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Posts by LB

Arrest This Man He Talks In Maths

Chronological thoughts on week numbers and week based flows.

Thanks Unsplash Source

I have never been a big fan of our calendar, the Gregorian calendar . I live in the real world so I cannot easily change what calendar we use but have always felt there must be a better way. This calendar breaks up the year into 12 months, each has days ranging from 28 through to 31 with February changing itself to suit our non-conformant traversal around our sun. The calendar we use today has a complex history with many accidents along the way. Including why February has fewer days than all the others and how the calendar is not really fully in sync with either the lunar months or our solar year.

Great video for a brief history of our calendar with a specific focus on February.

Rather than live each day in sorrow that the calendar we are forced to use in society is neither neat or logical I started researching alternatives. It turns out that many times in history people have tried to adjust our calendar to be either simpler or have a more logical approach to it. There also many other cultural and historic methods of calendars that are commonly used in parallel in some countries.

Positivist Calendar

My personal favourite calendar is the Positivist calendar proposed by Auguste Comte in 1849. This calendar was based on our solar year (not lunar months) and kept the Gregorian framework for determining years and leap years. Beyond that, it starts to get a bit different.

  • Thirteen months, all with different names to our current calendar.
  • Each month has exactly 28 days (13 x 28 = 364).
  • Day 365 was outside of the normal week cycle.
  • Leap years had a 366th day which was also outside the normal week cycle.

While this can seem very foreign at first, there is a beautiful simplicity to it, especially when you start digging into the numbers. For example, the 1st day of the first month would always be a Monday no matter what year it is. The first day of the fourth month, would also always be a Monday. Each month is a consistent set of four weeks no matter when it is. Compared to our months, we have approximately 4.3333 weeks per month and the 1st of January could be any weekday.

Thinking in Weeks

The core framework of the Positivist calendar is the concept of a week and keeping weeks as consistent as possible throughout the year. The reality of our solar year means that we have to work with a number that is not very friendly. 365 gives us only two workable factors, 5 and 73 — each of which could be very confusing if implemented. Imagine a calendar where we had 73 weeks a year, each with five days.

If we consider the leap year, we could look at a four-year cycle with each year being 365.25 accounting for the leap year fraction. This gives us a total of (365.25 x 4) 1461, this number has the following factors: 3 and 487 which is even less friendly.

So if we come from the other direction, looking at what we have today, one of the common structures is that of a week. A week contains seven days, and while not necessarily based on anything other than convention it is a nice number to work with. Dividing the year into weeks directly does not work too well, we end up with 365/7 = 52.143, again the four-year cycle 1461/7 = 208.714 does not help too much here either. However, if our year were a bit nicer and sat at 364 days, we end up with an equal number of weeks at 52. This is the beauty, and maybe ignorance, of the Positivist calendar it just looks at a framework where the year is close to what we no but works better for us mathematically.

364 has a lot more going for it, with a lovely array of factors to work with. All these amazing numbers; 2, 4, 7, 13, 14, 26, 28, 52, 91, 182.

This means we can look at our year with divisions of any of those numbers, this helps because we like to break our year up into smaller components to work within. Like our our clock, which is divided up into 12 parts, one of the main benefits is because it has more factors available (half, quarter, one-sixth).

Living in Weeks

Because I cannot easily change the calendar I live by, despite my desire to do so, I must learn to be flexible and compromise. Thankfully the International Standards Organisation have come to my rescue, by devising a way for us to break the year up into weeks in a standardised way (they do love standards at the ISO).

Enter, the ISO Week and ISO Week Date which is part of the ISO 8601 date standards.


Aside from the general awesomeness of this date standard, there is a section about weeks and week numbers.

Enter the Week Number


The definition for week 1 is the week with the Gregorian year’s first Thursday in it. Confusing at first but it means that there is a consistent first week of each year, with all weeks following in order until the end of the year.

  • Each week is our normal Monday to Sunday week. Some prefer to think of weeks as Sunday to Saturday but ISO see Monday as the first day of the week.
  • Weeks do not stop, there is a method for resolving which week it is across year boundaries.
  • There is a consistent method to resolve the Leap year issues.
  • The format is easy to process, sometimes shortened to just 2017W12.

Why Weeks Work

Weeks are a great single iteration unit, easy to comprehend, plan and think in. Weeks are consecutive and avoid the conflicting issue of months which can end at different dates and weekdays. A week works for staff who do one or five days as part of their employment. Many of our financial systems rely on weeks, most payroll is done as a weekly or fortnightly process. Reporting becomes simpler, especially when comparing year on year and you get more granular detail in your reports. If most reporting is done weekly, you are forced to think about the decisions you make today, not just ‘this month’.

There is a great post from a few years back on Wait But Why about viewing your life in weeks that is well worth the read.

Weeks can be further grouped using our factors listed above:

  • 2 week block = fortnight
  • 4 week block ~= month, but best to just call it a 4 week block
  • 13 week block ~= a quarter
  • 26 week block ~= half year
  • 52 week block ~= year

Finally, in the ISO standard, we can find a consistent approach that is implemented in lots of software and means a shared language about implementing weeks. The other great benefit is that we do not have to abandon our Gregorian calendar, weeks work within that system. This is good because my birthday is in the existing calendar system and I like presents.

When Weeks Don’t Work

Not everything is perfect in week land, the biggest issue is obviously intuitiveness. We spend our whole lives adjusting to the oddities of our year and month structure, with songs in our head to remember the days. Overcoming this seemingly natural approach is a bit of a roadblock, however after some time (I can attest), you start to think in weeks and have a rough idea of what week it is at all times.

Mechanically, there are other reasons such as most countries financial years are based on months. The other major roadblock is when years have 53 weeks, our pesky leap year comes into play here meaning that some years have their last week after week 52. In these years, depending on the nature of your business there are other ways to work with this, like grouping it in with quarter four.

Getting Started With Weeks

If you have read this far, you are either a family member or interested in exploring your world in weeks. Here are some great ways to add the ISO 8601 Week Number to your life.

Google (G-Suite) Calendar — Week Numbers

  1. Load up Google Calendar in your browser
  2. Click ‘other calendars’ on the left sidebar
  3. Click ‘browse interesting calendars’
  4. Think (wow, weeks are interesting)
  5. Click the ‘more’ tab
  6. Last on the list is ‘week numbers’, click subscribe

This will add a nice week number to your calendar, which will also be available for syncing with your phone.

Google Chrome Plugin

I have tried a lot of these and this one is my favourite, you even get to pick the colour.

Useful Week Number Website

Usually the top of a Google search, this website will always show you (and your colleagues) the current week if a URL is needed. Along with some handy references on how to get the week number in your favourite programming language.

Calver Variation

You could implement a Week Number variation for your software releases, it keeps you thinking about what is being worked on and shipped this week.


  • Format: YYYY.WW.Patch (Eg. 2017.14.00)
  • YYYY = year in full format
  • WW = zero padded week number according to ISO8601 week number
  • Patch for patches/changes released outside of the weekly release

Next Week

I am not sure if this all of this was helpful, but hopefully it explains thinking behind week numbers and why they can come in handy. If anything, it helps me see the world as a bit more ordered and I have found that the excuse of ‘next month’ is less reliable as we really only have ‘next week’.

Further Reading

There is also another similar calendar, the Thellid Calendar , which approaches the year with weeks in mind and used as inspiration for this post. The International Fixed Calendar is worth looking into and was used within Kodak for over 60 years, it has more user-friendly month naming conventions and placements of the ‘additional’ days in the year.

Have fun, let me know if you find any other epic resources about weeks.