Our magic carpet

As temperatures moderate and our towering snow banks diminish, the snowmelt largely runs off into municipal storm drains and finds its way into Narragansett Bay. Not so fifty years ago.

On the high plateau above Lake Erie, the two-hundred inch snowfall began to melt during late winter and turned the road to muck. Back then, the main highways were paved but many farm roads like ours were plain dirt. At worst dusty in the summer, during mud season they became impassable. Our salvation turned out to be the neighbor’s old two-banger John Deere tractors. Tall and sturdy, these machines had nearly three feet of ground clearance and needed every inch. Driving down the middle of the road, the front wheels would become buried to the top and steering was accomplished only by skilled application of individual braking to the huge rear wheels. The tractors would bog and complain, but always managed to deliver us up the hill.

Our cars were parked near the pavement at the bottom of the hill, nearly a mile away. We took turns shuttling each other back and forth using our communal magic carpets, these magnificent machines. There was no other way to travel unless one were willing to slog through knee deep, sucking mud.

Mud season was problematic because the cows never stopped their natural processes, and the byproduct thus produced still required daily collection and spreading in the fields. At times a tractor in such duty would sink a bit too much and become high-centered in the mud. But always the other would come to the rescue and pull the errant rig, tractor and spreader, to firmer ground. Tractors always work better in pairs, a truth that seems to be mirrored in good marriages.

In later years, copious dump-truck loads of gravel firmed up our road and allowed year-round access via automobile. But I will never forget the season of mud and the sturdy tractors that served as our lifeline to the outside world.

Mathematical illiteracy

Kevin Alexander Gray, in a recent opinion piece, is either mathematically illiterate or hoping that you are. I suspect the latter.

Mathematical literacy has more to do with logic and reasoning than it has to do with numbers. Fabulists such as Gray hope that you are either unable or just too lazy to think through their illogic.

Gray upbraids President Obama for abandoning the poor with his most recent budget proposals. The tool he uses to fool you is the mixing of time scales. When describing the President’s budget, Gray presents you with a list of annual budget figures:

- “proposed $3.73 trillion budget…”

- “cutting $2.5 billion…”

- “slash … the $350 million…”

Then Gray castigates the President for approving “$858 billion in tax cuts for the wealthiest Americans.” One is led to think that, if only that tax money had been captured, the budget reductions would be unnecessary. Only one problem - the infamous “tax cuts for the wealthy” is a ten year estimate, not annual. Just shift the decimal point to estimate the annual revenue impact of the tax cut: about $86 billion .

The Congressional Budget Office estimate of the 2011 deficit is $1,500 billion. If the President had been able to collect and apply one year of the “wealthy tax cuts” to this deficit, he would have been able to reduce it by 5.7% (from $1,500 to $1,414 billion). At that rate it would take 17 years to pay off the 2011 deficit. But in the meantime we would have accumulated an additional $25,500 billion in debt (at current rates).

The debate will continue to rage on job creation and GDP growth and taxation rates and how we enable the poor to participate in our productive economy. But those debates are not enhanced by mathematical illiteracy, intentional or otherwise.

"Uncle" Sam indeed

97 Orchard Street, on Manhattan’s lower east side, is a classic nineteenth century tenement house. Operated as a museum, the period-authentic apartments portray the lives of our immigrant ancestors. Featured are Irish, German, and Italian apartments with all the furniture, utensils, clothing, and bric-a -brac of everyday family life 75-150 years ago.

From our 21^st century perspective, we view it quaint that our progenitors often lived three generations to a household – babies, parents, and a grandparent or two all in crowded harmony. Nonna and Nonno provided babysitting and wise counsel while Mom and Dad worked and were in turn supported by these erstwhile, grateful adult children.

Today, the Massachusetts congressional contingent are complaining bitterly that folks in Alabama and West Virginia and North Dakota, et al, aren’t being forced to subsidize our senior housing and heating aid programs. Seems that Massachusetts could pay for that themselves without seizing other peoples' money.

In more bucolic times, we met our life needs primarily by self effort and responsibility. If unable for any reason, our family was the next bulwark. Failing that, churches or local charities. Then, only grudgingly and with some degree of ignominy, government, be it local, state, or federal.

It is a rather odd thought that the federal government, with its power of confiscation, should support Nonna and Nonno so that their children can cavort in Aruba.

How far we have come.

The winter of our contentment

It is challenging that we have had nearly 70 inches of snow near Boston this winter. Everyone is properly sick and tired of shoveling and slipping and sliding about. But hope abounds – spring will soon be here.

Memories abound as well. Late 1950s, high on a plateau above Lake Erie, with an unobstructed view 35 miles across the lake to Port Maitland, Ontario, Canada. In the winter, the snow clouds scudded low and dark across the lake and the wind howled out of the near Arctic north. Deep snow drifted heavily and became much deeper where the wind tired and dropped it.

At the top of the hill above us, the road peaked then dropped quickly to a T-intersection with another farm road. That particular winter, a storm dumped heavy snow and the wind sculpted it into lovely forms that buried the stop sign at Miller Road nearly thrice its height – a 25 foot deep drift. Now this is pure candy to children who tobogganed and sledded and tunneled in that great drift, but the county had the duty to bust the roadway clear.

First up were dual Oshkosh diesel trucks, mounted with massive v-plow blades which rammed and battered into the huge drift, one from the north and one from the south. But neither could break through; heavy black plumes of diesel exhaust stained the sky as the monsters rumbled to a stop, beaten by the huge pile of snow. We watched, entranced, retreating occasionally to a neighboring farm house for a warm interlude of hot chocolate, but soon back to see how the grownups would deal with this conundrum.

After some scratching of heads and puffing of pipes, the elders called up their course of last resort. Shortly after, a third truck pulling a large trailer arrived and unloaded a Caterpillar D6 bulldozer, fortunately equipped with an enclosed cab. The bulldozer operator fired her up and backed the 18 ton crawler off the trailer. Then, after the engine was thoroughly warmed, he raised the blade a few inches and advanced at top speed into the drift. As the engine strained and belched black smoke, the crawler slowed but continued and disappeared completely into the huge drift. As we watched, awestruck, the huge machine eventually emerged seventy five feet further up the road, having cleft the drift in twain. The operator emerged from the enclosed cab and brushed the packed snow from his gallant machine as the twin Oshkosh plows attacked with renewed vigor and success.

We will always remember the valley of snow thus created, twenty five feet deep with steep slopes on both sides which offered immense opportunity for climbing and sliding. It was with regret that we acknowledged the warming sun and longer days that marked the end of a most wonderful winter.

Statistical Illiteracy, or How Eating Ice Cream Causes Sunstroke

Dan Domenech is a highly educated man. The Executive Director of the American Association of School Administrators, Dr. Domenech was once Superintendent of the Fairfax County (Va.) Public schools (168,000 students) and holds a Ph.D from Hofstra University.

Domenech is also statistically illiterate. That’s a shame for one whose mission is to help school administrators advance the goals of public education and advocate for the children.

Statistical illiteracy is shockingly common in our society. As one wag observed, 8 out of 5 people suffer from it. More seriously, Gerd Gigerenzer, an eminent German psychologist, recently wrote that “Statistical literacy is a necessary precondition for an educated citizenship in a technological democracy.” He is absolutely correct. It is vital that voters, politicians, bureaucrats, journalists, health professionals, and all manner of businesspeople understand the numbers behind policy decisions that we must make.

What was Domenech’s statistical faux pas? In a recent interview with National Public Radio, Domenech weighed in on the case of an Ohio mother who sent her kids to another school district for a better education. She was found out, tried, convicted, and imprisoned (briefly) for lying about her residency. Domenech, decrying the disparity in education quality between districts, said: "The correlation between student achievement and zip code is 100 percent. The quality of education you receive is entirely predictable based on where you live."

First let’s review a brief definition of correlation. When two measurements tend to move together, they are said to be correlated. For instance, if you were to prepare a table of daily ice cream cone sales and daily high temperature, you would see that more ice cream is consumed at 90 degrees than at 30. Ice cream sales and temperature are said to be correlated. Similarly, a comparison of sunstroke incidents to temperature would show a kindred relationship. But one must be careful – correlation does not imply causation. If you looked only at sunstroke rates and ice cream cone sales, they would also be correlated, that is, high sunstroke rates occur with high ice cream sales and vice versa. But one cannot say that eating ice cream causes sunstroke. Behind the scenes, they are both correlated with a common variable – the temperature.

Correlation is represented by a number between zero and one that describes the degree of relationship between the two variables. A correlation of zero means that variables are completely unrelated, such as the cost of bubblegum and the distance between star clusters. A correlation of one, on the other hand, means that the variables are perfectly related, such as the number of pennies represented by various dollar amounts.

A discussion of direct vs. inverse and negative correlation will be postponed to a future topic.

So let’s return to Dr. Domenech. If the correlation between student achievement and zip code were indeed 100%, then all of the students in a given zip code must have the same grade. All students in 90210 must have a C grade, and all in 20511 a B, or the correlation is not 100%. But we know that that is untrue. Some students in 90210 get A grades, and some are awarded D grades. There is variation within the student body that is caused by will, ability, and parental expectation among other things. So it is patently untrue that “the correlation between student achievement and zip code is 100 percent.” Domenech should be made to sit in the corner with a dunce cap until he learns his lesson. (Perhaps the problem is that we no longer do such things).

As a responsible citizen and voter, the most important thing you can do to make informed decisions is to arm yourself with basic math skills and not be afraid to challenge those who appear to be speaking from a position of authority. Our intellectual and political elite are not always completely accurate, sometimes from ignorance and sometimes from calumniation. I’m sure that you are shocked.