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.
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.
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.
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.
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.
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"?
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)
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).
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.
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.
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 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?
First: I appreciate your pressing your points, as it's helpful for me to clarify my own reasoning. This hinges on a few points, and again the sense of ideas as interfaces / models is key for me. I'm less a believer in truth than of pragmatism of ideas, something I've been delving into through history of philosophy for a number of years now. And it's the utility of dividing systems into analogue vs. digital which seems key.
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 re...
> 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".
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.
I guess I would also appreciate the conversation if you had ever addressed my argument about attaching gears to a slower crystal, especially since that was in my very first very short comment. As is, I'm kind of annoyed.
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 didn't touch that one for a few reasons, mostly addressed to exhaustion above, viz: mechanical timepieces tend to be based on a regulated entropic source (watchspring, weights). It's not clear to me that a slow resonance oscillator would effectively couple to gearing, and I'm very far from enough of a watch/clock nerd to think of how this might be done or whether there are any current or historical examples of same. Basically: if you had a pure resonator, then a mechanical coupling seems to me very likely to degrade its regularity beyond use in timekeeping. An escapement design is preferable, and again, that's an inherently analogue mechanism.
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.
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.
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 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...
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 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.)
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.
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.
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 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.
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.
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 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.
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.
“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.
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.
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!
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. :)
The average of its errors is 0- ie it is not biased. Ofc, the average absolute error, which in English one could very reasonably refer to as "average error" is much greater than 0.
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.
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 :)
> 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.
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.
> 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.
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.
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.
Jonathan Agnew has a similar story about the late, great Australian cricket commentator Richie Benaud, although filling ~52 seconds rather than 5 minutes.
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
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.
With the lack of precision for clocks the way they are, and worries about variance in travel time due to traffic, distractions, potty emergencies, and so forth, the more natural way to handle precision is to give yourself a 5-to-15-minute-to-an-hour buffer to ensure that you're in your seat when the clock ticks from 11:59 to 12:00.
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.
> 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.
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.
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[ 2.7 ms ] story [ 357 ms ] threadMost 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.
https://www.bbc.com/news/world-asia-66028606.amp
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.
https://en.wikipedia.org/wiki/Quartz_clock
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 re...
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.
<https://news.ycombinator.com/item?id=42621419>
[1]: https://en.m.wikipedia.org/wiki/Automatic_quartz
[2]: https://en.m.wikipedia.org/wiki/Quartz_clock
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:
https://m.youtube.com/watch?v=ZArBfxaPzD8
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.
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.
https://en.wikipedia.org/wiki/Escapement
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.
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.
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.
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 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.
"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.
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.
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
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.
No, it's probably just autism.
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!
https://youtu.be/FsmtFZQJbHU
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!