One related fascinating historical artifact is the special purpose analogue computer designed by Lord Kelvin in the 1860s based on Fourier series, harmonic analysis. Think difference engine in it's cogs and cams glory, but special purpose.
https://en.m.wikipedia.org/wiki/Tide-predicting_machine
Possibly one of the first examples of Machine learning, with Machine in capital 'M'. It incorporated recent tidal observations to update it's prediction.
Note that sinusoids are universal approximators for a large class of functions, an honour that is by no means restricted to deep neural nets.
George Darwin (Charles Darwin's son) was a significant contributor in the design and upgrade of the machine.
https://en.m.wikipedia.org/wiki/George_Darwin
Other recognizable names who worked on tide prediction problem were Thomas Young (of double slit experiment fame) and Sir George Airy (of Airy disk fame).
There is of course an In Our Time episode https://www.bbc.co.uk/programmes/m0029qh3
Hyperlocal ocean modeling for science, defense, and recreational applications.
Anecdotally works very well in Tidal harbors with multiple rivers.
Is this intended to communicate positivity or negativity?
Predicting tides was known to the ancients; it would be lovely to explore the hubris of the modern narrative.
Edit: fundamentally, if hacker news has taught me anything, it's that "downvote = makes me feel bad and doesn't want to answer questions". The entire concept of democratic news aggregation was a lie.
I don't think anyone is claiming tide times were so unpredictable in 1945.
Guidelines:
> Please don't comment about the voting on comments. It never does any good, and it makes boring reading.
That it feels bad to not win the popular vote does not make democracy a lie, and there's no surprise in not winning favor when blanket discarding the current topic and describing it as "hubris", while not adding any new or constructive information.
It just says it was important to predict the tides. There is no positivity or negativity to it. Your question doesn’t make sense, hence the downvotes.
> Predicting tides was known to the ancients
Good. To which ancients? With what accuracy and how far into the future? What techniques did they use? Tell us more.
> it would be lovely to explore the hubris of the modern narrative.
Explore it then! Would love to read it. It is not like there is some conspiracy holding you back.
The earth itself is squashed like that with two bulges, but the water on the surface exhibits a more complex motion.
This explanation is so much better.
If people want to use big words they can say fluid dynamics, but yeah, it's a complex system with a big orbiting body pulling on it regularly, that gives the complex system rhythm but not order.
The mathematics involved in the theory of tides are formidable. Even in homogeneous, tidally locked systems things can get complicated very quickly.
But tides are nevertheless very important. One two objects pass very close to each other, tidal effects are substantial and can actual destroy one of the objects: https://en.wikipedia.org/wiki/Tidal_disruption_event
https://en.wikipedia.org/wiki/Roche_limit
https://en.wikipedia.org/wiki/Roche_lobe
Indeed given that we now think most of the heavy elements in the universe were created in type 1a mass-transfer supernovae, we can ultimately thank tidal phenomena for the existence of things like rocky planets and humans.
That links to this website which has a similar animation for the current day: https://www.tpxo.net/
To be fair to the course, it was much more interested in currents than tides (I don't remember really discussing tides in any depth at all)
This is a great answer!
This raises a question for me though: why do we show the tidal bulge graphic in any educational context? Like OP, the "far bulge" was always the most surprising and difficult-to-grasp part of the image. But this explanation would indicate that the far bulge is almost totally pointless as a concept, given the complexities of the system. Given it's the least intuitive part of the image, it invites additional consideration. But it's all the wrong consideration!
The model would be more useful if it only showed the bulge on the moon side, and excluded the far side bulge. It would still be wildly imprecise, kind of like the orbital model of atoms is wildly imprecise, but at least it would be a slightly more accurate (and useful) initial mental model.
I can't for the life of me understand why graduate level oceanography courses would be teaching it though.
So how was the existence of a far bulge justified?
It's similar to depiction of projectile motions as parabola s. The trajectories of artillery shells ar not like that, but helps get started.
Did read through stackexchange. It is indeed complicated. But the top response feels like paralysis by analysis. If we analyzed turbulent flow too much we would be unable to build rockets. Remember frictionless planes and point masses in high school? Those results are not exact either but a great way to model and understand what is going on.
Soooo .. could we make simplifying assumptions here? What if the earth was a smooth rigid sphere with a layer of water on the surface? The center of mass of Earth-Moon is at ~3/4ths of the earth's radius, from the earth's center. They are rotating about that center. The 12+ hour tides in many parts of the world start to make sense. Is there a mistake in this mental model?
Water can’t pass through landmasses, and that is a huge factor. If the earth had no landmasses, the tides would be entirely as you expect. However, if you look at a global visualization of tidal heights, you will see that a small landmass, NZ is a great example, can have highs and lows just miles apart. Same in Panama, what happens on the pacific coast is wildly different to what happens on the Caribbean.
In addition, the gravity of the sun comes to factor as well. Where I am, north of the 50th parallel, we simply don’t get very low tides during the day when we are near the winter solstice. The opposite happens in the summer.
The timing of the tides for any given spot tend to be predictable (where it is semi diurnal anyway, other places are a mess). But heights are extremely variable.
As is clear from the map, the tidal response is profoundly affected by land mass and ocean depth, which have complex shapes; so too the tidal response is as complex as it is, which is simple in comparison.
In your simplified model of the Earth, you would also need to make the ocean deep enough that the water could travel fast enough to keep up with the Earth's rotation (~22 km).
Am I the only one skeptical that Newton would confuse a force with a displacement? What am I missing?
Edit- I recommend actually reading it, especially the second answer.
There’s a brackish pond/lake in a park in Victoria BC, you go over a bridge from downtown to get to the main entrance, though the locals can cross a street.
If should actually be a bay, but under said bridge is a stone formation that forms the throat of this bay, which being so long and narrow, cannot fill up or drain as fast as the tides. So at high tide there is a waterfall flowing into the pond, and as the tides recede it’s a waterfall going the other direction.
Am I the only one skeptical that Newton would confuse a force with a displacement?
The Bernoulli principle is one.
You might be thinking the way it's often used to wrongly explain how airplane wings generate lift. Yeah, that's bullshit. I mean, the principle still applies, if applied correctly. The equal transit bullshit that it's often associated with, well yes, that's complete and utter bullshit.
Who would have guessed. Well, Laplace maybe.
