Clinging to outliers: hope springs eternal

Workout notes: though it has been a while, (it started with a scratchy throat on 18 February and peaked Sunday, 22 February; first workout back was 27 February) I am STILL not back near 100 percent. Yesterday’s “almost 5K (2.9 miles)” at a 8:35 pace left me sore. So I did work out, but I have an ever-present “mild fatigue” that hindered my performance:

Weights: pull ups, 4 sets of 10, 7, 1, 5. I couldn’t get that 5’th set of 10. Rest: rotator cuff and back exercises.
bench press: 10 x 135, 1 x 180 (not really strong), 4 x 170 (and THAT was hard),
incline: 135: 1 set of 3 (weights slid off; forgot to set one of the clips) and then a set of 5.
circuit: 3 sets of 10 on machines: rows (110), pull downs (130), military (90 each arm).

I was feeling a bit run down so I walked indoors though it was a pretty day: 4 miles in 50:09 (middle lane): 13:13, 12:36, 12:33, 11:46. It wasn’t a bad walk, but it wasn’t exactly blazing fast either.

Hope and outliers
Yesterday’s 5K run chopped off part of the usual course; this was apparent when I got to what should have been mile 2 (14:30…ok, 10 years ago…maybe?) and finished in 24:42; this was my best time last year (certified course). I came in tired and had heavy legs during the warm up; this was about 2.87-2.9 miles and equates to a 26:30-26:40 on a true 5K course, and THAT reflects where I was yesterday.

But I wanted to believe that this was a full 5K. It wasn’t.

That got me to thinking a bit more about denial. Early this season, our Division I basketball team lost to a Division III team 58-56. Now of course, many fans didn’t want to admit the obvious: our team was a very bad basketball team. Some fans went back to memory lane and remembered famous upsets like this one. And it is true: you can comb the annals of basketball history to see some legitimately good teams suffering embarrassing losses in the preseason or early in the season.

But those are the exception: the vast majority of a time, a D-1 team loses to a D-3 team because they aren’t any good. And yes, we finished 9-24 overall and 3-15 in conference play, though we did beat a 9-22, 6-12 team in the conference tournament…only to lose by 25 the next game.

And yes, you see this with regards to test scores; witness the satirical treatment of this rather dumb facebook meme:


Yes, on rare occasion, someone with a math ACT of 19 makes it past calculus 3; there is a CEO of a company who did poorly on a standardized test, and I know of one language professor whose GRE scores were a disaster…and her logical abilities were limited..but she was/is a genius with languages. No, those tests didn’t pick that up.

But those are outliers. Most of the time, the tests reflect reasonably well what the student knows and what their academic abilities.

It works the other way too. I remember watching the Boston Marathon in 2001 and seeing Lee Bong Ju win. During the race, the announcer said that, while he was in high school, he had set national records in Korea. At first I thought “wow”…then “DUH….what kind of person leads (and wins) the Boston Marathon?” That he had run some fast times while as a youngster is the least surprising thing in the world.

Yes, one Boston Marathon winner had started his running career as a recreational runner to lose weight! But that is the rare exception.

But dreams die hard. Think about lottery mania. I tried to tell my dad that he was wasting his time and money by buying a ticket. His response: “someone wins”. Well, “someone dies on their way to buy their ticket too” and, as we can see, the odds of dying while picking up a ticket are greater than buying the winning ticket!

The odds of dying by a car accident are 1.58 \times 10^{-8} per mile traveled. The odds of winning a lottery jackpot are about 5.7 \times 10^{-9}

So there you go.

March 8, 2015 Posted by | illness, running, sickness, statistics, weight training | , , | Leave a comment

Typical Spring…

Screen shot 2013-04-10 at 9.49.33 AM

42 F, 22 mph wind….brisk, to say the least. And yes, it drizzled a bit at times, and there were a couple of claps of thunder. But that is seasonal around here for early April; no room to complain.

I did wear a long sleeve t-shirt though for my hilly 6.4 mile (10.3 km) run which took 1:03:53 today. Up until last week, this would have been one of my faster times but today, this represented a “keep it easy” effort. Seriously; I barely broke a sweat. Then again, at 10 mpm (just under), I shouldn’t have.

I was 9:48 at 1.03, 24:4x at the 2.5 turn around, 36:09 at the start of the second loop, 13:3x for the second loop and 9:40 for the trip home.

On the way down Cornstalk (the first time) I saw a bespandexed lady come down from the building and get on the course right in front of me. I saw her build (slender), her gait (quick and efficient, compared to mine) and told myself “don’t EVEN think about it” (meaning: “don’t try to keep up with her”). Sure enough when I got down to the base of the hill, she was out of sight; I couldn’t even tell which way she had turned.

Being old, fat and slow SUCKS!!!! 🙂

Seriously, I enjoyed the run and thought about this weekend.

Foot: not an issue, but it isn’t fully well. I need to ice it after EVERY workout.

April 10, 2013 Posted by | injury, running, sickness | , | Leave a comment

Illusions, Frogs and Civility

workout notes
Basically, the usual minus a bit of intensity: rotator cuff, 5 sets of 10 pullups, bench: 10 x 135, 4 x 180, 7 x 170
inclines: 7 x 145, 9 x 140, rows: 3 sets of 10 x 200 Hammer, military: 2 sets of 12 x 50 dumbbell, 10 x 80 machine, curls: 3 sets of 10 (dumbbell 30, 57.5 pulley, 70 machine), pull downs 3 x 10 with 160, ab set (3 sets each: crunch, twist, sit back, v. crunch). I was only a tiny bit off.

Heel: it hurt a bit; it came on late last night. Was it the run? I felt NOTHING during the run. Or was it the bad shoes I was walking in; the pain mostly went away with a shoe change.

Sickness: stomach not quite right, but ok. Full speed ahead for this weekend’s half marathon spandex chase.

Illusion Watch how your brain plays tricks on you, even though you KNOW what is going on!

Lawsuit? Heck, I’d add a surcharge to have frogs on the property! Good thing I wasn’t on the jury…

Margaret Thatcher’s death
The Brits think about things a bit differently than Americans do; some openly celebrated (and I am not talking about bloggers or mere people on the street; I am talking about politicians too)

I saw this on Facebook (put out by a Brit, no doubt: notice how “privatized” is spelled:


Hey, Satan is a inefficient socialist, right?

This reminds me of this a bit: Christopher Hitchens was brought onto Hannity and Colmes to discuss Jerry Falwell right after his death. Fox News knew EXACTLY what they were doing when they did this; this is TV melodrama at its best.

Speaking of Christopher Hitchens, someone provided one of his quotes which explains exactly why I don’t like magazines like The Nation or Salon even though I mostly agree with their policy views:

“I had become too accustomed to the pseudo-Left new style, whereby if your opponent thought he had identified your lowest possible motive, he was quite certain that he had isolated the only real one. This vulgar method, which is now the norm and the standard in much non-Left journalism as well, is designed to have the effect of making any noisy moron into a master analyst.”

When I finish one of their articles, I am often no better informed than when I started the article. I guess that reading Paul Krugman, science blogs (written by scientists) and the New York Times has spoiled me a bit.

Crazy Rick Santorum might run again. I might have to back him again. 🙂

Social Policy
On facebook, I made a mistake and commented on this a bit too soon. The Arkansas State Senate passed a bill that would make people who sought unemployment benefits sign a waver to allow themselves to be drug tested (random drug testing). At first I thought “here we go again, just like Florida” but then realized that:
1. This was a different population: unemployment benefits are different from welfare
2. Many jobs require you to pass a drug test to be considered
3. This was random testing versus “testing everyone”.

It still might be bad policy; my knee jerk response was against it and still is; it “smells like” a “punish the miscreants” fetish. But I might be wrong; I’ll have to think about this a bit more.

Suicide Statistics
This is interesting:

A recent study out of the University of California, Riverside has discovered that there may be link between suicide, gun ownership and political conservatism.

Published in the February issue of Social Psychiatry & Psychiatric Epidemiology, the study found that states with high levels of firearm availability and a proclivity toward political conservatism tended toward higher rates of suicide.

However, church attendance, which is sometimes correlated to political conservatism, was shown to depress suicide rates.

The state with the highest suicide rate was Alaska, which is second only to Montana in firearm ownership. Montana, for its part, had the third highest suicide rate in the nation. Other states with high rates of conservatism, suicide and gun ownership include Wyoming, Idaho, Alabama and West Virginia.

The percentage of gun suicides were higher in the South and West than in the Northeast or Midwest.

The study measured “firearm availability” by calculating the average number of firearms per household in a given state and traced political conservatism based on the percentage of that state’s voters who cast a ballot for Republican George W. Bush in the 2000 presidential election.

“Persons living in states or localities with high suicide rates may have higher exposure to definitions favorable to suicide acceptance, and this in turn may increase their odds of committing suicide,” wrote Augustine J. Kposowa, who authored the study, and has researched the causes of suicide for two decades. “Prevailing social, economic and even political conditions in a state may further affect individual suicidal behavior by maintaining an environment in which people’s aspirations are thwarted and dreams of a better tomorrow are deferred.”

I’ll have to check out the data and cross tabs; there is excellent material for a statistics class here.

Of interest to me:
married people committed suicide at higher rates than single people, and divorced people had higher rates than either single or married (was this corrected for age?)

Whites and Hispanics had higher rates than Blacks or Asians.

Church goers had lower rates than non-church goers (not a surprise; I think that church membership DOES provide some fellowship benefits)

Access to weapons lead to higher rates. Note: this is what complicates the gun control debates. Firearm death rates (suicides, accidents, crime) are mostly caused by handguns, and it is assault rifles that have come up for debate.

April 9, 2013 Posted by | frogs, injury, politics, politics/social, republicans, rick santorum, sickness, weight training | , , | Leave a comment

Life is easier when you aren’t dumb

Workout notes I felt better this morning so I decided to run.
It was warm (compared to recent weather) 67 F, 79 percent humidity. Yeah, that is sweater weather in Texas. 🙂

I decided to try my Cornstalk classic 4.2 mile course (hilly)
It felt more difficult than expected; I felt slightly sick during the first mile so I told myself to relax; that came at 9:08 (for 1.03)
It was 3:19 down to the loop, 12:03 for the 1.3 (+) loop and 3:59 back up the hill, 8:45 back home. Time: 37:17, (8:52 mpm) for my fastest since July 2004 and my 5’th fastest since 2003. Ok, this used to be 33-34 when I was in 20 minute 5K shape. But last year it was a struggle to get 40:00.

But no, it was NOT an easy effort; it was work.

Now to shower, eat and do math. Still, I overdid it a bit; I am not 100 percent.

April 8, 2013 Posted by | running, sickness | Leave a comment


This is only for my records: last night saw me getting up a LOT and a LOT of pink bismuth. Otherwise, I don’t feel that bad; I was told by my spouse (who lovingly gave me this bug 🙂 ) that this should “pass” in a couple of more days.

I might walk again today and try something approaching a full workout tomorrow.

So, just a bit of humor:


April 8, 2013 Posted by | humor, mathematics, sickness | | Leave a comment

No Respect….

Workout notes Great weather; walked my Cornstalk classic course in about 58 minutes (by time of day; I had to wait to cross streets, etc.) This was about 13:30 mpm or so on a hilly course; it was just hard enough to get slightly damp with sweat.

I am feeling better, but this mini-workout took something (just a little) out of me. There is no way in Hades I could have done this 7 times in a row (enough to make 30 miles) today. And yes, I’ve walked 50 miles in a row at a faster pace…a LONG time ago.

Later, my wife tells me that one of her former students (in his early 30’s) ran his first half marathon in 1:54. “That’s good, right?” she asks. I reminded her that when I was 39 and 40, I had run a 1:42 (windy; a month after a marathon) and a 1:35 (peaked) and she had yelled “get going Lard-Butt!” at me as I finished (25-30 minutes behind the winner). So, is he (her former student) a lard-butt? “No…that’s different.”

No respect.

I got this e-mail message from Rick Santorum:

Screen shot 2013-04-07 at 2.04.32 PM

Screen shot 2013-04-07 at 2.05.00 PM

Grab the popcorn folks; this will be fun. 🙂


See the earth through Saturn’s rings…and Saturn, with rings, from the earth via the moon:


The view from the other direction:


April 7, 2013 Posted by | astronomy, politics, republicans, republicans politics, science, sickness, walking | , | Leave a comment

What I did with my day: the value of the x^n sin(pi/x) in calculus.

Cross posted in my math blog:

In my non-math life I am an avid runner and walker. Ok, my enthusiasm for these sports greatly excedes my talent and accomplishments for these sports; I once (ONCE) broke 40 minutes for the 10K run and that was in 1982; the winner (a fellow named Bill Rodgers) won that race and finished 11 minutes ahead of me that day! 🙂 Now I’ve gotten even slower; my fastest 10K is around 53 minutes and I haven’t broken 50 since 2005. 😦

But alas I got a minor bug and had to skip today’s planned races; hence I am using this morning to blog about some math.

Real Analysis and Calculus
I’ve said this before and I’ll say it again: one of my biggest struggles with real analysis and calculus was that I often didn’t see the point of the nuances in the proof of the big theorems. My immature intuition was one in which differentiable functions were, well, analytic (though I didn’t know that was my underlying assumption at the time). Their graphs were nice smooth lines, though I knew about corners (say, f(x) = |x| at x = 0 .

So, it appears to me that one of the way we can introduce the big theorems (along with the nuances) is to have a list of counter examples at the ready and be ready to present these PRIOR to the proof; that way we can say “ok, HERE is why we need to include this hypothesis” or “here is why this simple minded construction won’t work.”

So, what are my favorite examples? Well, one is the function f(x) =\left\{ \begin{array}{c}e^{\frac{-1}{x^2}}, x \ne 0 \\  0, x = 0  \end{array}\right. is a winner. This gives an example of a C^{\infty} function that is not analytic (on any open interval containing 0 ).

The family of examples I’d like to focus on today is f(x) =\left\{ \begin{array}{c}x^ksin(\frac{\pi}{ x}), x \ne 0 \\  0, x = 0  \end{array}\right. , k fixed, k \in {1, 2, 3,...}.

Note: henceforth, when I write f(x) = x^ksin(\frac{\pi}{x}) I’ll let it be understood that I mean the conditional function that I wrote above.

Use of this example:
1. Squeeze theorem in calculus: of course, |x| \ge |xsin(\frac{\pi}{x})| \ge 0 ; this is one time we can calculate a limit without using a function which one can merely “plug in”. It is easy to see that lim_{x \rightarrow 0 } |xsin(\frac{\pi}{x})| = 0 .

2. Use of the limit definition of derivative: one can see that lim_{h \rightarrow 0 }\frac{h^2sin(\frac{\pi}{h}) - 0}{h} =0 ; this is one case where we can’t merely “calculate”.

3. x^2sin(\frac{\pi}{x}) provides an example of a function that is differentiable at the origin but is not continuously differentiable there. It isn’t hard to see why; away from 0 the derivative is 2x sin(\frac{\pi}{x}) - \pi cos(\frac{\pi}{x}) and the limit as x approaches zero exists for the first term but not the second. Of course, by upping the power of k one can find a function that is k-1 times differentiable at the origin but not k-1 continuously differentiable.

4. The proof of the chain rule. Suppose f is differentiable at g(a) and g is differentiable at a. Then we know that f(g(x)) is differentiable at x=a and the derivative is f'(g(a))g'(a) . The “natural” proof (say, for g non-constant near x = a looks at the difference quotient: lim_{x \rightarrow a} \frac{f(g(x))-f(g(a))}{x-a} =lim_{x \rightarrow a} \frac{f(g(x))-f(g(a))}{g(x)-g(a)} \frac{g(x)-g(a)}{x-a} which works fine, so long as g(x) \ne g(a) . So what could possibly go wrong; surely the set of values of x for which g(x) = g(a) for a differentiable function is finite right? 🙂 That is where x^2sin(\frac{\pi}{x}) comes into play; this equals zero at an infinite number of points in any neighborhood of the origin.

Hence the proof of the chain rule needs a workaround of some sort. This is a decent article on this topic; it discusses the usual workaround: define G(x) =\left\{ \begin{array}{c}\frac{f(g(x))-f(g(a))}{g(x)-g(a)}, g(x)-g(a) \ne 0 \\  f'(g(x)), g(x)-g(a) = 0  \end{array}\right. . Then it is easy to see that lim_{x \rightarrow a} \frac{f(g(x))-f(g(a))}{x-a} = lim_{x \rightarrow a}G(x)\frac{g(x)-g(a)}{x-a} since the second factor of the last term is zero when x = a and the limit of G(x) exists at x = a .

Of course, one doesn’t have to worry about any of this if one introduces the “grown up” definition of derivative from the get-go (as in: best linear approximation) and if one has a very gifted class, why not?

5. The concept of “bounded variation” and the Riemann-Stiltjes integral: given functions f, g over some closed interval [a,b] and partitions P look at upper and lower sums of \sum_{x_i \in P} f(x_i)(g(x_{i}) - g(x_{i-1}) = \sum_{x_i \in P}f(x_i)\Delta g_i and if the upper and lower sums converge as the width of the partions go to zero, you have the integral \int^b_a f dg . But this works only if g has what is known as “bounded variation”: that is, there exists some number M > 0 such that M > \sum_{x_i \in P} |g(x_i)-g(x_{i-1})| for ALL partitions P. Now if g(x) is differentiable with a bounded derivative on [a,b] (e. g. g is continuously differentiable on [a,b] then it isn’t hard to see that g had bounded variation. Just let W be a bound for |g'(x)| and then use the Mean Value Theorem to replace each |g(x_i) - g(x_{i-1})| by |g'(x_i^*)||x_i - x_{i-1}| and the result follows easily.

So, what sort of function is continuous but NOT of bounded variation? Yep, you guessed it! Now to make the bookkeeping easier we’ll use its sibling function: xcos(\frac{\pi}{x}). 🙂 Now consider a partition of the following variety: P = \{0, \frac{1}{n}, \frac{1}{n-1}, ....\frac{1}{3}, \frac{1}{2}, 1\} . Example: say \{0, \frac{1}{5}, \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, 1\} . Compute the variation: |0-(- \frac{1}{5})|+  |(- \frac{1}{5}) - \frac{1}{4}| + |\frac{1}{4} - (-\frac{1}{3})|+ |-\frac{1}{3} - \frac{1}{2}| + |\frac{1}{2} -(-1)| = \frac{1}{5} + 2(\frac{1}{4} + \frac{1}{3} + \frac{1}{2}) + 1 . This leads to trouble as this sum has no limit as we progress with more points in the sequence of partitions; we end up with a divergent series (the Harmonic Series) as one term as points are added to the partition.

6. The concept of Absolute Continuity: this is important when one develops the Fundamental Theorem of Calculus for the Lebesgue integral. You know what it means for f to be continuous on an interval. You know what it means for f to be uniformly continuous on an interval (basically, for the whole interval, the same \delta works for a given \epsilon no matter where you are, and if the interval is a closed one, an easy “compactness” argument shows that continuity and uniform continuity are equivalent. Absolute continuity is like uniform continuity on steroids. I’ll state it for a closed interval: f is absolutely continuous on an interval [a,b] if, given any \epsilon > 0 there is a \delta > 0 such that for \sum |x_{i}-y_{i}|  < \delta, \sum |f(x_i) - f(y_{i})| < \epsilon where (x_i, y_{i}) are pairwise disjoint intervals. An example of a function that is continuous on a closed interval but not absolutely continuous? Yes; f(x) = xcos(\frac{\pi}{x}) on any interval containing 0 is an example; the work that we did in paragraph 5 works nicely; just make the intervals pairwise disjoint.

April 6, 2013 Posted by | mathematics, running, sickness | , , , , , | Leave a comment

Rats…no race for me

Well, I had signed up to do a brand spanking new 10K this morning, followed by a 8 pm 30 mile trail…well…hike for me.

Neither will happen; yesterday I woke up feeling a bit off; during my weight workout I was a bit off…then I got worse. I went to bed at 3 pm and mostly napped/slept; got a mild fever. It should be no big deal but running or walking is out of the question. I do feel better though; I should be “back in the saddle” come Monday.

I am glad that I kind of pushed the pace on a training run on Thursday; a course PR (ok, “PB over the past 3 years”) is always nice to have.


I don’t care too much about this; I think that this is a high stakes political poker game:

By tying his Social Security cuts to tax increases, President Obama has offered Republicans the same deal that he has been proposing for years. It is also a deal that will Republicans will never in a million years accept.

Reuters put the offer of cuts to Social Security in the lead, but the twist in in the paragraph below, “However, the president will only accept these spending cuts if congressional Republicans, for their part, agree to higher taxes, the official added. The President’s budget proposal is due to be laid out in full on Wednesday.”

The New York Times revealed that the President is using the offer of Social Security cuts to break the Republican resistance to tax hikes, “Congressional Republicans have dug in against any new tax revenues after higher taxes for the affluent were approved at the start of the year. The administration’s hope is to create cracks in Republicans’ antitax resistance, especially in the Senate, as constituents complain about the across-the-board cuts in military and domestic programs that took effect March 1.”

In other words, relax.

April 6, 2013 Posted by | economy, politics, politics/social, sickness | | 2 Comments

I feel bad

Well, I slept much of the day away; I have a mild fever. If I am not a lot better tomorrow morning, I’ll have to cancel.
If I feel ok, I might walk/jog the 10K course with Tracy and keep her company.

When Barbara had this, she was affected for about 12 hours.

Not knowing what to do

On policy grounds, it appears that Paul Krugman makes sense in this criticism of President Obama’s putting “the chained CPI” on the table. But every time I say “ok, the purity trolls are right; Obama is selling us out”, I end up with egg on my face. I’ve learned to NOT underestimate him.

So, on one hand, I want to be objective and critical where required. On the other hand, he appears to know what he is doing.

It is a fine line between earned trust and being a “bot”; I stopped giving the benefit of the doubt to President W. Bush after the State of the Union in 2003 when he said that we were going to war with Iraq.

April 6, 2013 Posted by | Barack Obama, bush-era, political/social, politics, sickness | | Leave a comment

Yin/Yang…running and economic negotiations

Workout notes
8 mile run eastpeoriatrail

I felt a bit run down (mild cough for the past 4-5 days) and not that peppy so I decided to only run 8 miles (shoot for 12 this weekend); I slogged to 42:03 at the turn around and did the second half in 35:21 (not that bad). It was 37 F and mostly calm; I encountered a few walkers and one “escaped dog” (playful).

But when I finished, I went to stretch and some old guy went to check on me; evidently I didn’t look too hot when I finished. I admit that I pushed the last mile in 8:10 (hard for me) and was bent over from the waist when I stopped to catch my breath. I didn’t FEEL that bad though; the stretching made me feel loose and I was able to stop at the grocery store on the way home.

We haven’t had snow yet (some is coming tomorrow) and we’ve had only a bit of cold weather. I admit that I don’t like it, but well..


The yin: it is frustrating that I am not fast enough to catch up to get a better look.
The yang: it speeds me up thereby giving me better workout that I would have ordinarily had.

Fiscal Cliff
Paul Krugman is worried about the negotiations; it appears to him that President Obama is in the process of doing all of the giving. To those who are worried: I recommend David Corn’s book Showdown; it describes how President Obama negotiates. He is shrewder than he might appear. In a nutshell: he does the calculation: “do the disadvantaged classes/people who need it the most get as much as reasonably possible”? If so, he’ll make the deal, even if it might appear that he got “rolled”. It took me some time to finish that book, but I can recommend it.

Huckabee is still clueless

Mr. Huckabee: there is no evidence that religion reduces homicide, either in the United States or in the world. No, these statistics won’t convince the fundamentalists but hopefully these will show that evidence for the conjecture “becoming more religious reduces homicide in a society” is simply not there; it fact it suggest that the reverse “might” be the case (data is too noisy to be convincing).

December 19, 2012 Posted by | Barack Obama, big butts, books, economy, huckabee, politics, politics/social, running, sickness, social/political, spandex | , , , | Leave a comment