Loving To Learn

Between the ages of three and five I learned to add, subtract, multiply, and divide numbers of any size. I also learned the US version of the prefixes million, billion, trillion, and so on, up to decillion. I found that I could add columns of figures quickly by either seeing them or hearing them. One day when I was five or six I was in the neighborhood grocery store with my mother and overheard the owner calling out the prices as he totaled up the customer’s bill on his adding machine. When he announced the answer, I said no, and gave him my number. He laughed good-naturedly, added the numbers again, and found I was right. To my delight he rewarded me with an ice-cream cone. After that I dropped by when I could and checked his totals. On the rare occasions when we disagreed, I was usually correct and would get another cone.

My father taught me to compute the square root of a number. I learned to do it with pencil and paper as well as to work out the answer in my head. Then I learned to do cube roots.

Before the advent of writing and books, human knowledge was memorized and transmitted down the generations by storytellers; but when this skill wasn’t necessary it declined. Similarly, in our time with the ubiquity of computers and hand calculators, the ability to carry out mental calculations has largely disappeared. Yet a person who knows just grammar school arithmetic can learn to do mental calculations comfortably and habitually.

This skill, especially to make rapid approximate calculations, remains valuable, particularly for assessing the quantitative statements that one continually encounters. For instance, listening to the business news on the way to my office one morning, I heard the reporter say, “The Dow Jones Industrial Average [DJIA] is down 9 points to 11,075 on fears of a further interest rate rise to quell an overheated economy.” I mentally estimated a typical (one standard deviation ) DJIA change from the previous close, by an hour after the open, at about 0.6 percent or about sixty-six points. The probability of the reported move of “at least” nine points, or less than a seventh of this, was about 90 percent, so the market action was, contrary to the report, very quiet and hardly indicative of any fearful response to the news. There was nothing to worry about. Simple math allowed me to separate hype from reality.

Another time, a well-known and respected mutual fund manager reported that Warren Buffett, since he took over Berkshire Hathaway, had compounded money after taxes at 23 to 24 percent annually. Then he said, “Those kind of numbers will not be achieved in the next ten years — he’d own the world.” A quick mental estimate of what $1 grows to in ten years compounded at 24 percent gave me a little over $8. (A calculator gives $8.59.) Since, at the time, Berkshire had a market cap of about $100 billion, this rate of growth would bring the company to a market value of roughly $859 billion. This falls far short of my guesstimate of $400 trillion for the present market value of the world. The notion of a market value for the whole world reminds me of a sign I saw on an office door in the Physics Department of the University of California, Irvine. It read earth people, this is god. you have thirty days to leave.i have a buyer for the property.

Just after I turned five I started kindergarten at Dever Grammar School in northwest Chicago. I was immediately puzzled by why everything we were asked to do was so easy. One day our teacher gave us all blank paper and told us to draw a copy of an outline of a horse from a picture she had given us. I put little dots on the picture and used a ruler to measure the distance from one to the next. Then I reproduced the dots on my piece of paper, using the ruler to make the distance between them the same as they were on the picture and with my eye estimating the proper angles. Next, I connected up the new dots smoothly, matching the curves as well as I could. The result was a close copy of the original sketch.

My father had shown me this method and also how to use it to draw magnified or reduced versions of a figure. For example, to draw at double scale, just double the distance between the dots on the original drawing, keeping angles the same when placing the new dots. To triple the scale, triple the distance between dots, and so on. I called the other kids over, showed them what I had done and how to do it, and they set to work. We all handed in copies using my method instead of the freehand sketches the teacher expected, and she wasn’t happy.

A few days later the teacher had to leave the room for a few minutes. We were told to entertain ourselves with some giant (to us) one-foot-sized hollow wooden blocks. I thought it would be fun to build a great wall so I organized the other kids and we quickly assembled a large terraced mass of blocks. Unfortunately my project totally blocked the rear door — and that was the one the teacher chose when she attempted to reenter the classroom.

The last straw came a few days later. I sat on one of the school’s tiny chairs meant for five-year-olds and discovered that one of the two vertical back struts was broken. A sharp splintered shard stuck up from the seat where it had separated from the rest of the strut, so the whole back was now fragilely supported only by the one remaining upright. The hazard was obvious, and something needed to be done. I found a small saw and quietly cut off both struts flush with the chair’s seat, neatly converting it into a perfect little stool. At this, the teacher sent me to the principal’s office and my parents were called in for a serious conference.

The principal interviewed me and immediately recommended that I be moved up to first grade. After a few days in my new class, it was clear that the work there also was much too easy. What to do? Another parent–teacher conference. The principal suggested skipping me again into second grade. But I had barely been old enough to qualify for kindergarten: I was a year and a half younger on average than my first- grade classmates. My parents felt that skipping another grade would leave me at an extreme social, emotional, and physical disadvantage. Looking back on twelve years of pre-college schooling, where I was among the smallest and always the youngest in my class, I think they were right.