What’s the Brightest Time on a Digital Clock?

Like many, I have spent many a night lying awake desperately trying to fall asleep. Counting sheep, meditation, trying not to fall asleep, pleading with a higher power… fruitless more often than not. And on these nights, in a hotel room or a friend’s couch or a grandparent’s floor, the darkness would be pierced by the light of a digital clock face. Could be on a microwave or a cable box or a plain old alarm clock, but one thing is for certain, the last thing a brain trying to fall asleep is for the only visual stimulant in the room to be a reminder of how much time is being wasted not sleeping.

I’ve found myself staring at the seven segment display and trying to think myself to sleep. Which segment is on the most? Bottom right. Which segments are on the least? Top left and bottom left. Which segments blink on and off the most? Bottom left and bottom middle. Are there any times where if you smushed the digits together, they’d form squares? Yes, 8:33 and 6:59.

But one thought comes to dominate these musings, especially when I roll over to ignore it and am met by its mocking glow illuminating the room: how bright is this thing anyway?

A Light in the Dark

There’s no way I could lay there and calculate the wattage equivalent of a lightbulb, but I can at least compare between different times. After all, the segments turn on and off, and the clock is brighter when more segments are on.

First off, the dimmest time is pretty simple: 1:11. Only three digits, each of them the fewest segments possible, a paltry six lit segments total. An insomnia-fighting hero, 1:11 is.

By the same token, the brightest time would be 18:88. Except that time is impossible. No hour has more than sixty minutes and my civilian life has no room for hours greater than 12.

Starting from the back, we can keep the final 8. Next up is the tens minute. Our options here are 0-5. The edge here goes to 0. So we’ve got :08. For the hour, 8 seems like a decent candidate, but we can do one better. We can add the one in the front for an extra two segments and sacrifice just one segment to move from 8 to 0. So there we have it, at a whopping twenty-one segments:

10:08

Wait, there’s more?

Here’s a table of the number of illuminated segments at each time on a digital clock. Hours across the top, minutes down the side. The brighter the background, the more segments are lit.

As you can see, there are dark bars for 1’s and 7’s and bright bars for 8’s, along with the vertical 10 and 12. Here’s a histogram of the frequency of each number of lit segments.

As we can see, the distribution is significantly left skewed. This is because the dimmest digit, 1 with its two lit segments, is farther from the median five lit segments than the brightest digit is, 8 with its seven lit segments. Of all of the times with eight or fewer lit segments, only 7:17 does not feature multiple 1’s.

Finally we’ll look at a line graph of how the brightness of the clock changes over the course of an hour. This graph only looks at the number of minute segments that are lit as the hour segments remain constant.

We can see that the number of lit segments stays constant every ten minutes between 2 and 3. It also holds each hour from 29 to 30, from 3:59 to 4:00, and from 8:59 to 9:00.

I think a convincing argument could be made that the most sleep-interrupting effect would result not from sheer brightness, but changes in brightness. With 10:08, that clock has been pretty bright for the last ten minutes. I’m not certain that twenty-first segment is as eyelid-burning as it’s cracked up to be.

Big drops of four segments in brightness can be found every ten minutes from 0 to 1, every hour from 10 to 11, and 12:59 to 1:00. The brightest and dimmest times each hour, 08 and 11, are separated by just three minutes, resulting in a rapid nine segment fall between them.

We also see brightness gains of four segments every ten minutes from 7 to 8, along with 1:59 to 2:00 and 11:59 to 12:00. These are the real wake-up calls, the defense against Mr. Sandman.

But one time change stands alone. The biggest brightness shift from any one time to the next, the one flip of the minute that goes from a false sense of security to comparative supernova at a mind-boggling five segment increase:

7:59 to 8:00

Good luck slumbering through that one tonight. I know I won’t.