I filled in to teach a class today..and then went to swim:
500 free, 250 of back/fly, 150 of side, 100 IM, 4 x (100 free, 100 pull, 100 fins)
pull ups: 5 sets of 10 (stronger than I had anticipated), super sets with
military (machine, 10 x 100 each arm)
rows( machine, 10 x 110)
Then incline presses: 10 x 135, 10 x 135, 5 x 135 (quit as I was getting tight)
But when I went home, Barbara’s cleaning woman was still there (she had started late), so I walked to the Vietnamese place for a buffet lunch.
It was good, but it was also more food than I was used to.
So when I tried to concentrate on a work topic…..zzzzzzz……and I ended up checking Facebook about 50 times…
There is a reason I eat a light lunch on most days.
FAIL I was looking at a math book (for a class that I am teaching) and read the phrase “…. for integral ” and I didn’t quite get the word “integral” (I had just taught calculus…) until my colleague patiently reminded me of the phrase “for integral multiples of ”
“slow brain + heavy lunch” = “embarrassing fails”.
I got up late (by my standards) and worked out late; today was a lazy summer day. I’ll do some work later today; I have been thinking about a mathematics problem.
Workout notes: weights, then a run.
Weights: surprisingly, I felt relatively strong.
pull ups: 5 sets of 10 (good set today)
incline bench (strong), 10 x 135, 7 x 150, 10 x 140
super set: military: 7 x 45 dumbbell (standing), 10 x 40 dumbbell, 10 x 100 (each arm) seated, machine
rows: 3 sets of 10 x 110
pull downs: 2 sets of 10 x 160 machine 1, 10 x 150 machine two.
run: 11 minutes treadmill, 10:16 mile on the track (aborted a 3 miler), 21:30 treadmill (started slowly, increased the speed); finished feeling better.
my left knee is bothering me and bothered me some yesterday. It is probably a weather ache.
I don’t want to admit that yesterday’s walking workout was harder on me that I thought that it “should” be.
Now to do some thinking; these sort of things will be on my mind:
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:
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