Chicago and Nash

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).

Well, one can place a circle in a plane (distortion is allowed) in different ways:

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).

May 26, 2015 Posted by | mathematics, swimming, travel | Leave a comment

More Krugman…

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.

First, the main factor in the decline of US manufacturing is NOT trade imbalance.

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:


May 19, 2015 Posted by | economics, economy, family, mathematics, running | , | Leave a comment

What I did this weekend:

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.

Pitiful. :-)

May 11, 2015 Posted by | mathematics | , , | Leave a comment

Bleah. Really. Sort of. Maybe?

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.

Final exam
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 a_{n+1} term). But the series does NOT telescope though it does factor and can be written \frac{1}{3} (\sum \frac{2k-1}{k^2-k+1} + \frac{1}{k+1})

May 6, 2015 Posted by | mathematics, Personal Issues, walking, weight training | | Leave a comment

Woo woo, satire and some math

Last night, The President had some fun with his critics:

Mathematics gets a should out (yay!)

But woo-woo gets front page at the Peoria Journal Star:

OTTAWA — In an age when science explains many of the natural world’s mysteries, there still exist things not fully understood.
As a licensed clinical professional counselor and a priest, the Rev. Michael Driscoll, a Peoria native, believes both science and the spiritual world should be considered in the realm of mental illness.
Driscoll’s new book, “Demons, Deliverance, and Discernment: Separating Fact from Fiction About The Spirit World,” employs modern thinking while addressing the age-old notion of demonic possession.
“We certainly don’t have everything figured out when it comes to mental health problems,” said Driscoll, during a telephone interview from Ottawa where he works as the chaplain and director of pastoral care at OSF Saint Elizabeth Medical Center. While there is greater understanding today about brain chemistry and other factors that lead to mental illness, spiritual issues should still be considered in the treatment of patients.


“I don’t want to say every mystery can be attributed to the devil, but some of us think, ‘Well, there’s a spirit world too, and maybe that explains some things.’”
Driscoll referenced a 2014 story in the Indianapolis Star about a Gary, Ind., woman who claimed she and her three children were possessed by demons. Several hospital workers and police officers witnessed extraordinary events — such as a 9-year-old boy walking backwards up a hospital wall — that made them believe. A series of exorcisms seemed to solve the problem.


The question became the subject of Driscoll’s dissertation several years later while he was working on his Ph.D. through Regent University in Virginia Beach, Va. The book contains the same information, but it is written with the aim of educating priests and the public about the differences between mental illness and demonic possession. Published by Catholic Answers Press, the book will be available by month’s end.

Oh dear. This reminds me of the “genuine psychics” signs I’ve seen.
I’d like to think that I don’t live in a 3’rd world backwater but evidently, I do.

April 26, 2015 Posted by | Barack Obama, health, mathematics, Peoria, political humor, political/social, politics/social, religion, superstition | Leave a comment

somewhat crazy this week

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 F = \{0, 1 \} and declare each individual point to be an “open set” (this is called the “discrete topology”. ) Pretty boring, huh?

Now consider F \times F \times F..... = \Pi^{\infty}_{i=1} F_i 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:













April 14, 2015 Posted by | mathematics | | Leave a comment

Math, abs and bench presses

Workout notes Weights first, then running.
Weights: pull ups: 10-10-10-10 (rotator cuff)
Bench: 10 x 135, 1 x 190, 1 x 180, 6 x 160 (got a spotter for 190) rotator cuff.
pull ups: 10
military (barbell); 10 x 85, 10 x 80, 10 x 80
superset with pull downs: 3 sets of 7 x 160 traditional, 7 x 100 low
rows: 3 sets of 10 with 110 (different machines and grips)

Then to the treadmill: I used on treadmill to warm up 32 minutes for 3 miles
second treadmill (passed on trying a mile): I played around with hills 1 to 2 minute intervals, 0-.5-1-2-3, etc. 32 minutes for 3 more.
It was warm in Markin and I didn’t want to overexert today.

This whole workout took just under 2 hours.

My former Congressman (from 2008 to 2012, when I was in IL-18) works out a lot and now is in a heap of trouble. Aaron Schock resigned and now is being investigated by Federal Prosecutors; his case is in front of a Grand Jury. Note: it is the Republicans that went after him.

Mathematics I worked on some…and was anguished at the elementary mistakes I made. Now if you want to see some of what world class mathematicians work on, read this. This is a “Scientific American” caliber article which shows how some work in algebra and number theory relates to string theory. The article isn’t technical but gives a flavor of what is going on.

April 10, 2015 Posted by | Aaron Schock, IL-18, mathematics, Peoria/local, politics/social, weight training | Leave a comment

Somewhat recovered

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 \Pi_{i=1}^{\infty} \{0, 1 \}_i

April 8, 2015 Posted by | mathematics, running, weight training | | Leave a comment


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.

February 18, 2015 Posted by | basketball, mathematics, running, weight training | , | Leave a comment

Me right now: Meh

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”:

Screen shot 2015-02-17 at 6.24.32 AM

And…well…if the shoe fits:

Screen shot 2015-02-17 at 6.25.08 AM

February 17, 2015 Posted by | mathematics | , , | Leave a comment


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