Flooring makes more sense in every case, from years to milliseconds and more. A few reasons:
You want to send a message at exactly 13:00:00, you have a digital clock that doesn't show seconds. What you do is that you watch your clock, and as soon as it goes from 12:59 to 13:00, you press the button. That's also how you set the time precisely by hand. With rounding, that would be 12:59:30, who wants to send a message at precisely 12:59:30 ?
You have a meeting at 13:00:00, you watch the clock to see if you are early or late. With flooring, if you see 13:00, you know you are late. With rounding, you are not sure.
It is common for digital clocks to have big numbers for hours and minutes and small numbers for seconds. If you are not interested in seconds, you can look quickly from afar and you have your usual, floored time. If you want to be precise, you look closer and get your seconds. Rounding the minutes would be wrong, because it wouldn't match the time with seconds. And you don't want clocks with a small display for seconds you may not even see to show a different time than those that don't.
And if you just want to know the approximate time and don't care about being precise to the second, then rounding up or down doesn't really matter.
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
Thanks for the feedback. I agree this is how I should have ended the article. If anything, the most important thing with conventions is that we all follow the same ones. So in the end I'm obviously not gonna move all my clocks forward by 30 seconds. This is just how I decided to write the article, but I concede I should have made the tongue-in-cheek tone more explicit.
You can still change the ending. It is your article and right now quite a few people will have read it, but if you keep it live for years many more will probably get to read it and there is no reason why you should keep some first version of it online if you think it should’ve been different.
You wouldn’t leave a v1 of an app online just because it is first
It seems to me many people are so amazed by the fact they for once had an original thought that at this moment they stop caring whether it is actually a good one.
It is crucial to maintain mental flexibility and one does that by thinking things through, killing your darlings, admitting when ideas are wrong or simply just mediocre. Only because it was me who had an idea doesn't mean I have to defend it at all cost. The idea isn't me.
I have been staring at this comment for over 2 hours. It is brilliant on so many levels... During that first hour, two people DMed me, and said a couple of my practices are genius.
I think that this is one of the very most important ideas I have ever read on YC:
"It is crucial to maintain mental flexibility and one does that by thinking things through."
One of the big downsides of the internet is the cold water it constantly pours on my idea of my own originality. Every time I think of a great idea I find someone else has already thought of it
> 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.
Because of how lots of reminders work. There isn't even a good way to tell Google calendar to always notify 1 minute before events - I had to do it through slack integration.
So instead the reminder usually tells you a meeting will be in 15min which quite often is a useless information. Then the app tells you the meeting started right now and you still need a few seconds to wrap things up and prepare.
> There isn't even a good way to tell Google calendar to always notify 1 minute before events
It's on the calendar settings. Settings for my calendars > Event Notifications. You can set 5 default notification options for all events created on that calendar.
Multiple notifications are a great feature. I use two: "10 minutes before" and "1 minute before".
Because 10 minutes is just enough to wrap up something I'm in the middle of, and simultaneously, 10 minutes is well past long enough to get distracted if I'm not already deep in the middle of something. :)
Need to check that when I am at my desk. I use 10 minutes and then remind me again in 5 minutes. Which isn't working all too well. If I miss the the first one by a minute, the second one comes 1 minute after the meeting started. So I'll join 2 minutes late. And in our company we take proud in not starting late.
Most people are not clear on two concepts: Be prepared, and on time is late.
Both of these are not math skills, they are leadership skills.
Its rather easy to establish a beat, and set two clocks to one clock ( seminar program clocks to USNO standard time, ). After a few hours, even the most inexpensive digital clocks will not vary a second, usually it takes a full day to drift that far.
Its quite uncommon for everyone to be ready, alert and available on time, even in integrity conversations.
Seems like there are important cultural differences in how appointment times are understood. Last week I was talking to a friend living in the Comoros, who mentioned that for them 13:59 is still 13:00 for this purpose.
As I understand, they're less stressed about having things at precise points in time and are fine with waiting. I guess they would say something like "13 zero zero" when necessary...
We consider it impolite, if you show up for an invitation at someone’s home before the time you were invited for. Many would say it is even impolite to show up less then 5 minutes late, and consider being 10-15 minutes late the best, and up to 30-45 minutes acceptable.
For a business appointment or doctor's appointment, where there is an assistant that opens the door and a waiting area, it's expected to be early, so that you are already in front of the correct room when the appointment starts.
I don't know if it's a Korean thing or my mom-specific thing but she had very strong opinion about being early. For her 15 minutes early == on time. To reinforce this notion, she would set the house clocks later by some random undetermined minutes. The clocks in her home would all differ slightly so you could never tell what time it actually was unless you looked at your phone but you'd know you're little bit early to things for sure. Good times.
She didn't by chance serve in the military or a civil auxiliary branch, did she?
"Early is on time, on time is late, and late is unacceptable" was drilled into me while doing Civil Air Patrol back in secondary school (high school) and I habitually set all my clocks 5 minutes ahead, still, to this day.
If the social group in question regards 13:00 as meaning between 13:00 and 13:10 then arriving at 13:05 is arriving on time and no one is bothered or inconvenienced.
Being late is not simply a property of the clock time but also of the society you are part of.
In England arriving early for a dinner party is going to get you at least a dirty look, arriving half an hour late just means that you might miss a pre-dinner drink. In Norway, if you are ten minutes late the host might send out a search party.
"Late" here means "arriving after the social expectation." In many places in the Americas, you can be (and are expected to be) an hour "late" for a party of any kind. That doesn't mean you are late.
In a Western business context, "late" comes about 1-2 minutes after the meeting starts.
This makes a lot of sense. But where it really matters, say train departure times, are there rules that the doors are closing precisly at X seconds? Or is it arbitrary?
What is specified is the actual departure time of the train. Before that it has to be decided to start closing the doors, the doors must be closing, the secure closure must be determined by the train leader and the train leader has to order the train driver to start driving. How long that takes depends on the train. For short-distance trains it's ~15seconds for long-distance ~1minute.
I'm usually early but I watch the preview until there are at least two other people in the call, then I join. I suspect many other do the same which sometimes results in implicit standoffs.
But not every clock would be like that - only those clocks which don't show the seconds precision would use this rounding.
The consequence of that would be that statements like "fireworks start at 12 AM" would mean two different points in time depending on how much precision your clocks have.
That's true if you catch the exact moment the clock changes. If you don't, the only thing you know with a truncating clock is that the fireworks started 0 to 59 seconds ago. With a rounding clock, you know the starting point is within [-30, 30] from now. So on average, you're closer to the starting point when seeing the clock show 12AM.
A good reason for truncating is that we have a strong bias against being late, but not really against being early.
> If you don't, the only thing you know with a truncating clock is that the fireworks started 0 to 59 seconds ago.
More importantly, I know whether the designated point in time passed or not. If you have a submission deadline set at 14:00, the most important thing you care about is whether you made it or not.
But what bothers me more is that this is inviting ambiguity into time definition. What 14:00 means (in addition to all the timezone complexity) now depends on the type of the clock you use. That's just bad.
> A good reason for truncating is that we have a strong bias against being late, but not really against being early.
This is a weirdly satisfying thought, if entirely unrealistic in a corporate setting: what if meetings in general were more of a consensus thing, and less of a rigid time slot thing.
I still think that flooring would be better; however, if you did insist to do this rounding instead then you could use a different convention for numbering seconds with e.g. -30 to +30 instead of 0 to 60. However, I think that this is not worth it, and that the existing use of flooring is much better, although if you want such precision with timing then you really should display the seconds, rather than using a clock that does not display seconds, anyways.
> This is especially apparent when you're trying to calculate "how much time until my next meeting?", and your next meeting is at noon. 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"!
Ok. But what does it mean for a meeting to start at 12:00 when people don't have clocks that will accurately show 12:00? They'll only know when the time is 11:59:30 or 12:00:30, anything between is just going to be a guess. So it seems to me that the start times would just align to the half-minute offsets instead, and we'd be back exactly where we started but with more complexity.
> 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.
I've done a lot of work with hosts on various shows. One guy stood out more than others on being so natural on the vamp/stretch to fill the time. Starting at 5mins, we give one minute signals. Not once did it ever sound unnatural in trying to rush or filled with ums, uhs, or ahs. Others struggled with the rushing being most noticeable.
Jonathan Agnew has a similar story about the late, great Australian cricket commentator Richie Benaud, although filling ~52 seconds rather than 5 minutes.
I think it's every host's worst nightmare when they see it when reading the teleprompter. It's my worst nightmare when watching local news feeds where they are clearly off prompter or vamping.
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.
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.
The point is that we use 12:00 to note a time between 12:00:00.0 (inclusive) and 12:01:00.0 (exclusive). Saying that 12:00 is a time between 11:59 and 12:01 implies that the range of error is twice as big as it actually is.
How long between 12:01:00.0 and 12:00 (as read on a clock)? Between 0 and 60 seconds.
How long between 11:59:00.0 and 12:00 (as read on a clock)? Between 60 and 120 seconds.
What I am saying is that that use is incorrect as well. There is only one way to understand numbers, and that is scientifically. I.e. significant digit.
Analogue clocks like the face of big ben are not like digital displays, and whether they "show seconds" in the context of the meaning of this article is not, like digital displays, down to whether there is a dedicated hand.
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).
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.
Again, 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. It is down to the number of beats per unit time for an analogue display as to what the minimum display resolution is (regardless of if the movement is analogue or digital itself).
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.
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.
The key to this mechanism is that the stepping of the minute hand is what unlocks the second hand. Pretty clever low-tech way to keep a LOT of clocks in really close sync.
Dutch train stations used to have these too, I loved to watch them in action while waiting for a train.
If you think of the design goals (synchronizing clocks across the train network) and the technology available at the time, the design is actually pretty clever. Knowing the exact second is not important - if the second hand actually completes a whole cycle in only 58 seconds, this is still good enough to be able to see how much of the minute has passed. Having the exact same minute on all clocks is much more important than that - especially since train departure times are usually "on the minute".
What technology wasn't invented by the time this clock was created??? And the design is bad, nothing clever about it, clocks can move their minutes hand to give the necessary indication
So name a single time tech and explain how the lack of it didn’t prevent other train station operators having clocks without jumping hands operating even before 1944?
(not sure, but think that the minute timetable resolution was pretty universal)
> 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.
> 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.
I think a slightly better term is "discrete" vs "continuous". Some analog clocks are discrete, some are continuous. Some digital clocks operate on a resolution so fine that they appear to move continuously. It's quite lovely to find those that invert your expectations when out in the real world.
There are analog clocks where all hands move continuously (like when there's a second hand with no discernable beats). There are analog clocks where all hands move discreetly once per second (60 BPM for all hands). There are analog clocks where the minute hand moves at 1 BPM (quantized to the floor of each minute) while the second hand does something else (perhaps discrete movement at 60 BPM, or perhaps continuous other than a pause at the top of each minute, etc.). And there are digital clocks!
You're correct, thanks for the clarification. I was going more with the colloquial understanding of the two (analog = continuous; digital = discrete) and was trying to touch on the vagueness of no true analog clock with the reference to ticks/resolution.
However, your explanation is definitely much better.
All universal statements like this are wrong and stem from basic ignorance
> So when it's actually 14:15:45, they'll show 14:15. And when the actual time goes from 14:15:59 to 14:16:00, then that's when your clock changes from 14:15 to 14:16.
No, that's a silly mistake, look at the picture (though much better - video) of the analogue clock to see it's not the case, the minutes hand moves continuously, so isn't at 15 at 15:59
> the meeting is in 5 minutes.
That's not the only question we ask about time. Has the meeting/game already started? You can't answer that with an average value
> for some context appropriate reason) you reply with just hours, you would say it's 11!
No, you reply would depend on the context, which you haven't specified.
> Please someone tell me I'm not crazy
Of course not, just trying to replace one ambiguity with another. Maybe instead come up with a more precise minutes display in digital clocks that adds more info like two dots flashing when it's past 30 sec and only 1 dot when it's before? (In phones you could use color or a few more pixels within all the padding?)
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!
Both of your pic examples are wrong though. That digital clock does show seconds and the London clock has its minute hand in between minute mark - showing progres between minute mark if you look closely. This is the same for all analogue clocks.
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.
Most analog (really, with a geared mechanism) clocks do not "snap" on exact minutes but slowly drive toward them (because that's simpler and thus cheaper).
This is true unless you look at something like a Seiko Spring Drive, which has a completely smooth second hand sweep, although it’s not entirely mechanical (and maybe only watch nerds care about this)
Pedantically, only above second granularities. They're continuous between second hand sweep movements at subsecond ones, no? I mean, there's no point on the watch that the second hand doesn't "hit" at some point, however small.
Or am I wrong that "intermittent, jerky, continuity is still continuity"?
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.
In movies when the villain has placed the hero in the mechanism of a clock-tower, the minute hand seems to always tick over a minute. I don't recall ever seeing it in real-life, but I don't look at clocks in clock-towers that often.
I have a round analog clock with a particularly strange arrangement: it has a second hand (that ticks every second), and it has a minute hand that only moves every fifteen seconds.
(It's a radio-controlled clock: it has the second and minute hand on separate motors presumably because syncing to the actual time if there were only a motor for the second hand like a conventional analog clock would take too long (and probably make determining position more complicated). There is no independent motor for the hour hand, so it does have to roll the minute hand around to move that one.)
There’s some very neat designs that only tick the minute hand once per minute, as it’s significantly more power efficient to do so. You just power the hand once per minute, as opposed to continuously driving the hand in small increments.
I see these clocks often in railway stations (I live in India). There is no seconds hand. The minute and hour hands move in clicks, not smoothly like most clocks.
The clocks in German railway stations have second hands which 'click'. It's particulary fun how the seconds hand runs slightly fast so that it can pause on the minute, waiting momentarily for a synchronization pulse:
Swiss stations are similar but have contiuously moving second hands. I could have sworn this clock characteristic was indeed called 'Swiss motion' but I can't find any such reference on the Web...
Quartz crystals are inherently digital, where the quartz crystal itself oscilates at a stable rate, 32,768 Hz in most timepieces.
That's counted by a digital accumulator, and a one-second advance occurs every 32,768 cycles.
The display of a quartz timepiece may be digital (as in a liquid crystal display, or any other discrete display), or analogue, as with a watch or clock with hands. But the underlying timekeeping is digital at its heart.
(One might make a similar argument for a pendulum- or spring-driven clock mechanism, with discrete periodic movements, or for an hourglass (discrete sand particles flowing through an orifice) though the more variable physical process tends to argue against this.)
There is very little that is "digital" about the crystal itself. Tuned oscillation is analog.
The accumulator attached to it is digital, but it only has to be that way because it's so hard to make gears that tiny. If quartz was slower you could use the signal to directly drive a gear and have nothing digital in the entire timepiece.
Digital in the sense that there's a set of discrete countable events.
Contrast with several other timekeeping systems: water clocks, hourglasses (sand glasses), sundials or astronomical observations (ultimately the definitive reference), in which periodic processes or entropic gradients serve as analogues to the passage of time.
Modern atomic clocks are also to my mind inherently digital or quantum, where counts of discrete events are tallied.
The discussion of DAC/ADC conversion process has some merits, but to me, thinking of ideas as interfaces, and as models of reality, "digital" fits far better than "analogue" in this case. Particularly as you'll find that same DAC/ADC process in what we manifestly call digital computers or digital memory/storage systems, where some other-than-discretely-varying signal is nonetheless abstracted to 1s and 0s.
As occurs when tallying quartz crystal oscillations in a timepiece.
The counterargument is that whilst the escapement of a spring-driven or pendulum clock is in a sense digital (as, for that matter, was a Jaquard loom's card-based governor), the driving mechanism (gravity weights, spring) isn't. But then, quartz-crystal clocks utilise a battery....
Again: ideas are interfaces, ways we get a grasp and shared understanding of reality, and are models of that reality. To that extent, all definitions are both arbitrary and flexible, but ultimately are governed by their utility.
Again: quartz crystal movements involve a manifestly digital accumulator which drives a display (character-based or analogue hands) based on accumulated ticks. The ticks are digital, a sequence of accumulated 1s and 0s, and are interpreted by logic rather than mechanism.
(Yes, logic itself can be mechanically implemented, but it remains a mechanical implementation of logic rather than a purely mechanical process.)
Escapement mechanisms lack such an accumulator, but rather utilise gears and cogs to match the movement's oscillation to the desired movement of hands on the display. That entire process is analogous of time, and hence, and analogue movement.
You said they "might" be in the same category and sounded unconvinced. Now that you're insisting on an expansive definition of digital, I'm addressing the problems it causes more directly.
> To that extent, all definitions are both arbitrary and flexible, but ultimately are governed by their utility.
And the utility of the term depends on clockwork clocks not being digital.
> (Yes, logic itself can be mechanically implemented, but it remains a mechanical implementation of logic rather than a purely mechanical process.)
Gears are a mechanical implementation of logic. If you make a distinction here, it puts clockwork clocks on the wrong side.
The logic here is just a divider. The same thing the gears already do in a clock.
Also you didn't really address one of my points, but I think it was an important one. If quartz crystals had a slower frequency, you could easily use them to directly push gears like a pendulum does. Since you're so focused on the crystal itself as being digital, would you call that a digital clock?
The quartz crystal itself is an analog component which resonates at some specific frequency. The crystal is placed within a feedback circuit to create a stable, sinusoidal oscillation; the analog sinusoid is then converted into digital pulses to be counted.
It's the same principle as a "pendulum- or spring-driven clock mechanism, with discrete periodic movements"; just on a microscopic scale -- you're taking an analog physical system which naturally resonates at some specific frequency, and then converting the continuous motion of the system into discrete pulses.
While automatic quartz watches do exist[1], “generally, some form of digital logic counts the cycles of this signal”[2], to the point of becoming a synonym.
Almost every clock based on mechanical escapement stops hands on each beat. That is where the ticking noise of classic mechanical movement comes from. For quartz clocks, smooth sweeping hands is a premium feature and I'm not sure are even those truly continuous motion or just higher frequency.
The output of the quartz oscillator is a high frequency electrical signal which is read by a digital frequency divider then fed back into a motor.
> The data line output from such a quartz resonator goes high and low 32768 times a second. This is fed into a flip-flop (which is essentially two transistors with a bit of cross-connection) which changes from low to high, or vice versa, whenever the line from the crystal goes from high to low. The output from that is fed into a second flip-flop, and so on through a chain of 15 flip-flops, each of which acts as an effective power of 2 frequency divider by dividing the frequency of the input signal by 2. The result is a 15-bit binary digital counter driven by the frequency that will overflow once per second, creating a digital pulse once per second.
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.
The only one that I know of as being an anachronism is saying "quarter of" or similar. At one point people decided that 'of' meant 'to' and after a while we forgot that because it was stupid. People still say quarter past though.
Also vaguely related, I've come to realize some people find metric measurements easier than feet and inches.
I find the fractions simpler. Need a half of that half? Just double the denominator.
My wife would seemingly rather keep counting .1 centimeters.
The same applies with clocks. It's easier for me to rough out how long I have if I just chop the face into fractions vs mental arithmetic, as brutal as that sounds. What do you mean this guy can't divide 30 in half?
The spatial representation on an analogue clockface is far more evident. Each 15 minute interval sweeps out a quarter of the face with the minute hand.
In Germany, that would be quarter 7, which means either the quarter in the 7th hour or the 7th time that a quarter has passed since the hour, which is of course that same. (Unless you are in a part, that got conquered by the US after 2WW, which now uses "English time".)
So do the public schools here, and we have 3 analog clocks in my house, but 3/4 of my children cannot read an analog clock, and 2/4 of them do not understand me when I say "quarter past" or "quarter to" no matter how many times I explain it.
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.
It's not really about flooring or rounding, but whether one thinks of time indices as ranges or moments.
Days, as the author points out, are though of with "flooring", but more accurately it could be said that a date is thought of as a range between the times belonging to the date.
Minutes one can consider as ranges or time indices. There the error comes, in switching the interpretation of a start of a duration to an actual estimate of a point of time index.
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.
Pointless remark about myself, but I always set my phone's clock to second precision (I think this setting is hidden somewhere, or even needs a third-party app to unlock), and I am annoyed there's no way to do this on the lockscreen. How is it possible that nobody else (apparently) wants it, and it's not the Android default? Why would I want a clock that is, on average, a half minute off?
> Why would I want a clock that is, on average, a half minute off?
Because in 99.9% of the cases I don't care about the seconds, it takes away space in the top status bar, and the constant changing of seconds in the top-left corner of the screen is distracting. And for the remaining 0.1% of cases, there is the clock app that shows seconds.
What benefit do you gain in daily life by having the time down to the second? The argument "so it's not half a minute off on average" seems a bit self-referential.
> What benefit do you gain in daily life by having the time down to the second?
I commute by public transport and am sometimes cutting it fine, so knowing whether it is hh:mm:05 or hh:mm:55 does make a difference in how much I have to hurry up sometimes.
> and I am annoyed there's no way to do this on the lockscreen
With some OEMs there is (personally I know that current-ish Sony phones offer a corresponding option), but yeah, it is a bit annoying that that isn't universal… part of the reason I still carry a regular watch.
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 may technically be correct, but it is incorrect in the real world. I submit that error is error in the real world. Mathematics can go jump off a cliff unless it wants to be helpful. :)
I don't think this applies to Elizabeth Tower/Big Ben, as it's an analogue clock and, from footage I can find[0], its minute hand appears to move continuously opposed to in steps. (or at least, not in full-minute steps)
Also, I believe it's wrong to say "the average error would be 0" if rounding to nearest minute. The average offset would be 0, but the average error would be 15, to my understanding.
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 :)
Hä?! A clock shows the period of time we are currently in. A clock only showing hours would for example indicate that we are in the 14th hour of the day, for the entire duration of that hour. That is not an error. Similarly, a hh:mm clock will show the hour and minute we are currently in for the duration of that minute.
No clock can display the exact current moment of time. That would require infinite digits, and even then those will be late, since lightspeed will ensure you recieve the femtoseconds and below really late.
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.
The fallacy is it’s a leap from logic to go from “average error is x” is the same as “is x late”.
Seeing the exact transition is often if not more useful than minimizing average displayed error.
This is nitpicking, but the transition from "the average error of a truncating clock is 30 seconds" to "therefore all clocks are 30 seconds late!" is seriously wrong. For one, the median is equal to the mean here, so about half of all clocks are less than 30 seconds late, which is a clear contradiction.
> Basically I'm arguing that rounding for clocks would be more useful than flooring. This is especially apparent when you're trying to calculate "how much time until my next meeting?"
Yet a rounding clock provides no way at all for you to know whether the meeting has already started or not.
Not sure where I've heard this, but an idea that's been stuck in my head is this: We don't look at clocks to see what time it is, we do so to know what time it isn't yet:
Have I missed the bus yet? Can I already go home? Am I late for this meeting? Do I still have time to cancel this cronjob? All questions that a rounded clock cannot precisely answer.
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.
> Hours: That's when mentally, I switch to rounding! At 15:48 I definitely feel like it's pretty much 16:00.
Disagree. I would never round to a full hour, only to nearest 5 minutes.
As far as minutes, for clocks that show discrete minutes, it'd be weird to see the minute-hand snap to the next number and think "oh, it's actually 29 seconds before that number". Seeing the snap motion means you're at :00 seconds.
Besides, for a clock that doesn't show seconds, it really doesn't matter. If you need more precision, you just use a timepiece with the extra precision.
Clocks show the time that is _passed/past_, that's the point. Hence flooring is correct approach.
Even when you involve physics, you are seeing the nanosecond past. Not the actual time. (The time that takes light to travel from clock to your eyes, then your brain's processing delay via neurons etc.)
Even the thought of being late is the same way. If something starts at 13:00 and you are not already there when it is 13:00:00.000, you are -by definition- late.
Good point, when you look at your watch your thought should be “3:15 has passed” or “3:15:40 has passed”. One is more precise but if you think of it as a time that has already passed you can budget accordingly. 3:15 tells you that 3:15:00 has definitely passed and as much as 3:15:59 might have passed.
While most analog clocks' minute hands sweep from minute to minute, jumping minute clocks have the issue the article brings up.
Depending on when / where you went to school, you may have had analog jumping minute clocks. The ones we had at one school would "give away" when the minute would change because the minute hand would move slightly counterclockwise before changing to the next minute.[0]
Per reddit, some Swiss Railway clocks had jumping minutes, but I have not seen one in person. [1]
Another school I attended had sweep second and minute hands, but would hold the clock at 59 seconds until it matched the master clock. Depending on the particular clock and how well it was maintained, these could be 5 - 10 seconds off. Seems like nothing as an adult, but as a kid wanting to go home, it seemed like an eternity, especially on the last day of class for the semester.
The Clock app in iOS works like this in timer mode. If you start a timer for 10 seconds, you'll see the 10 for half a second, then 9 through 1 for a second each, then 0 for half a second, then it beeps. In practice it's pretty stupid and not really useful, so I wish they'd fix it.
There's a reason why normal countdowns work the way they do. You care about the exact moment it hits zero, and with rounding you lose that.
Time intervals aren't floors or rounds but thresholds.
This is most evident above the level of hours, minutes, or seconds: we speak of a new day beginning (though the time at which this occurs has varied culturally and regionally), or a new year, decade, century, or millennium (with their own threshold arguments courtesy the AWOL Year Nil in the Julian/Gregorian calendrical system).
Birthdates are an interesting example. In Western/European cultures, it's typical to count by full years elapsed, such that an infant within its first 12 months is 0 years old. In Asian cultures, the age is given as "1", which is reflected in an occasionally-used Western notion of "being in my nth year". That is, a 49 year old is in their 50th year.
What a clock (or calendar) indicates generally is what time period you are presently in, that is, the second of a minute, the minute of an hour, the hour of a day, day of a month, etc., etc. And what's relevant from this point of view is that the threshold is what matters.
The other problem touched on in this essay is of estimating time remaining to a future threshold, and here, rounding is indeed useful. If you have a 10am meeting and the time presently reads 9:55 am, you have fewer than five minutes to arrive punctually. But that is planning and not timekeeping issue, strictly.
The writer makes an implicit assumption you just glance at the clock with no prior info.
Where seconds count, you can watch the clock until the moment it ticks. At that time you have greater precision. And due to your own innate sense of time, that precision decays for a little while (maybe even 30s?) rather than instantly disappearing.
I like to synchronize my clocks this way (when seconds are unavailable). Yes, it does mean I invest up to a minute more to set the time, and it's probably not worth it if you're doing so often (eg. area prone to power outages).
The same technique is how computer RTCs are set/read, but to sub-second precision instead of minute precision, because the most common register standard allows only storing whole seconds but they keep relatively accurate time.
Centuries are also 50 years late on average... And everyone is on average 6 months older than they say.
Also moving the rounding 1 place down doesn't solve anything. Now your second-resolution clock is on average 500ms late unless you move the decimal 1 place down again.
> If it's 11:55, you would usually mentally subtract and conclude: the meeting is in 5 minutes. But the most probable estimate given the available information is actually 4'30"!
Admittedly I'm being a bit pedantic, but this isn't true. The expectation value might be 4'30", but the time is as likely to be 4'59" as 4'30"; assuming it's 4'30" will simply minimize your expected error.
> It would be weird if we rounded for years, months and days, that's for sure. I think most people think of those scales as intervals. In other words, July is a period of time, with a start and an end. So are years, centuries, seasons. We are inside of it or outside.
I feel like my sense of time is different from the author's. While it can be useful to round the current hour/minute on some occasions, the information about which exact segment of the day/hour you're in can also be very useful. I can certainly tell that I ask the question of "when exactly is it going to be 12:00?" far more often than "how many seconds have statistically likely elapsed in the current minute?"
The biggest issue for me is that the precise moment of when one minute/hour transitions into the next is important for people. Like, when coordinating an event or meeting, would you prefer it if your clock indicated the precise moment when 12:59:59 becomes 13:00:00 and told you to start the meeting, or would it be better if the clock instead told you that it was "13ish" and you'd have to wait out ~30 seconds by counting in your head?
This also causes a jarring discontinuity - now clocks with a ticking hour hand appear to run 30 seconds late than clocks without, turning on the digital clock setting to show seconds offsets it, and so on. Some people celebrate New Year's or occasions that happen at a specific time 30 seconds early because they no longer have a strong reference point.
Clocks are used as inputs into decisions. So this doesn't matter as long as the decision process accounts for it. If I see that a meeting starts in 5 minutes, I'm not setting a timer get there in 300 seconds, I'm trying to decide if I have time to fill my water bottle on the way or not.
The post is a useful consideration to think if you are trying to do precise tasks though. See Keskival's post below about intervals vs moments to add some more precise ways of thinking.
I'd be very surprised if a smartphone, syncing itself to a reference, is ignoring seconds. Why would it?
To me, if a clock that doesn't display seconds is displaying 09:30, then I assume the time could be anywhere between 09:30:00 and 09:30:59.
Presumably when setting the time on a device that doesn't display seconds, the seconds are being reset to 0 (i.e. setting time to 09:30 is setting it to 09:30:00), so if someone really cares about sub-minute accuracy they can take this into account.
Does OP realize that people don't looks at 11:55 and think it means 11:55:00, but they think, it is just not 11:56 yet.
Computers and smart devices syncing to NTP doesn't have 30s average error rate, it is the author who has 30s average error rate in clock-reading if he reads a digital clock and think that the clock tells that no seconds has passed since the last time it added one minute.
If you had two rounding digital clocks, one with seconds and one without, they would switch to the next minute 29.5 seconds apart. Everyone would hate that.
Because it would be incorrect. Like the article's main premise. Flooring is the only correct behavior for minutes. And other time units.
Big Ben may not show seconds but people would notice if it started bonging 30 seconds early or late with new year. Which would be the case if it rounded. It bongs right on time. That kind of is the point. The news doesn't start half a minute early or late either. And people joining meetings after the minute changes in their clock are technically a few seconds late.
All of this is made redundant by just... knowing this is how clocks work.
If you don't have a seconds hand/counter, you can't predict how many seconds are left in the current minute. If it's 11:45:01, it's 11:45 without seconds. If it's 11:45:59, it's still inside the minute-long interval known to everyone as 11:45. The clock can always be one second away from flipping to the next minute. I just mentally subtract one minute if I'm actually planning on being somewhere down to the fraction of a minute, and planning what I can do beforehand. Mentally subtracting 30 seconds is not any easier.
I don't see this as even having some kind of gimmicky benefit...
Anyone who has done timer or countdown-based work has to think the opposite. Whether that's sports or event production, rocket launches, or so on. You're not thinking about the time you've past/expended. You're thinking of the time you still have left. "Two minutes left in game." "We're live in 30 seconds" etc.
NFL delay-of-game penalties are interesting for this, because when the clock first shows 0 seconds, that means that the team still has a full second to start the play.
“Drive to the hands is by an oblique shaft which drives bevel gears positioned centrally on a gantry above the clock, with four shafts running out to each dial. Because there is no remontoire the hands on the dials advance by 2 seconds every two seconds, i.e. at every swing of the pendulum“
⇒ if you look close enough, you can read the time at intervals of two seconds.
Drivers licenses would be more accurate if they showed place of birth. Maybe the kid grows up to move to an eastern timezone and is accused of drinking a few hours early!
When I make word clock, I make it change from "SATU LEBIH DUA" ("ONE PLUS TWO", 01:02:00) to "SATU LEBIH TIGA" ("ONE PLUS THREE", 01:03:00) at 01:02:30.
But if I make digital clock, I make it change from 01:02 to 01:03 at 01:03:00.
One wrinkle here is the choice of signed error instead of eg. RMSE; absolute error metrics don't care about rounding vs. flooring. Since the conclusion of the analysis hinges on this choice of error metric, I think some justification or discussion of that choice adds interesting context.
Signed error implies that clock-imprecision "cancels"; that being 20 seconds late to your meeting will be undone by being 20 seconds early to lunch afterwards. I'm not sure if this is quite how people reason about 'lateness' though. Obviously in some applications it makes sense (ex. recording event times of some phenomenon of interest), but in scheduling my daily life that's not really how I think about things.
I think RMSE is closer to how people evaluate scheduling of stuff; it doesn't matter if I'm late or early, both will have notable consequences in unique ways. The ambivalence of the RMSE error to rounding vs. flooring is the intuition I would put behind the counterargument fielded by the author:
> But this is just a convention! Truncating, rounding or even ceiling are all valid, as long as we pick one and stick to it.
I think you can also squeeze some juice out of playing with the error metric further. If you want a 'just-in-time' schedule (ie. you want to never be early to anything) then the flooring clock is superior to the rounding clock. If you want the opposite then a ceiling-ing clock would be the best choice.
> Personally, I would never say that it's 10 if the clock shows anything past 10:30
I like to floor my times to the nearest 15-minute interval (10, quarter-past, half-past, quarter-to), only rounding once I've reached ~10:55
While you could argue that it's flooring, it feels much more like truncating. We have a inner representation of time that's like yyyymmdd-hhmmss-mmmm and we truncate it to the precision we need for a given task. If we need the month we truncate to yyyymm, and if we need hours we truncate to yyyymmdd-hh.
That's quit intuitive for all kind of time precision, and the author's rounding solution would be somewhat counterintuitive, at least for me.
Summer starts at the solstice, when the day is the longest. But by then half the length of the season already passed with the day approaching that point. So I think the seasons are half a season off (seasonal lag notwithstanding).
I had a watchface on my Pebble smartwatch that only displayed time in five-minute intervals. This post is making me question whether it rounded up or not.
I have to assume it did because I didn't start being late for everything.
Well I was bothered by a similar problem when tweaking my StumpWM modeline long time ago.
I wanted to show the seconds in the clock on my modeline, but the modeline has a fixed refresh rate, which I set to 1HZ. Then I realized my clock can never be accurate.
Eventually I chose to hide the seconds to stop myself from having those nightmares, but I think they are coming back after reading this article.
I enable seconds on my PC and phone clocks, and basically anywhere it's an option. I enjoy seeing if two messages on IRC were just 3 seconds apart as it will often tell you the second person hasn't actually read the first person's message right before theirs (they were probably writing their messages at the same time). Something not obvious if you just see the minutes.
> 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"!
But if you want to say it's M minutes, then it's either 4 or 5, and 4:30 rounds to 5, so it all works out once more! :)
I have about a dozen of the absolute cheapest digital clocks around my house, and every single one, I set it to the next integer minute then waited for 00s to hit the button that makes the : blink. So, even if every other person on earth fails to do this, the average is below 30s just due to me.
This post is fascinating but I think it is more mundane than I realized. I thought everyone knew that when a cheap digital kitchen timer shows a time like “0 H 1 M”, that actually means you have exactly 60 seconds or fewer for its alarm to go off.
I might be wrong, but there was a Prince of Persia game (maybe for Game Boy?) that had the same timer behavior. It would show the time remaining to complete the level in minutes and would jump immediately from “1 minute” to 0.
The iOS podcast app is more sophisticated than that. It normally displays how many minutes remain in the playing podcast episode. But what is cool is that at the 30 second boundary, it will decrease one minute. For example, it is at -24:30 or -24:29 that it will go from saying “25 minutes remaining” to “24 minutes remaining.” Then when 30 seconds are left, it is nice enough to show you a countdown of the seconds.
Yeah, I've seen a lot of countdown UIs that incorrectly start beeping as soon as "1s" becomes "0s". In fact they should start beeping exaclty 1 second after that change.
I'm sure this is actually an intentional design decision because starting to beep at 0.99 (displayed 0) feels more correct, even though it isn't.
I agree this is an interesting take and fun to think about. But if clocks rounded to the nearest minute instead of truncating, the average error would be still be greater than 0 I think, and not 0, as the author claims. Assuming a sufficiently large number of measurements taken at random times, I think the average error would be 15 seconds.
The author meant "average error" in the systematic error sense, not the standard error sense. The minute display would be well calibrated, not precise to less than a minute.
A slightly related thing I think about someone's, is if I look at the time and it's 13:05 and then I do a task and when I finish a task it's 13:10, you could say that took 5 minutes, but because we can't see the seconds each time could be up to a minute out. So a total of 2 minutes error! Quite big if you're timing something small like 5 minutes!
Any clock which doesn't have a seconds display is probably not accurate to the second and is also very unlikely to have been set to the exact second. Those 2 factors together mean a good chance the time is > 30 seconds out, making the original point moot.
I am really annoyed that it is almost universal to show only minutes on clocks- when so much in my life at least depends on knowing time to the second. Even modern digital devices like an iPhone make it really hard to get a seconds readout, when the cost of doing so should be zero.
Some of the things I need precise seconds for frequently in my daily life: buying tickets to concerts, campsites, and kids camps before they sell out, checking into Southwest flights, sailboat race starts, and starting/joining virtual meetings I am hosting.
Am I that weird that this is something I need at least once a day that nobody else seems to need or want?
It’s wasteful of other peoples time to show up to a meeting late, and wasteful of my own to be early. I’d like to be as precise as practical. Meetings filled with high paid experts are incredibly expensive- one should get every detail right to save time. One little thing might not matter, but if you pay attention to a lot of little details in running a meeting efficiently- including starting as close to on time as you can, it saves a lot of time.
Side note. I’m more bothered by this issue on digital thermostats.
I don’t even know if they’re flooring or rounding. And sometimes half a degree makes all the difference. I do wish they’d do temperatures out to one decimal point.
If you do care about what second it is, you can still be 59s off: eg. if the "rounded" clock shows 12:30, it could be 12:29:30 all the way to 12:30:29.
The error is reduced on average if you only care how far away from exact minute you are, but you simultaneously never know when it is the exact minute.
The question is really about what's more generally useful: the offset of 30s is usually not important enough, which is why most clocks only show hours and minutes. Where it matters, higher precision is used.
Some of the social constructs would be less meaningful (like New Year countdown) as most watches and clocks would show midnight 30s early.
This could be a good allegory for sampling intervals. I’m forever having to explain to people that if they are looking at data every 60 seconds they can take a lot longer to notice a problem than common sense would suggest. Your new information shows up on average 30 seconds late and up to 59.99999 seconds late. If you’re trying to compare the last two samples to detect a problem then you’re going to see it up to 2 minutes after it already started, since it could start 1 ms after the first sample. Particularly in systems where multiple actors are using periodic actions.
This blog post is a really good argument. The kicker for me was that we all generally switch to rounding when asked for the hour (without minutes) but don't round when asked for the minute (without seconds). That's an inconsistency for which there doesn't seem to be a good reason.
However, this inconsistency only exists orally. When a device displays the time, it never rounds. Changing the convention would probably be very confusing for a lot of people, at least initially.
For now, I'm convinced that when communicating the minute orally, I should round to the nearest minute, just like I do with hours.
This is correct. In fact, in one sense our clocks could be argued to be minutes out, on average: originally time was measured by the sun. But by the sun, the earth doesn't rotate in exactly the same time each day during the year. So a clock assuming each day is the same length (like they all do) accumulates an error with respect to sun time of more than 16 minutes,and then loses it again, in a cycle.
But we just collectively decided that it was simpler not to bother with that. We changed the convention so that time is marked with respect to an average day length
While interesting this is just… wrong. Imagine a world where:
- I tell people I’m 50 years old but I’m really just 49 1/2
- My phone says it’s Jan 7th but it’s really afternoon on Jan 6th
- My coworker says they’re a sr engineer because they’ve been told that they’ll definitely be promoted soon
Rounding shouldn’t be applied everywhere. Some things in life are supposed to use a floor function; common sense applies and most folks intuitively know that 1:00pm means ‘between 1:00 and 1:01pm’.
The article is claiming that clocks that only show time truncated to a minute are off by an average of 30 seconds, which just isn't true in practice. When I say or hear 11:30, I assume it can be within 11:30:00 and 11:30:59. Humans rarely need accuracy to the second beyond this, so clocks intended to be used by humans truncate to the minute without causing problems. To say they are "late" is a real leap.
I mean, you can reduce this to absurdity too. A clock truncating to seconds is off by an average of 500 milliseconds! The problem is no one cares in day to day usage which is what human readable clocks are made for.
> When I say or hear 11:30, I assume it can be within 11:30:00 and 11:30:59.
And if you cared about seconds-precision, you would assume 11:30:30, and thus your error would average the same 15s.
The difference is that when you observe a minute change, you know that's exactly at zero seconds (instead of 30 — or 31 if you apply the same rounding rule to seconds).
It is fair to ask a question if rounding would be more useful (nope), but the entire article is incoherent and speaks mostly of the author's confusion.
Amusingly, one of my kids gets very frustrated with how I answer what time it is on most requests. Most of my answers will be of what the nearest relevant time is. I will never bother determining what the exact minute is from my watch. As I just can't see the value of that. Even from a digital watch, I don't see the need in giving a majorly different answer to the same question within 5 minutes or so.
That's how people commonly give time in my language, I suspect mainly out of convenience:
Quarter hour precision is possible to achieve with at most five syllables (and typically just two); compare that to minute-level precision, which usually takes at least 5 and sometimes as many as 10.
Interestingly, spoken times also commonly use the 12 hour clock, while times are almost exclusively written as 23 hours.
I was always annoyed at my parents for doing this when I was a kid. When anyone asks me the time I always read out the minutes for whatever time my phone shows me. Maybe someone wants to make a particular bus or train and the more precise timing is appreciated, who knows!
Analog clocks mostly don't have the problem the author is complaining about since most minute hands move once per second and you can easily see (depending on your eyesight and distance to the clock) that the minute is partially consumed.
I agree though that this is a downside to digital clocks which don't show seconds, though whether the best fix is to round instead of averaging is hard to say.
A delightful read, though I disagree. Unless we were going to introduce half-minute units (which decreases the scale of the error, but makes it twice as numerous) then shifting our minute units by a half value doesn't seem to actually solve the problem, doesn't it only shift it to a slightly different location?
One often unappreciated and amazing thing about the GPS-on-cellphones era is that nowadays everyone has the exact time. Up to the late 20th century it wasn't trivial to have the right time, in fact there was a three digit phone number you could call to get the right time (up to the minute).
I don't think rounding clocks would be any more useful in the scenario about mentally calculating how many minutes until the meeting at noon, because a rounding clock would show noon 30 seconds earlier, so the average difference between 11:55 and noon in a rounded clock vs a floor clock is still 4.5 minutes.
Yes, and it's infuriating if software draws the conclusion that, simply because I happen to be in region x (or even worse, using language x), I must also want date presentation, units of temperature and distance etc. to be according to customs in x.
At least macOS/iOS at this point mostly allow customizing many of these, but some native apps and date picker widgets still don't respect my preferences, driving me nuts every time I have to schedule a reminder or meeting.
Just sitting here with my mechanical automatic watch like some kind of renaissance fair re-enactor. Probably off by a few seconds, but probably less than 30.
TFA fatally misunderstands what clocks actually measure. They measure the amount of time that has elapsed. When we say "it's quarter after noon" what we really mean is that 12 hours and 15 minutes have elapsed since 00:00. The reason clocks don't round up is because that's simply wrong.
A minute hasn't elapsed at xx:xx:36, it has only elapsed after :59
tl;dr The author of TFA doesn't actually understand what clocks measure.
> Is it the same for the current minute of the current hour ? I'm not so sure.
Yes it is. Appointments start at the beginning of the minute, not the average. (And while changing clocks WOULD change that, I'm not sure it makes a lot of sense)
This is true across other domains! If trains are spaced exactly 10 minutes apart and you arrive at a random time, the expected waiting time is 5 minutes, for example.
It is. It's just taking something obvious and recontextualizing in language that sounds like a Mysterious Conspiracy when it's really just a banal truth we all take for granted because all the other options make less sense. Like using tau over pi in geometry.
Technically Big Ben is the bell, the clock has typically been referred to as the Great Clock because that's sufficient explanation of what you meant. The tower, which like the clock is often referred to just as "Big Ben" colloquially, was formally named "Elizabeth Tower" in honour of the late Queen some years ago.
I don't think so, because the sweeping motion of minute hand is effectively continuous rather than discrete, so there's no truncation. At 4:53:30 the minute hand will be correctly in between 4:53 and 4:54, if one (like the author) cares about such precision.
Not really. A mechanical analog clock will typically have smooth motion, so 30 seconds into a minute, the minute hand will be halfway between two values.
Most quartz watches with analog displays work the same. I don't know about Big Ben, but it's possible the author is wrong about that example.
There was a clock on HN a while ago (which I cannot now find) - it has one mode in which the clock only updates itself every random number of seconds, or ticks at different times within each second, oor ticks according to a MIDI tune as well as it can while staying within 30 seconds of the real time.
So, while you can just set your clock forward 30 seconds and be done with it, there are some variations that someone who likes thinking about this are worth playing with.
[My favorite mode of the referenced clock, sets the clock randomly ahead between 1-5 min. Since you don't know how much your clock is off by, you have to assume your clock is on time, and that will give you an average 2.5 minutes to actually show up on time.]
The argument is a bit like saying decimals are wrong because the one in "10" jumps to one after you counted to 9, which is 90% of the range and not 50%.
But that is the point of using multiple digits. Similarily the point of using multiple units of time is that each of the parts is in it self correct. 15:30 always means it is after the 15th hour and after the 30th minute.
If you want to know it more precisely you either wait till the minute changes or you get a clock with seconds. With the proposed system you would not know if the time is before or after the 30th minute. Also: why stop at the minute? You could also round the hour.. But that would introduce a weird jump and the minute would suddenly be negative 30.
This author is either an idiot or does not understand the concept of precision.
It's very surprising that this article has engendered so much discussion...in support of what he is saying.
10:01:01 and 10:01:59 are both still 10:01, because a minute is a discrete unit of time. Rounding the minute to the next minute is simply wrong. Similarly, rounding to the next hour is also wrong and nobody does this except apparently the author. (Note: 15:48 is almost 1600 but is not 1600.) People might round to the nearest five or ten minutes for convenience (i.e., when reading an analog clock) but that hasn't been a thing since the switch to digital clocks.
RMSE of current digital clocks rounding down is roughly 34.5 seconds.
RMSE of proposed rounding to closest is 17.5 seconds.
The new method is roughly 17 seconds more accurate on average.
Does this reduced error make a significant difference? Probably not. There are very annoying practical issues with this proposal though.
Rounding down makes it clear what minute has already passed. If your clock says 3:00, you know the current time is definitely some point after 3:00. If something needs to happen at 3:00, and your clock says 3:00, it is time to start.
With this proposed method, 3:00 could mean anywhere from 2:29:30 to 3:00:30. When do you start? Do you start as soon as your clock says 3:00? Then you're starting 30 seconds early. Do you wait until your clock says 3:01? Then you're starting 30 seconds late.
And how do you set a clock that uses this scheme? If I want to set the clock to 3:00, do I wait until 2:59:30 and then set the clock to 3:00?
The headaches that arise from this scheme are not worth the trivial error reduction.
Flooring makes more sense in every case, from years to milliseconds and more. A few reasons:
You want to send a message at exactly 13:00:00, you have a digital clock that doesn't show seconds. What you do is that you watch your clock, and as soon as it goes from 12:59 to 13:00, you press the button. That's also how you set the time precisely by hand. With rounding, that would be 12:59:30, who wants to send a message at precisely 12:59:30 ?
You have a meeting at 13:00:00, you watch the clock to see if you are early or late. With flooring, if you see 13:00, you know you are late. With rounding, you are not sure.
It is common for digital clocks to have big numbers for hours and minutes and small numbers for seconds. If you are not interested in seconds, you can look quickly from afar and you have your usual, floored time. If you want to be precise, you look closer and get your seconds. Rounding the minutes would be wrong, because it wouldn't match the time with seconds. And you don't want clocks with a small display for seconds you may not even see to show a different time than those that don't.
And if you just want to know the approximate time and don't care about being precise to the second, then rounding up or down doesn't really matter.
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
Thanks for the feedback. I agree this is how I should have ended the article. If anything, the most important thing with conventions is that we all follow the same ones. So in the end I'm obviously not gonna move all my clocks forward by 30 seconds. This is just how I decided to write the article, but I concede I should have made the tongue-in-cheek tone more explicit.
You can still change the ending. It is your article and right now quite a few people will have read it, but if you keep it live for years many more will probably get to read it and there is no reason why you should keep some first version of it online if you think it should’ve been different.
You wouldn’t leave a v1 of an app online just because it is first
It seems to me many people are so amazed by the fact they for once had an original thought that at this moment they stop caring whether it is actually a good one.
It is crucial to maintain mental flexibility and one does that by thinking things through, killing your darlings, admitting when ideas are wrong or simply just mediocre. Only because it was me who had an idea doesn't mean I have to defend it at all cost. The idea isn't me.
I have been staring at this comment for over 2 hours. It is brilliant on so many levels... During that first hour, two people DMed me, and said a couple of my practices are genius.
I think that this is one of the very most important ideas I have ever read on YC:
"It is crucial to maintain mental flexibility and one does that by thinking things through."
One of the big downsides of the internet is the cold water it constantly pours on my idea of my own originality. Every time I think of a great idea I find someone else has already thought of it
(well, almost every time)
> Every time I think of a great idea I find someone else has already thought of it
that's because an idea's greatness does not come from the creator, but from the other people affected by the idea. And most ideas dont affect anyone.
Originality does not exist, humans are not capable of purely original thought.
Closest you can get are unique sentences.
I am sure this is not an original thought.
It may have been for them.
I could have phrased it as "convinced themselves they had an original thought" but that sounded too cynical even for me.
> 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.
Because of how lots of reminders work. There isn't even a good way to tell Google calendar to always notify 1 minute before events - I had to do it through slack integration.
So instead the reminder usually tells you a meeting will be in 15min which quite often is a useless information. Then the app tells you the meeting started right now and you still need a few seconds to wrap things up and prepare.
> There isn't even a good way to tell Google calendar to always notify 1 minute before events
It's on the calendar settings. Settings for my calendars > Event Notifications. You can set 5 default notification options for all events created on that calendar.
Multiple notifications are a great feature. I use two: "10 minutes before" and "1 minute before".
Because 10 minutes is just enough to wrap up something I'm in the middle of, and simultaneously, 10 minutes is well past long enough to get distracted if I'm not already deep in the middle of something. :)
Need to check that when I am at my desk. I use 10 minutes and then remind me again in 5 minutes. Which isn't working all too well. If I miss the the first one by a minute, the second one comes 1 minute after the meeting started. So I'll join 2 minutes late. And in our company we take proud in not starting late.
Most people are not clear on two concepts: Be prepared, and on time is late. Both of these are not math skills, they are leadership skills.
Its rather easy to establish a beat, and set two clocks to one clock ( seminar program clocks to USNO standard time, ). After a few hours, even the most inexpensive digital clocks will not vary a second, usually it takes a full day to drift that far.
Its quite uncommon for everyone to be ready, alert and available on time, even in integrity conversations.
Seems like there are important cultural differences in how appointment times are understood. Last week I was talking to a friend living in the Comoros, who mentioned that for them 13:59 is still 13:00 for this purpose.
So they ignore minutes entirely and just live in hours?
As I understand, they're less stressed about having things at precise points in time and are fine with waiting. I guess they would say something like "13 zero zero" when necessary...
I have friends who treat dinner party invitation times in this manner
I tell my kids this aphorism:
Early is on-time. On-time is late.
This vastly depends on culture and context.
We consider it impolite, if you show up for an invitation at someone’s home before the time you were invited for. Many would say it is even impolite to show up less then 5 minutes late, and consider being 10-15 minutes late the best, and up to 30-45 minutes acceptable.
For a business appointment or doctor's appointment, where there is an assistant that opens the door and a waiting area, it's expected to be early, so that you are already in front of the correct room when the appointment starts.
I have a funny anecdote.
I don't know if it's a Korean thing or my mom-specific thing but she had very strong opinion about being early. For her 15 minutes early == on time. To reinforce this notion, she would set the house clocks later by some random undetermined minutes. The clocks in her home would all differ slightly so you could never tell what time it actually was unless you looked at your phone but you'd know you're little bit early to things for sure. Good times.
She didn't by chance serve in the military or a civil auxiliary branch, did she?
"Early is on time, on time is late, and late is unacceptable" was drilled into me while doing Civil Air Patrol back in secondary school (high school) and I habitually set all my clocks 5 minutes ahead, still, to this day.
She did not, but I would not be surprised if she picked it up for my granddad (he was in the UDU - precursor to the now ROK UDT/Flotilla).
It’s an aphorism
The other person already said that.
But for anyone living in an area where it's mostly wrong, it's not an aphorism for them.
You shouldn't nitpick an aphorism. But if it's wrong a sufficiently large amount of the time, rejecting it is fine.
Showing up early just makes other people feel like they did something wrong by showing up on time.
It could be argued that people can’t be made to feel anything, apart from pain. How people react, on the other hand, may be quite different.
True. Probably wouldn't be a very good argument though.
Other people's feelings about a dimension don't change the dimension.
In a social context, almost everything some people do changes how other people feel.
Depends on the power dynamic and the goals for the meeting, and what position you hold, no?
No it does not. Time is not a dimension that changes depending upon power dynamic.
Time isn't, but punctuality, as a social as opposed to physical phenomenon, most certainly is.
It's disrespectful to be late no matter the power dynamic. In some power dynamics, it's okay to be disrespectful, though.
If the social group in question regards 13:00 as meaning between 13:00 and 13:10 then arriving at 13:05 is arriving on time and no one is bothered or inconvenienced.
Being late is not simply a property of the clock time but also of the society you are part of.
In England arriving early for a dinner party is going to get you at least a dirty look, arriving half an hour late just means that you might miss a pre-dinner drink. In Norway, if you are ten minutes late the host might send out a search party.
"Late" here means "arriving after the social expectation." In many places in the Americas, you can be (and are expected to be) an hour "late" for a party of any kind. That doesn't mean you are late.
In a Western business context, "late" comes about 1-2 minutes after the meeting starts.
This makes a lot of sense. But where it really matters, say train departure times, are there rules that the doors are closing precisly at X seconds? Or is it arbitrary?
What is specified is the actual departure time of the train. Before that it has to be decided to start closing the doors, the doors must be closing, the secure closure must be determined by the train leader and the train leader has to order the train driver to start driving. How long that takes depends on the train. For short-distance trains it's ~15seconds for long-distance ~1minute.
In the UK the doors close 30 seconds before the advertised departure time.
In the UK you're lucky if the train has even arrived 30 seconds before the advertised departure time.
That's not really true. In my experience (London), the trains are on-time more often than not.
Won't be a problem if you're there on-time.
Early is on-time. On-time is late. Late is how most people behave.
We always taught our kids that if you’re not five minutes early, you’re late.
One boy took it to heart and is very prompt.
The other, eh, not so much. He was almost late to his own wedding.
Technically speaking you can’t be late to your own wedding. If you’re not there, it isn’t your wedding. ;)
I'm usually early but I watch the preview until there are at least two other people in the call, then I join. I suspect many other do the same which sometimes results in implicit standoffs.
I live by joining before
:58 if presenter
:59 if core
:00 if contributor
:01 if observer
Many colleagues seem to +:01 this.
But if every clock was like that, then 12:59:30 would be the new 13:00:00
But not every clock would be like that - only those clocks which don't show the seconds precision would use this rounding.
The consequence of that would be that statements like "fireworks start at 12 AM" would mean two different points in time depending on how much precision your clocks have.
That's true if you catch the exact moment the clock changes. If you don't, the only thing you know with a truncating clock is that the fireworks started 0 to 59 seconds ago. With a rounding clock, you know the starting point is within [-30, 30] from now. So on average, you're closer to the starting point when seeing the clock show 12AM.
A good reason for truncating is that we have a strong bias against being late, but not really against being early.
> If you don't, the only thing you know with a truncating clock is that the fireworks started 0 to 59 seconds ago.
More importantly, I know whether the designated point in time passed or not. If you have a submission deadline set at 14:00, the most important thing you care about is whether you made it or not.
But what bothers me more is that this is inviting ambiguity into time definition. What 14:00 means (in addition to all the timezone complexity) now depends on the type of the clock you use. That's just bad.
> A good reason for truncating is that we have a strong bias against being late, but not really against being early.
TBH I don't understand what you're saying here.
So if my watch shows seconds, I'd be late at 12:59:31?
If someone without seconds on their clock starts the meeting, yes.
This is a weirdly satisfying thought, if entirely unrealistic in a corporate setting: what if meetings in general were more of a consensus thing, and less of a rigid time slot thing.
How does 12:59:30 floor to 13:00:00? Wouldn't that be the result of ceil?
Only until the next article saying that "all clocks are 0.5 seconds early" and we then switch to randomized rounding.
I still think that flooring would be better; however, if you did insist to do this rounding instead then you could use a different convention for numbering seconds with e.g. -30 to +30 instead of 0 to 60. However, I think that this is not worth it, and that the existing use of flooring is much better, although if you want such precision with timing then you really should display the seconds, rather than using a clock that does not display seconds, anyways.
> This is especially apparent when you're trying to calculate "how much time until my next meeting?", and your next meeting is at noon. 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"!
Ok. But what does it mean for a meeting to start at 12:00 when people don't have clocks that will accurately show 12:00? They'll only know when the time is 11:59:30 or 12:00:30, anything between is just going to be a guess. So it seems to me that the start times would just align to the half-minute offsets instead, and we'd be back exactly where we started but with more complexity.
> 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.
I've done a lot of work with hosts on various shows. One guy stood out more than others on being so natural on the vamp/stretch to fill the time. Starting at 5mins, we give one minute signals. Not once did it ever sound unnatural in trying to rush or filled with ums, uhs, or ahs. Others struggled with the rushing being most noticeable.
Jonathan Agnew has a similar story about the late, great Australian cricket commentator Richie Benaud, although filling ~52 seconds rather than 5 minutes.
https://youtu.be/FsmtFZQJbHU
> vamp
Thanks for teaching me a new term!
I think it's every host's worst nightmare when they see it when reading the teleprompter. It's my worst nightmare when watching local news feeds where they are clearly off prompter or vamping.
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.
The point is that we use 12:00 to note a time between 12:00:00.0 (inclusive) and 12:01:00.0 (exclusive). Saying that 12:00 is a time between 11:59 and 12:01 implies that the range of error is twice as big as it actually is.
How long between 12:01:00.0 and 12:00 (as read on a clock)? Between 0 and 60 seconds.
How long between 11:59:00.0 and 12:00 (as read on a clock)? Between 60 and 120 seconds.
What I am saying is that that use is incorrect as well. There is only one way to understand numbers, and that is scientifically. I.e. significant digit.
Good luck educating people on why they should change lifelong habits that actually even make more sense most of the time too.
Exactly, this article can be summed up on one sentence: "Look at me, I'm so clever"
I apologise for my "but, actually...":
Analogue clocks like the face of big ben are not like digital displays, and whether they "show seconds" in the context of the meaning of this article is not, like digital displays, down to whether there is a dedicated hand.
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).
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.
Again, 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. It is down to the number of beats per unit time for an analogue display as to what the minimum display resolution is (regardless of if the movement is analogue or digital itself).
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 key to this mechanism is that the stepping of the minute hand is what unlocks the second hand. Pretty clever low-tech way to keep a LOT of clocks in really close sync.
Dutch train stations used to have these too, I loved to watch them in action while waiting for a train.
On a wristwatch it's also easy - and probable - to set a minutes hand out-of-sync with the seconds, so they don't both line up at 12 at the hour.
Thanks for the video, what a silly design, especially given the Swiss reputation when it comes to clocks...
If you think of the design goals (synchronizing clocks across the train network) and the technology available at the time, the design is actually pretty clever. Knowing the exact second is not important - if the second hand actually completes a whole cycle in only 58 seconds, this is still good enough to be able to see how much of the minute has passed. Having the exact same minute on all clocks is much more important than that - especially since train departure times are usually "on the minute".
What technology wasn't invented by the time this clock was created??? And the design is bad, nothing clever about it, clocks can move their minutes hand to give the necessary indication
What technology wasn't available in 1944 (https://en.wikipedia.org/wiki/Swiss_railway_clock#Technology) compared to today? Quite a lot...
So name a single time tech and explain how the lack of it didn’t prevent other train station operators having clocks without jumping hands operating even before 1944? (not sure, but think that the minute timetable resolution was pretty universal)
>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...
> 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.
> 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.
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.
I think a slightly better term is "discrete" vs "continuous". Some analog clocks are discrete, some are continuous. Some digital clocks operate on a resolution so fine that they appear to move continuously. It's quite lovely to find those that invert your expectations when out in the real world.
It's a bit more than that:
There are analog clocks where all hands move continuously (like when there's a second hand with no discernable beats). There are analog clocks where all hands move discreetly once per second (60 BPM for all hands). There are analog clocks where the minute hand moves at 1 BPM (quantized to the floor of each minute) while the second hand does something else (perhaps discrete movement at 60 BPM, or perhaps continuous other than a pause at the top of each minute, etc.). And there are digital clocks!
You're correct, thanks for the clarification. I was going more with the colloquial understanding of the two (analog = continuous; digital = discrete) and was trying to touch on the vagueness of no true analog clock with the reference to ticks/resolution.
However, your explanation is definitely much better.
All universal statements like this are wrong and stem from basic ignorance
> So when it's actually 14:15:45, they'll show 14:15. And when the actual time goes from 14:15:59 to 14:16:00, then that's when your clock changes from 14:15 to 14:16.
No, that's a silly mistake, look at the picture (though much better - video) of the analogue clock to see it's not the case, the minutes hand moves continuously, so isn't at 15 at 15:59
> the meeting is in 5 minutes.
That's not the only question we ask about time. Has the meeting/game already started? You can't answer that with an average value
> for some context appropriate reason) you reply with just hours, you would say it's 11!
No, you reply would depend on the context, which you haven't specified.
> Please someone tell me I'm not crazy
Of course not, just trying to replace one ambiguity with another. Maybe instead come up with a more precise minutes display in digital clocks that adds more info like two dots flashing when it's past 30 sec and only 1 dot when it's before? (In phones you could use color or a few more pixels within all the padding?)
> 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!
Interesting take!
Both of your pic examples are wrong though. That digital clock does show seconds and the London clock has its minute hand in between minute mark - showing progres between minute mark if you look closely. This is the same for all analogue clocks.
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.
Most analog (really, with a geared mechanism) clocks do not "snap" on exact minutes but slowly drive toward them (because that's simpler and thus cheaper).
Analog Clock movements with second hands! The seconds hand is rarely smooth, we want the tick, but the minute hand and hour hands are smooth.
Except those of us (like my SO) who are bothered by the ticking sound at the edge of audibility, and prefer smooth seconds motion.
Unless it's an old AC-motor clock
All escapement driven clocks are discrete.
This is true unless you look at something like a Seiko Spring Drive, which has a completely smooth second hand sweep, although it’s not entirely mechanical (and maybe only watch nerds care about this)
https://www.hodinkee.com/articles/does-spring-drive-have-an-...
Pedantically, only above second granularities. They're continuous between second hand sweep movements at subsecond ones, no? I mean, there's no point on the watch that the second hand doesn't "hit" at some point, however small.
Or am I wrong that "intermittent, jerky, continuity is still continuity"?
Well it depends on the interval. Taken to the limit, this would be a very nerdy way to rediscover calculus.
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.
I have never seen a round clock with hands that ticks over a minute! And I look at clocks. Most that have second hands tick over seconds, though.
Where do you live?
In movies when the villain has placed the hero in the mechanism of a clock-tower, the minute hand seems to always tick over a minute. I don't recall ever seeing it in real-life, but I don't look at clocks in clock-towers that often.
I have a round analog clock with a particularly strange arrangement: it has a second hand (that ticks every second), and it has a minute hand that only moves every fifteen seconds.
(It's a radio-controlled clock: it has the second and minute hand on separate motors presumably because syncing to the actual time if there were only a motor for the second hand like a conventional analog clock would take too long (and probably make determining position more complicated). There is no independent motor for the hour hand, so it does have to roll the minute hand around to move that one.)
There’s some very neat designs that only tick the minute hand once per minute, as it’s significantly more power efficient to do so. You just power the hand once per minute, as opposed to continuously driving the hand in small increments.
I see these clocks often in railway stations (I live in India). There is no seconds hand. The minute and hour hands move in clicks, not smoothly like most clocks.
The clocks in German railway stations have second hands which 'click'. It's particulary fun how the seconds hand runs slightly fast so that it can pause on the minute, waiting momentarily for a synchronization pulse:
https://www.youtube.com/watch?v=wMSBJzN35u0
Swiss stations are similar but have contiuously moving second hands. I could have sworn this clock characteristic was indeed called 'Swiss motion' but I can't find any such reference on the Web...
Maybe; I think of analog clocks as ones with an analog, continuous mechanism. As such they happen to use a sweep hand display.
Quartz and the like CAN also use non-digital displays, but I wouldn't consider them analog timekeepers.
Quartz is an analog mechanism like a pendulum. It doesn't stop at each cycle.
Quartz crystals are inherently digital, where the quartz crystal itself oscilates at a stable rate, 32,768 Hz in most timepieces.
That's counted by a digital accumulator, and a one-second advance occurs every 32,768 cycles.
The display of a quartz timepiece may be digital (as in a liquid crystal display, or any other discrete display), or analogue, as with a watch or clock with hands. But the underlying timekeeping is digital at its heart.
(One might make a similar argument for a pendulum- or spring-driven clock mechanism, with discrete periodic movements, or for an hourglass (discrete sand particles flowing through an orifice) though the more variable physical process tends to argue against this.)
There is very little that is "digital" about the crystal itself. Tuned oscillation is analog.
The accumulator attached to it is digital, but it only has to be that way because it's so hard to make gears that tiny. If quartz was slower you could use the signal to directly drive a gear and have nothing digital in the entire timepiece.
Digital in the sense that there's a set of discrete countable events.
Contrast with several other timekeeping systems: water clocks, hourglasses (sand glasses), sundials or astronomical observations (ultimately the definitive reference), in which periodic processes or entropic gradients serve as analogues to the passage of time.
Modern atomic clocks are also to my mind inherently digital or quantum, where counts of discrete events are tallied.
The discussion of DAC/ADC conversion process has some merits, but to me, thinking of ideas as interfaces, and as models of reality, "digital" fits far better than "analogue" in this case. Particularly as you'll find that same DAC/ADC process in what we manifestly call digital computers or digital memory/storage systems, where some other-than-discretely-varying signal is nonetheless abstracted to 1s and 0s.
As occurs when tallying quartz crystal oscillations in a timepiece.
That defines any clockwork clock as digital rather than analog and I think at that point the definition you're using needs to be rejected.
I'd noted that in my initial comment.
The counterargument is that whilst the escapement of a spring-driven or pendulum clock is in a sense digital (as, for that matter, was a Jaquard loom's card-based governor), the driving mechanism (gravity weights, spring) isn't. But then, quartz-crystal clocks utilise a battery....
Again: ideas are interfaces, ways we get a grasp and shared understanding of reality, and are models of that reality. To that extent, all definitions are both arbitrary and flexible, but ultimately are governed by their utility.
Again: quartz crystal movements involve a manifestly digital accumulator which drives a display (character-based or analogue hands) based on accumulated ticks. The ticks are digital, a sequence of accumulated 1s and 0s, and are interpreted by logic rather than mechanism.
(Yes, logic itself can be mechanically implemented, but it remains a mechanical implementation of logic rather than a purely mechanical process.)
Escapement mechanisms lack such an accumulator, but rather utilise gears and cogs to match the movement's oscillation to the desired movement of hands on the display. That entire process is analogous of time, and hence, and analogue movement.
> I'd noted that in my initial comment.
You said they "might" be in the same category and sounded unconvinced. Now that you're insisting on an expansive definition of digital, I'm addressing the problems it causes more directly.
> To that extent, all definitions are both arbitrary and flexible, but ultimately are governed by their utility.
And the utility of the term depends on clockwork clocks not being digital.
> (Yes, logic itself can be mechanically implemented, but it remains a mechanical implementation of logic rather than a purely mechanical process.)
Gears are a mechanical implementation of logic. If you make a distinction here, it puts clockwork clocks on the wrong side.
The logic here is just a divider. The same thing the gears already do in a clock.
Also you didn't really address one of my points, but I think it was an important one. If quartz crystals had a slower frequency, you could easily use them to directly push gears like a pendulum does. Since you're so focused on the crystal itself as being digital, would you call that a digital clock?
The quartz crystal itself is an analog component which resonates at some specific frequency. The crystal is placed within a feedback circuit to create a stable, sinusoidal oscillation; the analog sinusoid is then converted into digital pulses to be counted.
It's the same principle as a "pendulum- or spring-driven clock mechanism, with discrete periodic movements"; just on a microscopic scale -- you're taking an analog physical system which naturally resonates at some specific frequency, and then converting the continuous motion of the system into discrete pulses.
While automatic quartz watches do exist[1], “generally, some form of digital logic counts the cycles of this signal”[2], to the point of becoming a synonym.
[1]: https://en.m.wikipedia.org/wiki/Automatic_quartz
[2]: https://en.m.wikipedia.org/wiki/Quartz_clock
Almost every clock based on mechanical escapement stops hands on each beat. That is where the ticking noise of classic mechanical movement comes from. For quartz clocks, smooth sweeping hands is a premium feature and I'm not sure are even those truly continuous motion or just higher frequency.
Quartz is an analog mechanism, but AFAIK it's always read/used digitally.
No. Most analog wrist watches use a quartz mechanism.
The output of the quartz oscillator is a high frequency electrical signal which is read by a digital frequency divider then fed back into a motor.
> The data line output from such a quartz resonator goes high and low 32768 times a second. This is fed into a flip-flop (which is essentially two transistors with a bit of cross-connection) which changes from low to high, or vice versa, whenever the line from the crystal goes from high to low. The output from that is fed into a second flip-flop, and so on through a chain of 15 flip-flops, each of which acts as an effective power of 2 frequency divider by dividing the frequency of the input signal by 2. The result is a 15-bit binary digital counter driven by the frequency that will overflow once per second, creating a digital pulse once per second.
https://en.wikipedia.org/wiki/Quartz_clock
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.
The only one that I know of as being an anachronism is saying "quarter of" or similar. At one point people decided that 'of' meant 'to' and after a while we forgot that because it was stupid. People still say quarter past though.
My teenage daughter needs me to explain it to her every time I say either "quarter past" or "quarter to"
past and to are pretty self explanatory if you know English at all.
Also vaguely related, I've come to realize some people find metric measurements easier than feet and inches.
I find the fractions simpler. Need a half of that half? Just double the denominator.
My wife would seemingly rather keep counting .1 centimeters.
The same applies with clocks. It's easier for me to rough out how long I have if I just chop the face into fractions vs mental arithmetic, as brutal as that sounds. What do you mean this guy can't divide 30 in half?
If only we were a species with six fingers per hand.
Romans were using both : "metric/decimal" for numbers, but "imperial/dozenal" for fractions :
https://en.m.wikipedia.org/wiki/Roman_abacus
(Base 12x5=60 was of course used by their Babylonian predecessors.)
But 15 minutes is a quarter of an hour regardless of whether you are using an analog or a digital clock to read the time.
The spatial representation on an analogue clockface is far more evident. Each 15 minute interval sweeps out a quarter of the face with the minute hand.
a "quarter" means 1/4th -- it's a "quarter" turn of rotation on a physical clock, but 60/4 is always 15.
or were you making the distinction between "quarter past" and "quarter after", because I'd agree that the former is a lot less common.
I'm not sure, but either way, "it's a quarter past 6" has gotten me blank stares.
In Germany, that would be quarter 7, which means either the quarter in the 7th hour or the 7th time that a quarter has passed since the hour, which is of course that same. (Unless you are in a part, that got conquered by the US after 2WW, which now uses "English time".)
Technology Connections did it:
https://m.youtube.com/watch?v=NeopkvAP-ag
Bonus on analog vs digital mechanism in flip clocks:
https://m.youtube.com/watch?v=ZArBfxaPzD8
Public schools here in suburban Boston MA still teach analog first.
So do the public schools here, and we have 3 analog clocks in my house, but 3/4 of my children cannot read an analog clock, and 2/4 of them do not understand me when I say "quarter past" or "quarter to" no matter how many times I explain it.
Don't kids know how to tell the time before they go to school?
Mine did. Most don't.
This is regional. US never used quarters afaik.
What do you mean? People in the US routinely use "quarter after" and "quarter to" when telling time.
I've only ever lived in NE USA, but I have traveled, and I definitely don't think it's regional.
Generational though, sure.
Oh yes, I grew saying "quarter past four." Probably don't anymore, but it was definitely in the vernacular in the US in years past.
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.
This is why analog clocks are superior to digital
It's not really about flooring or rounding, but whether one thinks of time indices as ranges or moments.
Days, as the author points out, are though of with "flooring", but more accurately it could be said that a date is thought of as a range between the times belonging to the date.
Minutes one can consider as ranges or time indices. There the error comes, in switching the interpretation of a start of a duration to an actual estimate of a point of time index.
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.
Pointless remark about myself, but I always set my phone's clock to second precision (I think this setting is hidden somewhere, or even needs a third-party app to unlock), and I am annoyed there's no way to do this on the lockscreen. How is it possible that nobody else (apparently) wants it, and it's not the Android default? Why would I want a clock that is, on average, a half minute off?
> Why would I want a clock that is, on average, a half minute off?
Because in 99.9% of the cases I don't care about the seconds, it takes away space in the top status bar, and the constant changing of seconds in the top-left corner of the screen is distracting. And for the remaining 0.1% of cases, there is the clock app that shows seconds.
What benefit do you gain in daily life by having the time down to the second? The argument "so it's not half a minute off on average" seems a bit self-referential.
> What benefit do you gain in daily life by having the time down to the second?
I commute by public transport and am sometimes cutting it fine, so knowing whether it is hh:mm:05 or hh:mm:55 does make a difference in how much I have to hurry up sometimes.
> and I am annoyed there's no way to do this on the lockscreen
With some OEMs there is (personally I know that current-ish Sony phones offer a corresponding option), but yeah, it is a bit annoying that that isn't universal… part of the reason I still carry a regular watch.
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.
I can get behind this idea, however, this sentence is wrong:
"If clocks rounded to the nearest minute instead of truncating, the average error would be 0.”
The negative and the positive error don’t cancel each other out. They are both error. The absolute value needs to be used.
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.
By this logic, a broken 24 hour clock stuck at mid day has 0 error.
That may technically be correct, but it is incorrect in the real world. I submit that error is error in the real world. Mathematics can go jump off a cliff unless it wants to be helpful. :)
Zero average error conveys something important though: the error that there is, isn't biased positive or negative.
That's language failing us, not maths :-)
What are you talking about? Error is a metric.
That's a very fair nitpick, but even with a more rigorous error function the point still stands, I think.
Agreed. There will be less error, just not zero. I thought it was a silly error that detracted from the point, rather than defeated the point.
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?
I don't think this applies to Elizabeth Tower/Big Ben, as it's an analogue clock and, from footage I can find[0], its minute hand appears to move continuously opposed to in steps. (or at least, not in full-minute steps)
Also, I believe it's wrong to say "the average error would be 0" if rounding to nearest minute. The average offset would be 0, but the average error would be 15, to my understanding.
[0]: https://www.youtube.com/watch?v=eUP3DsiqkzA
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 :)
The jumping ones are mostly electrically activated. Big Ben from 1854 is gloriously mechanical - some of the mechanism: https://www.youtube.com/watch?v=G-WSzdAF8b8 pendulum https://youtu.be/U8gkgWoFBAw guy who winds it https://youtu.be/dMT-OOrLBik
Hä?! A clock shows the period of time we are currently in. A clock only showing hours would for example indicate that we are in the 14th hour of the day, for the entire duration of that hour. That is not an error. Similarly, a hh:mm clock will show the hour and minute we are currently in for the duration of that minute.
No clock can display the exact current moment of time. That would require infinite digits, and even then those will be late, since lightspeed will ensure you recieve the femtoseconds and below really late.
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.
The fallacy is it’s a leap from logic to go from “average error is x” is the same as “is x late”. Seeing the exact transition is often if not more useful than minimizing average displayed error.
This is nitpicking, but the transition from "the average error of a truncating clock is 30 seconds" to "therefore all clocks are 30 seconds late!" is seriously wrong. For one, the median is equal to the mean here, so about half of all clocks are less than 30 seconds late, which is a clear contradiction.
> Basically I'm arguing that rounding for clocks would be more useful than flooring. This is especially apparent when you're trying to calculate "how much time until my next meeting?"
Yet a rounding clock provides no way at all for you to know whether the meeting has already started or not.
Not sure where I've heard this, but an idea that's been stuck in my head is this: We don't look at clocks to see what time it is, we do so to know what time it isn't yet:
Have I missed the bus yet? Can I already go home? Am I late for this meeting? Do I still have time to cancel this cronjob? All questions that a rounded clock cannot precisely answer.
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.
> Hours: That's when mentally, I switch to rounding! At 15:48 I definitely feel like it's pretty much 16:00.
Disagree. I would never round to a full hour, only to nearest 5 minutes.
As far as minutes, for clocks that show discrete minutes, it'd be weird to see the minute-hand snap to the next number and think "oh, it's actually 29 seconds before that number". Seeing the snap motion means you're at :00 seconds.
Besides, for a clock that doesn't show seconds, it really doesn't matter. If you need more precision, you just use a timepiece with the extra precision.
Clocks show the time that is _passed/past_, that's the point. Hence flooring is correct approach.
Even when you involve physics, you are seeing the nanosecond past. Not the actual time. (The time that takes light to travel from clock to your eyes, then your brain's processing delay via neurons etc.)
Even the thought of being late is the same way. If something starts at 13:00 and you are not already there when it is 13:00:00.000, you are -by definition- late.
Good point, when you look at your watch your thought should be “3:15 has passed” or “3:15:40 has passed”. One is more precise but if you think of it as a time that has already passed you can budget accordingly. 3:15 tells you that 3:15:00 has definitely passed and as much as 3:15:59 might have passed.
While most analog clocks' minute hands sweep from minute to minute, jumping minute clocks have the issue the article brings up.
Depending on when / where you went to school, you may have had analog jumping minute clocks. The ones we had at one school would "give away" when the minute would change because the minute hand would move slightly counterclockwise before changing to the next minute.[0]
Per reddit, some Swiss Railway clocks had jumping minutes, but I have not seen one in person. [1]
Another school I attended had sweep second and minute hands, but would hold the clock at 59 seconds until it matched the master clock. Depending on the particular clock and how well it was maintained, these could be 5 - 10 seconds off. Seems like nothing as an adult, but as a kid wanting to go home, it seemed like an eternity, especially on the last day of class for the semester.
[0] This video shows how clocks worked at my school: https://www.youtube.com/watch?v=jpU_lG_TPP4
[1] https://www.reddit.com/r/clocks/comments/10714a1/hard_time_f...
The Clock app in iOS works like this in timer mode. If you start a timer for 10 seconds, you'll see the 10 for half a second, then 9 through 1 for a second each, then 0 for half a second, then it beeps. In practice it's pretty stupid and not really useful, so I wish they'd fix it.
There's a reason why normal countdowns work the way they do. You care about the exact moment it hits zero, and with rounding you lose that.
Clocks are not 30 seconds late.
Time intervals aren't floors or rounds but thresholds.
This is most evident above the level of hours, minutes, or seconds: we speak of a new day beginning (though the time at which this occurs has varied culturally and regionally), or a new year, decade, century, or millennium (with their own threshold arguments courtesy the AWOL Year Nil in the Julian/Gregorian calendrical system).
Birthdates are an interesting example. In Western/European cultures, it's typical to count by full years elapsed, such that an infant within its first 12 months is 0 years old. In Asian cultures, the age is given as "1", which is reflected in an occasionally-used Western notion of "being in my nth year". That is, a 49 year old is in their 50th year.
What a clock (or calendar) indicates generally is what time period you are presently in, that is, the second of a minute, the minute of an hour, the hour of a day, day of a month, etc., etc. And what's relevant from this point of view is that the threshold is what matters.
The other problem touched on in this essay is of estimating time remaining to a future threshold, and here, rounding is indeed useful. If you have a 10am meeting and the time presently reads 9:55 am, you have fewer than five minutes to arrive punctually. But that is planning and not timekeeping issue, strictly.
By this logic, the author must also tell people it's "2024" until July 3, and that we're still in the 20th Century until 2051.
No, if you read the article, you'll see that he addresses this point.
It's addressed by "I'm not so sure."
Let me unlock your hidden precision.
The writer makes an implicit assumption you just glance at the clock with no prior info.
Where seconds count, you can watch the clock until the moment it ticks. At that time you have greater precision. And due to your own innate sense of time, that precision decays for a little while (maybe even 30s?) rather than instantly disappearing.
I like to synchronize my clocks this way (when seconds are unavailable). Yes, it does mean I invest up to a minute more to set the time, and it's probably not worth it if you're doing so often (eg. area prone to power outages).
The same technique is how computer RTCs are set/read, but to sub-second precision instead of minute precision, because the most common register standard allows only storing whole seconds but they keep relatively accurate time.
Centuries are also 50 years late on average... And everyone is on average 6 months older than they say.
Also moving the rounding 1 place down doesn't solve anything. Now your second-resolution clock is on average 500ms late unless you move the decimal 1 place down again.
> If it's 11:55, you would usually mentally subtract and conclude: the meeting is in 5 minutes. But the most probable estimate given the available information is actually 4'30"!
Admittedly I'm being a bit pedantic, but this isn't true. The expectation value might be 4'30", but the time is as likely to be 4'59" as 4'30"; assuming it's 4'30" will simply minimize your expected error.
> It would be weird if we rounded for years, months and days, that's for sure. I think most people think of those scales as intervals. In other words, July is a period of time, with a start and an end. So are years, centuries, seasons. We are inside of it or outside.
I feel like my sense of time is different from the author's. While it can be useful to round the current hour/minute on some occasions, the information about which exact segment of the day/hour you're in can also be very useful. I can certainly tell that I ask the question of "when exactly is it going to be 12:00?" far more often than "how many seconds have statistically likely elapsed in the current minute?"
The biggest issue for me is that the precise moment of when one minute/hour transitions into the next is important for people. Like, when coordinating an event or meeting, would you prefer it if your clock indicated the precise moment when 12:59:59 becomes 13:00:00 and told you to start the meeting, or would it be better if the clock instead told you that it was "13ish" and you'd have to wait out ~30 seconds by counting in your head?
This also causes a jarring discontinuity - now clocks with a ticking hour hand appear to run 30 seconds late than clocks without, turning on the digital clock setting to show seconds offsets it, and so on. Some people celebrate New Year's or occasions that happen at a specific time 30 seconds early because they no longer have a strong reference point.
Clocks are used as inputs into decisions. So this doesn't matter as long as the decision process accounts for it. If I see that a meeting starts in 5 minutes, I'm not setting a timer get there in 300 seconds, I'm trying to decide if I have time to fill my water bottle on the way or not.
The post is a useful consideration to think if you are trying to do precise tasks though. See Keskival's post below about intervals vs moments to add some more precise ways of thinking.
I'd be very surprised if a smartphone, syncing itself to a reference, is ignoring seconds. Why would it?
To me, if a clock that doesn't display seconds is displaying 09:30, then I assume the time could be anywhere between 09:30:00 and 09:30:59.
Presumably when setting the time on a device that doesn't display seconds, the seconds are being reset to 0 (i.e. setting time to 09:30 is setting it to 09:30:00), so if someone really cares about sub-minute accuracy they can take this into account.
Does OP realize that people don't looks at 11:55 and think it means 11:55:00, but they think, it is just not 11:56 yet.
Computers and smart devices syncing to NTP doesn't have 30s average error rate, it is the author who has 30s average error rate in clock-reading if he reads a digital clock and think that the clock tells that no seconds has passed since the last time it added one minute.
What a nonsensical article. I could've used the 30 seconds I skimmed it back.
If you had two rounding digital clocks, one with seconds and one without, they would switch to the next minute 29.5 seconds apart. Everyone would hate that.
Because it would be incorrect. Like the article's main premise. Flooring is the only correct behavior for minutes. And other time units.
Big Ben may not show seconds but people would notice if it started bonging 30 seconds early or late with new year. Which would be the case if it rounded. It bongs right on time. That kind of is the point. The news doesn't start half a minute early or late either. And people joining meetings after the minute changes in their clock are technically a few seconds late.
Somehow I do not think that the Big Ben transitions the minute`s hand by using the floor function from Python.
But neither is it continuous. It ticks. The mechanism might be made from iron, but a part of it is not unlike a floor function.
https://en.wikipedia.org/wiki/Escapement
Smart enough to make the proposition, but not smart enough to disprove it. Middling intelligence might be the greatest threat to society.
All of this is made redundant by just... knowing this is how clocks work.
If you don't have a seconds hand/counter, you can't predict how many seconds are left in the current minute. If it's 11:45:01, it's 11:45 without seconds. If it's 11:45:59, it's still inside the minute-long interval known to everyone as 11:45. The clock can always be one second away from flipping to the next minute. I just mentally subtract one minute if I'm actually planning on being somewhere down to the fraction of a minute, and planning what I can do beforehand. Mentally subtracting 30 seconds is not any easier.
I don't see this as even having some kind of gimmicky benefit...
I use a certain trick a lot when cooking, or timing anything with precision of a several minutes:
0) Suppose I am steaming vegetables for 8 minutes
1) I will check what time I started them (say 5:30)
2) I will forget the number of seconds that were on the clock when I started
3) I will pull the vegetables off at 5:38:30
The intended interpretation for clocks IMO is "we are now past this time".
Like a mile marker when you are running down a jogging track.
It doesn't matter if the granularity is one-day or even one-year, like the ball drop in Times Square on New Year's Eve.
Anyone who has done timer or countdown-based work has to think the opposite. Whether that's sports or event production, rocket launches, or so on. You're not thinking about the time you've past/expended. You're thinking of the time you still have left. "Two minutes left in game." "We're live in 30 seconds" etc.
NFL delay-of-game penalties are interesting for this, because when the clock first shows 0 seconds, that means that the team still has a full second to start the play.
Countdown clocks run backwards, not forwards.
FTA: All the above clocks have one thing in common: they don't show seconds
One of those clocks is Big Ben in London. http://www.bigben.freeservers.com/clocmech.html:
“Drive to the hands is by an oblique shaft which drives bevel gears positioned centrally on a gantry above the clock, with four shafts running out to each dial. Because there is no remontoire the hands on the dials advance by 2 seconds every two seconds, i.e. at every swing of the pendulum“
⇒ if you look close enough, you can read the time at intervals of two seconds.
I can imagine a 20 and a half year old in the US arguing this logic when fighting an underage drinking charge.
Drivers licenses would be more accurate if they showed place of birth. Maybe the kid grows up to move to an eastern timezone and is accused of drinking a few hours early!
Interesting,
When I make word clock, I make it change from "SATU LEBIH DUA" ("ONE PLUS TWO", 01:02:00) to "SATU LEBIH TIGA" ("ONE PLUS THREE", 01:03:00) at 01:02:30.
But if I make digital clock, I make it change from 01:02 to 01:03 at 01:03:00.
One wrinkle here is the choice of signed error instead of eg. RMSE; absolute error metrics don't care about rounding vs. flooring. Since the conclusion of the analysis hinges on this choice of error metric, I think some justification or discussion of that choice adds interesting context.
Signed error implies that clock-imprecision "cancels"; that being 20 seconds late to your meeting will be undone by being 20 seconds early to lunch afterwards. I'm not sure if this is quite how people reason about 'lateness' though. Obviously in some applications it makes sense (ex. recording event times of some phenomenon of interest), but in scheduling my daily life that's not really how I think about things.
I think RMSE is closer to how people evaluate scheduling of stuff; it doesn't matter if I'm late or early, both will have notable consequences in unique ways. The ambivalence of the RMSE error to rounding vs. flooring is the intuition I would put behind the counterargument fielded by the author:
> But this is just a convention! Truncating, rounding or even ceiling are all valid, as long as we pick one and stick to it.
I think you can also squeeze some juice out of playing with the error metric further. If you want a 'just-in-time' schedule (ie. you want to never be early to anything) then the flooring clock is superior to the rounding clock. If you want the opposite then a ceiling-ing clock would be the best choice.
> Personally, I would never say that it's 10 if the clock shows anything past 10:30
I like to floor my times to the nearest 15-minute interval (10, quarter-past, half-past, quarter-to), only rounding once I've reached ~10:55
While you could argue that it's flooring, it feels much more like truncating. We have a inner representation of time that's like yyyymmdd-hhmmss-mmmm and we truncate it to the precision we need for a given task. If we need the month we truncate to yyyymm, and if we need hours we truncate to yyyymmdd-hh.
That's quit intuitive for all kind of time precision, and the author's rounding solution would be somewhat counterintuitive, at least for me.
Summer starts at the solstice, when the day is the longest. But by then half the length of the season already passed with the day approaching that point. So I think the seasons are half a season off (seasonal lag notwithstanding).
I had a watchface on my Pebble smartwatch that only displayed time in five-minute intervals. This post is making me question whether it rounded up or not.
I have to assume it did because I didn't start being late for everything.
In case you want to see it: https://pebblestyle.com/watchface/BVmexStjq3j/
That's only the case if you interpret them as HH:MM:00. The issue is fixed if you interpret them as HH:MM:30 instead.
Well I was bothered by a similar problem when tweaking my StumpWM modeline long time ago.
I wanted to show the seconds in the clock on my modeline, but the modeline has a fixed refresh rate, which I set to 1HZ. Then I realized my clock can never be accurate.
Eventually I chose to hide the seconds to stop myself from having those nightmares, but I think they are coming back after reading this article.
I enable seconds on my PC and phone clocks, and basically anywhere it's an option. I enjoy seeing if two messages on IRC were just 3 seconds apart as it will often tell you the second person hasn't actually read the first person's message right before theirs (they were probably writing their messages at the same time). Something not obvious if you just see the minutes.
> 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"!
But if you want to say it's M minutes, then it's either 4 or 5, and 4:30 rounds to 5, so it all works out once more! :)
I have about a dozen of the absolute cheapest digital clocks around my house, and every single one, I set it to the next integer minute then waited for 00s to hit the button that makes the : blink. So, even if every other person on earth fails to do this, the average is below 30s just due to me.
This post is fascinating but I think it is more mundane than I realized. I thought everyone knew that when a cheap digital kitchen timer shows a time like “0 H 1 M”, that actually means you have exactly 60 seconds or fewer for its alarm to go off.
I might be wrong, but there was a Prince of Persia game (maybe for Game Boy?) that had the same timer behavior. It would show the time remaining to complete the level in minutes and would jump immediately from “1 minute” to 0.
The iOS podcast app is more sophisticated than that. It normally displays how many minutes remain in the playing podcast episode. But what is cool is that at the 30 second boundary, it will decrease one minute. For example, it is at -24:30 or -24:29 that it will go from saying “25 minutes remaining” to “24 minutes remaining.” Then when 30 seconds are left, it is nice enough to show you a countdown of the seconds.
Yeah, I've seen a lot of countdown UIs that incorrectly start beeping as soon as "1s" becomes "0s". In fact they should start beeping exaclty 1 second after that change.
I'm sure this is actually an intentional design decision because starting to beep at 0.99 (displayed 0) feels more correct, even though it isn't.
I agree this is an interesting take and fun to think about. But if clocks rounded to the nearest minute instead of truncating, the average error would be still be greater than 0 I think, and not 0, as the author claims. Assuming a sufficiently large number of measurements taken at random times, I think the average error would be 15 seconds.
The author meant "average error" in the systematic error sense, not the standard error sense. The minute display would be well calibrated, not precise to less than a minute.
A slightly related thing I think about someone's, is if I look at the time and it's 13:05 and then I do a task and when I finish a task it's 13:10, you could say that took 5 minutes, but because we can't see the seconds each time could be up to a minute out. So a total of 2 minutes error! Quite big if you're timing something small like 5 minutes!
Any clock which doesn't have a seconds display is probably not accurate to the second and is also very unlikely to have been set to the exact second. Those 2 factors together mean a good chance the time is > 30 seconds out, making the original point moot.
I am really annoyed that it is almost universal to show only minutes on clocks- when so much in my life at least depends on knowing time to the second. Even modern digital devices like an iPhone make it really hard to get a seconds readout, when the cost of doing so should be zero.
Some of the things I need precise seconds for frequently in my daily life: buying tickets to concerts, campsites, and kids camps before they sell out, checking into Southwest flights, sailboat race starts, and starting/joining virtual meetings I am hosting.
Am I that weird that this is something I need at least once a day that nobody else seems to need or want?
Almost nothing in my life or career to date has depended on knowing time to the second.
Why does it matter if your noon meeting starts at 11:59 or 12:01?
It’s wasteful of other peoples time to show up to a meeting late, and wasteful of my own to be early. I’d like to be as precise as practical. Meetings filled with high paid experts are incredibly expensive- one should get every detail right to save time. One little thing might not matter, but if you pay attention to a lot of little details in running a meeting efficiently- including starting as close to on time as you can, it saves a lot of time.
Side note. I’m more bothered by this issue on digital thermostats.
I don’t even know if they’re flooring or rounding. And sometimes half a degree makes all the difference. I do wish they’d do temperatures out to one decimal point.
If you do care about what second it is, you can still be 59s off: eg. if the "rounded" clock shows 12:30, it could be 12:29:30 all the way to 12:30:29.
The error is reduced on average if you only care how far away from exact minute you are, but you simultaneously never know when it is the exact minute.
The question is really about what's more generally useful: the offset of 30s is usually not important enough, which is why most clocks only show hours and minutes. Where it matters, higher precision is used.
Some of the social constructs would be less meaningful (like New Year countdown) as most watches and clocks would show midnight 30s early.
This could be a good allegory for sampling intervals. I’m forever having to explain to people that if they are looking at data every 60 seconds they can take a lot longer to notice a problem than common sense would suggest. Your new information shows up on average 30 seconds late and up to 59.99999 seconds late. If you’re trying to compare the last two samples to detect a problem then you’re going to see it up to 2 minutes after it already started, since it could start 1 ms after the first sample. Particularly in systems where multiple actors are using periodic actions.
This blog post is a really good argument. The kicker for me was that we all generally switch to rounding when asked for the hour (without minutes) but don't round when asked for the minute (without seconds). That's an inconsistency for which there doesn't seem to be a good reason.
However, this inconsistency only exists orally. When a device displays the time, it never rounds. Changing the convention would probably be very confusing for a lot of people, at least initially.
For now, I'm convinced that when communicating the minute orally, I should round to the nearest minute, just like I do with hours.
Verbally, IME, people mostly round to quarters of an hour (exact hour, quarter past, half past, quarter to).
I've never heard anyone say it's 4pm when it was 3.31pm.
"It's just a convention"
This is correct. In fact, in one sense our clocks could be argued to be minutes out, on average: originally time was measured by the sun. But by the sun, the earth doesn't rotate in exactly the same time each day during the year. So a clock assuming each day is the same length (like they all do) accumulates an error with respect to sun time of more than 16 minutes,and then loses it again, in a cycle.
But we just collectively decided that it was simpler not to bother with that. We changed the convention so that time is marked with respect to an average day length
While interesting this is just… wrong. Imagine a world where:
- I tell people I’m 50 years old but I’m really just 49 1/2
- My phone says it’s Jan 7th but it’s really afternoon on Jan 6th
- My coworker says they’re a sr engineer because they’ve been told that they’ll definitely be promoted soon
Rounding shouldn’t be applied everywhere. Some things in life are supposed to use a floor function; common sense applies and most folks intuitively know that 1:00pm means ‘between 1:00 and 1:01pm’.
TFA goes into the author's opinion around when to floor and when to round, and notes that "hours" is the largest interval where rounding feels right.
The article is claiming that clocks that only show time truncated to a minute are off by an average of 30 seconds, which just isn't true in practice. When I say or hear 11:30, I assume it can be within 11:30:00 and 11:30:59. Humans rarely need accuracy to the second beyond this, so clocks intended to be used by humans truncate to the minute without causing problems. To say they are "late" is a real leap.
I mean, you can reduce this to absurdity too. A clock truncating to seconds is off by an average of 500 milliseconds! The problem is no one cares in day to day usage which is what human readable clocks are made for.
> When I say or hear 11:30, I assume it can be within 11:30:00 and 11:30:59.
And if you cared about seconds-precision, you would assume 11:30:30, and thus your error would average the same 15s.
The difference is that when you observe a minute change, you know that's exactly at zero seconds (instead of 30 — or 31 if you apply the same rounding rule to seconds).
It is fair to ask a question if rounding would be more useful (nope), but the entire article is incoherent and speaks mostly of the author's confusion.
> It would be weird if we rounded for years, months and days, that's for sure ...
> Is it the same for the current minute of the current hour ?
> I'm not so sure.
I'm sure - it's the same.
If I actually have to be on time and it says 11:55, I’m not going to wait 5 minutes. I would wait 4 minutes.
If it’s more fluid, then 5 minutes is a fine estimation.
OP’s suggestion of rounding the minutes wouldn’t change anything except make what I’m doing complex.
My computer's clock say "twenty five past ten" and I don't even take offense about the missing "-" in twenty five. It's close enough for me.
Amusingly, one of my kids gets very frustrated with how I answer what time it is on most requests. Most of my answers will be of what the nearest relevant time is. I will never bother determining what the exact minute is from my watch. As I just can't see the value of that. Even from a digital watch, I don't see the need in giving a majorly different answer to the same question within 5 minutes or so.
That's how people commonly give time in my language, I suspect mainly out of convenience:
Quarter hour precision is possible to achieve with at most five syllables (and typically just two); compare that to minute-level precision, which usually takes at least 5 and sometimes as many as 10.
Interestingly, spoken times also commonly use the 12 hour clock, while times are almost exclusively written as 23 hours.
I was always annoyed at my parents for doing this when I was a kid. When anyone asks me the time I always read out the minutes for whatever time my phone shows me. Maybe someone wants to make a particular bus or train and the more precise timing is appreciated, who knows!
I would same, that at is communicated by the length of the stare you get after telling the time.
Analog clocks mostly don't have the problem the author is complaining about since most minute hands move once per second and you can easily see (depending on your eyesight and distance to the clock) that the minute is partially consumed.
I agree though that this is a downside to digital clocks which don't show seconds, though whether the best fix is to round instead of averaging is hard to say.
Time Cube redux?
https://en.wikipedia.org/wiki/Time_Cube
I would argue that eg 13:00 represents an interval, not a moment. So there is no error. But I appreciate the nerdy level of detail.
I think a good part of this comes from how we often mention time: "It's half past two" is interpreted to mean: "it's at least half past two"
If we round seconds, why not microseconds/etc?
Ticking clocks let us know what time it is "at least" and uses the minutes :00 as the "barrier" Shifting that to :30 only causes more confusion IMO
> "It's half past two" is interpreted to mean: "it's at least half past two"
I think most people would have no issue calling 14:28 "half past two". There's no "at least" to it, just an approximation.
If it was 2:27 and I asked you the time, I would be much happier with "half past two" than "quarter past two"
The Hunt for Red October gave us "He always goes to starboard in the bottom half of the hour."
You said it yourself, the data is truncated. We shouldn't be rounding time one way or the other, just truncating it.
A delightful read, though I disagree. Unless we were going to introduce half-minute units (which decreases the scale of the error, but makes it twice as numerous) then shifting our minute units by a half value doesn't seem to actually solve the problem, doesn't it only shift it to a slightly different location?
We don’t floor clocks, we usually put them up on the wall..
One often unappreciated and amazing thing about the GPS-on-cellphones era is that nowadays everyone has the exact time. Up to the late 20th century it wasn't trivial to have the right time, in fact there was a three digit phone number you could call to get the right time (up to the minute).
I don't think rounding clocks would be any more useful in the scenario about mentally calculating how many minutes until the meeting at noon, because a rounding clock would show noon 30 seconds earlier, so the average difference between 11:55 and noon in a rounded clock vs a floor clock is still 4.5 minutes.
So this is not about all clocks but more about all clocks that do not show seconds. In that case, sure.
This article tries to redefine the correct time by pointing to clocks that are not precise.
If you use round instead of floor an error persists. So all clocks that don't show seconds are always wrong.
Has anyone ever wondered why in the US the week starts on Sunday, but in Europe and Asia it starts on Monday?
Yes, and it's infuriating if software draws the conclusion that, simply because I happen to be in region x (or even worse, using language x), I must also want date presentation, units of temperature and distance etc. to be according to customs in x.
At least macOS/iOS at this point mostly allow customizing many of these, but some native apps and date picker widgets still don't respect my preferences, driving me nuts every time I have to schedule a reminder or meeting.
I work in Europe...my week starts on a Sunday.
Where in Europe is that?
Just sitting here with my mechanical automatic watch like some kind of renaissance fair re-enactor. Probably off by a few seconds, but probably less than 30.
TFA fatally misunderstands what clocks actually measure. They measure the amount of time that has elapsed. When we say "it's quarter after noon" what we really mean is that 12 hours and 15 minutes have elapsed since 00:00. The reason clocks don't round up is because that's simply wrong.
A minute hasn't elapsed at xx:xx:36, it has only elapsed after :59
tl;dr The author of TFA doesn't actually understand what clocks measure.
> Is it the same for the current minute of the current hour ? I'm not so sure.
Yes it is. Appointments start at the beginning of the minute, not the average. (And while changing clocks WOULD change that, I'm not sure it makes a lot of sense)
Perhaps, to be more precise, "How should clocks without a second-hand round?"
I enjoyed this article for it's tongue-in-cheek approach. Thanks Victor!
I definitely start saying I'm $age+1 as I approach that birthday, as it seems more accurate. Round, not floor.
Although I have to say I've not really encountered other people doing this.
I also thought it was interesting when basketball essentially added 1 second to each game by including tenths on the game clock
I'm not trying to be snarky but I really don't see why this matters. It's just a convention. We are not robots, not everything has to be 100% precise.
Only robots floor, humans truncate.
This is true across other domains! If trains are spaced exactly 10 minutes apart and you arrive at a random time, the expected waiting time is 5 minutes, for example.
This makes me wonder how train countdown clocks are programmed, and if "1 minute away" means "60-120 seconds away" or "30-90 seconds away".
What a waste of 30 seconds of my life reading that
Perhaps we could retitle the link, as it stands a bit click-baity.
Perhaps, average error of clocks is 30 seconds higher because minutes use .floor() nor .round()
The whole post feels like nonsense.
It is. It's just taking something obvious and recontextualizing in language that sounds like a Mysterious Conspiracy when it's really just a banal truth we all take for granted because all the other options make less sense. Like using tau over pi in geometry.
I like to think of it as TRUNC
For positive numbers, both the FLOOR() and TRUNC() functions return the same values
And for negative numbers it's CEIL()!
And in SQL Server, ROUND() with a nonzero number for the third parameter for truncate, and CELING() for ceiling.
This hall monitor mentality in every comments section is more annoying than titles ever are.
People are usually interested in the transients.
It's been 2025 for 6 months already...
"It would be weird if we rounded for years, months and days, that's for sure. "
We round years too, otherwise I would be in my 30s.
That’s a bit of a cup half-empty way to think about it, innit
Worse yet, our calendars are all 12 hours off!
I'm sorry, you are crazy.
I thought about it as a kid, you're definitely not crazy Victor, and I appreciate that you wrote this piece
Fun scissor. Seems to depend on your personal definition of "error", with respect to time.
Except analog clocks, remember those?
Yes. My Casio on my wrist has a minute hand that creeps slowly from minute to minute.
The article does have a picture of an analog clock (The Big Ben) I think. The problem is not analog but showing seconds or not.
Technically Big Ben is the bell, the clock has typically been referred to as the Great Clock because that's sufficient explanation of what you meant. The tower, which like the clock is often referred to just as "Big Ben" colloquially, was formally named "Elizabeth Tower" in honour of the late Queen some years ago.
Depends if the analog clock “ticks” on the minute or if it does a constant movement during the minute.
I don't think so, because the sweeping motion of minute hand is effectively continuous rather than discrete, so there's no truncation. At 4:53:30 the minute hand will be correctly in between 4:53 and 4:54, if one (like the author) cares about such precision.
Not really. A mechanical analog clock will typically have smooth motion, so 30 seconds into a minute, the minute hand will be halfway between two values.
Most quartz watches with analog displays work the same. I don't know about Big Ben, but it's possible the author is wrong about that example.
Yup. I have my clocks in the house set 30 seconds ahead to counteract exactly this.
Plenty of nitpicking here, for me this piece was a fun and clever thought-ride.
A clock is not showing you what time it is, a clock is showing you what time it most recently was. It is marking time, not embodying time.
All this does is move when the issue he claims exists presents itself.
If we flip the minute display at the 30, then the same problem occurs because if you start timing from the 20, the minute will change in ten seconds.
This article is just kind of stupid masquerading as smart.
On a larger analog clock, you can clearly see the minute hand progress from one minute mark to another.
It doesn't have to be large: My wristwatch does it.
i don't think the above comment is saying it has to be large, just that it's less obvious on a smaller clock
This is like asserting that all calendars are 12 hours late.
I think truncating down allows us to procrastinate a little more :)
All the way to the miliseconds I strongly disagree!
This is why I dislike clocks without seconds.
There was a clock on HN a while ago (which I cannot now find) - it has one mode in which the clock only updates itself every random number of seconds, or ticks at different times within each second, oor ticks according to a MIDI tune as well as it can while staying within 30 seconds of the real time.
So, while you can just set your clock forward 30 seconds and be done with it, there are some variations that someone who likes thinking about this are worth playing with.
[My favorite mode of the referenced clock, sets the clock randomly ahead between 1-5 min. Since you don't know how much your clock is off by, you have to assume your clock is on time, and that will give you an average 2.5 minutes to actually show up on time.]
Wow, I’ve never read a wronger take in my life, and that’s saying something!
Like even flat earth is more reasonable than this
Another perfect example of wasted disk space and bandwidth on the internet 8-/
Not to mention a waste of the one truely nonrenewable resource, our time...
>Please someone tell me I'm not crazy
No, it's probably just autism.
The argument is a bit like saying decimals are wrong because the one in "10" jumps to one after you counted to 9, which is 90% of the range and not 50%.
But that is the point of using multiple digits. Similarily the point of using multiple units of time is that each of the parts is in it self correct. 15:30 always means it is after the 15th hour and after the 30th minute.
If you want to know it more precisely you either wait till the minute changes or you get a clock with seconds. With the proposed system you would not know if the time is before or after the 30th minute. Also: why stop at the minute? You could also round the hour.. But that would introduce a weird jump and the minute would suddenly be negative 30.
Unrelated, but I've always wanted a clock that is randomly fast so that I never know exactly how fast it is.
At worst, maybe I can set a maximum "fastness" setting.
Then peeking at the actual time has minimal value over the long run.
I'm sure this already exists. But I haven't come across it yet.
What about ages?
i vote we move to the korean system where everyone gets a year older on January 1st
That was a fun one but I think they changed it already.
https://www.bbc.com/news/world-asia-66028606.amp
This author is either an idiot or does not understand the concept of precision.
It's very surprising that this article has engendered so much discussion...in support of what he is saying.
10:01:01 and 10:01:59 are both still 10:01, because a minute is a discrete unit of time. Rounding the minute to the next minute is simply wrong. Similarly, rounding to the next hour is also wrong and nobody does this except apparently the author. (Note: 15:48 is almost 1600 but is not 1600.) People might round to the nearest five or ten minutes for convenience (i.e., when reading an analog clock) but that hasn't been a thing since the switch to digital clocks.
RMSE of current digital clocks rounding down is roughly 34.5 seconds.
RMSE of proposed rounding to closest is 17.5 seconds.
The new method is roughly 17 seconds more accurate on average.
Does this reduced error make a significant difference? Probably not. There are very annoying practical issues with this proposal though.
Rounding down makes it clear what minute has already passed. If your clock says 3:00, you know the current time is definitely some point after 3:00. If something needs to happen at 3:00, and your clock says 3:00, it is time to start.
With this proposed method, 3:00 could mean anywhere from 2:29:30 to 3:00:30. When do you start? Do you start as soon as your clock says 3:00? Then you're starting 30 seconds early. Do you wait until your clock says 3:01? Then you're starting 30 seconds late.
And how do you set a clock that uses this scheme? If I want to set the clock to 3:00, do I wait until 2:59:30 and then set the clock to 3:00?
The headaches that arise from this scheme are not worth the trivial error reduction.
Great example of the pitfalls of RMSE.
I show seconds in windows clock
Now I need to extrapolate this to explain why I am 10-30minutes late every time.
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