I thought I’d veer off into esoterica today. I don’t know why it came to mind a couple of weeks ago, but since it came to mind, I have found myself pondering the matter. Now I’ll share it with you and get your input.

The matter at issue is the numeral designator for half. If we write 2 days, there is no question what is meant. Similarly, if we write 2.5 days, readers correctly translate that to two-and-a-half days. But is it really correct?

I suppose that it is because it has been accepted and understood as correct for decades, if not for centuries. But shouldn’t time be more accurately represented? If a day has 24 hours, then a half day has 12 hours, which means that 2.5 really means two days plus 5 hours. Yet if we were to write 2.12 days, no one would understand that means 2 days plus 12 hours or two-and-a-half days.

Time has always been treated differently from other yardsticks. Probably because time is so important in our daily lives. We have coalesced around certain conventions, correct or not, that are now the accepted methods for portraying time, especially decimally.

Consider the matter of years. we all know and accept that 6 months equals one-half year. Yet we do not write 1.6 years to represent one-and-one-half years; as with days, we write 1.5 years and we all know what is meant.

I work on nonfiction books, which has led me to occasionally wonder if an error will occur when measure shorthands aren’t correlated with the written out version; that is, how likely is it that some reader will mistake 1.5 days for 1 day 5 hours, so I should write one-and-one-half days rather than 1.5 days?

Of course, I only wonder and do not spell it out because I understand that we have accommodated our use of language so that there is no likelihood of misinterpretation. But that doesn’t move me away from wondering how this came about and why such imprecision is accepted by communities that require precision elsewhere.

Not only have we accommodated our use of language to .5 representing one-half, but this accommodation appears to be fairly universal among languages. Writing 1.5 days will not mislead a French, Italian, Slovakian, Chinese, or Malayan speaker any more than it misleads an English speaker. The convention has crossed linguistic borders (someone once said that math is a universal language, so perhaps the fault for this accommodation lies in math’s universality).

I’m not interested in trying to change the accommodation (some brick walls truly are meant to stand forever), but I am curious about how we came to universally accept and understand that 1.5 days means one-and-one-half days and not one day, five hours.

What is your theory?

It is simply the standard notation for 1/2 expressed as a decimal fraction. This way of writing decimal fractions was introduced by the mathematician John Napier in the late sixteenth century.

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Comment by Lawrence — January 23, 2012 @ 4:33 am |

I agree that math is a universal language here. It would feel more natural (for me at least) to represent 2 days and 5 hours as 2:5 days as it would be more in line with the convention used for separating hours, minutes, seconds. But then would there perhaps be confusion with the use of the double colon?

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Comment by Indie Ebooks — January 23, 2012 @ 5:50 am |

Whether it’s 2.5 or 1.5 or 10.5, the “.5” will always mean 1/2 (one half of whatever it is we are referring to) and this is very clear for any person used to metric annotation.

For the 5 to mean 5 hours, another convention should be invented to stand for days, say, 2 d 5 h, or 2* 5′, etc.

By the way, shouldn’t it be time for USA to change to metric? Seems to be you are the only country left with miles, yards, feet, etc.

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Comment by Marcela — January 23, 2012 @ 8:03 am |

Cher American Editor,

Could it be the influence of the metric system?

When you use 1.6 years, you are mixing two units, year and month.

In 1.5 years, you only have one unit.

The same goes for 1.5 days.

Measuring a plank of wood is a good exemple:

in the imperial system, a carpenter will mix foot, inche and line (ligne in french);

in the metric system, the same man will only use meter and a percentage of that unit that can be refered too in subsets of the same unit: decimeter, centimiter, millimeter, etc..

That is my theory this morning!

luc

PS:

I just discovered your blog.

You are doing a fantastic job!

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Comment by Luc Prévost (@AutoPublication) — January 23, 2012 @ 8:50 am |

Maybe I haven’t had enough coffee yet this morning, but I don’t understand the question. The .5 in 1.5 refers to half of a whole; half of 1. It has nothing to do with the number of hours in a day (or days in week, months in a year, quarts in a gallon, centimeters in a meter, books on a shelf, etc.). It’s just … half of a whole. It’s a universal measurement that can apply to anything. If 24 is the whole of something, then half of it is 12, but that 12 is still .5 – half – of that whole.

Maybe the question should be why .5 plus .5 = 1.

Then again, math was never my strong point …

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Comment by Ruth E. Thaler-Carter — January 23, 2012 @ 8:57 am |

It’s just math.

In mathematical notation, 5 is five (obviously).

.5 is five-tenths (5/10).

.05 is five-hundreths (5/100).

.005 is five-thousands (5/1000).

Ten-tenths (10/10, ten divided by ten) equals one, which means that five-tenths (.5, 5/10, 5 divided by 10) equals half of one. So 1.5 is one and a half. And it’s one and a half of *anything*–days, years, sandwiches, whatever. It has nothing to do with units and subunits, such as days and hours.

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Comment by EditorJack — January 23, 2012 @ 12:01 pm |

It will take me 1.5 days to think about which format I think is best, right, confusing.

Alan

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Comment by Alan — January 23, 2012 @ 6:24 pm |

Rich, we live in a decimal system. Numbers like 1.5 are called decimals because they’re ten-based. It wouldn’t have to be this way. The Egyptians apparently experimented with base 12 numbers (counting the number of knuckles in the non-thumb fingers rather than individual digits). The Mesopotamians used a base 60 mathematics. In these mathematics, 1.5 would not be understood as one and a half, but as one and five whatever other place units (e.g., 1 and 5 60ths). I think that the 12 hour clock and the 12 months in the year descend from earlier use of base 12 arithmetic but these were probably invented before place-based arithmetic and hence don’t use the decimal point. Basically, in our world, we count our fingers and we’ve learned that things come in tens.

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Comment by Rob Preece — January 24, 2012 @ 1:16 am |

“how likely is it that some reader will mistake 1.5 days for 1 day 5 hours, so I should write one-and-one-half days rather than 1.5 days?”

That would depend on the book. If you’re writing for HS students, some might not know the difference between 1.5 and 1:5. If you’re writing a science book, every reader would be familiar with the decimal system. In gray areas, it would be better to write out, depending in part on they style you’ve chosen for that book.

However, I’ve never seen a colon used for anything but hours, minutes, and seconds. Have others?

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Comment by Gretchen — January 24, 2012 @ 7:46 am |

I’m just catching up with emails after being on vacation.

In keeping with most of the above comments I would never have thought to interpret 1.5 days as one day and five hours and was surprised to see the matter even queried. Is it an American custom? How about pounds and ounces? I can’t imagine a recipe book would ever specify 1.5 lbs of sugar with the intention that the cook used one pound and five ounces rather than one pound and eight ounces. If there was likely to be any ambiguity in a book/document I would specify the period of time as 1d 5h or 1d 12h (depending on what was intended) but would avoid using a colon, as suggested above, because of the resemblance to a ratio.

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Comment by Thiers — February 7, 2012 @ 1:59 am |

No, it isn’t an Americanism. We, too, think of 1.5 as one and one-half. This was more of a whimsical query than anything else. My thoughts tend to wander in an Alice-in-Wonderland manner.🙂

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Comment by americaneditor — February 7, 2012 @ 2:27 am |