All clocks are 30 seconds late

I think that’s the problem with the article - that it sticks to its guns.

It starts with an outrageous statement, goes on to show that it’s actually correct. Then it relates it to similar things and instead of saying “yeah, just like we floor years and hours it makes sense to do it for minutes too, but it was fun to think about” it goes on to say “but for minutes this is bad”

If it had backtracked and said “flooring is actually the better choice” I would have appreciated the article as a whole much more

> With flooring, if you see 13:00 you know you are late

I always though that you are late from 13:01. Common these days with Teams meetings etc. It seems most people join during the minute from 13:00 to 13:01.

But if every clock was like that, then 12:59:30 would be the new 13:00:00

> If it's 11:55, you would usually mentally subtract and conclude: the meeting is in 5 minutes. That's how I always do it myself anyway! But the most probable estimate given the available information is actually 4'30"!

The way I like to think about it is "the meeting is in less than 5 minutes". Which is always correct since my reaction time to seeing the clock switching to 11:55 is greater than zero.

It could even be less than 4 minutes if it has already switched to 11:56 and I haven't had time to react to that change, but that's OK - my assessment that I have less than 5 minutes to get to the meeting is still correct.

All broadcast studios are equipped with master clocks that show seconds to deal with this ambiguity.

You can look at your own watch and anticipate when program transitions in radio or TV are supposed to take place (usually the minute and 30 second marks). Also, get a sense when a host is filling time to get to the transition.

This is a good point. There's tons of times when I'm watching a clock to watch for a precise moment (like buying concert tickets, limited edition merchandise, stock market opening). Losing the ability to see when a 12:00:00 happens would be annoying

If you care about starting a meeting to within better precision than a minute, use a clock that shows seconds. If I want to start a meeting at noon, I don't block off the minute display of my clock and wait for the 11 -> 12 transition to start the meeting.

> If it's 11:55, you would usually mentally subtract and conclude: the meeting is in 5 minutes. That's how I always do it myself anyway

And if you showed up to the meeting in exactly 5 minutes, you’d be on time!

> If it's 11:55, you would usually mentally subtract and conclude: the meeting is in 5 minutes.

Even that part is wrong. I guess I‘m not the only one who knows and thinks it’s less than 5 minutes.

The technically correct thing to do would be to educate on precision, perhaps even display it, such that people know that 12:00 means a time between 11:59 and 12:01, not 12:00.000.

Exactly, this article can be summed up on one sentence: "Look at me, I'm so clever"

Unlike digital displays, the largest denomination hand on an analogue clock display contains all of the information that the smaller hands do (depending on the movement in some cases).

You would be surprised. When I was a kid, I sometimes used to stare at the clocks with an analog face at the train station while waiting for the train to school to arrive.

Interestingly enough the seconds hand would go slightly faster than actual seconds and at the 60 seconds the seconds hand would get stuck for a moment as if it was pushing the minutes hand and then the minutes hand would flip to the next minute.

Found a video here:

https://www.youtube.com/watch?v=ruGggPYQqHI

The description describes how they work, which seems like a mixture of digital and analog (due to the use of both cogs and relays + propagation of pulses from central to local clocks), translated:

- The seconds hand makes a revolution of 57-58 seconds and is then stuck for 2-3 seconds.

- The seconds hand is driven using 230V.

- The minutes hand get a 12V or 24V pulse once every 60 seconds. The polarity has to swap every 60 seconds. The swapping of the polarity can be done using a relay or specially-made components.

- The hours hand is driven by the minutes hand using cogs.

Edit: more information and references here: https://en.wikipedia.org/wiki/Swiss_railway_clock#Technology

>The easiest way to realise this is to imagine a clock without the minute hand.

No need to imagine it, it's been invented many years ago and it's called a perigraph. Meistersinger makes one of the nicest I've seen: https://www.relogios.pt/meistersinger-perigraph-relogio-auto...

> it depends on the movement, but it is not out of the question that your minute hand is moving once every second, and not every minute.

I think the only place where I've seen the minute hand move by the minute has been on TV, in those climactic moments where the camera zooms in on the clock and strikes a certain time. Maybe it's a trope, for emotional tension, like mines that don't explode until you step off.

> The easiest way to realise this is to imagine a clock without the minute hand. Can you tell when it's half-past the hour? You can. The hour hand is half way between the two hours.

Can I? Many analog clocks actually "tick" the second and minute hand. I've even seen some that tick the hour hand.

You literally just defined the difference between digital (binary) and analog (gradation).

A digital clock is 1:01 or 1:02. An analog clock is some tick of some range (depending on the resolution, as you abstracted), at all times.

> All universal statements like this are wrong and stem from basic ignorance

Yup, I think the "has the {thing} already started" is, for many people, the most useful function of precise time anyway. All sorts of work and personal meetings, transportation schedules, doctor's appointments, and so on.

Knowing the ballpark in the form of "it's 15:30-ish", even if more precise, is strictly less useful than "you're late to the 15:30 meeting with your manager".

Fun article nonetheless, and interesting perspectives on both sides!

I’m ready for the rebuttal post: “different clocks have different approaches to conveying information about seconds within a minute” which uses the same photos as examples.

No my digital clock doesn't show seconds. As for the london one, I was actually wondering about that! I know it depends, because some analog clocks work like digital one and snap to the next minute by discrete increments.

Not all analogue clocks smoothly move the minute hand to show progress in the current minute. Many of them tick over, truncating the information to the minute like what digital clocks do.

Vaguely related: I don't think people are being taught how to read analog clock faces nearly as much anymore, and apparently phrases like "quarter past ten" are becoming, so to speak, anachronisms.

I feel you're missing the elephant in the room with the clock observation:

Time is a cube, not a cuboid.

Yes. Though analog second hands often "tick" the seconds. (Some move the second hand smoothly.)

>That digital clock does show seconds

It most certainly does not.

I see HH:MM, temperature in Celsius, humidity in percent, alarm status, alarm time, day of the week, and DD/MM. None of those are seconds. It is a truncating digital clock that rounds down.

>the London clock has its minute hand in between minute mark - showing progres between minute mark if you look closely.

"If you look closely" isn't really how analog clocks work in practice. Without a second hand, the limits of human vision prevent us from fully calculating the time between minutes, as each second only represents a 0.1° change in angle of the minute hand, and most mechanical analog clocks aren't designed for the minute hand to move perfectly linearly between minutes.

A minute is an insignificant period for most daily tasks, so the convention "show me when the minute changes" is simple and pragmatic. If your task needs precise count of seconds, you get a clock that shows when the second changes, and now you are half a second late on average.

You can keep playing with increasingly smaller time units until you conclude, like Zeno's arrow paradox, that you're always infinitely late.

I think that's about right.

Another way of thinking about this is that the author is confusing time as measurement (how much time) with time as rule (what time is it). If you wanted to measure the duration as a difference in clock times, yes, there would be a certain amount of measurement error incurred by the way clocks are displayed. But if you want to know the time, in the sense of whether a certain time has been reached, or a certain graduation has been crossed, it doesn't make sense to round to the nearest minute.

The question of "how much is this clock off?" is only meaningful with reference to a certain use or interpretation of the numbers being displayed. If you say it's "8:56" people know it could be anything up to but not including 8:57, but greater than or equal to 8:56. The number means a threshold in time, not a quantity.

That's a good point, I was actually wondering about that. I've seen a lot of jumping analog clocks so I incorrectly assumed Big Ben was the same. I should have checked :)

Good catch. RMS (root mean square) error is typical in signal processing to avoid this undesirable cancellation.

The average error is in fact 0! The average absolute error is reduced but not 0.

That's a very fair nitpick, but even with a more rigorous error function the point still stands, I think.

It depends on the application. Are you summing times (as with a pay clock at a job), or are you paying for error in both directions for some reason?

An analog clock does show the exact current moment of time (if the hands move in a linear motion and don't jump).

What time it is, is just made up, it's something we can decide freely through social power, as evidenced by timezones and daylight savings and leap seconds.

Commonly the resolution is something like minutes or a few of them, that's the margin we'll typically accept for starting meetings or precision in public transport like buses.

The utility of femtoseconds in deciding what time it is seems pretty slim.

Yeah, I think labelling it "error" is a bit of a strange way to look at it to be honest.

It's only error if you're trying to measure time in seconds, but are doing it with a clock that can only measure hours and minutes. If you want to know the current minute, then a clock that can measure minutes it is 100% correct.

It's an interesting thought experiment, but really all it's saying is that half of the time 10:00 is closer to 10:01:00 than 10:00:00, but this imply you care about measuring time to the second which prompts the question why it's being measured in minutes?

To be charitable, I suppose in the real world we might occasionally care about how close 10:00 is to 10:01 in seconds, but the time shown on phones can't tell us that so on average we will be about 30 seconds out.

Those are all questions no clock can answer though. They require state from the physical world over and above knowing the current time.

It’s a wild misconception to think that a flooring clock is somehow more late than a rounding clock and it’s if anything an even more crazy misconception to think that a clock can tell you whether something in the physical world has or hasn’t happened.