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).
TomK32 · 3h ago
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.
Anecdotally works very well in Tidal harbors with multiple rivers.
srean · 11h ago
That was so fascinating. Thank you.
synalx · 10h ago
If you're ever in SF, it's really worth going to see. Such a cool mixture of art and technology.
rhdjsjebshjffn · 4h ago
> 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.
grues-dinner · 9m ago
I think there are two ways to interpret that sentence: "it would have been important": one which implies tidal prediction was unavailable at D-day but would have been useful, and one that implies it was indeed available (subjunctive conditional or "the Anderson case", apparently, per Wikipedia)
I don't think anyone is claiming tide times were so unpredictable in 1945.
HPsquared · 12h ago
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.
tomxor · 10h ago
> 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.
II2II · 9h ago
That would be akin to describing a computer as a complicated arrangement of switches that control each other through pulses of electricity to do useful stuff. While it may satisfy a bunch of people who aren't really interested in how computers work, and it may even inspire a few people who are intrigued by how such a simple notion could produce incredible results, it doesn't really explain how computers work.
darkerside · 5h ago
But it is actually a bit more accurate than saying, electricity goes in and information comes out
dexwiz · 1h ago
Information and electricity go in and information and heat go out, to be pedantic about a simplification.
antognini · 11h ago
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
hinkley · 8h ago
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.
zabzonk · 9h ago
destruction (or nearly) via tidal mechanics happens in several of larry niven's short sf stories
ghaff · 8h ago
As I recall there were issues with the math in Neutron Star though still a very good story.
CommenterPerson · 7h ago
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?
dghlsakjg · 5h ago
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.
TomK32 · 2h ago
And then there's the Solent which for Springs has a double high tide as the western end of the Solent is quite narrow and the tide racing around the Isle of White and in from the wider eastern side.
https://www.nci.org.uk/solent-tides/
kgwgk · 2h ago
> Your clock was off. Tides advance ~30 minutes per day.
“roughly 12 hours”
jhanschoo · 4h ago
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.
red369 · 5h ago
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).
chermi · 13h ago
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.
alejohausner · 11h ago
In the animations, New Zealand stood out: the high and low tide chase each other counterclockwise around the islands!
Calwestjobs · 9h ago
earth is 3D not 2D ;) "bulges" same. that is where confusion comes from. also tesseract is nonsense.
why_at · 9h ago
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.
coolcase · 11h ago
Try to get your head around this while simultaneously not thinking of gravity as a force but curvature in spacetime.
senderista · 9h ago
No, don't! Use the simplest model that applies in your context!
coolcase · 7h ago
I agree, I meant to add "as a mind bending exercise to realize how complex nature is!"
Calwestjobs · 9h ago
exactly, like water is excellent model for electricity, but youtubers want to be edgy, provocative so they intentionally drop something which needs 20+ years of intentional thinking / education on high schoolers.
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 :-).
Retric · 13h ago
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.
joshmarinacci · 12h ago
I think of it not as Newton was wrong, but rather his explanation was incomplete.
Calwestjobs · 9h ago
Most kind way of saying Newton was a simple man.
umanwizard · 12h ago
So, yet another thing I learned at school was bullshit. Pretty interesting to know!
an0malous · 10h ago
What are the others?
The Bernoulli principle is one.
roelschroeven · 9h ago
The Bernoulli principle is not bullshit -- it is very valid physics.
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.
umanwizard · 2h ago
“Serious companies will require you to comment every line of code”
daveguy · 11h ago
Turns out teachers are people and general understanding evolves over time and not all at once.
Who would have guessed. Well, Laplace maybe.
0xbadcafebee · 12h ago
> one of Newton's few mistakes
fwiw, Newton was bipolar. High-strung, antisocial, egotistical, domineering, rage-filled. He fought with people often and refused to share his work out of fear of criticism. Most people really didn't like him and he was often severely depressed. Later in life, in part because of the torment of just being himself and having to work with peers, he refused to continue researching science, and instead became obsessed with God and alchemy.
The dude made mostly mistakes throughout his life, he just happened to be brilliant some of the time.
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.
srean · 10h ago
> I think at the end of the day he was just a gifted flawed human.
And what gifts !
Imagine anyone doing Principia at an age of 24 (the book was published much later, but he had the results by then).
He would have been notable even if he had borrowed an established discipline of calculus to elaborate it's Physical consequences. No he had to develop it himself first and double check the results by translating that into geometry, into power series to be sure they are correct.
Einstein and Newton are often spoken of in the same breath, but by sheer body of work it seems a no-contest to me. Einstein had the luxury of being able to borrow tensor calculus, by then well formed. Perhaps the person who comes closest to Newton would be Archimedes, considering the time that Archimedes was doing his thing.
shakna · 10h ago
This reads like you think no one with bipolar can live without ruining the people around them.
IAmBroom · 11h ago
We ALL mostly make mistakes throughout our lives.
Newton just happened to be much more brilliant than most others - and exhaustively documented his scientific thoughts.
s1artibartfast · 7h ago
Well some people do nothing worthy of note at all.
srean · 12h ago
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.
That might explain his behaviour.
parpfish · 11h ago
And to top it all off, that dang apple hit him on the head
ahazred8ta · 3h ago
Newton - "the sole mortal who could grapple,
Since Adam, with a fall or with an apple."
— Byron
A calculus fit to compute on,
White light and a head to drop fruit on,
A mind to absorb it,
And soar into orbit —
That's all that it takes to be Newton. — Gina Berkeley
srean · 10h ago
Is that so ?
I have to email hn@news.ycombinator.com about it. Those Apples are just too freaking expensive to throw around like that, Dang.
hollerith · 10h ago
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).
btilly · 11h ago
Can we at this distance tell the difference between bipolar, mercury poisoning, and repressed homosexual?
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.
senderista · 9h ago
Executing counterfeiters is certainly distasteful to us today, but I find it less distasteful than ideologically motivated crimes by modern scientists such as Lakatos (one of my intellectual heroes who I find it difficult not to despise as a person).
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.
https://www.current-lab.com
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.
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.
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.
“roughly 12 hours”
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).
Edit- I recommend actually reading it, especially the second answer.
https://www.youtube.com/watch?v=C3gnNpYK3lo
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.
fwiw, Newton was bipolar. High-strung, antisocial, egotistical, domineering, rage-filled. He fought with people often and refused to share his work out of fear of criticism. Most people really didn't like him and he was often severely depressed. Later in life, in part because of the torment of just being himself and having to work with peers, he refused to continue researching science, and instead became obsessed with God and alchemy.
The dude made mostly mistakes throughout his life, he just happened to be brilliant some of the time.
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.
And what gifts !
Imagine anyone doing Principia at an age of 24 (the book was published much later, but he had the results by then).
He would have been notable even if he had borrowed an established discipline of calculus to elaborate it's Physical consequences. No he had to develop it himself first and double check the results by translating that into geometry, into power series to be sure they are correct.
Einstein and Newton are often spoken of in the same breath, but by sheer body of work it seems a no-contest to me. Einstein had the luxury of being able to borrow tensor calculus, by then well formed. Perhaps the person who comes closest to Newton would be Archimedes, considering the time that Archimedes was doing his thing.
Newton just happened to be much more brilliant than most others - and exhaustively documented his scientific thoughts.
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.
A calculus fit to compute on, White light and a head to drop fruit on, A mind to absorb it, And soar into orbit — That's all that it takes to be Newton. — Gina Berkeley
I have to email hn@news.ycombinator.com about it. Those Apples are just too freaking expensive to throw around like that, Dang.
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.