Framed

 

 

- Hello ChatGPT, can you please explain why in some cases, like old LP sound records, a continuous signal is recorded, but in other recording systems, like film projection, a sequence of frames with gaps between them is recorded. For example, Waymo cars seem to be using a frame record for its Lidar and Sonar systems.

Absolutely. The key idea is that “continuous” and “frame-based” are two different ways of representing something that may itself be continuous in time. The choice is mostly driven by what the physical system can conveniently measure, store, and reproduce.

There is a nice historical progression from phonograph → film → radar/LiDAR → digital cameras that makes this particularly clear.

1. An LP is essentially a continuous-time record

With an old LP, the sound is a continuously varying pressure wave:

air pressure → microphone → electrical voltage → cutting lathe → physical groove

The cutting stylus moves continuously as the audio waveform changes. The groove is therefore an analog spatial representation of the waveform.

If the voltage goes:

~~~~~

the groove's lateral motion goes correspondingly:

~~~~~

There aren't supposed to be individual "sound frames" separated by blank intervals. The groove is one continuously varying physical object.

Of course, the signal isn't infinitely continuous in reality. The atoms, mechanical vibrations, finite stylus size, etc. impose limits. But conceptually it is continuous.

---

2. Film is different because you're trying to capture images

Suppose you're filming someone walking.

Their motion is continuous:

person → moves continuously → continuously changing image

But film photography takes a snapshot during an exposure:

exposure → stop → move film → exposure → stop → move film → ...

So you get:

[FRAME] [FRAME] [FRAME] [FRAME] [FRAME]

rather than one continuously varying picture.

There's an important subtlety here: the gaps aren't really missing chunks of time in the visual scene. They're largely a consequence of how the camera/projector handles the film.

A movie camera typically exposes one frame, advances the film, exposes the next, and so forth. A projector does essentially the reverse. It holds one frame stationary in front of the light for a moment, then rapidly moves the film to the next frame while a shutter blocks the light.

Your eye/brain integrates those successive images into the perception of continuous motion.

At 24 frames/s, for example:

1 → 2 → 3 → 4 → 5 → ...

becomes:

motion

rather than:

a person teleporting 24 times per second.

The interesting thing is that film could theoretically be exposed while moving continuously. There have been continuous-motion cinematographic techniques. The intermittent frame mechanism won because it makes sharp individual exposures and projection much easier.

---

3. Now LiDAR starts looking much more like film

This is where your Waymo example is especially interesting.

A LiDAR sensor isn't normally producing one enormous continuous "picture of the world." It sends out individual optical pulses and measures their returns.

Conceptually:

laser pulse → wait for reflections → measure → laser pulse → measure → ...

Each return gives you something like:

"There is an object approximately 37.2 meters away in this direction."

Do that over many directions and you accumulate a point cloud.

After some period of scanning, you have something like:

          •       •
     •          •       •
         CAR
   •   ••••••••    •
       •      •

That's a snapshot-like data structure, even though the measurements that produced it occurred sequentially.

And this is a crucial distinction:

A LiDAR "frame" does not mean the world was frozen.

If the LiDAR takes 100 ms to construct a point cloud, point #1 might have been measured 100 ms before point #10,000.

So the point cloud is actually a little bit of time smeared into space.

That is one reason autonomous-driving systems have to do a lot of temporal compensation and sensor fusion.

---

4. Why not just record LiDAR continuously?

You actually can record the underlying measurements continuously, at least conceptually.

But consider what the computer needs to do.

Suppose a LiDAR produces:

2 million measurements per second.

You could simply have a stream:

time       direction       distance
10.000001     ...             ...
10.000002     ...             ...
10.000003     ...             ...
10.000004     ...             ...

That's a perfectly legitimate representation.

But software generally wants to reason about things such as:

"Where are all the objects right now?"

So the sensor data is grouped into time windows, perhaps something conceptually like:

Frame 1: 0.000–0.100 s
Frame 2: 0.100–0.200 s
Frame 3: 0.200–0.300 s
...

Each group becomes a point cloud or other representation.

It's rather like saying:

"Instead of giving me every raindrop individually, give me a photograph of the rainfall pattern every 100 milliseconds."

The underlying phenomenon is continuous. The representation is sampled and packetized.

---

5. Cameras are actually doing the same thing

A digital camera makes this particularly obvious.

The outside world doesn't operate at 30 frames/sec.

It is continuously changing.

Yet your camera might produce:

30 images/sec.

So:

continuous world
       ↓
   exposure
       ↓
 digital image
       ↓
   exposure
       ↓
 digital image
       ↓
      ...

That's fundamentally the same conceptual operation as a movie camera.

And LiDAR can be thought of similarly:

continuous world
       ↓
LiDAR measurements
       ↓
 point cloud
       ↓
LiDAR measurements
       ↓
 point cloud
       ↓
      ...

The big difference is that a camera measures light intensity/color over a 2D array, whereas LiDAR measures distance from reflected laser light, typically across many directions.

---

6. And there's another very important reason for frames: computation

This is probably the deepest reason modern systems like autonomous vehicles use frame-like data structures.

Imagine trying to answer:

"Is that object a pedestrian?"

You could feed the AI a never-ending stream of individual photons/laser returns.

That's possible, but computationally awkward.

Instead, you organize the information into manageable chunks:

          SENSOR
             │
             ▼
       measurements
             │
             ▼
      ┌─────────────┐
      │   FRAME     │
      │             │
      │ 2D image    │
      │ or          │
      │ 3D points   │
      └─────────────┘
             │
             ▼
       perception
             │
             ▼
     "pedestrian here"

Frames give algorithms a common temporal coordinate system.

You can then say:

Camera frame 153 occurred at time T.
LiDAR frame 87 occurred at approximately T.
Radar measurements around T also correspond to that scene.

That makes sensor fusion much easier.

---

7. There is an interesting philosophical distinction

You can think of three layers:

Reality

Continuous:

World(t)

The physical world changes continuously with time.

Measurement

Often discrete:

M(t₁), M(t₂), M(t₃), ...

The sensor samples reality at particular moments.

Representation

May be grouped:

Frame₁, Frame₂, Frame₃, ...

The computer packages those measurements into convenient objects.

So a "frame" doesn't necessarily mean:

"Reality consists of separate frames."

It means:

"We have chosen to represent a continuously changing reality as a sequence of samples."

That's a much more general concept than film.

---

8. And this explains the LP/LiDAR contrast beautifully

An LP designer asks:

What physical quantity can I continuously encode into a groove?

Answer: the instantaneous audio waveform.

So continuous spatial variation works wonderfully.

A LiDAR designer asks:

What physical quantity can I efficiently measure with pulses and timing electronics?

Answer: discrete distance measurements.

And a computer engineer then asks:

How should I organize millions of those measurements so the rest of the system can process them?

Answer: time-stamped packets, scans, point clouds, frames, etc.

So the difference isn't really analog versus digital.

It's more fundamentally:

What does the sensor measure naturally, and what representation is useful to the downstream system?

In fact, you can have a continuous analog signal, a discrete digital signal, a continuous physical phenomenon represented digitally, or a digital system processing a stream that never conceptually becomes a "frame."

And there's a particularly fascinating next step here: LiDAR "frames" are not quite analogous to movie frames because the LiDAR is scanning the scene sequentially rather than capturing the entire scene simultaneously. That creates some wonderfully weird effects when the car or objects are moving. If you'd like, I can explain how a rotating LiDAR can make a moving car appear warped in its point cloud, and why autonomous vehicles have to "de-skew" LiDAR frames. 

- I don't completely understand yet. If Lidar scans, isn't it scanning a frame? If not, how does the scanning work?

Yes, and this is exactly where the terminology gets slippery. A LiDAR can produce a “frame,” but it usually doesn't capture that frame all at once. It builds the frame by scanning.

Think of it as the difference between a camera taking a photograph and a person painting a photograph one dot at a time.

Imagine a very simple LiDAR

Suppose it has a laser that can point in different directions:

             ↑
          ↗  |  ↖
        ↗    |    ↖
      ↗      |      ↖
    ↗        🚗        ↖
  ↙          |          ↘
             ↓

It sends out a laser pulse in one direction.

The pulse hits something, comes back, and the LiDAR measures the travel time.

If light takes 200 nanoseconds to make the round trip, the system can calculate the distance:

distance = (speed of light × travel time) / 2

Then it points the laser somewhere else:

1. → measure
2. ↗ measure
3. ↑ measure
4. ↖ measure
5. ← measure
6. ↙ measure
7. ↓ measure
...

After thousands or millions of these measurements, it has constructed a 3D point cloud.

So when someone says:

"The LiDAR captured a frame"

what they often really mean is:

"The LiDAR collected a batch of measurements over a particular interval of time and we're treating that batch as one frame."

That's the subtle part.

---

A camera and LiDAR do it differently

Imagine looking at a car.

Camera

A camera might expose essentially all of its pixels during one exposure:

TIME = 10.000 s

┌───────────────────────┐
│ · · · · · · · · · · · │
│ · · · 🚗 · · · · · · │
│ · · · · · · · · · · · │
└───────────────────────┘

       one exposure

You get the whole 2D image at approximately the same time.

Scanning LiDAR

A scanning LiDAR might instead do:

10.000 s    •
10.001 s      •
10.002 s        •
10.003 s          •
10.004 s            •
10.005 s              •
...

It's moving its measurement direction through space.

Consequently, the eventual 3D picture might have been assembled over, say, 0.1 second.

So:

                 FRAME
       ┌──────────────────────┐
       │ • • • • • • • • • • │
       │ • • 🚗 • • • • • •  │
       │ • • • • • • • • • • │
       └──────────────────────┘
       ↑                      ↑
    first measurement     last measurement
             100 ms apart

The "frame" is therefore a bookkeeping concept, not necessarily a single instant.

---

There's an even more interesting wrinkle

Different LiDAR designs scan differently.

A traditional spinning automotive LiDAR might have laser emitters/detectors arranged vertically and rotate the entire optical assembly:

                  ↑
                  |
             ↗    |    ↖
          ↗       |       ↖
       ↗          |          ↖

              [LiDAR]
                 ↻

As it rotates, it sweeps its beams around the vehicle.

One rotation gives you something resembling a complete 360° scan.

But even that isn't instantaneous.

At the beginning of the rotation:

        scan begins
             ↓
       [LiDAR] →→→

and 100 ms later:

        scan finishes
             ↓
       [LiDAR] →→→

During those 100 ms, the car, pedestrians, and other vehicles have moved.

Therefore the resulting point cloud is a mixture of measurements made at slightly different times.

---

This is why a moving object can look bizarre

Suppose a LiDAR scans from left to right while a car is moving.

At the beginning:

          🚗

Halfway through the scan, the car has moved:

             🚗

At the end:

                  🚗

But the LiDAR combines all those measurements into one point cloud.

You can consequently get something resembling:

       •••
          •••
             •••
                •••

instead of a nice rigid car.

The car has effectively been drawn at several different positions during one "frame."

This is called motion distortion or skew in LiDAR data, and autonomous-driving systems can compensate for it if they know the measurement timestamps and the vehicle's motion.

---

So what does "scan" actually mean?

Here's the distinction I'd keep in your head:

Scanning = moving the measurement across space.

Frame = grouping a set of measurements together in time.

Those aren't the same thing.

A LiDAR can therefore do:

             SCANNING
                 ↓
       • → • → • → • → •
       ↓   ↓   ↓   ↓   ↓
       •   •   •   •   •
       ↓   ↓   ↓   ↓   ↓
       •   •   •   •   •

                 ↓
        group measurements
                 ↓
             FRAME

The frame is something we construct from the scan.

And this is the key difference from a movie camera:

Movie camera: capture a spatial image, then advance to the next frame.

Scanning LiDAR: sweep through spatial directions, accumulate measurements, and then treat the resulting collection as a frame.

So your instinct was right: yes, LiDAR is "scanning a frame" in the loose sense. But technically, it is usually scanning the scene to construct a frame rather than capturing the entire frame simultaneously.

If you want, I can next show you exactly what happens inside one laser pulse, from “fire laser” → “photon comes back” → “distance measured” → “point appears in the 3-D frame.” That makes the whole thing click rather nicely. 

Thanks, I think I understand now. I wonder if there are other examples, like the LP vinyl records, of entirely continuous recording which does not ever record or construct a frame?

Yes. And you've put your finger on a really useful distinction: some systems are naturally “streams,” while others naturally become “frames.”

There are quite a few examples of genuinely continuous recording, although they are less common in modern digital systems.

Good examples of continuous recording

1. Analog magnetic tape

An ordinary analog audio tape is very much in the LP family.

A microphone produces a continuously varying voltage, and the tape's magnetic properties vary continuously along the tape:

time ───────────────────────────→

signal     ~~~~\/~~~~\___/~~~~~~
             ↓
magnetic    ~~~~\/~~~~\___/~~~~~~
tape

There is no sequence of audio "frames" that has to be assembled. The waveform simply progresses along the tape.

Interestingly, analog videotape could also record a continuously varying signal, although the physical arrangement became much more complicated because enormous amounts of bandwidth were required.

---

2. Optical sound on motion-picture film

This is a particularly beautiful example because it sits right next to the film-frame example.

Old film can have an optical soundtrack running continuously along the edge of the film. The varying shape or density of the soundtrack represents the audio waveform.

So the same piece of film can contain:

┌──────────────────────────────────────────┐
│ [FRAME][FRAME][FRAME][FRAME][FRAME]      │
│                                          │
│ ~~~~~~~ continuously varying soundtrack  │
└──────────────────────────────────────────┘

The picture is frame-based, while the soundtrack is essentially continuous.

That's a wonderful demonstration that the choice isn't really about the recording medium. It's about what you're trying to encode.

---

3. Analog seismographs

A traditional seismograph can physically move a pen continuously across a rotating drum.

Earthquake motion:

ground motion
     ↓
mechanical movement
     ↓
pen
     ↓
~~~~~~~~~~~~~~~~~~~~~~~~

The resulting trace is a continuous spatial record of the continuously varying ground motion.

No "earthquake frames" are needed.

---

4. Old chart recorders

Factories, laboratories, hospitals, power plants, etc. used mechanical or analog chart recorders.

For example, temperature could be recorded by a pen moving continuously across a roll of paper:

temperature
    ↑
    │       /\       /\
    │  /\  /  \__/\_/  \__
    │_/  \/
    └────────────────────→ time

Again, it's essentially:

continuous physical quantity → continuous physical trace.

---

Here's the really interesting counterexample: audio CDs

An audio CD sounds like it should be continuous because music plays continuously.

But its representation is fundamentally different from an LP.

The microphone signal is sampled:

continuous waveform

       ~~~~~~~
     ~~       ~~
---•---•---•---•---•---•---
   samples

Each sample is a number.

So the CD is not storing the continuously varying waveform itself. It's storing a sequence of measurements from which the waveform is reconstructed during playback.

But notice something subtle:

A sequence of samples isn't necessarily a sequence of frames.

This is an important refinement to our earlier discussion.

You can have:

continuous signal → samples → continuous stream

without ever having:

sample → frame → sample → frame → ...

Audio is usually treated as a stream of samples, not as discrete "audio pictures."

---

And this gives us three different concepts

I think this may be the conceptual map you've been looking for.

A. Continuous representation

The recording itself varies continuously.

LP groove

analog tape

mechanical chart recorder

analog optical soundtrack

~~~~~~~~~~~~~~~

There isn't a collection of individual measurements.

---

B. Discrete stream

The recording consists of individual measurements, but they're simply an ongoing sequence.

digital audio

telemetry

many sensor measurements

• • • • • • • • • • • • • • •

There may be millions of samples, but nobody needs to say "this is frame 173."

---

C. Frames

Measurements are deliberately collected into chunks representing some interval or snapshot.

movie film

digital photographs

video

LiDAR point clouds

[••••••] [••••••] [••••••] [••••••]
 Frame 1   Frame 2   Frame 3   Frame 4

And now we can see that LiDAR isn't necessarily fundamentally frame-based either. Its underlying measurements can be regarded as a stream of individual range measurements. The system chooses to package some of them into scans/point clouds because that's useful for perception.

---

The LP is therefore special in a subtle way

The LP isn't merely "analog" while LiDAR is "digital."

It's more specific:

The LP uses a continuous spatial variable to encode a continuous temporal signal.

The groove itself is the recording. There isn't an underlying collection of samples that gets assembled into a waveform.

That's why the LP feels almost mathematically elegant:

time → position along groove

and

audio amplitude → physical displacement of groove

So playing the record is essentially reversing that mapping:

groove position → displacement → electrical signal → sound

No frame construction is necessary at any point.

And that same principle is why a mechanical clock's continuously moving hands, a seismograph trace, or an analog tape recording feel fundamentally different from a movie or a digital camera. They aren't making a succession of little pictures of the phenomenon. They are making one continuously varying physical trace of it.

There is also a fascinating middle ground: analog television. It is neither quite like an LP nor quite like modern digital video, because the picture itself is represented as a continuous electrical signal that is nevertheless scanned line-by-line. That example really blurs the boundary between "continuous" and "frame-based."

- Analog television seems to be very much like Lidar? Also, the continuous second hand movement of a clock is actually a succession of separate movements.

Yes. Those are both excellent corrections to what I said.

Analog television really is surprisingly close to LiDAR

The crucial idea is scanning.

An old analog TV signal doesn't transmit a whole picture instantaneously. The camera scans the image:

──────────────→
──────────────→
──────────────→
──────────────→

The brightness at each point is converted into a continuously varying electrical signal. The receiver then scans its screen in synchrony and recreates the image.

So conceptually:

camera:
spatial image → sequential scan → continuous electrical signal

LiDAR:
spatial scene → sequential range measurements → digital data stream

They are cousins.

There is one major difference: analog TV's scan is usually a continuous sweep of a raster, whereas scanning LiDAR makes discrete range measurements at particular directions. But in both cases, the system explores the spatial scene sequentially rather than capturing every location simultaneously.

And there is a lovely historical irony here: analog TV is continuous in its signal, but spatially scanned. So "continuous" and "scanned" aren't opposites.

---

And yes, the clock example was a bad one

You're exactly right.

A conventional mechanical clock's second hand doesn't move in a mathematically continuous fashion. Its motion is produced by the escapement:

tick → tiny movement → tick → tiny movement → ...

So the apparent continuous sweep of some clocks is actually a succession of very small mechanical steps.

There are clocks with genuinely continuous-looking movement, though. An electric synchronous motor clock, for example, can rotate its hand continuously (within the mechanical limitations of the system).

But even there, if we get sufficiently microscopic, everything becomes complicated. The motor consists of electromagnetic interactions, gears, friction, molecular motion, etc. Asking whether anything is "truly continuous" eventually becomes a question about physics rather than recording technology.

---

And I think this reveals the more precise question you're really asking

It's not:

"Is the thing continuous or made of frames?"

It's:

"Does the recording contain a continuously varying representation of the signal, or does it contain discrete samples of the signal?"

Those are different questions.

For example:

System	What gets recorded?	Continuous or discrete?
LP	Groove displacement	Continuous
Analog audio tape	Magnetic variation	Continuous
Seismograph trace	Pen position	Continuous
Analog TV	Electrical waveform	Continuous, but spatially scanned
Digital audio	Amplitude samples	Discrete, but usually a continuous stream
Digital camera	Pixel values	Discrete frame
Scanning LiDAR	Range samples	Discrete measurements, often grouped into scans/frames

And here's the particularly interesting case:

Analog TV is actually much closer to an LP than it first appears.

An LP converts:

time → position along a groove

and

signal amplitude → groove displacement

Analog TV converts:

position in the image → position in time during the scan

and

brightness → instantaneous electrical voltage

So the television signal is effectively a one-dimensional temporal traversal of a two-dimensional image.

The TV isn't recording a succession of photographs. It's recording a continuously varying signal produced while sweeping through the photograph.

That's quite different from a modern digital video camera, where you really do have:

image → pixels → frame → pixels → frame → ...

And LiDAR sits somewhere between these worlds, because its underlying sensor output is a stream of discrete spatial measurements, which software may subsequently package into "frames."

So I think you've uncovered a very useful distinction: "frame" is not synonymous with "scan," and "continuous" is not synonymous with "not scanned." Those two axes can vary independently. 

- Before watches used a quartz crystal vibration to act in place of mechanical escapement, which would be a case of digital counting I think, the electrical current powering the watch from the battery somehow moved the second hand, but could that movement be described as continuous?

 

Yes, and there's a beautiful distinction here between how the time is generated and how the hands are moved.

For a traditional quartz watch, you're basically right about the first part:

battery → electrical oscillator → counting circuit → motor → gears → hands

The quartz crystal oscillates at a very stable frequency, commonly 32,768 Hz. The electronics count those oscillations and divide the frequency down until they produce one pulse per second.

So in that sense, quartz timekeeping is indeed digital counting.

But then something interesting happens.

The motor doesn't continuously rotate the second hand

In the most common quartz watch:

32,768 crystal oscillations/sec
              ↓
       electronic divider
              ↓
       1 electrical pulse/sec
              ↓
        tiny stepper motor
              ↓
          gear train
              ↓
       second hand moves
             ↑
       one small step
       every second

The second hand therefore typically does:

tick → move → stop → tick → move → stop

rather than continuously sweeping around the dial.

So it is actually a lovely hybrid:

digital time reference → mechanical movement.

The quartz oscillator itself is oscillating continuously (to a very good approximation), but the electronics count its cycles. The counting produces discrete events, and those events cause discrete mechanical movements.

---

But here's the really interesting part

The motor itself doesn't necessarily make a giant jump of exactly one second.

A typical quartz watch's stepper motor rotates by a small fixed angle when it receives a pulse. The gear train converts that into the second hand's movement.

So imagine:

       pulse       pulse       pulse
         ↓           ↓           ↓
        ┌─┐         ┌─┐         ┌─┐
        │ │         │ │         │ │
────────┘ └─────────┘ └─────────┘ └──── time

hand:    ↑
         │
         └─ small movement
                    ↑
                    └─ small movement
                               ↑
                               └─ small movement

The hand is stationary for most of each second and moves rapidly through a small angle.

Your eye interprets the sequence as one tick per second.

---

But some quartz watches do have continuous-looking hands

And this is where your question gets especially interesting.

There are quartz watches designed so that the hand moves in many smaller increments per second, or in some cases uses a motor arrangement that produces a very smooth sweep.

For example, instead of:

one step/second

you could have:

10 steps/second

or:

20 steps/second

The underlying timing is still digital:

quartz oscillations → counting → electrical pulses

but the mechanical output becomes increasingly smooth.

So we get this fascinating chain:

continuous physical oscillation
↓
digital counting
↓
discrete electrical commands
↓
mechanical motion

The same digital clock can therefore produce either a visibly discrete or apparently continuous physical output.

---

And this connects directly back to your LP question

You've now uncovered something important.

A system can have discrete information internally but produce a continuous physical output.

For example:

Quartz watch:

discrete electrical pulses → mechanical hand movement

Digital audio:

discrete samples → reconstructed continuous voltage → speaker movement

Digital video:

discrete frames → display → continuously varying light during each frame

So "digital" doesn't necessarily mean "the thing you ultimately observe moves in discrete steps."

Conversely, something can be physically continuous while being sampled by a digital system.

That's exactly what happens with the quartz crystal: its vibration is a physical oscillation, but the watch doesn't need to measure its amplitude continuously. It essentially says:

one oscillation, two oscillations, three oscillations... 32,768 oscillations... one second!

And then starts counting again.

So your phrase "digital counting" is actually a very good way of thinking about a quartz watch. The fascinating thing is that the digital counting is only the timekeeping reference. The final act of displaying that time can be digital, mechanical, or a mixture of both.

- Before the invention of the quartz movement electric clocks were widespread that produced what looked like a continuous motion. Was it really continuous or a different kind of digital output that is perceived as continuous?

Yes. And there were two quite different kinds of electric clocks, which is probably the source of the distinction you're noticing.

The short answer is:

Some pre-quartz electric clocks really did produce genuinely continuous mechanical motion. Others produced discrete mechanical steps that were small and frequent enough to look continuous.

The important thing is that electricity itself does not imply digital operation.

The classic continuously moving electric clock

An early electric clock could use a synchronous motor. Alternating current from the power grid has a continuously alternating electromagnetic field, and a motor can use that field to rotate continuously.

The chain was roughly:

AC electricity → rotating magnetic field → motor rotates → gears rotate → hands rotate

The second hand could therefore physically rotate continuously:

                    hand
                     ↓
        ───────────────────────→ time

        continuously rotating

There was no electronic counter saying "one, two, three..." and then commanding the hand to move.

The motor was being driven by an analog, continuously varying electromagnetic process.

There were also electrically wound mechanical clocks in which an electromagnetic mechanism periodically rewound a spring or supplied energy to a pendulum. In those, the timekeeping could remain fundamentally mechanical even though electricity supplied the energy.

---

But here's the fascinating catch

Even a continuously rotating second hand isn't necessarily telling you that the time measurement itself is continuous.

Suppose a motor turns at exactly one revolution per minute:

motor rotation → gear reduction → second hand

The angular position of the hand is then a continuous variable:

θ(t)

and you can read the time from its position.

That's quite different from a quartz watch:

quartz oscillations → count 32,768 cycles → generate pulse → step motor → advance hand

The latter is explicitly based on discrete events.

So we could make this comparison:

Clock	Time reference	Hand movement
Pendulum clock	mechanical oscillation	usually continuous-ish or stepped
Electric synchronous clock	AC frequency / motor	potentially continuous
Electric impulse clock	discrete electromagnetic impulses	stepped
Quartz watch	counted crystal oscillations	usually stepped
Smooth-sweep quartz	counted crystal oscillations	many tiny steps, appears continuous

---

And there's a wonderful paradox here

Even the "continuous" electric clock is ultimately being driven by alternating current, which reverses direction 50 or 60 times per second.

So if we keep zooming in, we can ask:

Is the motor really receiving a continuous rotation, or is it responding to a succession of electromagnetic cycles?

That's where the word continuous becomes slippery.

At the level relevant to the clock's hand, the motor can produce essentially continuous rotation.

At a deeper physical level, the motor's torque is periodically varying with the AC waveform.

And at an even deeper level, quantum physics makes our everyday idea of a perfectly continuous physical process considerably more complicated.

But we don't need to go that far for the engineering distinction.

The useful dividing line is this:

Continuous mechanism:

A continuously varying physical quantity directly determines the output.

Stepped/digital mechanism:

A sequence of discrete events determines the output.

So a synchronous-motor clock can genuinely belong in the first category, even though its power source is electrical.

And this is a nice correction to the direction our conversation was taking earlier: "digital" and "electrical" are not synonyms, and "mechanical" and "continuous" aren't synonyms either. A mechanical clock can step, and an electric clock can rotate continuously.

In fact, the old electric synchronous clock is probably a better example of genuinely continuous recording/display than my earlier clock-hand example was. Your objection about the mechanical second hand was exactly on target.

- So we come to the strange conclusion of the similarity (continuous movement) of the LP record and the AC regulated electric clock!

 

Exactly! And I think you've found a genuinely elegant connection.

The LP record and the old AC synchronous clock belong to the same broad family:

A continuously varying physical process is mapped directly onto a continuously varying physical quantity.

For the LP:

time-varying sound pressure
→ electrical waveform
→ continuously varying groove shape
→ stylus motion
→ sound

For the AC synchronous clock:

time-varying AC electromagnetic field
→ continuously rotating motor
→ continuously rotating gears
→ continuously moving hands

In both cases, there is no need for a sequence of discrete "events" saying:

now advance to the next value.

Instead, the instantaneous state of one physical system continuously determines the state of another.

And there's an especially beautiful parallel

An LP essentially performs:

time → distance along the groove

The clock performs:

time → angular position

So if we froze each at an arbitrary instant:

• the LP stylus would be at a particular position along the groove
• the clock hand would be at a particular angle

Both are analog representations of a continuously evolving quantity.

You could almost write them mathematically as:

LP:
groove position x(t) encodes audio amplitude A(t)

clock:
hand angle θ(t) encodes time t

The remarkable thing is that neither needs a digital counter to establish the correspondence.

And that makes your original question about LiDAR even more interesting. LiDAR is fundamentally different because its basic measurement is more like:

distance₁, distance₂, distance₃, distance₄...

It samples the world into discrete values and then constructs a spatial representation from them.

So we have a little taxonomy emerging:

LP: continuous → continuous
AC synchronous clock: continuous → continuous
analog TV: continuous signal, but spatially scanned
quartz clock: oscillation → counting → discrete impulses
digital audio: samples → digital stream → reconstructed continuous sound
LiDAR: discrete measurements → accumulated spatial representation

And there's one delicious wrinkle: AC itself is a waveform, so the synchronous clock is using an analog physical oscillation as its time reference, whereas the quartz watch takes a physical oscillation and turns it into a digital count.

In other words, the quartz revolution didn't merely replace a mechanical clock with an electrical one. It changed the kind of relationship between the time reference and the displayed time.

That's a much more interesting story than "old clocks were mechanical, quartz clocks were electronic."

Yes. Thanks, we seem to have explored the question from end to end now.

 

Indeed. We managed to travel from vinyl grooves → film frames → LiDAR scans → analog television → clock escapements → quartz counting → AC synchronous motors, and somehow ended up with a fairly useful little theory of continuous versus discrete representation. 😄

The particularly satisfying conclusion is that “continuous,” “scanned,” “electrical,” “mechanical,” and “digital” are independent dimensions, rather than opposing categories.

And your LP ↔ AC clock connection is a very good one: both are examples where a continuously varying physical process can directly produce a continuously varying physical representation.

A surprisingly deep rabbit hole from a question about vinyl records. 🌀

Glad we got all the way to the bottom of it.

- Excellent! see you later.

 

See you later! 👋 It was a pleasure following that particular intellectual rabbit hole with you. Until the next one!