Daylight Saving Time is Mathematically Illogical

Published by patrick honner on

I’ve always found daylight saving time confusing, and now I know why:  mathematically, it doesn’t make sense.

As summer turns to winter and our part of the Earth spends less time in the sun, the length of the day contracts.  This kind of transformation is known as a dilation–a shrinking or stretching of something.

The yellow part of the graph represents the amount of sunlight per day.  This part dilates, while the times-of-day on the clock stay fixed.

In order to increase the amount of productive daylight, we translate the times-of-day.  Naturally, this doesn’t change the amount of available sunlight; it simply shifts the clock-times so that more of that sunlight occurs during preferred times-of-day .

Thus, the new day looks like this.

Essentially, daylight saving time tries to counteract a dilation with a translation.  But mathematically, the way to truly counteract a dilation is with another dilation!  Thus, the mathematical logic of daylight saving time is faulty.

Now that I fully understand the source of my confusion, I can rest easier.  And for an extra hour!

patrick honner

Math teacher in Brooklyn, New York


Ahmed Gouda · November 7, 2010 at 12:57 pm

I always saw Day Light Savings time as something farmer related. Make it so that 6 in the morning is still when the sun comes up so that they don’t “waste sunlight”.

Richard · November 26, 2010 at 3:21 pm

Benjamin Franklin often gets credit (or blame) for inventing Daylight Saving Time (known as summer time in Europe) because he wrote an essay in 1784 suggesting that the French could save money on candles and oil by waking up earlier, thereby getting more done during daylight hours. Franklin’s essay also “suggested” ringing church bells and firing cannons at dawn to ensure that nobody would be excluded from his benevolent gesture.

MrHonner · November 27, 2010 at 7:06 pm

Thanks for the back-story Richard–it’s always encouraging to remember that even the giants swung and missed every now and then.

Andy Huynh · November 6, 2011 at 1:14 pm

The change that occurs in the Fall is going from Daylight Savings time to Standard time. The change in the Spring is going from Standard time to Daylight Savings time. This means that time just got changed back to “normal” and in the Spring, the clock gets moved ahead to “save time.” What all of this means, I don’t know.

MrHonner · November 6, 2011 at 2:16 pm

“What all of this means, I don’t know. ”

My sentiments exactly.

David Radcliffe · November 6, 2011 at 7:38 pm

As I understand it, the purpose of DST is to gain an extra hour of daylight during summer evenings, at the cost of an hour of daylight in the morning. This would be rational if you value daylight more in the evening than in the morning. But why not just encourage people to alter their schedules during the summer instead of adjusting the clocks? Perhaps the solution is to institute year-round Daylight Saving Time.

MrHonner · November 6, 2011 at 11:19 pm

What reasons do people give when arguing that an hour of daylight in the evening is more valuable than one in the morning? And yeah, if that’s the case, why not always rig it so 5-6 pm at night is always daylight?

Certainly would make more sense for people just to alter their schedules.

Colin Beveridge (@icecolbeveridge) · March 11, 2012 at 9:38 am

Personally, I think we should decimalise time and just go by Unix timestamps. People would be able work whatever kiloseconds they choose, and there’s no such thing as a rush myriasecond anymore.

Maybe _this_ is why the Mayan calendar ends in 2012 – they realised it would become obsolete this year!

mcg · November 2, 2013 at 9:46 pm

But the purpose of daylight savings time is not to compensate for winter dilation at all. In fact, the actual shift is occurring I the summer, not the winter; summer time is shifted ahead. It’s actually meant to trade some of the morning daylight for more evening daylight, where (in theory at least) it will be better utilized. I am no fan of the shifts myself; but if I were dictator, I would probably just keep us on shifted summer time all year round!

Susan Russo · November 3, 2013 at 7:32 am

Interesting. I’ve always thought of it as a vertical shift (+1) followed by a vertical shift (-1) regarding sunrise times.

Now I get the sun in my eyes for the next few weeks on my way to school again.

Jonathan · November 6, 2016 at 8:37 am

It’s not a mathematical problem, but a social one. The amount of daylight varies… In New York City we go from over 15 hours in the summer to 9 hours and 15 minutes just before Christmas.

DST was first seriously proposed around 1900 – adopted by some localities (I have a source that says in Canada) with the first whole country adoption being Germany in 1916.

This has nothing to do with agrarian society – farmers lived by the animals (and the sun) not by the clock. It has everything to do with “clock society” – it’s an urban issue – and saving energy.

In New York City, would daylight be more useful from 4:30 to 5:30 AM, or from 7:30 to 8:30 PM?

There have been experiments with dropping time changes – many countries (including Britain, the USSR, and the US did so during WWII), and also experiments with moving the clock more than an hour (British war time was “double summer time” – 2 hours). And several countries today don’t move clocks, not sure if they count as winter time, summer time, or just time.

Pat · November 6, 2017 at 9:21 am

The purpose is that it’s easier to just change the time than it is to change the hours at which everyone congregates and works. Like if the farmers market opens at say 8, it’s easier to just change the time as the amount of daylight dilates throughout the year than it is to suddenly change the time at which we do business. Easier to change time abruptly than to say businesses now open at 7 instead of 8. In a perfect world we would have one time and have businesses and work open when dawn is actually occurring.

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