” Ono says. “This provocative sequence evokes wonder, and has long fascinated mathematicians.”

By definition, partition numbers are tantalizingly simple. But until the breakthroughs by Ono’s team, no one was unable to unlock the secret of the complex pattern underlying this rapid growth.

Economics: what you know about “socialist Europe” isn’t necessarily so:

One simple indicator is the fraction of prime-working-age adults — that is, 25-54 — that are, in fact, employed. Why focus on that age group? Because employment rates for the young are strongly affected by things like student aid policy, while those for the over-55 set are strongly affected by retirement policy; so if you want to know how many of the people who really should be working are managing to find jobs, the 25-54 sample is useful. Here’s America versus the cheese-eaters over the years:

n the 90s, with US employment surging while France (and much of Europe) was having trouble creating jobs, there was a lot of talk about the European employment problem. By the eve of the current crisis, however, the European job picture had changed a lot for the better, while even a business-cycle recovery didn’t seem to do much for US jobs.

Read on and see another graph comparing the EU to the US.

Religion: well, just read:

Authorities have charged a South Carolina woman with felony animal cruelty, saying she hanged her nephew’s pit bull from a tree with an electrical cord and burned its body because the dog chewed on her Bible.

Animal control officers said Monday that 65-year-old Miriam Smith told them she killed a female dog named Diamond because it was a “devil dog” and she worried it could harm neighborhood children. Authorities said bond wasn’t immediately set for Smith, who remains jailed in Spartanburg County after her weekend arrest.
[...]

Hmm, the DOG is of the devil?

Advertisement