Time Math: Part I

Think you’re good with numbers? Think that addition and subtraction are simple? Actually, it’s likely that you’re only capable of performing arithmetic when operating within the decimal numerical system.

Whether by nature or nurture, our minds are conditioned to think in base 10, which explains why some anniversaries are more significant than others. Binary and hexadecimal are examples of numeric systems that do not have a base of 10, but we don’t need to enter those worlds in order to encounter difficulties, for we regularly deal with units of measure that do not scale by tens. Let’s look at some examples.

How many inches tall is a 6.25 foot person? Chances are the answer didn’t immediately spring into your mind, so you did some simple math to find the answer.

6 * 12 + .25 * 12 = 75

But what if we have to deal with a more complex problem, like 5 miles, 61 yards and 2 feet minus 10,000 inches?

(5 * 5,280 + 61 * 3 + 2) * 12 – 10,000 = 309,020

Suddenly the impracticality of the imperial system becomes apparent, and the metric option seems like an attractive alternative. Although the metric system makes measuring mass, volume and distance quite simple, we have yet to devise a viable solution for time measurement. Time is by far the most perplexing system of measurement for a number of reasons.

First, the base of the units of time vary. This is why entering 75 on your microwave will cook your food 15 seconds longer than entering 100. This is not a problem unique to time, but the amount of variation here is extreme. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, 7 days in a week, around 4.33 weeks in a month and 12 months in a year. In addition to these variations, most of the world uses a 12-hour clock, which means that a day is made up of a hidden base 12 unit. To complicate things even further, the term day may refer either to a 24-hour period or only a section of the same period between sunrise and sunset.

The second reason for the complication is that the units of time are not uniform in duration. Although the smaller units don’t vary, the length of months and years does change. A month can be anywhere from 28 to 31 days, and a year, though usually 365 days, is sometimes 366. A day can also vary in duration. In nations that use daylight savings time, one day every year is 23 hours long and another is 25 hours. On top of all that, time changes depending on where and when we are. Time zones make keeping time difficult during travel and also cause many people to miss their favorite television programs. These inconsistencies may not seem strange, but if we were told that a foot wasn’t always 12 inches or a kilogram wasn’t always 1,000 grams, we would surely question it.

Third and finally, humans share a close link with time, and standard time is our first language. However, unlike our relationship with other dimensions, velocity and direction through time can not yet be altered. Because of this, our behavior is influenced heavily by the time of day, the day of the week and the month of the year. Our relationship with time is part of the reason why it’s so difficult to change the system (yet we are somehow able to suddenly decide that it’s an hour in the future during daylight savings time).

In light of the intricate and unique nature of time, let’s look at progressively difficult series of problems in order to understand just how challenging time math can be.

  • How many minutes are in November?
  • How many hours are between 3:00 AM and 7:00 PM?
  • How many days are between July 3 and September 19?
  • How many hours are between 5:00 PM on Monday and 9:00 AM on Wednesday?
  • If January 14th is a Wednesday, then what day of the week is February 5th?
  • How many minutes are between 11:43 AM on January 3 and 1:17 PM on November 19?
  • What time is 1,000,000 seconds after 10:10 PM on January 1?
  • How many seconds are between 5:19:31 PM on September 5, 231 BC in Rome and 3:26:04 AM on August 22, 1746 in Central China?

Doing math with time in our current system is extremely convoluted. However, metric time isn’t the quick fix that it is for other units. We’ll explore some possible solutions in part II.