Interest in Numbers

I’ve been interested in math all my life but I’m not what is commonly understood as being a mathematician. I like numbers but mainly for their entertainment and useful benefits.

As a child, I once computed all possible fractional values from 1 to 154 to four or more places; I don’t remember exactly. These included such fractions as ½, 1/3, 1/4, etc., to 1/154; also 2/3, 2/4, 2/5, etc., to 2/154, etc. There were perhaps about 12,000 calculations needed and I spread the work over a long period of time. In doing this I observed that there are many shortcuts that could be used; for example, 1/2 has the same value as 2/4, 3/6, 4/8, etc., and 1/3 has the same value as 2/6, 3/9, 4/12, etc.

I don’t know why I did this; it seemed like a good idea at the time. When I became a computer programmer, I was able to write a very short program that accomplished the same task in only a few minutes.

At a time when I should have known better, I wrote a letter to a local TV station that said, “Concerning your decision to show movies on your channel, 1,000,000 thanks.” Then I had the computer print the letter including one million “thank you”s automatically printed. I had no idea that this would require a lot of paper. I stopped the printout when I saw a stack of paper that was getting larger and larger by the second. A quick calculation showed that I would have needed over 1500 sheets of paper to print all these thanks. I changed the letter to say, “many thanks” and printed a single sheet of them.

When teaching computers, I enjoyed telling the story of the kid who got rich. He convinced his parents that they should pay him for doing chores in June for one cent the first day, two cents the second, four cents the next, etc., doubling the number of cents paid until he had worked under this arrangement on June 30th. The amount he needed to be paid came as a monumental surprise to the parents.

I’m dismayed that these days, many persons can’t do simple arithmetic for everyday living when al that is really necessary is knowing how to add, subtract, multiply, divide, understand fractions, decimals, and percentages.

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Ten Teaching Rules

As a teacher of computers and computer science for forty years, I feel I can list the test most important rules about teaching. They may not apply to all forms of teaching but, I feel, I can offer them for teaching scientific material. The rules that follow are not in any special order. They are all important. You are the one who determines which is the most important at any given moment.

1 Know the material. You need to fully understand at least twice as much as you plan to teach. The more you know the better.

2. Have a good command of the English language. You can’t afford to be vague about what you’ll be telling student.

3. Know your students’ names. Make this a personal experience for students. Have them understand that they are persons to you, not just faces in an audience.

4. Learn, at least, a little of what they already know about the subject and why they are taking your course.

5. Present material at about one-third the speed that you might, at first, believe is needed. This is all new to students and they require a little time for it to be absorbed.

6. Know your students. Begin at a point that is comfortable to at least ninety percent of your audience. Define or review terms you will be starting with.

7. Repeat important points frequently. Use different words than you did the first time if necessary. Use examples to illustrate your points.

8. Watch your students to ensure that they are understanding what you’re saying. If you see puzzled faces, back off, resume at some point where students are with you.

9. Be open to questions. Questions often reveal something you may have not explained or not fully explained.

10. Exercise patience. Never show annoyance over someone not understanding or not understanding readily enough.

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Seven Lucky Factors in Choosing a Good Stock

When I’m preparing to purchase a stock that I’ve currently don’t own, I look for these qualities:

1. The stocks needs to have a long history of earnings growth over at least the last five years, quarter after quarter with rare exceptions. If there have been exceptions, they should not in the most recent reports.

2. The stock needs to pay a regular dividend. The yield can be as little as one percent. Two or three percent would be better.

3. The company that issued the stock should have a long history of having paid a dividend and a long history of having increased its amount.

4. The P/E ratio should be somewhere between 10 and 20; right in the middle would be ideal. This ratio could be somewhat higher in bull markets and somewhat lower in bear markets.

4. The stock should be one of the 30 industrial stocks in the Dow Jones Average or one that has every bit the recognition and reputation factors.

5. The company’s business should be global.

6. It should have good management. This may be difficult to ascertain.

7. It should have a relatively low debt. A total absence of debt would be ideal.

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To Stamp Out Inflation

It was around 1952. I was with General Electric. GE had launched a campaign against inflation. We employees were being asked to agree that inflation was bad. I didn’t see it as clearly as I do now that was correct. I thought that a little inflation was actually good since it would make money easier to get and debts like those for a mortgage would be easier to pay off.

General Electric started a contest. Any employee could submit a motto, saying, or proverb depicting the evils of inflation. The winner was to receive a prize. I decided to enter.

I sent in this little jingle:

To stamp out inflation, there’s only one way.
Give an honest day’s work for an honest day’s pay.

This won first prize and my picture appeared in the G. E. News standing next to a GE Hi-fi Phonograph Player. General Electric had many thousands of employees at that time and the News was published weekly. I became an instant celebrity with the workers near me.

General Electric was right. Inflation is an insidious hidden tax on everyone. As time goes by, money becomes worth less and less. It’s a slow process so people don’t see its affect over the short time. But given a few years, it’s easy to see what happens. Money that one saves buys less over time. Over a period of forty or fifty years only about one-tenth of what it could before. The value of your home, which sees huge in comparison with what you bought it for, has dwindled to the point where there is virtually no gain. A worker earns a lot more but the cost of everything as gone up more. When a person retires, he or she often finds that a life style that seemed affordable suddenly begins to strain the budget almost to the bursting point.

I’m good with slogans and invented this one:

We get born and spend the rest of our lives striving to stay out of the poor house.

I say this with tongue in cheek. This doesn’t happen to everyone. And if I avoid retiring indefinitely, I may be able to avoid this eventuality completely. But it may seem to be a hollow victory to state at the last moment, “Well, at least, I stayed out of the poor house!”

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Betting on the Numbers

In 1941, when I started my first job at The American Locomotive Company in Schenectady, I met a numbers runner for the first time. An individual would come to the area where I work and take bets from workers. There was a game the workers played. If I guessed what the number to come out the next day was going to be, I’d get $540 for every dollar that I bet. The number to guess could have three digits from 000 to 999. This was a marvelous reward, I thought, and tried doing it for a while. I didn’t win anything so I reduced the amount bet to ten cents and made ten bets each day. My reasoning was that I had ten times as much chance to win. My bets were no more successful with this strategy than they had been before.

I thought about the problem and hit upon an idea that I thought might work. I asked the runner if he could give me a list of the winning numbers for the last several years. He was able to do this and did. I divided the numbers into 100 groups of ten numbers each. (There are 1000 possible numbers between the numbers 000 and 999. ) I numbered each group from 1 to 100 and made a table that showed how many time a number had won in each group. Some groups had one or two winning numbers, some six or seven, some none. I felt that if there had been no winning number in a particular group for a long time that group was due! That is, if a group had not had a winning number within it, the chances of that group receiving a winning number was better than they were for the groups that had had a few or even many winning numbers. I restricted my bets to groups that had not had a winning number for the longest time.

As before, none of my bets won. This puzzled me greatly. Where had my logic gone wrong? I stopped betting feeling that the numbers knew me and didn’t want to give me any winners. It was long time before I finally learned that numbers have no memory. The chances that any one number would win on any particular day were 1000 to 1 against winning. These were the chances for every number every day. It did not matter how long a number or a number within a group had not come out.

The reward of 540 to 1 was not at all generous. The mathematics of what I had been doing showed me that for every thousand dollars I played in this game, I would lose $460.

This experience soured me against gambling in general. I do invest in stocks. Some people might deem this to be gambling.

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