Time to Move?

The Institute for Health Metrics and Evaluation has a map up on their website that shows the life expectancy for men and women from 1989 to 2009 on a county by county basis. That means you can look for your county and find out, on average, how much longer you've got based on where you live. For Lake County, Illinois (next to Lake Michigan and the Wisconsin border) the life expectancy for men is 79.1 years and for women 82.3 years.  So I have about 18 years to go if I'm average. Although the number for Auglaize County in Ohio is 76.1 and my dad is 91. So maybe I still have some time to write that novel.   

There are a number of interesting details on the map. You can stroll through the years one by one and see how things have changed for your county. When you click on your county, it also tells you how far behind the top county you are (2.5 years for me). The top county for men is Marin County, California. It's also interesting that counties in the northern half of the United States are nearly uniformly higher in life expectancy than those in the southern half, especially in the southeastern part of the U.S. Several counties in Mississippi are more than 14 years behind the top county. But the way I understand it, time moves more slowly down there, so maybe it all balances out.  

I can't afford to move to the California coast to get those extra two and a half years. By that time the Illinois state legislature will have eliminated my teacher pension completely and we'll be living with Nate or Mike (probably on a rotating basis - No! It's your turn), so I'll leave it up to them.   

3/14 is Pi Day - Let's Celebrate

Every year, math teachers around the world celebrate Pi Day on March 14 (as in 3/14 or 3.14).We sometimes say that pi is 3.14, but we really mean that pi to two decimal places is 3.14. In fact pi doesn't have a decimal expansion that terminates (1/2 = .5) or repeats (1/3 = .33333 repeating forever). Pi is an example of an irrational number - it cannot be expressed as a ratio of two integers. There are some interesting irrational numbers:

i) pi - the ratio of the circumference of a circle to its diameter (about 3.14);
ii) e - the base for the natural logarithms and an important constant in population growth (about 2.718);
iii) the square root of 2 (about 1.414);

but there are a lot of irrational numbers that are just random collections of digits without any particular purpose. That would be OK if it didn't turn out that there are so many of them. In the late 1800's German mathematician George Cantor was turning mathematics upside down with his study of infinite sets. He stated that even though we can't count all the elements in an infinite set, we can assign them a "count" by putting them into a one - to - one correspondence with another set. From there he postulated that infinite sets come in different sizes. The smallest infinite set is the set of natural numbers -  1, 2, 3, 4, and so on. He used the Hebrew symbol aleph for counting infinite sets and assigned the size of the natural numbers to aleph null (here null is like zero).
That's where it started to get a little weird. Unlike finite sets, infinite sets don't behave well when you add elements. For example, suppose we looked at the set of integers: . . ., -3, -2, -1, 0, 1, 2, 3, . . . You might think this set is roughly twice as big as the natural numbers. But Cantor said that this set is the same size as the natural numbers. And he showed it by matching up the two sets

naturals       1     2      3     4      5      6      7      8      9     10     11      . . .

integers       0     1     -1     2     -2      3     -3     4     -4      5      -5      . . .

Neither set is going to run out before the other one does, so there is a one - to - one correspondence between the two sets. Therefore the sets are the same size. Cantor went on to show that the set of all rational numbers, i. e., fractions like 2/3, 17/5, -6/11, and so on, is the same size as the natural numbers as well. At that point, we might be forgiven if we think that, OK,  all infinite sets of numbers are the same size. It turns out the irrational numbers are a bigger set than aleph null. Here's how we show that. The key to matching up to the natural numbers is to put your set in some kind of order. If you look up a few lines, you can see that's what we did with the integers. We found a way to list them in an order that could then be matched up with 1, 2, 3, 4, and so on. Suppose we had some kind of order for all the irrational numbers.

first:        .328123986512970245 and so on
second:   .776823919374529476 and so on
third:      .554376920472539402 and so on
fourth:    .019283524377253628 and so on

It doesn't matter what the order is, just assume we have one and every irrational number is somewhere on the list. We can now make a new number that can't be on our list. We do that by making a decimal that is different from the first one in the first decimal place, different from the second one in the second decimal place, different from the third one in the third decimal place, and so on. Let's arbitrarily go one bigger each time with a 9 rolling over to a 0. Looking at our ordering, a new irrational number would have a 4 in the first decimal place (one bigger than the 3 in the first number), an 8 in the second decimal place (one bigger than the 7 in the second number), a 5 in the third decimal place (one bigger than the 4 in the third number), and a 3 in the fourth decimal place (one bigger than the 2 in the fourth number). Remember each irrational number keeps going to the right forever and our list keeps going down forever. So we keep up the process we outlined above. The new number we make is different from the first number (4 instead of 3), different from the second number (8 instead of 7), different from the third number (5 instead of 4), and so on forever. So it's a new number that wasn't on the list. So our ordering can't include every irrational number and the set of irrational numbers must be bigger than the set of natural numbers.Ta da!

Unfortunately, Cantor raised almost as many questions as he answered. The set of real numbers, which includes the rational and irrational numbers together, is commonly called the continuum, and the letter c is used to stand for the size of the set of real numbers. They couldn't use an aleph name because they didn't know if it should be aleph - one or aleph - two or whatever (remember aleph - zero was the natural numbers). So the continuum hypothesis is that c is really aleph - one, that is, the real numbers form the next size of infinity up from the naturals. Unfortunately nobody has been able to prove or disprove this in the 120 years since the question was first posed.

So, enjoy Pi day. I prefer apple or pecan or cherry pie myself, but it's the thought that counts. You may not be a pie person, but there are a lot of them out there. For example, as Nathan would tell you, if you hang around with World War 2 veterans for any length of time, you're going to eat a lot of pie.

HAPPY  PI  DAY !!!

You Can't Make This Stuff Up

Scientific American writer Davide Castelvecchi posts the following clip from a newspaper article about how much we Americans hate mathematics.    

 

What more can I say? I could offer my math tutoring services, but I mostly tutor high school or college calculus students, not 3rd graders studying basic fractions. I would hope we wouldn't need a full hour to go over this. Maybe instead of the library where I usually meet the students, we could meet at a pizza place. Hands - on manipulatives would probably help.     

Big Fish, Again

Back in 2011, when Marshmallow Fight was asking people to list their top ten movies, I had Big Fish at number 9 on my list.It has always been a movie that makes me tear up, because its all about family, fathers and sons. It is a Tim Burton movie, but don't let that stop you from watching. Some people aren't big Burton fans like I am, but this movie has just the right touch of the fantastic. And Ewan McGregor as the young Edward Bloom is great.    

              


On my top ten movie list, I included this exchange from Big Fish between old Edward Bloom (Albert Finney) and his son Will (Billy Crudup):  

Senior Ed Bloom: You are in for a surprise.
Will Bloom: Am I?
Senior Ed Bloom: Havin' a kid changes everything. There's burping, the midnight feeding, and the changing.
Will Bloom: You do any of that?
Senior Ed Bloom: No. But I hear it's terrible. Then you spend years trying to corrupt and mislead this child, fill his head with nonsense, and still it turns out perfectly fine.
Will Bloom: You think I'm up for it?
Senior Ed Bloom: You learned from the best.   

What brings the movie back to mind is that the original novel Big Fish by Daniel Wallace is being turned into  a Broadway musical. And, as many of them do, it opens in Chicago for five weeks first to get the bugs out. And, I now have tickets for the show on April 30th. Ann and I are treating it as a delayed 40th wedding anniversary outing. I think Nate and Dana are going with us. If anyone else would like to join us, please check at Broadway in Chicago for tickets. We're in center orchestra section, row U. Let us know if you are coming. We'll find a good place to eat afterwards.   

And on a related note, it is time for Marshmallow Fight to come up with a new list. So far, we have done songs, movies, and books. If you have a suggestion for a new list, let me know. Top five foods, vacation destinations, dog names (Barf Bag is still my favorite), whatever you can think of. Once we get a topic, we'll let everybody know to start sending in lists.  Thanks.    

The Disappearing Middle Class

Came across this video on YouTube that had been highlighted on Dan Ariely's blog on behavioral economics. Thought it was really interesting.  





In many ways, I think my generation is probably the last to have a legitimate chance to aspire to a true middle class. Ann and I were both public school teachers. We enjoyed what we did and felt we made a difference to our students. Because of that, we passed on the chance to get rich. But we did expect (and were able) to make a decent living, buy a house, provide for our kids, and have a comfortable retirement. The next generation is finding that a more difficult task. The amount of money available to the middle class is significantly smaller than it was thirty years ago and a much larger number of people are going to be in that lower middle class where home ownership may be a stretch. It will be much harder to make the kind of living that we took for granted. And it is taking longer for them to reach the stage where they can be truly independent. I talked to a mom today whose daughter is 27 and living at home because she can't get a job that would allow her to be on her own. Notice I didn't say "Can't get a job." She has what we would have considered a good job: assistant editor at a local newspaper. Unfortunately, it pays $27,000 a year. Even with a roommate, rent and utilities would take 35 to 40 % of her take-home pay. That wouldn't leave a lot to pay for groceries, car and insurance (needed to work in the suburbs), health insurance (not fully included in her job) and other essentials, let alone save for buying a house. So I worry about where our kids and their kids are going to end up in thirty years.    

It's Not the Donut, It's You!

The Science 2.0 website has an article by Greg Critser about the current war on obesity. It is an interesting approach to a difficult problem. How do we get Americans to stop eating so much sugar and junk food and exercising more? And the answer, according to the researchers that Critser talked to, is, "We don't." Slowly, these heretics in the field of nutritional science are saying that, in spite of the huge push in the last ten years about eating healthy and exercising, we haven't made a significant dent in obesity. Did we really think that outlawing the Big Gulp was going to make us all skinny? That's just stupid (or legislative, but I'm being redundant). These new researchers are "slowly and painstakingly shifting their inquiry to a more basic issue: homeostasis--the body’s innate capacities to recover from any kind of disturbance--and how we can strengthen those balancing mechanisms."  

Theirs is not a difficult premise to understand. Consider: The human phenotype--the body our genes and environment dictate--has been shaped by evolution to adapt, to bend and flex and return to balance when confronted with a challenge, be it a Big Gulp or bad air. You eat a huge hit of sugar, your body pumps out insulin to make it possible for your cells to use it and return to balance. It’s an intricate, elegant system that worked just fine until we engineered an environment that made sugar virtually free and almost everywhere present. Then the system crashed, and we got our intertwined epidemics of obesity and diabetes.     

So, the focus is on strengthening those balancing mechanisms in the body to counteract the bad stuff that comes in.   One such study, by a renowned diabetes researcher in Sweden involved adding a rye grain mix to type 2 diabetic's food in the evening, then having a traditional (non heart healthy) meal the next morning for breakfast (ham, eggs, bacon, etc.). In the study, the group fed the rye mixture handled the breakfast the way any normal non-diabetic would. Those not fed the rye mix beforehand had insulin and blood sugar responses that were impaired and diseased.   

“We don’t know why it works,” Inger Bjorck says. “But we have some idea. We think it involves some kind of gastric memory, maybe driven by fermentation in the gut, that we, as humans, once possessed, but which we lost when we began consuming our modern wheat mono-culture.”   

This approach is not going to sit well with the billion dollar "healthy lifestyle" industry. But in the long run, it may have more impact than telling people to change what they've been doing for forty years.  On the researchers' side is a nearly universally held vision of what health means:  

As articulated by one of its earliest 20th century proponents, the brilliant Johns Hopkins' pioneer Henry Sigerest, health “is not just the absence of disease. It is something positive, a joyful attitude to life, and a cheerful acceptance of the responsibilities that life puts upon the individual... A healthy individual is a man who is well balanced bodily and mentally, and well adjusted to his physical and social environment."   

There aren't a lot of "joyful attitudes to life" that I hear about when I'm preached to about why I'm overweight.  Mostly it's more the "Bad dog!" finger pointing. "Why can't you be more like us - skinny and in shape? What's wrong with you?" 

Gee, I wonder why the "healthy lifestyle" people are not having much success, other than in making money.  

 

Week 2 Almost Over

So, the morning after my hip replacement surgery, the surgeon stops by to see how I'm doing and gives me an x-ray picture of my new hip.   

 

I half expected him to give me the old hip parts like they used to do at the car repair place, just so I knew he had done something. The bright shape on the left of the picture is my new ball and socket joint right hip, stainless steel, I think. You can see dimly on the right of the picture, my original left hip to compare it to. I still don't know if this thing will set off the scanners at the airport.  

Lots of milestones in days 7 through 13 after the surgery:  

Physical therapy moved from walker to cane and even some walking yesterday and today without a cane.  I waddle badly, but I'm getting stronger and steadier. And Whimzy is happier with no cane because Dad with a stick is pretty scary.

Sleeping on my side now instead of my back. The therapist had to show me how to get there, and there are more pillows involved than you would imagine. The two major hip precautions everybody keeps repeating are: i) the angle between your thigh and your upper body can never be less than 90 degrees, and ii) never cross your legs. So, when you sit, you have to lean back and you can't lean forward to reach for something.

Access to the desktop computer. I can sit in the office chair now without any problems getting up.

Able to get out of the house. Last night we went out to dinner with Mary and Dave. It was nice to be somewhere else.  I got around fine with my cane. Even better, it means I can go to my school board meeting Thursday. Ann will have to drive me, but that's not a problem.

Most importantly, I've been cleared to take showers again. That was a long ten days. Luckily, the incision looks fine and has healed over nicely.   

I still haven't tried to take the dog outside yet. Ann has been on dog patrol. I'm mostly worried about what Whimzy would do if we went out the door and there was a squirrel in the driveway. But we'll work on that this week. Plus 8 inches of snow forecast for Monday night and Tuesday will raise some issues about getting around to go to my meetings.    

Anyway, I'm making really good progress. Might be able to catch a Bulls game in late March after all. If I'm able to come back and watch, Derrick Rose should be able to play again, right?