What follows 99,999?
—the ‘Range
Rider’ knows—Los Angeles
Times, March 22, 1976
I came across a true
artifact not long ago while browsing through some old notes and textbooks. It is, beyond a doubt, one of the oldest items
I have from those days when school wasn’t synonymous with training for a job.
This relic, my 1953
edition of a third-grade arithmetic book, Range
Rider: Adventures with Numbers, is older than my Boy Scout manual, my coin collection
or my English racer.
In the two decades that
have passed since I learned to add, subtract, multiply and divide, I have
steadily advanced, climbing to such heights as trigonometry, calculus,
differential and statistical analysis.
But no course, no text has provided the pleasure rekindled by
discovering this 23-year old edition of Range
Rider.
In degree of
difficulty, it followed immediately after Busy
Beavers and preceded Straight
Shooters and Airplane Aces. It was several courses removed from the more
difficult Home Run Hitters and Cage Champions.
These titles, while
quaint and possibly amusing, actually fail to describe just what the particular
subject matter was. For this reason, I shall offer a quick rundown of what we
learned in the third grade, thanks to Range
Rider.
In the beginning—to
paraphrase another author whose habit it was to delve into the past—there was
reading and writing numbers up to 99,999. This was where third grade stopped
and what an appropriate place to pause. Imagine the suspense of waiting all
summer to find out what came after 99,999.
From this meager
beginning we leaped ahead to multiplying and dividing. But the most exciting
facet of Range Rider is not what it
taught, but how it taught. After reading countless college texts, I am
convinced that they purposely remove any colorful tidbit of information that
might make the lesson the least bit enjoyable. Not so in the third grade, and
definitely not so in my Range Rider.
It was a veritable treasure house of vital but unfortunately forgotten information.
For instance, I
have always thought the Mississippi to be our longest river. Not so! The
Mississippi is only 2,486 miles long; The Missouri is 2,945. Simple
subtraction, as explained on the same page, shows that the Missouri is longer by
459 miles. There is no excuse for not knowing this.
Likewise, I can
only assume that I was daydreaming about recess or writing notes to Sally when
the following valuable figures were presented, for I have no recollection of
them at all. The crown of the King of England contains 2,783 diamonds and 277
pearls. It’s all there on page 3 under the heading, “More Big Numbers from
Geography.” The obvious question—and the book asks it—is, how many more diamonds
are there than pearls? But I’m not giving away any more answers.
It wasn’t until I
reached page 40 that I made my most important discovery. It was there that I
learned, after 20 years of working with numbers, that I have been doing one
procedure all wrong.
What I
misunderstood so totally was the chapter on “Ghost Figures,” which explained
the process of carrying over numbers when subtracting a large number from a
smaller.
In the example, 727
minus 269, I now realize it is necessary to borrow the 10 from the 2 to make
the 7 a 17, resulting in the 2, which is really a 20, becoming a 10. Simple enough—and yet I have never in my life
worked out a problem in this manner.
For some mysterious
reason I have always followed the practice of adding 10 to the top making the 7
a 17 by simply picking it out of nowhere. Of course, since I added 10 to the
top, I naturally had to do the same to the bottom, and so, I made the 60 a 70.
Again, I picked this 10 from out of nowhere.
How could I have
gone so wrong? Again, I’m going to blame
Sally.
The authors of Range Rider conclude this section with a
very important final message. It enables us to become accountants, engineers
and bankers. It enables us to build spaceships and calculate bowling scores. It
is the message without which the computer, large and small, could not and would
not exist.
The message is
simply: One “ghost” follows another.
This rule meant
nothing to me because I wasn’t using “ghost” figures—at least I wasn’t using
their “ghost” figures the way they were using their “ghost” figures. I was
simply pulling numbers out of thin air—and I didn’t give them fancy names.
Of course, not everything
covered in Range Rider was of such
earth-shaking proportions. Some of it
was much lower keyed.
Page 277, for
instance. Here we find Bobby in his
garden. The date is May 10, and he has just planted some carrot seeds. The
package says the carrots will be ready to eat in 70 days. Bobby does some quick calculating and runs
into the house to tell his mother to plan on cooking carrots for supper on July
19. No need to worry about dry spells or cold spells. No down time, no margin
of error, no calculated risk. Definitely no rabbit sneaking into the garden. If
only life were so simple!
In college, I used
a slide rule. My kids used calculators. Today, people use their iPhone to
determine how big a tip to leave the waitress. Not only can they subtract 269
from 727, but they can do logarithms. They are all amazing tools. They have
made books like the Range Rider obsolete.
But they can never make doing math as fun as Range Rider did.
To misquote Doc
McCoy from Star Trek, I’m not a
mathematician, I’m a writer. So it’s time to put my Range Rider, Adventures with numbers aside and check in on the
adventures of Sally, Dick and Jane.
Like the time when
Jane poured Puff’s milk in the bowl and Spot ran into her, splashing milk all
over her and Dick. Now there’s a tale worth telling.
Postscript: This is a minor re-write of
the original article, because I didn’t have kids at the time of the original or
an iPhone back then.