The training process evolves models to do predictions. The actual underlying mechanisms are not too relevant because the prediction function is an emergent property.

You brain is just biochemistry and biochemistry isn't intelligent and yet you are. Think of the number three and all you know about it. There is not a single neuron in your brain that has any idea what the concept of three even means. It's an emergent behavior.

Sphere with radius zero. Problem solved 🤣

I'm not a native speaker, but that sounds like semantics to me. How would you, when chatting, differentiate if the other end is "knowledgeable" or if it "merely contains knowledge"?

I don't get your analogy. Put your brain through a shredder. Is it still intelligent? All the atoms are still there.

Exactly. And that's also true for young children. Reading digital clocks is exactly that... reading. It doesn't mean you understand what it means or how to interpret it. Analog clocks however are a great tool at actually get a feeling for time.

I think the biggest issue judging by the comment section is that most Americans (at least it seems that way) are almost never exposed to analog clocks.

Do you have a link or something that explains "progression towards the equinoxes". I never heard of that and can't find anything about it.

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 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.

Thank you for taking the time to read it.

I still don't see a number ;-) but you can take a look at the meme to see other people with math degrees shouting at each other.

I tried to be careful to not suggest that scientist only use strong juxtaposition. They use both but are typically very careful to not write ambiguous stuff and practically never write implicit multiplications between numbers because they just simplify it.

At this point it's probably to late to really fix it and the only viable option is to be aware why and how this ambiguous and not write it that way.

As stated in the "even more ambiguous math notations" it's far from the only ambiguous situation and it's practically impossible (and not really necessary) to fix.

Scientist and engineers also know the issue and navigate around it. It's really a non-issue for experts and the problem is only how and what the general population is taught.