# blueollie

## My main post of the evening…

You can find it here.

Have you ever used a drawing program on the computer? Well, the program that draws curved lines uses the concept of the Bézier curve and the post I linked to is from my math blog; I wrote up some notes for my numerical analysis students and decided to post them on my math blog.

Yes, I post about topics OTHER than: politics, football/basketball running/walking/swimming/weight lifting and women’s bespandexed gluteal muscles.

March 9, 2014

Yes, I know, there are different formulas that work. So suppose we want ” 3 + 5″ to “equal” -28. What we want is the first digests (the constant coefficient upwards) to be the sum of the numbers, and the “leading” digits to be “a-b” with a correct sign; that is: a “+” b = (a-b, a+b) with the comma removed so as to make a single integer (the inputs are integers).

So the “cute” problem: get a spread sheet to do this.

To get full credit: you must get the correct answer for both a greater than b and a “less than” b.

February 21, 2014

## Different start and a couple of thoughts…Good Old Days and Bill Nye’s debate

Today, I woke up, checked some e-mail and yes, did some math. That might be a way to start my Tuesday/Thursday when I start to teach late: get up, start my duties and THEN break for a run/walk as I’ll take in a few moments.

It will be indoors, again:

Our neighborhood streets are solid compressed snow and ice.

What I am working on: it is somewhat technical. But imagine you want to find solve $f(x) = 0$ where the solution is impossible to solve “in closed form” (e. g. solve it like you did in algebra class). There are numerical techniques that you can use a computer for. If you’ve had calculus, you might recognize Newton’s method where if $x_{n}$ is an approximation to the solution, $x_{n+1} = x_n -\frac{f(x_n)}{f'(x_n)}$ where $f'(x)$ is the derivative of $f$. Never mind that; the point is that one generates a series of approximations to the solution (provided certain conditions are met): $x_1, x_2, x_3, .....x_n, x_{n+1}, ....$ which are hopefully getting closer to the desired solution. If you met the correct “starting requirements” and the solution exists, this sequence of numbers WILL get close to your desired solution.

One problem though: “how many times do you have to do this?” is an important question. One reason: the computer can’t store every number exactly; hence there is round off error, and that error grows with each calculation.
So, if it is the case where each approximation $x_n$ has error inherently built in, it might be possible (if certain conditions are met) to take your series of approximations and manipulate them so that the larger “inherent errors” subtract off and one gets close to the solution in a fewer number of steps. One adds calculation early (adding round off error) to save many more calculations later (greatly reducing round off error).

One such process is called the Aitken Delta-squared process and that is what I was working on.

Two thoughts

Thought one: the Good Old Days:

Okay, I’m just going to say this once more: No, I don’t miss the days when gas was 15 cents a gallon, and your curfew was “when the street lights came on,” and kids were more afraid of their parents than of the cops…..
Because back then, women, minorities, gays, and other marginalized people had even fewer rights than they have now. Crime is not really significantly worse now than it was then. It’s just than when a man beats his wife to a pulp, he can be convicted and jailed for it now, whereas back then, it was just seen as a domestic issue and no business of anyone else. People are still killing other people. People are still loving other people. People are still dying of curable diseases. People are still committing random acts of kindness.
And what a lot of conservatives don’t like to admit, but what the facts support, is that even the white, male, heterosexual population is better off when non-whites, females, gays, and any marginalized segments of society gain strength and power. Power is a renewable resource, increasing for the whole when it increases for a part; not a finite, limited supply.
In general, more of us are better off than we were 20, 40 years ago. I wouldn’t trade my penny candy memories for gas-guzzling over-poluting cars and institutionalized misogyny, not ever.

She is right, of course. I think that when we remember the past, we remember the good but not the bad. And change is NEVER all good; for example we live longer (most of us anyway) but that means there are more elderly who live long enough to lose their minds through dementia and Alzheimer’s disease.

What was curious though was one of the replies she got (she is religious and has religious friends):

In matters of the flesh, it certainly does seem things are better than they were.

But in matters of the Spirit, we are not better off, we are worse off and it is deteriorating from there.

We are abandoning God. That is never a sign that things are “better”, no matter the outward appearance that they are.

That leads to the next point. There are those who use religion to better their own lives in the hear-and-now, but to all too many, there is an inherent virtue to accepting some woo-woo supernatural claim (THEIR claim, of course) and rejecting it is a type of evil.

I can’t have an intellectual discussion with someone who is that delusional.

Which leads me to discuss the Bill Nye “The Science Guy” (educator) versus Ken Ham (owner of the creation museum).

I might watch the debate later

There are two schools of thought:

1. Bill Nye didn’t understand that this was an exercise in politics: hence he lost by merely showing up.

2. Bill Nye won the day by presenting some science to people who don’t see a lot of it. Maybe, just maybe, he planted a seed of science that might later germinate in a young mind.

Ok, there is a third, less popular school of thought: show up and insult the creationist as a charlatan. Here, the scientist started off by making some blunt accusations against the creationist and then offered the creationist a chance to electrocute himself:

Prior to the debate, I was in camp 1, but after the debate (which I didn’t watch), I thought ….well…remembered as a kid I once believed that superstitious nonsense….maybe? Then again, I kind of “evolved” out of it by basically living among more educated people. I have deep respect for those who manage to find their way out while staying in the same environment.

Ok, time to get it….

February 6, 2014

## Why mathematics shows that I am doomed to be a “put upon” spouse…..

My wife has recovered nicely from her broken foot. There was a time when she required quite a bit of assistance around the house. This has been too frequent for us; she has had some “assistance required” aliments over the past decade and a half (knee replacements, foot surgeries, trip to get coughing under control, etc.) Fortunately, they’ve always had a happy ending.

But when the “assistance time” was past, I felt “ok, now it is time for me to BE LEFT ALONE for a while.” But instead this meant that she could now do more….and she isn’t as introverted as I am. Grumble.

“But Honey, we are the only family that XXX can visit…he is so lonely.” Me: “lonely…what I wouldn’t give to be lonely for a while….”

So I thought about my “ideal spouse” who would be as fiercely introverted as I am.

Reality: I’d never meet her.

I thought about the friends that I have; the ones that I visit and share personal stuff with.

ALL but one (an unusual case) are very much “people” people. They LIKE people. Me: my regret is that I didn’t go in to WMD research. (ok, just kidding there…)

Ok, I am not quite that bad. But with the exception of one good friend, most people I really talk to have been outgoing to everyone type people and I am anything but that.

Hence, were I to get another wife there is a good chance she’d be pretty much like the one I have, at least in that regard.

What I am describing is part of what is known as the Friendship paradox and is actually well studied.

On Facebook: if you are like most people, your Facebook friends have more friends than you do.

In your profession: those you have heard of are more successful than you are (you are mostly unaware of those who are less successful; you remember the lead speaker but probably not many of the minor ones and probably even fewer of the ones who weren’t at the conference.

At the running races: I know about the 100 who beat me, but often little about the 200 that I beat. My eyes are in the FRONT of my head. Ok, I don’t like how that ratio is changing with time….

But here is the easiest example: think of airports. Most are small that only fly to a few airports. But the airports that they fly to have connections to LOTS of airports. Hence most airports connect to airports that have MORE connections than they do.

It is just mathematics and statistics.

January 28, 2014

## Not a problem for me in my department or at math meetings

Even when I do publish stuff (as I did recently), I get some feedback; recently I got a paper sent to me by a research mathematician which showed me some substantial extensions of the result I presented.

Sure, my paper wasn’t a wasted effort as it was, in part, bringing a higher level result to those who teach calculus, but in terms of the actual math, it was but the tip of an iceberg.

I LOVE smart people.

## GOP governor’s debate, math and science

Workout notes
short version: weights plus elliptical: elliptical was 30 minutes, much of it on “butt” setting.
weights: did the rotator cuff series and McKenzie set afterward; hip hikes and Achilles during.
pull ups: 5 or 6 sets of 10; lost count.
bench: 10 x 135, 4 x 180, 7 x 170 (more challenging than expected)
military press (dumbbell): 3 x (12 x 50)
upright row (dumbbell): 3 x (10 x 25)
dumbbell curl: 3 x (10 x 30)
pull downs: 3 x (10 x 160)
rows (Hammer): 3 x (10 x 220)
abs: 3 sets of 10: crunch, v. crunch, sit back, twist.

Posts
It is still cold (3 F, or -16 C) , and the neighborhood streets are still mostly the type of ice that comes from cars driving over snow. The city plows do just enough to bury the sidewalks in ice but not enough to really plow the streets to pavement. Peoria, IL is a nasty city during wintertime.

But while this is one of the two really bad recent winters, it isn’t out of the ordinary by HISTORICAL standards:

Based on preliminary data, the average temperature statewide is 20.0 degrees. That is 6.3 degrees below average and ranked as the 17th coldest January on record. Of course, if the forecast holds for the rest of January, we would end up colder. Here is a list of the 20 coldest monthly average temperatures in January. The column marked “Temperature” is for the January statewide temperature and the column marked “Departure” is for the departure from the 1981-2010 average of 26.3 degrees.

Surf to the link to see the rest; note that 1994, 2009, 2010 make the list.

And yes, we are hearing “global warming is a hoax”:

(hat tip: Why Evolution is True)

More science
There is a type of shrimp that has eyes with more color receptors (12) than human eyes have (3). But:

It’s tempting to think that with 12 color receptors, mantis shrimp see a rainbow humans can’t even conceive. But Marshall and his colleagues found the opposite. They trained mantis shrimp to associate certain wavelengths of light with food. As the wavelength of light defines its color, this meant that the shrimp saw certain colors as harbingers of treats.

They then showed the shrimp two colored-lights and let them choose the one that would get them treats by grabbing or tapping at it with their claws. By altering the wavelength of the lights, the researchers could figure out how good the shrimp were at telling one hue from another.

As it turned out, the shrimp could differentiate wavelengths that were about 25 nanometers apart, essentially the difference that separates orange and yellow. In comparison, humans can discriminate shades that are as little as 1 nanometer to 4 nanometers apart.

“They’re definitely not seeing the world of color in as much detail as other animals,” Marshall said of the shrimp.

So why keep the 12-receptor system? Marshall and his colleagues aren’t sure how it works yet, but they suspect the shrimps process color very quickly by setting up patterns of receptor excitation that correspond to certain colors. Imagine, for example, that every receptor is an empty bucket. If a couple of buckets on one end of the spectrum appear full, the shrimp knows it’s seeing red. On the other end of the spectrum, the buckets represent blue.

In other words, mantis shrimp might not so much process colors in the brain as recognize them in the eye, a technique that could help the animals quickly pick out colors in their brilliant reef environment.

Note: some internet memes get this wrong. Surprised?

Speaking of coloring: this blog post discusses an aspect of knot theory and, by mathematics standards, is very readable. So if you want a glimpse of what I think about from time to time, surf there.

Now on the opposite end of the intellectual scale

The Republicans had a governor candidates debate last night; it was 90 minutes and I saw about 65 minutes of it.

The line up: treasurer (Rutherford) (won his race when Gov. Quinn got reelected), political novice BUT A BUSINESSMAN (Rauner) (and the leader in the polls ..), the state senator that Gov. Quinn beat last time (Brady, a creationist) and another double chinned state lawmaker (Dillard).

From my point of view, this was the quote of the day:

In one of the few barbs during the debate, Rutherford pledged he wouldn’t have need “training wheels” to start running the state — a veiled shot at Rauner, who has never run for political office.

“I’m a reasonable Republican. I’m not a Republican with a horn and a tail,” Rutherford said.

But Rauner didn’t back down, proudly portraying himself as a government outsider.

“I’m the only one who hasn’t been in Springfield for decades,” he said.

Since Rutherford stressed his reasonableness and openly said that diversity (racial, religious and cultural) is a good thing, and stressed that knowing what one is doing is a good thing, he has no chance in the GOP primary.

Most of the debate: “Chicago sucks, marijuana is bad, we need more educational funding but lower taxes”, etc.

Before too long, this race might devolve into “which candidate will execute more witches”.

If that remark seems too snarky, you might be underestimating how dumb the Republicans in Illinois are.

Susanne Atanus, one of two Republicans taking aim at U.S. Rep. Jan Schakowsky’s seat representing Illinois’ 9th congressional district covering Chicago’s Far North Side and the North Shore suburbs, spoke out about the incumbent’s liberal reputation during an interview with the Daily Herald this week.

“I am not in favor of abortions, I am not in favor of gay rights,” Atanus, who has staged two previous unsuccessful runs for Congress, said during a videotaped portion of the interview, before going into more detail with the paper.

“God is angry. We are provoking him with abortions and same-sex marriage and civil unions,” she added, blaming natural disasters like tornadoes and diseases including autism and dementia on recent advances in the LGBT movement. “Same-sex activity is going to increase AIDS. If it’s in our military it will weaken our military. We need to respect God.”

David Earl Williams III, Atanus’ primary opponent, can be seen smirking through much of Atanus’ statements in the Herald video and said he was offended by her comments, though he also does not support marriage equality for same-sex couples.

Yes, these remarks have drawn rebukes from some Republican leaders, but they are not that far off what many of the GOP primary voters believe.

January 24, 2014

## Woo-woos and quantum mechanics

Physics has quite a few counter-intuitive results; many of them are in quantum mechanics. That opens the door to the woo-woos, just as evolution draws attackers from religious fundamentalists.

Fortunately, mathematics is spared most of this, though we have a few cranks and crackpots; here is one of the worst cases (this guy thinks that he has shown that “countably infinite” is the same as “uncountably infinite”).

## Onward to the semester (ugh…)

Workout notes I did a slow 6 miles on the home treadmill; that was probably a mistake. I went too slow and the gait irritated that upper thigh “ding”. A “pulling” motion isn’t the best thing for it. Time: 1:06:30 (approximately).

It was bitterly cold outside and we had a bit of snow; because of the wind parts of our walk were still dry, other parts were covered with drifts. Never mind; a city plow managed to bury the “clear” part.

So I shoveled; part of it was snow that stuck to the cement (could be best cleared by a broom), with powder over it with a top “crust” layer. I can see why some would think that a snow culture would have different words for snow…though what I learned in grade school (about the Inuit having lots of words for different kinds of snow) might not be correct.

One thing I’d like to search for: gloves that let you handle something like a shovel that keeps your fingers warm.

Sometimes people use the old “I worked X hours” as some sort of badge of honor. Yeah, sometimes the work is required, but often NOT:

And then there were the breakfast meetings. I can understand why busy, productive people might sometimes want to meet at 7 AM. But what soon became completely clear was that the people who insisted on those early meetings were precisely the least competent and productive guys — the economics team at the NSC, which was totally hopeless in the Reagan years, the team at Agriculture (ditto), and so on. (No offense to current personnel, who I hope are in a completely different class; there were a lot of really strange people allegedly doing economics in the early Reagan period.) It was hard not to conclude that they were making a show of being incredibly busy and hard-working; they probably went back to their offices after breakfast and read Ayn Rand novels or something.

Meanwhile, people at USTR and the Fed, who really did know what they were doing, showed no similar fetish.

To the extent that this is a problem, I guess rules are the answer. But you wonder whether the urge to signal will just pop up somewhere else.

Yes, the above was written by someone who understands success way better than most of us.

Math: as seen
Someone caused a stir with this video, which says that one can say $1+2+3+4+....+k +.... = -\frac{1}{12}$.

Now I can understand why this makes the heads of some mathematics professors explode. We spend a LOT of time trying (with varying degrees of success) to teach students about infinite series…only to be seemingly undermined by stuff like this.

Now math professors understand the issue: what is really going on here is that there exists some well defined map between the set of sequences of real numbers to the real numbers that assigns the sequence $(1, 2, 3, 4, 5, ....)$ the number $-\frac{1}{12}$. The trouble is that the term “sum” is used, and when one hears the term “sum”, one expects some sort of compatibility with ordinary addition; that is, if $f$ is the map, then if $f$ deserves the title “sum” at all, then one would expect something like $f(1,2,3,4...) = 1 + f(2,3,4,5,....) = 3 + f(3, 4, 5,.....)$, etc. Needless to say, the compatibility with ordinary addition will be a problem here, and it isn’t with the definition of “infinite sum” that we usually (attempt to) teach our calculus students.

And yes, string theory (THAT string theory) uses this weird assignment to this particular “series”.

And speaking of math: such a tiny minority of people understand it at even an elementary level that “art” like this is produced:

There is nothing here that a freshman in a technical curriculum wouldn’t recognize; there is the limit definition for $f(x) = x^n$ evaluate at $x = 1$, and I think that they meant to write $F = \frac{dp}{dt}$ instead of $F = \frac{\Delta p}{\Delta t}$. But on the whole, aside from being common expressions in freshmen level courses, these are unrelated and just put there at random.

January 21, 2014

January 19, 2014

## Goals for 2014

Ok, these aren’t resolutions as I might not meet these.

Athletic goals:

Set of 20 pull ups (chin over that bar) without a break. Currently I can do 15.

Five 5K runs under 25 (did one last year; had several under 25:30).

Finish a walking marathon under 5:30 OR a trail 50K/30 mile under 9 hours OR a 50 mile under (14/20 hours: 14 road course, 20: trail course) OR a walking 100 km in under 24 hours.

Return to swimming; 2000 yards three times a week (build up to it)

Run a half marathon in under 2 hours (I did 2:01 two different times last year).

Run/walk 2000 miles in 2014.

STAY HEALTHY; no doctor’s visits other than routine check-ups.

Professional goals

Publish another math paper.

Finish my current referring job (next two weeks).

Submit proposal for one book.

Learn something new every week.

Charity goals

Give whole blood twice.

January 1, 2014 Posted by | mathematics, running | | 2 Comments