The problem of predicting tides was so important that it attracted many Physics and Maths heavy weights. You can well imagine how important predicting tides would have been for D-day landing.
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.
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.
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).
The Battle of Clontarf on April 23rd 1014 springs to mind. While the high tide was of favour for the invading Vikings (who had already founded and still ruled Dublin) at 5:30 in the morn, the battle lasted all day and the next high tide at 17:55 cut off their way to a nearby wood and many killed or drowned as their were pushed against the tide. The times were calculated in 1860 by Samuel Haughton.
> You can well imagine how important predicting tides would have been for D-day landing.
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.
So it's a bunch of complicated splashy water that is excited by the moon moving past, and follows along at the same frequency - but it's not a simple wave travelling around the world, for various reasons.
The earth itself is squashed like that with two bulges, but the water on the surface exhibits a more complex motion.
> So it's a bunch of complicated splashy water that is excited by the moon moving past
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.
When I was in grad school in astronomy, one of my professors told me "many a promising young researcher has run their career aground on the rocky shores of tides."
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
There’s been some backpedaling lately in the astrophysics community about whether a tidally locked planet could still maintain an atmosphere and potentially support life. More modeling on how such at atmosphere might work has turned from “no” to “maybe”.
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.
The explanation is phenomenal. I particularly like the elevation heat map, which helps me intuitively grasp what is going on.
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 expect because without the far bulge, 12 hour tides can't be explained. One bulge would mean 24 hour tides. Not that either explanation is actually correct, but the two bulge explanation matches the obseved periodicity, which is all most people would ever need or care to know about tides these days.
I can't for the life of me understand why graduate level oceanography courses would be teaching it though.
It's an idealized model, accurate if Earth had only a single all encompassing deep ocean. Idealized models are good pedagogic tools to build corrections upon.
It's similar to depiction of projectile motions as parabola s. The trajectories of artillery shells ar not like that, but helps get started.
Six months ago, I spent a week at the shore. It happened to be full moon. We were out walking late at night while the moon was high up, and had to slog through ankle deep water on the way back. It was like clockwork roughly 12 hours apart.
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?
Your clock was off. Tides advance ~30 minutes per day. But not exactly 30 minutes. Sometimes more. Sometimes less. Sometimes it doesn’t follow a semi diurnal pattern.
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.
The SE answer gave you a nice map. The points where the white lines coalesce experience no change in height. The blue regions experience low tidal amplitude, whereas the red regions experience high tidal amplitudes. The white lines are the lines of equal phase: if a point on the line is experiencing its high tide, so is every other point on the line, and likewise for low tide.
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.
From reading the accepted StackExchange answer, I think the answer to your last questions is that this model might still be too simplified.
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).
Good point. I'd be curious if anyone actually has the text showing he said this. It's in principia I guess. My bet was that he never gave a full description, but rather just said that it is moon/sun that *causes* the tides.-- I'd wager he acknowledged the incompleteness of it.
Which would still be mostly accurate. It's hard to imagine him knowing about the complicated tides in England and saying definitively he had a full model of the tides.
TL;DR newton basically got the FORCES right, but forces don't tell the whole story because of (mainly ) 1) insufficient propagation speed because ocean is deep 2) think of it kind of like a diff eq, the boundary conditions (largely from land masses) from the actual structure of the earth make the solutions much more interesting than F=ma might suggest.
Edit- I recommend actually reading it, especially the second answer.
I was asked why there are two tides a day in an interview for my undergraduate University place. I blundered through to the classic answer. This stackexchange discussion made me realize I was even more of an imposter than I thought :-).
If it makes you feel better, the crust of the earth does bulge more in line with the classic answer due to the flow of the underlying magma being effectively uninterrupted by solid obstructions. Which then means the classic tidal answer is technically correct, except what we observe as tides is a delta between land and ocean.
Water has to flow. It doesn’t just appear where it “needs” to be.
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.
Damn, I just had one of those moments where you go from thinking you understand something to realizing it's really complicated and you don't understand it at all.
The term “newtonian solution” just implies that you’re using gravitational and kinematic approaches to the model. I think Newton probably would have done much better had he made an earnest study with the resources he had available. People in shipping towns knew when tides and currents would be favorable and ships would try to leave at those times.
I think you are doing the man a disservice summarising him in such a way.
His interest in unorthodox/heretical religion was at least since he was at university. He spent a significant amount of time on alchemy.
Newton was the President of the Royal Society for over two decades, an MP for a similar amount of time which I would think required a lot of interpersonal relationships and socialising.
He seemed to get along well with family who cared with and lived with him and described him as loving.
The traits of holding grudges and raging were probably as common in academia then as they are today (tech is benign in comparison), but are otherwise sociable and genuinely trying to be good, albeit flawed, people.
He made numerous statements of modesty, the most famous being "If I have seen further it is by standing on the shoulders of giants." This has, IMHO, been unfairly reinterpreted in recent times as being a insult to a rival rather than taken at face value.
If every comment, action, HN comment, tweet etc. of any person's entire life was interpreted in the least charitable light we would all be recorded in history as being as vile as you describe him.
I think at the end of the day he was just a gifted flawed human.
His childhood was quite emotionally traumatic. I can imagine severe abandonment wounds given his situation.
Not only would he have felt abandoned, when his mother quickly remarried after his father's death, he could actually see the distant steeple where her mother had to relocate after her marriage - source of affection and emotional connect just tantalizingly out of reach.
Perhaps the person that did the most to raise our standard of living (by basically inventing modern science). I basically don't care about how miserable it would be to sit next to him on a long airplane ride (or carriage ride).
srean|9 months ago
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).
TomK32|9 months ago
There is of course an In Our Time episode https://www.bbc.co.uk/programmes/m0029qh3
CGMthrowaway|9 months ago
neilfrndes|9 months ago
rhdjsjebshjffn|9 months ago
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.
HPsquared|9 months ago
The earth itself is squashed like that with two bulges, but the water on the surface exhibits a more complex motion.
tomxor|9 months ago
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.
antognini|9 months ago
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
hinkley|9 months ago
Sharlin|9 months ago
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.
zabzonk|9 months ago
mkl|9 months ago
That links to this website which has a similar animation for the current day: https://www.tpxo.net/
MostlyStable|9 months ago
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!
tylervigen|9 months ago
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.
Bjartr|9 months ago
I can't for the life of me understand why graduate level oceanography courses would be teaching it though.
srean|9 months ago
It's similar to depiction of projectile motions as parabola s. The trajectories of artillery shells ar not like that, but helps get started.
sixo|9 months ago
CommenterPerson|9 months ago
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?
dghlsakjg|9 months ago
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.
jhanschoo|9 months ago
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.
red369|9 months ago
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).
alejohausner|9 months ago
Calwestjobs|9 months ago
fransje26|9 months ago
jxjnskkzxxhx|9 months ago
Am I the only one skeptical that Newton would confuse a force with a displacement? What am I missing?
chermi|9 months ago
chermi|9 months ago
Edit- I recommend actually reading it, especially the second answer.
imurray|9 months ago
Retric|9 months ago
coolcase|9 months ago
senderista|9 months ago
hinkley|9 months ago
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.
cwmoore|9 months ago
https://en.wikipedia.org/wiki/Amphidromic_point
why_at|9 months ago
jxjnskkzxxhx|9 months ago
Am I the only one skeptical that Newton would confuse a force with a displacement?
throwaway173738|9 months ago
joshmarinacci|9 months ago
Calwestjobs|9 months ago
umanwizard|9 months ago
an0malous|9 months ago
The Bernoulli principle is one.
daveguy|9 months ago
Who would have guessed. Well, Laplace maybe.
Clood5|9 months ago
[deleted]
unknown|9 months ago
[deleted]
0xbadcafebee|9 months ago
[deleted]
teruakohatu|9 months ago
I think you are doing the man a disservice summarising him in such a way.
His interest in unorthodox/heretical religion was at least since he was at university. He spent a significant amount of time on alchemy.
Newton was the President of the Royal Society for over two decades, an MP for a similar amount of time which I would think required a lot of interpersonal relationships and socialising.
He seemed to get along well with family who cared with and lived with him and described him as loving.
The traits of holding grudges and raging were probably as common in academia then as they are today (tech is benign in comparison), but are otherwise sociable and genuinely trying to be good, albeit flawed, people.
He made numerous statements of modesty, the most famous being "If I have seen further it is by standing on the shoulders of giants." This has, IMHO, been unfairly reinterpreted in recent times as being a insult to a rival rather than taken at face value.
If every comment, action, HN comment, tweet etc. of any person's entire life was interpreted in the least charitable light we would all be recorded in history as being as vile as you describe him.
I think at the end of the day he was just a gifted flawed human.
shakna|9 months ago
IAmBroom|9 months ago
Newton just happened to be much more brilliant than most others - and exhaustively documented his scientific thoughts.
srean|9 months ago
Not only would he have felt abandoned, when his mother quickly remarried after his father's death, he could actually see the distant steeple where her mother had to relocate after her marriage - source of affection and emotional connect just tantalizingly out of reach.
That might explain his behaviour.
hollerith|9 months ago
btilly|9 months ago
He was also responsible for the execution of a couple of dozen people. These executions were connected to his position as master of the mint.