There’s social security in numerous numerate letters about license plates and telephones

My ineptitude with numbers has been well demonstrated here. I can barely manage to do simple sums in arithmetic, and I have no facility for calculating very large ones.

My ignorance was showing the other day when I misspelled femtosecond (a quadrillionth of a second) as femosecond . As Robert E. Kelly Jr. pointed out, a “femosecond” is “an all-too brief period of time spent with an attractive but unobtainable lady.”

So I was easily taken in by some of my readers who questioned the necessity for seven-digit license plates and for dialing 1 before long-distance codes.

For example, Paul Sandorff of Granada Hills wrote that “there are only 120 area codes in the telephone book; the three-digit code, with leading zeros and ones omitted, would comfortably handle six times as many. Then why do we need to dial or punch a 1 when we identify the area code?”

An answer comes from Theron Stanford of Caltech:

“There is a simple explanation for why we dial 1 before making long-distance calls out of our own area. When area codes were first used for long-distance dialing, Ma Bell needed a way to determine whether the first three digits dialed were the prefix or the area code. To solve this dilemma, it was decided that area codes would begin with a digit from 2 to 9, end with a digit from 1 to 9 and have a middle digit of 0 or 1, with the added restriction that no area code would end in 11--these numbers were reserved, apparently, for special services, such as directory assistance (411) and the new emergency number 911. (Notice that Los Angeles’ new 818 and New York’s new 718 both obey this principle.)

“This would give 8 x 9 x 2 - 8 = 136 area codes, of which 128 are now in use. Furthermore, prefixes were then prohibited from taking the form of an area code, so the switchboard could tell them apart. However, I suppose it soon became clear that not even this would be able to handle the growth of telephone usage in North America, so the phone company set out to find more numbers.

“Instead of making the consumer memorize a longer telephone number, though, the phone company decided to free up the restrictions on the form of the prefix, allowing 1,360,000 more phone numbers per area code, but then also required the caller to dial 1 to alert the switchboard when he was about to dial an area code instead of a prefix. . . .

“I see it as a nice thing for the phone company to do to keep our phone numbers as short as possible so that we can remember more of our friends.”

Have you got that?

Sandorff is also challenged on his figures for license plates. He said:

“The obsolete six-character display was good for at least 2 billion different vehicles, 50 times as many as we now have. . . . However, seven characters has allowed us the pleasure of personalized plates, even if it makes it impossible to remember our own.”

Steve Cherry of Costa Mesa answers:

“Mr. Sandorff is incorrect in stating that the six-character license plate would be good for at least 2 billion vehicles. The arrangement of three letters and three numbers would yield a total of 17,576,000 combinations. Of this total, DMV would eliminate certain letter combinations as inappropriate.

“I seem to recall that the six-character license plate was exhausted within 10 years. The present arrangement of three letters and four numbers will yield a total of 175,760,000 combinations, which should last almost 100 years (if the gasoline holds out).”

Douglas W. Caldwell confirms these figures:

“A six-character display yields 2.2 billion different plates only if all 36 letters and numbers are possible in each position. The DMV was very wise to limit the possible valid plates to have three digits followed by three letters, since 123 XYZ is considerably more readable than A2QRK1.

“Unfortunately, with this limitation there are only 17.6 million possible plates. As the order of the letter and digit groups used to be reversed, the six-character plates were used up after 35.2 million vehicles, about 5 million shy of those Mr. Sandorff asserts we need. The new seven-character plates allow us 176 million plates, assuming personalized plates contribute negligibly to the total.”

Further proof comes from David O’Harris of UC Santa Barbara, who observes, quite correctly, that “unfortunately most people have no comprehension of the magnitudes of numbers much larger or smaller than 1--you apparently included.”

As for license plates, he points out: “There are 17,576,000 different letter/number combinations on license plates (six characters 000 AAA through 999 ZZZ); i.e., 10 x 10 x 10 x 26 x 26 x 26--which is not even one per each Californian. Adding a seventh digit still doesn’t give 2 billion; nor does an 8th. . . . “

Several readers have pointed out a peculiarity of the match code number William Swan of Glendale found on his bill from The Times: 31703DO438120200031703DO4381202000, which I miscounted as 35 digits.

James C. McCormick points out that the series contains only 34 digits, not 35, and that they are actually two identical series of 17 digits each, like this:

31703D04381202000

31703D04381202000

“I fail to see,” McCormick says, “how just repeating the same sequence can add any new information. It just consumes time in programming the computer and in printing the bills.”

Although I work at The Times, I’m not going to ask why they repeat a 17-digit match code on their bills. I’m simply going to take the advice I gave (which McCormick says he followed) and pay my bill.