Additional Math Pages & Resources

Friday, July 22, 2011

Who decides which goes first?

One of the most common discussions on the playground is "which one goes first." That's an occasional discussion among adults too - especially on the road when two lanes are converging into one. There general rules for this sort of thing but often we ignore the rules and do what we feel like doing.

It happens in the math world too. Someone has to decide who goes first. For example, someone decided that addition and multiplication are performed BEFORE subtraction and division.

In previous blogs I've discussed times and dates and calendars. ( Here's one on time zones. Here's another on leap years. And another on setting your clocks for daylight savings. )

Today's blog was prompted by a customer's visit this week, asking "why is Sunday the first day of the week in Excel Math, when everyone knows it's the 7th day of the week?"

My answer was, Not everyone knows or thinks that Monday is first. 

A DAY Seems Simple, but it's not! Bear with me now as I get into this. We need to know when a day starts in order to know when to start the week (a collection of 7 days).


Hebrew and Islamic traditions begin their days at sunset. Or to be more precise, some said, from the moment that the sun's disk stands distant from the horizon by the length of its own diameter.


The US Naval Institute of Standards says:

  • Sunrise and sunset are the exact times when the upper edge of the disc of the Sun is at the horizon. 
  • Dawn occurs when the geometric center of the Sun is 18° below the horizon in the morning. 
  • Dusk occurs when the geometric center of the Sun is 18° below the horizon in the evening.
  • Twilight refers to periods between dawn and sunrise or sunset and dusk.
Twilight's hazy light is an effect caused by the scattering of sunlight in Earth's upper atmosphere. The brightness of twilight is subjective, depending upon on your location and elevation, the time of year and local weather conditions. Twilight is divided into 3 categories based on the angle of the Sun below the horizon.
  • Astronomical twilight is the period when the Sun is between 18° and 12° below the horizon. 
  • Nautical twilight is the period when the Sun is between 12° and 6° below the horizon.
  • Civil twilight is the period when the Sun is between 6° below the horizon until sunrise. 
The same designations are used for periods of evening twilight.

Roman and Western European medieval monastic days began at 6:00 am. In the Western world today, we normally end and start the day at midnight (the middle of the night).

  • Halfway between dusk and dawn? Not exactly. That depends on where you are.
  • How about 12 hours or opposite from noon? Ok, but when's noon?
  • Noon used to be when the sun was directly over your head, but that definition changed with Time Zones.
  • Noon is when the sun crosses the meridian, or is at its highest elevation in the sky. Solar noon varies depending on your longitude and the date.

The US government style manual recommends: use 12 a.m. for midnight and 12 p.m. for noon. Time up to midnight (but not including it) is PM and time after midnight (but not including it) and before noon (but not including it) is AM. 

The US Naval Institute of Standards says: 12 a.m. and 12 p.m. are ambiguous and should not be used.  The shortest measurable duration after noon should be designated as PM. For example, a digital clock changing from 11:59:59 a.m. to 12:00:00 should indicate PM as soon as it the 12:00 appears, and not delay the display of PM for a minute, or even a second.

Depending on your digital clock, midnight could be 12:00 or 00:00  


Traditionally, countries whose primary religion was based on the Bible (Judaism, Christianity and Islam) have generally considered the first day of the week to be Sunday.

Some countries do not use the naming structure of Sunday Monday Tuesday (Domingo, Lunes, Martes, etc.) but instead say First Day, Second Day, etc. These might use Monday as the first day.

In China, Sunday means "week day".  Monday is "first day of the (seven-day) week cycle", Tuesday is "second day of the (seven-day) week cycle", etc. When China adopted the Western calendar Sunday was at the beginning of the calendar week, but now Monday is preferred.

In Swahili a traditional day begins at sunrise, rather than sunset. It is twelve hours before Arabic and Hebrew calendars, so some countries may consider Saturday as the first day of the week.  


In the USA for the last 10 years or so Sunday been considered the last day of the week, as our more secular view now places Monday at the top of the pyramid of importance. When Janice Raymond created Excel Math (1978), Sunday was definitely the first day of the week in the US school systems.  As I began revising the curriculum in 2000, we reduced the places where kids were asked to count days of the week and solve math problems with those numbers.

It all comes down to how you want to display your weeks on a calendar. Most of the calendars in my house start with Sunday and end on Saturday. How about yours? There is no right answer.

The international standards organisation (ISO) decided describing the time of day was an important issue, and created Standard 8601 to answer all our questions. Here's a paraphrase of the introduction:

Although ISO standards have been available since 1971, various ways to represent dates and times are used in different countries. Where this happens across national borders, misinterpretation can occur, resulting in confusion, errors and economic loss. The purpose of this International Standard is to reduce the risk of misinterpretation. 

We include specifications for numerically showing the date and time. In order to achieve similar formats for calendar dates, ordinal dates, week-number dates, time intervals, recurring time intervals, combined date and time of day, and local time or Coordinated Universal Time, it is necessary to use numeric characters, single alphabetic characters and/or one or more other graphic characters.

The Standard provides a unique representation of any date and/or time. It retains commonly-used expressions for date and time of day, and provides unique representations for some new expressions. It can be used with computers and should eliminate errors and misinterpretation. It will facilitate interchange across international boundaries, improve the portability of software, and ease  communication within and between organizations.

Stay tuned for the next blog! It comes After Midnight.

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