Does Earth have two high-tide bulges on opposite sides? (2014)
physics.stackexchange.com277 points by imurray a day ago
277 points by imurray a day ago
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.
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).
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.
There is of course an In Our Time episode https://www.bbc.co.uk/programmes/m0029qh3
Have you seen the SF bay model? https://www.youtube.com/watch?v=i70wkxmumAw
Check out current lab
Hyperlocal ocean modeling for science, defense, and recreational applications.
Anecdotally works very well in Tidal harbors with multiple rivers.
That was so fascinating. Thank you.
If you're ever in SF, it's really worth going to see. Such a cool mixture of art and technology.
Veritasium made a video on this topic a couple of years ago: https://www.youtube.com/watch?v=IgF3OX8nT0w
> 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.
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.
They were predictable. Interestingly, Rommel misunderstood how tides affected landings. He thought the landings would be done at high tide, so the invading troops wouldn't have to advance across wide expanses of beach. In reality, the allies wanted to invade on a rising tide, so the landing craft, grounded to let out troops, would refloat and be able to move back out. Also, invading at lower tide meant beach obstacles would be exposed and unable to damage the landing craft.
> 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.
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.
> Is this intended to communicate positivity or negativity?
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.
>> Predicting tides was known to the ancients
> Good. To which ancients?
To the ancients of 1944 for sure.
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.
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.
Splashy complicated water is an accurate but imprecise description, which is exactly what you want for an introduction. It's a complex chaotic system.
Computers are a terrible analogy for this type of minimal explanation of natural phenomena because computers are layers of designed complexity built by exploiting an understanding of multiple distinct natural phenomena... At the composite scale computers are a very unatural human construct, not something emergent that can be accurately expressed informally.
But it is actually a bit more accurate than saying, electricity goes in and information comes out
Information and electricity go in and information and heat go out, to be pedantic about a simplification.
Electricity and possibly information, unless you're considering the structure itself to be information. Some ASICs only need to be powered on, for example.
If you're going to be pedantic, information and heat go into and come out of just about everything
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”.
See also:
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.
destruction (or nearly) via tidal mechanics happens in several of larry niven's short sf stories
As I recall there were issues with the math in Neutron Star though still a very good story.
I believe the issue is that the ship leaves the star in a spin, perhaps too fast to be survivable.
That animation is great. I found the person who made it: https://ceoas.oregonstate.edu/directory/svetlana-erofeeva
That links to this website which has a similar animation for the current day: https://www.tpxo.net/
I took a graduate level physical oceanography course and never learned this and still believed the tidal bulge story.
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!
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.
If the bulges were caused by water being attracted to the moon, there should not be a "far bulge"?
So how was the existence of a far bulge justified?
It's not justified for any rigorous setting at all.
In a layperson setting, it's as justified as saying the speed of light slows down in non-vacuum. It doesn't, but it's a close enough explanation for most people most of the time, and if you squint it's sort of saying the right thing, but missing all of the details. In the same way as the observed speed of light is slower in air, the tides happen every 12 hours. But c doesn't change and there aren't two bulges.
It 100% does not, every single photon is moving at the full c speed of light at all times. It's not even that the photons are bouncing around and so they, on average do not make progress as fast. I believe it's a factor of how the moving EM field of the photon nudges particles like electrons a little, whose now moving field results in a lower net wave phase velocity such that observed propagation time is < c, but every photon still moves at exactly c.
The Moon's gravity isn't just pulling on the water, it's pulling on the Earth as a whole. It's pulling more on the Earth as a whole than on the water on the far side. In the Earth's frame of reference, that looks like it is pushing the water on the far side away a little bit.
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.
Well, a single all encompassing deep ocean of something in which waves could travel 1600 km/h, since that's one of the major constraints, too.
So it appears that the answer is that the bulges are a forcing function, not a displacement.
Am I the only one skeptical that Newton would confuse a force with a displacement? What am I missing?
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.
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.
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/
> Your clock was off. Tides advance ~30 minutes per day.
“roughly 12 hours”
Thank you. I still feel the stackexchange post misses the forest for the trees (and weeds). Take a look at the NOAA global map showing coasts that have semidiurnal tides (that is, one in roughly ~12 hours) [1].
Most all of the coast of Africa is semidiurnal. So is east coast of North America, a lot of South America. Bay of Bengal, a lot of Europe. If you see the map on the RWU [2] site it shows Greenland and the north coast of Russia (although stretched due to the latitude) are also semidiurnal. This is a major part of the global coastline. The simple mental model explains this. I feel that going to partial differential equations, fourier series, etc. etc. is a little too complicated.
[1] https://oceanservice.noaa.gov/education/tutorial_tides/tides... [2] https://rwu.pressbooks.pub/webboceanography/chapter/11-3-tid... -
Wind can have a large effect the Chesapeake Bay's tides during large wind events in the atalanitc can effect water levels by feet.
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).
In the animations, New Zealand stood out: the high and low tide chase each other counterclockwise around the islands!
earth is 3D not 2D ;) "bulges" same. that is where confusion comes from. also tesseract is nonsense.
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.
Try to get your head around this while simultaneously not thinking of gravity as a force but curvature in spacetime.
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.
No, don't! Use the simplest model that applies in your context!
I agree, I meant to add "as a mind bending exercise to realize how complex nature is!"
Its all models in the end. Half of physics is just putting things in the easiest frame or model to solve the problem you want to solve. And the other half is often simplifying things down to the proverbial spherical cow in a vacuum.
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.
So it appears that the answer is that the bulges are a forcing function, not a displacement.
Am I the only one skeptical that Newton would confuse a force with a displacement?
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.
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.
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.
I think of it not as Newton was wrong, but rather his explanation was incomplete.
So, yet another thing I learned at school was bullshit. Pretty interesting to know!
What are the others?
The Bernoulli principle is one.
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.
Bernoulli apparently caused some serious problems during peak shipping on the Thames. Big boats navigating in opposite directions having to work not to bump into each other.
Turns out teachers are people and general understanding evolves over time and not all at once.
Who would have guessed. Well, Laplace maybe.
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> High-strung, antisocial, egotistical, domineering, rage-filled.
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.
> 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.
This reads like you think no one with bipolar can live without ruining the people around them.
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.
And to top it all off, that dang apple hit him on the head
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
My favorite:
Nature and Nature's laws lay hid in night:
God said, Let Newton be!
And all was light.
-- Alexander Pope
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.
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).
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.
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).