What is progression towards the equinoxes? You mean precession of the equinoxes? That takes millennia and is very much negligible when reading sun dials on a day to day basis, or even year to year basis.

The orbital motions of the objects in our solar system is pretty messy and you are right that there goes more into designing accurate sun dials than just a stick in the ground, but I'd still argue that that's not part of "reading a sun dial" - which was the question I answered.

It's about how far the hand moves in a given time. On a normal 12h circle analog clock the hand moves 30° per hour. On a 24h analog clock that's halfed to 15° per hour.

You can teach three year olds to read analog clocks (see my other post) but I've yet so see three year olds reading and understanding digital clocks. I get the feeling in this thread that everybody that has issues with analog clocks is from the US and that might come from the fact that the US (at least it seems based on this thread) has almost no exposure to analog clocks.

Analog clocks are mechanical imitations of sun dials. Ever wondered why clockwise is the way it is? It's because the sun moved that way (on the historically a bit more dominant northern hemisphere)

Why/How are analog clocks annoying?

24h analog clocks exist but they are pretty useless because you lose angular resolution. So unless you are a vampire that's up 24/7 a 12 hour wall clock has better angular resolution than a clock with 33% wasted area you'll never use/see because you are asleep

Analog clocks imitate sun dials and of you have amazing eye sight/precision you would only need the hour hand. If the hand is exactly on 3, it's 3 o'clock. If the hand is exactly in the middle between 3 and 4 it's half past 3. If the hand is 4° after 5 it's 04:08. But because our eye sight doesn't have super resolution we just add another hand that makes a full circle when the hour hand moves an hour. And same with seconds. Second hand makes a full circle for 1 minute.

Back to birthdays - you can do that on the other direction as well but I wouldn't call it a clock, it's a circular calendar. Think about a disk (like a wall clock with only one hand) and seven equal segments. The days of the week, every morning we move the hand to the next day. Another disk with 31 segments (day of the month) and another separate disk with 12 segments. We typically move that one on the first of the month to the next step.

Now of we discuss events I can point to a segment and even though she is a young kid she immediately gets the scale of things because of something happens in a few hours (let's say she is meeting a friend) I show it to her on the normal analog clock with focus on the hour hand. But if she ask about Christmas I point on the "month" dial and she knows that it takes a very long time for that hand to move.

Typical analog clocks have all the hands on the same disk (for convenience and because it's compact). Our "child-clock" started originally as an normal analog clock with only the hour hand and is now a normal analog clock with hour and minute hand and three more separate disks for day of the week, day of the month and month of the year.

I hope you are not serious. If the shadow (hand) is on two, it's two o'clock. If it's on three, it's three o'clock. If it's exactly between those two ticks it's half past two. There isn't even anything to learn (at least when they were invented). That's exactly how the hour hand on a clock works.

(Note: Today it would be a bit more complicated if you want wall-clock-time because the sun dial always tells local solar time and if you want the time in your time zone you would have to adjust for DST and use the equation of time for some smaller corrections)

Are you from the US? I'm completely amazed that there are counties we you are almost never exposed to analog clocks. I'm from Europe and analog clocks are everywhere. Every train station, public buildings, churches, clock towers, homes, wrist watches. Heck we even have tons of (but more because of esthetics instead of serious time keeping) sun dials on walls (which the analog clock and the clock wise direction is based on - for the north hemisphere). Many appliances/devices have digital clocks but that's not because the are more modern/better but because they are way cheaper to produce and have less moving parts.

Analog clocks are dated? Let's get rid of books because we have kindles. Just something was invented a very long time ago doesn't make it obsolete by any means. Or should we get rid of spoons or hammers? Those things are really somewhat dated.

My daughter got analog clocks before she could read when she was about three years old. IMHO it's a teaching skill issue. Take a normal wall clock, remove all hands except the hour hand, split the day into segments (brushing teeth, lunch, Kindergarten, etc.) and draw (did that in Gimp) some nice symbols and colors. Done. Explain stuff every time she asks "when" using that wall clock. Let that sink in for a year. Now add the minute hand back in.

Analog clocks are not really "obsolete" if you ask me. Hands on a circle aren't used enough. We have "clocks" (this time inverted - the circle spins and the hand/indicator is fixed) out of cardboards for a week to learn the days of the week, including "activity" symbols for kindergarten, "weekend", "music lesson", etc. a wheel for "day of the month", and one for month of the year also showing seasons.

The total amount of time that was invested in building those was about three or four hours but the value is huge when you have something to point to when she asks anything about time no matter it's about when we go to sleep, birthdays, holidays, etc.

There is not "brain transplant". That's called "full body transplant" IMO.