Try pencil and paper, forget the calculator

Bob Doyle, Columnist

One of my biggest concerns about our society is the growing alienation from numbers. With few exceptions, most of us rarely focus on numbers.

Some exceptions are when we review our income tax forms, compare the prices on a restaurant’s menu or plunk coins in a vending machine.

The swiping of credit/debit cards, automatically paying one’s monthly bills with our credit cards and direct deposit of our paychecks or social security checks into our bank accounts are ways that these financial exchanges are kept concealed from us. Then it becomes quite easy to have your credit card balance grow to thousands of dollars.

Being unaware of numbers also led many people to acquire homes beyond their means, leading to the high rates of foreclosure. (Bank officers were also complicit in the granting of these mortgages.)

How can we become more comfortable with numbers? In teaching my students in doing problems, it helps to break down each problem into a number of small steps, with each step written out on the board. By putting the steps down on paper, you can see how the numbers are developing and progressing towards the answer.

It is also easier to spot mistakes in the various stages of the problem. If one tries to get the answer by using a calculator and a long series of key strokes, most students end up with an wrong answer, often much larger or much smaller than the correct answer.

Here’s a problem regarding radioactivity. A radioactive atom or nucleus is unstable due to either too many protons (+ charge) or too many neutrons (no charge). For every type of radioactive nucleus there is a half life, a time over which half of these nuclei will decay or change into another element. The half lives are calculated using nuclear physics, the field that explains how the sun shines and predicts the heat flow in a nuclear reactor.

A special kind of radioactive nucleus is Carbon-14, about 1 carbon in a million. The C-14 half life is 5730 Earth years. Carbon-14 dating is used by archeologists to determine how old skeletons are, the charcoal in a fireplace, the age of the bandages around mummies, etc.

The Carbon-4 concentration in your body is fixed as very fast charged particles from outer space create Carbon-14 in our atmosphere at a constant rate; this Carbon-14 is inhaled by plants, which we eat or in the plants which our farm cattle, pigs or chickens eat.

So as we consume pork, chicken or beef, we also take in Carbon-14. Suppose an old skull contains 1/8 as much Carbon-14 as a fresh bone.

The fraction of 1/8 = 1/2 x 1/2 x 1/2; this means that three half lives have elapsed. Three half lives will be three times one half life or 3 x 5730 = 17,200 years, the age (since death) of the skull.

Another problem is to determine the distance that light travels in one year. The speed of light is 186,300 miles per second Thus 186,300 miles is the distance that light travels in 1 second. How many seconds are there in an hour? There are 60 seconds in each minute and 60 minutes in an hour so the number of seconds in an hour are 60 x 60 = 3600 seconds.

How many hours are there in a year? There are 24 hours each day and 365.25 days in a year, so the number of hours in a year is 24 x 365.25 = 8766 hours per year. Then if each hour has 3600 seconds, then total number of seconds per year will be 3600 x 8766 seconds = 31,560,000 seconds.

Lastly we multiply the distance light travels in a second by the number of seconds in a year, we get a huge number of 5.88 trillion miles where a trillion has 12 zeroes (as many zeroes as the number of eggs in a carton).

By breaking up every problem into a series of small steps and writing down these intermediate results, you are much more likely to detect any blunders and thus be more certain of a correct final answer.

Our corner show & egg moon

Our new April program at the Planetarium is “Earth from Our Corner of the Galaxy.” The night sky is speckled with relatively nearby neighbor suns, members of a vast galaxy of billions of suns.

In our March program, we considered how the Earth would be viewed by both distant and the nearest dense star clusters in our galaxy. Using the concept of look back time (the farther away an object is, the farther back you are looking back in time), the views from these objects would reveal the key events in the story of Homo Sapiens, our species.

Our April program considers the most impressive objects in our corner of the galaxy (within a distance of 15,000 light years); these include stunningly beautiful gas clouds, open star clusters and some of the most powerful suns seen in the current evening sky.

The Earth views of these objects would witness the first human settlements, the development of the river valley cultures, the rise and fall of mighty empires and the development of modern science from 1600 to 1900.

Our free public programs are held today, April 19 and 26 at 4 p.m. and 7 p.m. The Planetarium is in Tawes 302, just off the front lobby as you enter Tawes from the side nearest Compton Science Center.

Call (301) 687-7799 to request a free bookmark that includes a small campus map, showing convenient free parking near the Planetarium. April sky charts are available, too.

This Thursday, the moon is full, appearing near the star Spica of Virgo. This full moon can be called the Egg Moon, as it is the full moon preceding Easter (next Sunday). There will be no planetarium programs next Sunday.

Readers are invited to comment or ask questions; either call the above number or email rdoyle@frostburg.edu .