Workout notes: swam: 2000 straight laps (not timed; counted laps by 5: that is, 8 x 250 with no rests), then 200 pull.
I then took my daughter to Chicago Midway; we left at 9 am, I took her through the boarding pass line and to security; then I drove home and got home at 2:45. That was as fast as I’ve ever made this trip (round trip).
News: John Nash was killed in a traffic accident a couple of days ago. He was the focus of the book/movie A Beautiful Mind. He is known for the Nash equilibrium (in game theory); it was for that he won a Nobel in economics. But he had other great mathematics results; one of these was the Nash Embedding Theorem. The statement is somewhat technical but I think that I can give a flavor of what it was about.
Consider the circle. It is an object known as a “1-manifold” in that, if one examined the circle very “locally”, one would see that it was impossible to distinguish from a straight line. Example: if a tiny, near sided creature lived on a circle, it would look like a line to the creature, just like our spherical earth looks flat to us (locally).
Look at the two closed curves above. Those are “embeddings” (one to one, continuous maps from the circle). The one of the left: two points on the circle itself are “distant” from each other if and only if they are distant from each other as points on the plane. That is said to be an “isometric” embedding of the circle; points on the circle are far away from each other if and only if they are far away from each other in the plane.
Now look at the bent “circle”. See how two points of the circle are “close together” as points on the plane, but if one was forced to go from one of those points to the other point WHILE STAYING ON THE CURVE, one would have to travel a much further distance. That is a non-isometric embedding of the circle as two points are close together as points in the plane but NOT close as points on the circle.
So, the Nash embedding theorem deals with isometric embecdings; he gives a mathematical condition which guarantees that an arbitrary embedding can be approximated by an isometric embedding (as well as a dimensional criteria).
Workout notes On my own: I did the Cornstalk 8.1 in 1:28:44 (44:34/44:10); slow and it was chilly ….just perfect running weather. It was basically a “no effort expended” run, at least until my last mile.
I saw the university women’s track team headed toward me; they said “hi” as usual and I just wanted to disappear. The contrast between them and me was stark. :-)
That is another sign of age: 32-33 years ago I WANTED people to see me run. Now I want to be invisible. :-)
But it was very enjoyable…probably due to the chilly conditions.
Later: I walked just over 2 miles with Barbara and Olivia (about 20 minutes per mile).
I like these articles mostly because of the reasoning that they display.
Yes, cutting spending during a recession stalls growth. Here, Paul Krugman gets exasperated by some being unable to understand the difference between the economy’s level and its growth rate; that is, being unable to distinguish between a function and its derivative.
Now he attacks those who are supporting the TPP “fast track” by using bad reasoning:
And the selling of TPP just keeps getting worse.
William Daley’s pro-TPP op-ed in today’s Times is just awful, on multiple levels. No acknowledgment that the real arguments are not about trade but about intellectual property and dispute settlement; on top of that a crude mercantilist claim that trade liberalization is good because it means more exports; some Dean Baker bait with numbers — $31 billion in trade surplus! All of 0.2 percent of GDP!
But what really annoyed me, even if it’s not necessarily the worst bit, was this:
But today, of the 40 largest economies, the United States ranks 39th in the share of our gross domestic product that comes from exports. This is because our products face very high barriers to entry overseas in the form of tariffs, quotas and outright discrimination.
Actually, no. We have a low export share because we’re a big country. Here’s population versus exports as a percentage of GDP for OECD countries:
Well, I walked. I ran a race. I graded papers (two sets of final exams graded!).
And I wrote this “fun” blog post about the volume of the n-dimensional ball. Yes, I was thinking about this before the race and during my longish walk.
I didn’t have the a lot of sleep last night and woke up early…though when I was asleep, I slept soundly. But I was up at the crack of dawn…
Weights: 3 sets of 10 pull ups; Achilles exercises and rotator cuff
bench: 10 x 135, 3 x 180, 6 x 170, 8 x 160 (rotator cuff)
pull ups: 2 sets of 10 superset with
military: 2 sets of 12 x 50 dumbbell (seated, supported)
superset: 3 sets of 10 x 150 pull down (different machine) with
rows: 3 sets of 10 x 110 superset with
military: 2 sets of 10 x 40 dumbbell (standing)
That got me outside where I walked 5.1 miles from 7:50 to 9:04 (included 2 traffic stops). Pretty, though I did see a dead raccoon. The walk felt fine.
To say that my office hours were sparsely attended would be an understatement.
Yes, I am teaching calculus 3 and yes, the integrals on my exam will be harder than the spherical coordinates integral in this cartoon.
Note: 1, 3 and 4 are straight forward. 2: the series converges (alternating series test) and it is a simple matter to get the sum within a desired error bound (the absolute value of the term). But the series does NOT telescope though it does factor and can be written
I am going to have to rummage through archives for things in my personal history and talk to my bank. And I can’t forget about classes and the like.
One thing that I am thinking about: consider the two point set and declare each individual point to be an “open set” (this is called the “discrete topology”. ) Pretty boring, huh?
Now consider in the product topology. Seriously, this topological space is anything but boring, as simple as it appears to be. The elements of it are simply sequences of 0’s ans 1’s. There is more here.
These things appear all over the place in mathematics including in chaos theory.
Now to run and lift a little bit and get busy.
But yeah, these are all pictures which depict this space in one or more of its common forms:
It was slightly slick outside and foggy so that, plus my legs brought me to workout inside.
Run: treadmill: 2 miles 21:20
Track (middle lane): 7:49 (3:55/3:53)
4 lap walk, 4 lap jog (1 mile)
2.25 treadmill (2 in 20:20)
Weights (had to change my shirt; too sweaty):
pull ups: 15-10-10-10-(5-5) changed grip on the last set. rotator cuff recoveries.
bench: 10 x 135, 1 x 180 (ok), 6 x 160 (weak)
incline: 10 x 135
military: 2 sets of 10 x 40 standing (dumbbells, each arm)
pull downs: 2 sets of 10 x 160 (traditional)
Superset: 3 sets of 10 x 110 row, with 10 x 90 (each arm) military, 10 x 130 pull down in between.
This wasn’t my toughest workout ever, but was good enough and I got in at least a little bit of “less glacial” running.
I spent the academic morning writing about Cantor sets and spaces, under the guise of
Workout notes: weights went fine, the run was a mental struggle.
pull ups: 5 sets of 10 (ok), rotator cuff
bench: 10 x 135, 6 x 170, 5 x 170 (rotator cuff)
incline: 10 x 135
military: 3 sets of 10 x 40 dumbbell, standing.
machine stuff: 3 sets of 10 x 110 row
machine stuff: 3 sets of 10 x 130 pull down (wide grip)
machine: 10 x 90 (each arm) military
But I was surprisingly tired and thought my run would be iffy.
Still: it all went well for the first 12 of “start at 5.5, incline 0.5, up by 0.1 mph every 4 minutes” then at 49:33, I was at mile 5 and dialed it back..walked for 30-40 seconds at 5.3 and then got back up to 59:44 (mile 6) and walked .25 cool down miles.
But I was tired when I finished; was it the dinner last night?
During the day: grading marathon, and wondering about an a math problem that is bedeviling me.
Now: watching Wichita play Southern Illinois; lots of empty seats but an entertaining game.
I admit that the quality of writing in this blog has suffered. It is mostly workouts, the basketball team, and not much else.
I HAVE been writing challenging stuff, but mostly here.
The challenge: present the material in a way that is most useful to the students; so some of the proofs I have use have not been the most elegant ones that a mathematics professional would use. And it has been humbling; I am finding out that I don’t know the answer to some “natural” questions.
I do have some comics that I found funny:
No, I am NOT a “people person”:
And…well…if the shoe fits:
- 2008 Election
- 2010 election
- 2012 election
- 2014 midterm
- Aaron Schock
- affirmative action
- Agricultural Commisioner
- alternative energy
- April 1
- Barack Obama
- barback obama
- Barbara Boxer
- big butts
- bill maher on mosque
- bill richardson
- blog humor
- blood donation
- Bobby Jindal
- business & economy
- Cheri Bustos
- civil liberties
- Claire McCaskill
- climate change
- college football
- d k hirner
- dark energy
- dave koehler
- Dick Durbin
- Dick Morris
- dk hirner
- draw Mohammad day
- draw Muhammad day
- Fox News Lies Again
- free speech
- glenn beck
- glenn hubbard
- green news
- ground zero mosque
- gwen ifill
- haunting songs
- health care
- Herman Cain
- High Speed Rail
- hillary clinton
- human sexuality
- if rich people have to pay taxes
- immigration. racial profiling
- internet issues
- Intrade Prediction
- jan brewer
- jim lehrer
- Joe Biden
- John McCain
- jon stewart
- Judicial nominations
- knee rehabilitation
- laughing at myself
- michelle bachmann
- Mid Life Crisis
- Middle East
- Mike Huckabee
- mike's blog round up
- Mitt Romney
- national disgrace
- Navel Staring
- Newt Gingrich
- north america
- north carolina
- NSFW humor
- Olympic Spandex
- Personal Issues
- Political Ad
- political humor
- public policy and discussion from NPR public radio program Science Friday with host Ira Flatow. Science Videos
- rebulican party
- republican party
- republican senate minority leader
- republicans political/social
- republicans politics
- rick perry
- rick santorum
- Rush Limbaugh
- sarah palin
- Science Friday teachers
- Science Friday teens.
- shoulder rehabilitation
- Spineless Democrats
- stem cells
- stephen colbert
- tax cuts
- the colbert report
- Tim Pawlenty
- time trial/ race
- war on drugs
- weight training
- wise cracks
- world events