All clocks are 30 seconds late
victorpoughon.fr
victorpoughon.fr
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.
Your boss won't like hearing "well technically I wasn't late because you see your clock has the seconds rounded to minutes so you can't actually know if I'm late".
The best possible outcome you could get from that is that the meeting starts at 12:59:30 now.
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.
A good reason for truncating is that we have a strong bias against being late, but not really against being early.
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.
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.
Early is on-time. On-time is late.
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.
In a Western business context, "late" comes about 1-2 minutes after the meeting starts.
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.
"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.
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.
I strive to be on time for work things, but don't mind being a little late to parties -- and this drives me and my my wife nuts, because my wife wants to be on time for parties.
One boy took it to heart and is very prompt.
The other, eh, not so much. He was almost late to his own wedding.
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.
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.
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. :)
:58 if presenter
:59 if core
:00 if contributor
:01 if observer
Many colleagues seem to +:01 this.
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.
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
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.
(well, almost every time)
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.
Closest you can get are unique sentences.
There is no parallel chains of unconnected thought.
We are barely, rarely more than the sum of our parts on average.
We have very convincing illusions of free will though - like the apparent exhibition of agency.
Does that mean, that the idea is commonly known? Not necessarily.
It is also still an original idea in terms of you having thought, that was not easily derived from what you know (but probably somehow derived, like all thought likely is).
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."
Those who want to create great things cannot afford to fall into love with them. You can fall into love with a particular problem or question, but not with a specific solution, especially not if you came up with it.
You wouldn’t leave a v1 of an app online just because it is first
One of the things that intrigues me about Google's Plus Code addressing system is how it converts longitude and lattitude into "area block intervals" -- the first four digits represent a large area, the next four + three represent a small area, and if you know the large area, you can specify only the latter seven, or if the area is big enough, you could ignore the last three digits after +, or if you're talking about a ranch or a campground, you could even specify just the last three digits. The first four are analogous to "year", the second four to "month", and the last three to "day". This can even be continued into smaller and smaller intervals, just as we can divide a "day" into "hours" and "minutes" and "seconds" and so forth, we can specify smaller and smaller areas with plus codes.
The goal in messaging is almost always not about the send time (who cares?), but the receive time, when it is available to be read. If the goal is to have the message received at 1:00, then, as you note in the second example, sending it precisely at 1:00:00.000 guarantees it will be received late.
In any case, if you're that focused on intra-minute precision, you should probably be relying on clocks that incorporate seconds anyway.
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.
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.
Thanks for teaching me a new term!
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.
And yes, 5-to-15-to-an-hour is something that varies, depending on the length of your trip. 5 is appropriate when you're in your office and you need to get to the conference room, 15 if you're driving from your nearby home, an hour if you're flying in, or if you have to drive 200 miles or so -- particularly if it's a trip you don't regularly take!
For meetings, I actually give myself 16 "precise" minutes -- one minute less than 15, with 4-minute-30-second snoozes, so I can have both adequate warning, and regular pokes, to make sure I can do something on time.
Even that part is wrong. I guess I‘m not the only one who knows and thinks it’s less than 5 minutes.
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.
And if you showed up to the meeting in exactly 5 minutes, you’d be on time!
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.
Or am I wrong that "intermittent, jerky, continuity is still continuity"?
https://www.hodinkee.com/articles/does-spring-drive-have-an-...
Quartz and the like CAN also use non-digital displays, but I wouldn't consider them analog timekeepers.
> 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.
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.)
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.
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?
And again, this allows for differences and distinctions, one of which is your view, which again I find less useful and clear. That is, crystal-driven timepieces strike me as more usefully considered as digital rather than analogue.
On the distinction between a mechanically-implemented logic vs. an electronically implemented one: the degree is largely of complexity, scale, and speed, but in general once you've ventured into the electronic domain, it becomes infeasible to provide a comparable utility or function by mechanical means. We've tried mechanical digital calculators and computers. We've abandoned them on account of cost, slowness, unreliability, size, and power consumption. Mechanical systems cost too much, ran too slowly, broke down too often, and simply could not scale in the way that semiconductor-based systems could.
To the extent that a mechanical function (say, a mulitiplier gear) represents a pure logical function, we can abstract that functioning from the gear itself, much as writing conveys meaning independent of medium.
It's less possible to divorce the mechanical functioning of such a system from its inherent parts: their materials, mass, size, and the like. If we look at purely mechanical systems, they're very tightly linked to the inherent material constituents in a way that pure digital logic isn't. Let me give two examples.
The printing press (as a mechanical system, I'm not arguing its digital attributes if any) saw a profound development over the course of the 19th century. At the beginning of same, it was little evolved from Gutenberg's early adapted wine press, and with skilled operators might produce ~120 impressions an hour, a sheet every 30 seconds. Converting from a wood to a cast-iron frame roughly doubled that. Further developments: electrical power, cylindrical plates, web-based paper feed, increased that by the end of the century to one million impressions per hour, four orders of magnitude faster. That is, the function and capability of the machine was intrinsically bounded by materials (and power sources and paper characterstics, etc., etc.) from which it was constructed. Taking this further, modern Web servers / application servers are capable of millions of requests per second, another three orders of magnitude faster.
(In general, only one or two orders of magnitude is a fundamental revolution in capabilities: walking (5 kph) to bicycle (32 kph) to automobile (130 kph) to jet airliner (1000 kph) are separated by roughly 1.5 -- 2.5 orders of magnitude, with the largest step (e^2.2) being between the first two.)
Of digital systems, the unrelatedness to fundamental materials is probably best exemplified by virtualisation. That is, we see tremendous adoption of entirely virtualised systems in which the basic logic functions occur entirely independently of the underlying hardware implementation. A digital watch can fundamentally be implemented entirely in software, in ways that I'll venture a hardware watch cannot be. Though here again we trip up on my ideas / language / models distinction: is modelling a hardware system in software the same as emulation? I'm ... going to stick with "no", Because Reasons, though I'll acknowledge the question, though a large part would be that a model is a simplification of the reference system, whilst emulation is a complete functional equivalence.
Similarly, we can run identical software on entirely different CPU architectures, command sets, and semiconductor substrates with few if any practical considerations. Operation is divorced from hardware.
Keep in mind that the function of a transistor itself is equivalent to that of a gate or valve: a small controlling input leads to a large controlled input, and indeed these are often called gates or valves in the field / historically. There have been mechanical and hydraulic computers of limited capabilities. But again, moving from mechanical to electronic components
I'm not arguing that gears aren't capable of logic. I am arguing that gear-based logics severely restrict the capabilities and increase the physicality and physical constraints in ways in ways which fundamentally differ from those of purely electronic systems, and are best considered "analogue".
There's also the point that gears ... rotate continuously, rather than discretely. We can modify that (e.g., with cams or similar designs), but there's still that continous rotational motion at core.
But the only electronic part you actually need is a toggle (well, a handful of them in series). That doesn't increase your capabilities beyond gears, except that you can pick up a faster signal (and then the only thing you can do with it is slow it back down).
> A digital watch can fundamentally be implemented entirely in software, in ways that I'll venture a hardware watch cannot be.
If you say hardware can't truly be represented, then neither can the quartz crystal, and I would argue that output hardware can't truly be represented either. So the two things you're doing entirely in software are the conversion from 32kHz down to 1Hz, and the conversion from 1Hz to a series of digits.
But the type of watch we're talking about doesn't have a digits display so discard that.
Now the only thing you're doing in software is dividing by 2 a few times, maybe also dividing by 60. That's not beyond the capabilities of a simple mechanical system. There's no need to have "software" involved either. "Software" is orders of magnitude more complex than dividing by 2.
Or, another way to look at things: A watch just like a quartz watch can be implemented completely in hardware, if you put in a """crystal""" that wiggles at 8Hz instead of 32768Hz.
I see your point about speed being a meaningful difference in many areas, but in this case the only thing done at high speed is slow it back down.
> There's also the point that gears ... rotate continuously, rather than discretely. We can modify that (e.g., with cams or similar designs), but there's still that continous rotational motion at core.
The gears right at the core of a mechanical clock are moving in pulses. It's not very far off from what the transistors or vacuum tubes would be doing.
Overall, I think the things you're saying about the expressiveness and power of digital logic are valid, but I don't think they really apply here when the logic is so minimal and could in theory be removed entirely.
I can find no examples of an acoustically-based mechanical timekeeping mechanism. If you're aware of any I'd be interested in seeing them.
I can also remember when mechanical stopwatches were still A Thing, used in sport timing when I was a wee'un. I suspect that these were the highest-precision timepieces reasonably mass-produced (and likely expensive nonetheless), and they could reach 1/10th second accuracy. Far cheaper digital stopwatches came available shortly after, were less expensive, and had 1/100th s accuracy. They could easily have recorded to greater accuracy but the limits of human perception and reaction would have made that redundant.
Current prices seem to range from ~US25 to ~$150 for mechanical stopwatches, versus ~$2 to $20 for digital electronic stopwatches, going off Amazon.
Even now, timed events are generally only measured and judged to 1/100th of a second, given that unavoidable variances (e.g., in track or lane length for track or swimming events, or course lengths for others) would introduce variability not strictly addressed by an athlete's capability.
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.
Where do you live?
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...
(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.)
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 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?
https://en.m.wikipedia.org/wiki/Roman_abacus
(Base 12x5=60 was of course used by their Babylonian predecessors.)
https://m.youtube.com/watch?v=NeopkvAP-ag
Bonus on analog vs digital mechanism in flip clocks:
Generational though, sure.
You can confirm this by searching "quarter past" at any significant US website, e.g., the NY Times:
<https://duckduckgo.com/?q=site%3Anytimes.com+%22quarter+past>
"Quarter of" or "quarter to" are less frequent, but can be found and heard.
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.
Time is a cube, not a cuboid.
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).
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.
However, your explanation is definitely much better.
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!
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 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
Dutch train stations used to have these too, I loved to watch them in action while waiting for a train.
Can I? Many analog clocks actually "tick" the second and minute hand. I've even seen some that tick the hour 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...
> 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?)
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!
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.
You can keep playing with increasingly smaller time units until you conclude, like Zeno's arrow paradox, that you're always infinitely late.
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.
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.
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.
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.
"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.
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.
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.
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.
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.
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.
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.
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...
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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 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...
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
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.
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.
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.
That's quit intuitive for all kind of time precision, and the author's rounding solution would be somewhat counterintuitive, at least for me.
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
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/
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.
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.
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.
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.]
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.
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.
Or eschew the entire class of problem of daylight savings and drift with a GNSS- or radio time beacon-controlled clock.
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.
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?
Why does it matter if your noon meeting starts at 11:59 or 12:01?
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.
I've never heard anyone say it's 4pm when it was 3.31pm.
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
- 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’.
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.
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.
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 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 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.
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! :)
Not to mention a waste of the one truely nonrenewable resource, our time...
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
I think most people would have no issue calling 14:28 "half past two". There's no "at least" to it, just an approximation.
12:00 meetings now start at 11:59:30 and you're still late
Get a seconds precision watch if you care about seconds level accuracy
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.
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.
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.
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.
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)
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.
Although I have to say I've not really encountered other people doing this.
> Is it the same for the current minute of the current hour ?
> I'm not so sure.
I'm sure - it's the same.
No, it's probably just autism.
Perhaps, average error of clocks is 30 seconds higher because minutes use .floor() nor .round()
And in SQL Server, ROUND() with a nonzero number for the third parameter for truncate, and CELING() for ceiling.
We round years too, otherwise I would be in my 30s.
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.