All of Earth's water in a single sphere (2019)(usgs.gov)
usgs.gov
All of Earth's water in a single sphere (2019)
https://www.usgs.gov/media/images/all-earths-water-a-single-sphere
289 comments
> More recent research, from about 2017, suggests that there's about as much water in Earth's mantle as in all the oceans, so we either need another drop roughly the size of the first, or the second drop should be greatly expanded.
Specifically: given that the volume of a sphere is 4/3πR^3, doubling the volume is equivalent to increasing the radius by ~26%.
Specifically: given that the volume of a sphere is 4/3πR^3, doubling the volume is equivalent to increasing the radius by ~26%.
Good call, I've swapped "size" for "volume" to be clearer.
> The water discovered in the mantle is not in a form familiar to us – it is not liquid, ice, or vapor. Instead, it is trapped inside the molecular structure of the minerals in the mantle rock.
IMHO this is not a productive comparison. Hydrogen and oxygen ions inside minerals in rock is far too much of a stretch of imagination to call as water.
https://www.earth.com/news/ringwoodite-mineral-confirms-vast...
IMHO this is not a productive comparison. Hydrogen and oxygen ions inside minerals in rock is far too much of a stretch of imagination to call as water.
https://www.earth.com/news/ringwoodite-mineral-confirms-vast...
I don't think it's "hydrogen and oxygen ions"; that doesn't really meet the definition of water. I'd assume it's more like ebsom salts, where H2O is a part of the crystalline structure of the chemical compound. If you heat up epsom salts enough then the bonds are broken and steam is released.
> Hydrogen and oxygen ions inside minerals in rock is far too much of a stretch of imagination to call as water.
Agreed and to follow that thread to the end: We can't impact that water in a meaningful way.
We can't pollute it in dozens of ecosystem-altering ways.
We can't alter it's ability to host systems that sustain life.
We can't bulk-melt the frozen part & in turn alter the salinity + elevation of a liquid part.
We can't pump dry the parts that we desperately need to remain where they are.
Agreed and to follow that thread to the end: We can't impact that water in a meaningful way.
We can't pollute it in dozens of ecosystem-altering ways.
We can't alter it's ability to host systems that sustain life.
We can't bulk-melt the frozen part & in turn alter the salinity + elevation of a liquid part.
We can't pump dry the parts that we desperately need to remain where they are.
Are you sure we can’t do any of these things, or are you just not thinking big enough? Give me a couple million dollars of VC money and I bet I could have an MVP that could conceivably accomplish at least one of these. I’d obviously need to raise another round of funds to find a market for such a product before taking the necessary steps to fit my product into that particular market (after raising more funds again, obviously). This hypothetical startup could be a net benefit to investors and shareholders by 2035, and a net detriment to all others by 2028. “Disruptive” is an understatement for what we could do for the environment and society.
If you had the means to reach the mantle economically, there are a lot of other uses you'd be put to first. Magma geothermal comes to mind.
When I see these infographics I think of non-technical audiences like policy makers and politicians consuming the same information, and I avoid making these fine distinctions. In this case, I would not mention the water in the mantle at all.
In a separate, private graphic, I’d show the available water next to the number of 1 GW reactors, the pile of annual uranium mining output to feed those reactors, and annual calendars it would take to assemble all that to extract the water and dispose of the waste in a way that won’t harm our ecosystem further to express, “if you want this water in a form you colloquially understand, the species possibly can’t afford it”. In case some wise ass decides to bring up that mantle water. But that additional detail would even help technically inclined audiences reading the infographic.
In a separate, private graphic, I’d show the available water next to the number of 1 GW reactors, the pile of annual uranium mining output to feed those reactors, and annual calendars it would take to assemble all that to extract the water and dispose of the waste in a way that won’t harm our ecosystem further to express, “if you want this water in a form you colloquially understand, the species possibly can’t afford it”. In case some wise ass decides to bring up that mantle water. But that additional detail would even help technically inclined audiences reading the infographic.
Does any of that water, though, ever make it onto the Earth's surface? I'm guessing not, or only miniscule amounts over geologic time through volcanism.
For all intents and purposes, I think only counting "surface" water is more useful and intuitive. It's essentially any water that can participate in the hydrologic cycle on Earth, and that water locked beneath the crust doesn't really "matter" for what I think the intended purpose of this graphic is.
For all intents and purposes, I think only counting "surface" water is more useful and intuitive. It's essentially any water that can participate in the hydrologic cycle on Earth, and that water locked beneath the crust doesn't really "matter" for what I think the intended purpose of this graphic is.
The fundamental problem with complex phenomena is in defining the domain(s) of interest.
If we want to talk about the total amount of H2O around, on, or in the Earth then inclusion makes sense.
If we want to talk about water interacting with the surface environment (atmospheric, sea, ice cap, fresh, and subsurface aquifers and tectonic water), then splitting those into distinct categories probably also makes sense. In which case we can also show the subsurface water.
How much mantle water does make it to the surface over time is a good question. I've no idea though I'd suspect that some does through geothermal and tectonic activity. The more interesting question might be how we'd determine this (all but certainly through isotopic composition), and if a net flux could be determined.
Over geological time, additional reservoirs of water are significant simply because surface water boils off into space over time, with estimates I've seen of up to 25% of Earth's original allotment having done so over 4.5 billion years or so. As the Sun eventually grows warmer, this rate will increase. At the same time, tectonic activity will slow.
Note that there's a fair bit of water transport through the lower crust / upper mantle as oceanic plates subduct under continental plates, with the water absorbed into the oceanic plates playing a major role in volcanism at those plate boundaries, e.g., along the "Rim of Fire" surrounding the Pacific basin.
If we want to talk about the total amount of H2O around, on, or in the Earth then inclusion makes sense.
If we want to talk about water interacting with the surface environment (atmospheric, sea, ice cap, fresh, and subsurface aquifers and tectonic water), then splitting those into distinct categories probably also makes sense. In which case we can also show the subsurface water.
How much mantle water does make it to the surface over time is a good question. I've no idea though I'd suspect that some does through geothermal and tectonic activity. The more interesting question might be how we'd determine this (all but certainly through isotopic composition), and if a net flux could be determined.
Over geological time, additional reservoirs of water are significant simply because surface water boils off into space over time, with estimates I've seen of up to 25% of Earth's original allotment having done so over 4.5 billion years or so. As the Sun eventually grows warmer, this rate will increase. At the same time, tectonic activity will slow.
Note that there's a fair bit of water transport through the lower crust / upper mantle as oceanic plates subduct under continental plates, with the water absorbed into the oceanic plates playing a major role in volcanism at those plate boundaries, e.g., along the "Rim of Fire" surrounding the Pacific basin.
Earth is lucky to have a strong magnetic field and ozone layer limiting the loss of hydrogen to the solar wind. Mars, for example, has lost much more of its allotment.
The article has a strong focus on "available to humans" and "that humans depend on". Many of the water beneath the crust is exactly that, pumping it up is an important source of drinking water. (In my country, the Netherlands, it's the primary, almost only, source of drinking water)
The Netherlands doesn't pump water from beneath the crust! Groundwater is included in the larger freshwater sphere. Water in the mantle would be an additional sphere (not sure if it's freshwater or saltwater).
TIL. I did not get that that from the article. Thanks for correcting me.
I simply presumed that water that's pumped from layers 100m or lower below the surface, water that's sometimes 10.000 years "old", wasn't surface water. But it makes sense to lump it in there too.
I simply presumed that water that's pumped from layers 100m or lower below the surface, water that's sometimes 10.000 years "old", wasn't surface water. But it makes sense to lump it in there too.
The crust is about 40km thick. The deepest anyone has ever dug is ~12km[0]. It is quite weird to think we live on this crust which has a gigantic mass inside that we can't get to.
[0] https://en.wikipedia.org/wiki/Kola_Superdeep_Borehole
[0] https://en.wikipedia.org/wiki/Kola_Superdeep_Borehole
If you think that's weird, you'll love this. Go look at another human. There's a skeleton in there!
An interesting point, perhaps it's just me, but my initial reaction to this was that, for purposes of comparison, the volume of "usable" or maybe inhabitable land be measured instead, as opposed to the volume of the entire planet including mantle, core, etc. this graphic seems very prone to misinterpretation and usage as a memetic weapon against globalization, as it is.
It's similarly misleading to color coding a map of a nation's or a region's land area to show how the people who occupy various parts of that land area voted in an election. The graphic representation tells a story about the land that deceptively implies facts about the people that are not true.
I completely agree with you. Let's add to the fact that volume, being three-dimensional, is being represented on two dimensions (graphics on a computer screen), which might cause some loss of perspective, fundamental for comparison. Perhaps a better way to represent it would have been the volume of inhabitable land (as you suggest) vs the volume of available water but extrapolated to two dimensions?
It does separate liquid fresh water from surface lakes and rivers which makes me believe the middle ball includes reasonably accessible ground water.
My read is that the two smaller spheres are non-exclusive, and that the smallest is included in the 2nd.
The breakout is for comparison: surface freshwater (total) and surface freshwater (lakes and rivers) relatively.
The breakout is for comparison: surface freshwater (total) and surface freshwater (lakes and rivers) relatively.
Yes they're pretty clearly subsets of each other. There's a better graphic on this page: https://www.usgs.gov/special-topics/water-science-school/sci...
Direct link: https://d9-wret.s3.us-west-2.amazonaws.com/assets/palladium/...
That one actually has percentages on the subsets too for interesting differences like glacier and icecap volume vs ground water (which I think still excludes the kind of deep mantle water mentioned up thread because it's not usably extractable).
That one actually has percentages on the subsets too for interesting differences like glacier and icecap volume vs ground water (which I think still excludes the kind of deep mantle water mentioned up thread because it's not usably extractable).
PFAS have reportedly contaminated water everywhere on Earth including the water in springs, confined aquifers, and even the rain that falls.
Is the water pumped from beneath the crust in the Netherlands poisoned too or have you guys got the last of the good stuff?
Is the water pumped from beneath the crust in the Netherlands poisoned too or have you guys got the last of the good stuff?
We don't have access to any part of the planet below a depth of 2.5 miles, so the image should compare the volume of accessible water to the volume of accessible Earth, except then it would fail in its dishonest mission to make people say "gosh that sphere looks relatively small compared to the other sphere, I must restrict myself to ten-second showers."
Even if it was accessible water to accessible non-water I don't really see how the metric is relevant in any decision making. Is it warning against a half-baked plan to mix water with every available cubic meter of soil or rock? Because there wouldn't be enough water to do that crazy thing? Thanks, I'll bear that in mind.
Even if it was accessible water to accessible non-water I don't really see how the metric is relevant in any decision making. Is it warning against a half-baked plan to mix water with every available cubic meter of soil or rock? Because there wouldn't be enough water to do that crazy thing? Thanks, I'll bear that in mind.
You seem really upset about what to me looks like a quite neutrally presented fact. There are lots of interesting aspects to this picture which don't have anything to do with criticizing you or the length of your morning shower.
>We don't have access to any part of the planet below a depth of 2.5 miles
Given how many miles I can travel over land or through the air, 2.5 miles _into_ the earth is amazingly shallow in similar ways to how the article already anticipated my amazement of how small the spheres of water were.
Given how many miles I can travel over land or through the air, 2.5 miles _into_ the earth is amazingly shallow in similar ways to how the article already anticipated my amazement of how small the spheres of water were.
It’s just an interesting infographic that is factually correct. You can disagree that the chosen facts are relatively the best ones, but, not everything has to have an agenda. Calling facts dishonest because they make you uncomfortable is what I consider yucky.
I think a neat follow-up image would be a sphere containing the top 2.5 miles of Earth’s crust for comparison to the water.
> or the second drop should be greatly expanded.
The second drop is called "liquid fresh water".
I'm not sure if I would want to categorize the water in the mantle as either "liquid" or "fresh". Most of that stuff is way above the critical point, not to mention saturated with rocky salts.
The second drop is called "liquid fresh water".
I'm not sure if I would want to categorize the water in the mantle as either "liquid" or "fresh". Most of that stuff is way above the critical point, not to mention saturated with rocky salts.
> second drop should be greatly expanded
Radius of said sphere would only increase by ∛2. ;)
Radius of said sphere would only increase by ∛2. ;)
Seems that Jules Verne (1867) in 'Journey to the Center of the Earth' was onto something when he invented his subterranean ocean.
I long assumed that the Earth is a "water planet" because water is mostly what you see from a distance. It wasn't until I did the math that I realized that is really about wet rocks in space vs dry rocks in space.
Earth isn't made of water, it's just a damp rock. Or a bowling ball that you squirted a dozen times with a spray bottle.
Earth isn't made of water, it's just a damp rock. Or a bowling ball that you squirted a dozen times with a spray bottle.
The ballpark math is easy to do in your head too. The diameter of Earth is 8,000 miles, and the deepest point in the ocean, the Mariana Trench, is only 7 miles deep. It's immediately apparent that the oceans are tiny by comparison to the rest of the mass that is Earth.
Neil DeGrasse Tyson says the earth scaled down to the size of a billiard ball would be smoother than any billiard ball ever made.
This was analyzed and the results were mixed...
https://billiards.colostate.edu/bd_articles/2013/june13.pdf
>So, based on the data, just how smooth is a CB? And how does this smoothness compare to the surface of the Earth? The highest point on earth is Mount Everest, which is about 29,000 feet above sea level; and the lowest point (in the earth’s crust) is Mariana’s Trench, which is about 36,000 feet below sea level. The larger number (36,000 feet) corresponds to about 1700 parts per million (0.17%) as compared to the average radius of the Earth (about 4000 miles). The largest peak or trench for all of the balls I tested was about 3 microns (for the Elephant Practice Ball). This corresponds to about 100 parts per million (0.01%) as compared to the radius of a pool ball (1 1/8 inch). Therefore, it would appear that a pool ball (even the worst one tested) is much smoother than the Earth would be if it were shrunk down to the size of a pool ball. However, the Earth is actually much smoother than the numbers imply over most of its surface. A 1x1 millimeter area on a pool ball (the physical size of the images) corresponds to about a 140x140 mile area on the Earth. Such a small area certainly doesn’t include things like Mount Everest and Mariana’s Trench in the same locale. And in many places, especially places like Louisiana, where I grew up, the Earth’s surface is very flat and smooth over this area size. Therefore, much of the Earth’s surface would be much smoother than a pool ball if it were shrunk down to the same size.
https://billiards.colostate.edu/bd_articles/2013/june13.pdf
>So, based on the data, just how smooth is a CB? And how does this smoothness compare to the surface of the Earth? The highest point on earth is Mount Everest, which is about 29,000 feet above sea level; and the lowest point (in the earth’s crust) is Mariana’s Trench, which is about 36,000 feet below sea level. The larger number (36,000 feet) corresponds to about 1700 parts per million (0.17%) as compared to the average radius of the Earth (about 4000 miles). The largest peak or trench for all of the balls I tested was about 3 microns (for the Elephant Practice Ball). This corresponds to about 100 parts per million (0.01%) as compared to the radius of a pool ball (1 1/8 inch). Therefore, it would appear that a pool ball (even the worst one tested) is much smoother than the Earth would be if it were shrunk down to the size of a pool ball. However, the Earth is actually much smoother than the numbers imply over most of its surface. A 1x1 millimeter area on a pool ball (the physical size of the images) corresponds to about a 140x140 mile area on the Earth. Such a small area certainly doesn’t include things like Mount Everest and Mariana’s Trench in the same locale. And in many places, especially places like Louisiana, where I grew up, the Earth’s surface is very flat and smooth over this area size. Therefore, much of the Earth’s surface would be much smoother than a pool ball if it were shrunk down to the same size.
Not completely accurate, it depends on your definition of smoothness. The Earth scaled down to the size of a billiard ball would have a texture more like sandpaper, certainly not what most people would consider smooth.
Sandpaper also come in different roughness. So in this case maybe a 300-400 grit sandpaper?
[deleted]
An interesting exercise is to do this exact same calculation with the atmosphere.
It's fun to scale down the Earth's depth to a 8 metre long measuring tape on the floor and then having kids guess things lik, how deep is the ocean, how deep is the deepest hole we've ever dug, how high is the atmosphere.
Adding in how far of a drive is it to X place or how far of a walk is it, is also fun.
Adding in how far of a drive is it to X place or how far of a walk is it, is also fun.
"Squirt with a spray bottle" is a nice euphemism for throwing asteroids at.
https://en.wikipedia.org/wiki/Origin_of_water_on_Earth#Aster...
https://en.wikipedia.org/wiki/Origin_of_water_on_Earth#Aster...
They mean in terms of the ratio of water to rock.
Well, the spray bottle was more to spread the water out into a thin layer as opposed to something like crashing an icy asteroid in at one spot.
I have a mental image of a gigantic cosmic being grabbing the Earth, wiping off the wet stuff with a rag, and bowling it at Proxima Centauri.
I have a mental image of a gigantic cosmic being grabbing the Earth, wiping off the wet stuff with a rag, and bowling it at Proxima Centauri.
Reminds me of the ending of Men In Black (1997).
There are moons out there that are more like giant snowballs - so much water that it dwarfs even our reserves.
There was an old sci-fi trope that the reason aliens attack earth is to get at our water.
The problem with that was, 1. there are better sources of water (the oort cloud) and 2. they aren't stuck in an gravity well.
The problem with that was, 1. there are better sources of water (the oort cloud) and 2. they aren't stuck in an gravity well.
Earth isn't even really a "rock", it's mostly a ball of iron.
It's a ball of iron covered with rocks (i.e. metal oxides) cover with water (i.e. hydrogen oxide).
It's a ball of iron covered with rocks (i.e. metal oxides) cover with water (i.e. hydrogen oxide).
I don't buy it. Even allowing counting iron as separate from what rocks can be composed of (and using mass instead of volume) you still have 30.1%+15.1%=45.2% of the Earth as oxygen and silicon (which are most certainly part of what makes a rock) at which point you've already disproved the claim Earth is more a ball of iron than a ball of rock.
A ball of iron covered with a ball of rocks is a more fair statement though, and I'd agree with that. It's just that center ball isn't most of what makes up the Earth (by any measure).
A ball of iron covered with a ball of rocks is a more fair statement though, and I'd agree with that. It's just that center ball isn't most of what makes up the Earth (by any measure).
https://s3-us-west-2.amazonaws.com/courses-images-archive-re...
Everything up to and including the mantle is either iron or has a lot of iron. But to your point the mantle also has a lot of silica. So I guess it depends on your definition of "mostly".
Everything up to and including the mantle is either iron or has a lot of iron. But to your point the mantle also has a lot of silica. So I guess it depends on your definition of "mostly".
Mass is the defining characteristic of a quantity of matter. Given that much of the iron is under far higher compression than the outer layers of silicate rock, this also advantages iron.
By mass, iron (32.1%) is still a minority constituent of the Earth.
<https://en.wikipedia.org/wiki/Abundance_of_the_chemical_elem...>
By mass, iron (32.1%) is still a minority constituent of the Earth.
<https://en.wikipedia.org/wiki/Abundance_of_the_chemical_elem...>
Closer to a bowling ball that picked up a drop of beer from your hands.
This didn't sound right, so I did the math.
The volume of all water is 1,386,000,000 km^3, which is then 1.386e+21 liters, or right about the same number of kilograms.
The mass of Earth is about 5.972e+24 kg. So the percent fraction by mass is 0.0232%.
A "drop" is typically estimated at 1/20th of one mL, which is then 0.05 grams. We can estimate the mass of a small-ish bowling ball at 5kg, or 5000 grams. 0.05 / 5000 * 100 = 0.001%.
So it's an order of magnitude shy, but that's still closer than I expected! It's about 1 ml of beer on a bowling ball - a small splash. Or maybe a very large drop.
The volume of all water is 1,386,000,000 km^3, which is then 1.386e+21 liters, or right about the same number of kilograms.
The mass of Earth is about 5.972e+24 kg. So the percent fraction by mass is 0.0232%.
A "drop" is typically estimated at 1/20th of one mL, which is then 0.05 grams. We can estimate the mass of a small-ish bowling ball at 5kg, or 5000 grams. 0.05 / 5000 * 100 = 0.001%.
So it's an order of magnitude shy, but that's still closer than I expected! It's about 1 ml of beer on a bowling ball - a small splash. Or maybe a very large drop.
You'd have to use the volume of earth, not the mass. Google tells me that lava is ~3x denser than water.
Lava is not really representative of the Earth as a whole, as it turns out. The mantle (which is the vast majority of Earth's volume) isn't a liquid, it's a squishy deformable solid. Magma that comes from the mantle is only liquid because of the removal of pressure or the addition of water; it wasn't liquid down there. And a lot of lava comes from crustal melting, not mantle material.
Earth as a whole has a density about 5.5x that of water.
Earth as a whole has a density about 5.5x that of water.
Thanks. This really put it in perspective for me better than the image or other analogies!
The picture already answers this question. If the earth was a bowling ball the blue sphere would be much bigger than a single drop, maybe slightly bigger than a popping boba, the size of a small grape?
The sphere of water would have a surface gravity of 0.016 g, 1.6% of Earth's gravity, 1/10th of the Moon's gravity.
Alas, the atmosphere it could hold would be insufficient to avoid it all vaporizing.
A dash.
It is quite incredible that there is just enough water for a continuous ocean and also dry land, not either just a couple ponds or a waterworld.
Oceanus's ocean tosses with slow, tall waves, beneath a pale blue sky. The colonists live in tall cities of steel and concrete with buildings sealed against the planet's harsh environment, on platforms floating on the planet-wide ocean. They spend their time pursuing art, leisure, and spiritual fulfilment, while automatic machines take care of their material needs.
> I long assumed
Understandably, since, in this case, surface area is more intuitively captured by our brains than volume.
Also because we are very small. The amount of water, from our perspective, makes it look like a water planet.
Understandably, since, in this case, surface area is more intuitively captured by our brains than volume.
Also because we are very small. The amount of water, from our perspective, makes it look like a water planet.
rock that moves and is hot inside so a magnetic fields generates from its motion and protect us from the sun particles
Mars is the same, right? Just the water is locked 20 - 200km beneath the surface from recent discoveries.
This water is locked away in the form of ice
> Earth isn't made of water, it's just a damp rock. Or a bowling ball that you squirted a dozen times with a spray bottle.
Yeah, the image with the oceans being dry is wow-inducing... On further thought, of course it'd be very close a sphere, because gravity forces it to be. A sphere where e.g. a slice of it is water (imagine a clementine with one of its segments being water) would be very wobbly if even possible at all..
Yeah, the image with the oceans being dry is wow-inducing... On further thought, of course it'd be very close a sphere, because gravity forces it to be. A sphere where e.g. a slice of it is water (imagine a clementine with one of its segments being water) would be very wobbly if even possible at all..
Yup, the mere fact that we can have oceans and continents on a planet means we can only have so much water, lest we become a water world or something more like mars.
I do wonder if the OP includes water locked away in rocks though, to my understanding the majority of the water is in the mantle and not even the oceans, but my source is my butt for that one
I do wonder if the OP includes water locked away in rocks though, to my understanding the majority of the water is in the mantle and not even the oceans, but my source is my butt for that one
> damp rock
lol it's funny when you put it that way
lol it's funny when you put it that way
I don't really follow a lot of comments questioning the choice of shape, methodology, exclusion of water in the mantle etc.
I believe the purpose of the image is to evoke sense of preciousness and responsibility towards the water we have - maybe how much for granted we take our "blue planet".
To me, this is an amazingly effective and visually poignant way of doing just that.
I believe the purpose of the image is to evoke sense of preciousness and responsibility towards the water we have - maybe how much for granted we take our "blue planet".
To me, this is an amazingly effective and visually poignant way of doing just that.
> This sphere includes all of the water in the oceans, ice caps, lakes, rivers, groundwater, atmospheric water, and even the water in you, your dog, and your tomato plant.
Does it include water in the mantle? (https://www.bnl.gov/newsroom/news.php?a=111648)
or other non-liquid water for that matter like hydrates (ebsom salts, etc)
Does it include water in the mantle? (https://www.bnl.gov/newsroom/news.php?a=111648)
or other non-liquid water for that matter like hydrates (ebsom salts, etc)
Given that the quantity of water in the mantle is thought to be equivalent to that in all the oceans (large drop), I'd presume not.
The mantle-water research is fairly new, with this report from 2017:
"There’s as much water in Earth’s mantle as in all the oceans"
<https://www.newscientist.com/article/2133963-theres-as-much-...>
The USGS detail pages are based on a 1993 publication, Igor Shiklomanov's chapter "World fresh water resources" in Peter H. Gleick (editor), Water in Crisis: A Guide to the World's Fresh Water Resources (Oxford University Press, New York).
<https://www.usgs.gov/special-topics/water-science-school/sci...> and <https://www.usgs.gov/special-topics/water-science-school/sci...>
The mantle-water research is fairly new, with this report from 2017:
"There’s as much water in Earth’s mantle as in all the oceans"
<https://www.newscientist.com/article/2133963-theres-as-much-...>
The USGS detail pages are based on a 1993 publication, Igor Shiklomanov's chapter "World fresh water resources" in Peter H. Gleick (editor), Water in Crisis: A Guide to the World's Fresh Water Resources (Oxford University Press, New York).
<https://www.usgs.gov/special-topics/water-science-school/sci...> and <https://www.usgs.gov/special-topics/water-science-school/sci...>
Yep, it's quite misleading since the region where they looked for water at all is an incredibly thin layer on the outside of the planet, but they show it all as if it applied to all of the volume.
There’s nothing wrong with their representation. You’re describing a different comparison.
It's not bad on purpose if that what you understood.
But the comments here are full of "it's so little!" variants, where if you took the rest of the Crust and smashed as a sphere, it wouldn't be much larger than the water one.
It did evidently mislead a large number of people.
But the comments here are full of "it's so little!" variants, where if you took the rest of the Crust and smashed as a sphere, it wouldn't be much larger than the water one.
It did evidently mislead a large number of people.
No, it doesn't. It includes all of the water in the oceans, ice caps, lakes, rivers, groundwater, atmospheric water, and even the water in you, your dog, and your tomato plant.
"Groundwater" is a little ambiguous - H2O in the mantle is also "ground water", no?
No, that "water" is actually hydroxyl groups in minerals.
No it comes out of the tap as water.
No tap water comes from the mantle.
That's water going into the mantle.
No, it’s completely inaccessible. Unless you are just playing word games, then sure.
Geologically it probably isn’t. If all surface oceans disappeared, some of that water would likely come out to the surface and form new bodies of water, over millions of years.
It's not. The mantle is hundreds of kilometers further down.
Same question I've got, but I imagine USGS is only considering reachable surface, atmospheric water.
The sphere for all liquid water seems to be close in size to the asteroid Ceres.
https://lightsinthedark.com/wp-content/uploads/2013/06/ceres...
https://lightsinthedark.com/wp-content/uploads/2013/06/ceres...
But would this sphere of water have enough mass to hold itself together as a sphere in space? Put aside it freezing into a ball of ice as a thought exercise.
The freezing-into-a-ball-of-ice is relevant here. A body that small can't hold on to water vapor at anything a human would consider a reasonable temperature; the average velocity of light gases at human-sane temperatures is high enough to overcome their escape velocity. See [1] for a log-log plot of what gases a body can hold onto - even Mars, which is much larger and denser than a Ceres-sized ball of water, has lost most of its water (although other factors like the solar wind are contributors there).
A cold enough body, though, has a low enough vapor pressure that this isn't relevant even over cosmological timescales. That's why Europa can can have a stable icy surface. It's far enough from the Sun (and has a low enough albedo) that it's very very cold (about 100K), and at that temperature ice doesn't sublimate very much.
TLDR: a Ceres-sized ball of water could hold itself together, but only as long as it stayed water. But it wouldn't be able to. Either it'd be cold enough to freeze over at the surface, or hot enough to evaporate into vapor that would escape.
[1] https://en.wikipedia.org/wiki/Atmosphere#/media/File:Solar_s...
A cold enough body, though, has a low enough vapor pressure that this isn't relevant even over cosmological timescales. That's why Europa can can have a stable icy surface. It's far enough from the Sun (and has a low enough albedo) that it's very very cold (about 100K), and at that temperature ice doesn't sublimate very much.
TLDR: a Ceres-sized ball of water could hold itself together, but only as long as it stayed water. But it wouldn't be able to. Either it'd be cold enough to freeze over at the surface, or hot enough to evaporate into vapor that would escape.
[1] https://en.wikipedia.org/wiki/Atmosphere#/media/File:Solar_s...
Given that water gets lighter when cooling down right above its fusion temperature, and that ice is a pretty good insulator. You'd have liquid water below an ice crust for a lot of time. It would eventually freeze entirely and be slowly eaten by the Sun's radiations. But that would take a pretty long time (well on a human scale).
Yeah, that's why I specified freeze over and not freeze through, although without doing the math I'm pretty sure it'd still freeze through on solar system timescales without radioactive (as in Earth's own mantle's case) or tidal (Enceladus, Europa, possibly Triton and Ganymede) heating.
Indeed, it will slowly freeze though and evaporate at the same time.
Freezing? Wouldn't it boil instead due to the low pressure?
Depends on the temperature. At Earth-like temperatures, yes, it would. The transition between the two is around 175 K, give or take; below about 150 K ice is quite stable in a vacuum even over astronomical timescales; above 200 K it sublimates rapidly. (Surface liquid water is never stable in a vacuum or thin atmosphere regardless.)
The rate of evaporation ramps up exponentially, from ~irrelevant at the bottom of that range to fast at the top. (For a body of this size, any resulting vapor would be quickly lost at these temperatures, so the rate of evaporation is effectively the rate of water loss as well.)
This is why Jupiter can have icy moons (temperature ~100 K), but ice sublimates quickly on Mars (~200 K).
The rate of evaporation ramps up exponentially, from ~irrelevant at the bottom of that range to fast at the top. (For a body of this size, any resulting vapor would be quickly lost at these temperatures, so the rate of evaporation is effectively the rate of water loss as well.)
This is why Jupiter can have icy moons (temperature ~100 K), but ice sublimates quickly on Mars (~200 K).
Going from a liquid to a gas takes energy, which rapidly lowers the temperature of what remains. Net result most of the water freezes without some external energy source. Sublimation then lowers the temperature of the ice until near absolute zero, again unless there’s some external energy source.
i knew there would be someone to just try to get out of the answer by failing to just go with the spirit of the question by being pedantic. even my own attempt at dispel pedantry just allowed for even more pedantry.
I don't know what you wanted.
If you wanted to ask whether that amount can hold together and become spherical, then just by comparing to Ceres doesn't that make it plenty?
It's not crazy to interpret "hold itself together" as more complex and including vapor escape.
If you wanted to ask whether that amount can hold together and become spherical, then just by comparing to Ceres doesn't that make it plenty?
It's not crazy to interpret "hold itself together" as more complex and including vapor escape.
The sphere of water would have a surface gravity of 0.016 g, 1.6% of Earth's gravity, 1/10th of the Moon's gravity. So yes, it would gravitate into a ball shape, aside from slowly boiling off if it's inside the orbit of Mars (our 32°F Goldilocks Zone) or freezing if it's farther out.
The wording of the legend description says all the war in, on and above the earth so we have to assume that is does take it into account.
Sources say otherwise, see my immediate prior comment.
Water dissolving and removing
There is water at the bottom of the ocean
Largest ocean in our solar system isn't even on Earth, apparently:
> ... Ganymede’s ocean is even bigger than Europa’s—and might be the largest in the entire solar system. “The Ganymede ocean is believed to contain more water than the Europan one,” he says. “Six times more water in Ganymede’s ocean than in Earth's ocean, and three times more than Europa.”
https://www.scientificamerican.com/article/overlooked-ocean-...
> ... Ganymede’s ocean is even bigger than Europa’s—and might be the largest in the entire solar system. “The Ganymede ocean is believed to contain more water than the Europan one,” he says. “Six times more water in Ganymede’s ocean than in Earth's ocean, and three times more than Europa.”
https://www.scientificamerican.com/article/overlooked-ocean-...
https://www.businessinsider.nl/earth-water-ice-volume-versus...
Ganymede vs. Earth is indeed very surprising!
Ganymede vs. Earth is indeed very surprising!
The largest ocean in the solar system actually is on Jupiter [1]. The gas planet has an absolute massive amount of liquid hydrogen on its "surface". But yeah, liquid hydrogen isn't water, so it might be the biggest ocean, but not the biggest ocean made out of water in our solar system :).
[1]: https://science.nasa.gov/jupiter/jupiter-facts/ (Under "Structure")
[1]: https://science.nasa.gov/jupiter/jupiter-facts/ (Under "Structure")
> Ganymede’s ocean is even bigger than Europa’s
Europa Clipper launches in October [1]. I've seen talk of crashing it into Ganymede to give JUICE novel data [2].
[1] https://en.wikipedia.org/wiki/Europa_Clipper
[2] https://www.space.com/europa-clipper-might-crash-into-ganyme...
Europa Clipper launches in October [1]. I've seen talk of crashing it into Ganymede to give JUICE novel data [2].
[1] https://en.wikipedia.org/wiki/Europa_Clipper
[2] https://www.space.com/europa-clipper-might-crash-into-ganyme...
We could probably terraform Mars if we crashed Europa into Mars.
It would make Mars warmer. It would melt all the ice and CO2. It would give Mars an ocean. Of liquid rock. This is assuming that it doesn't destroy Mars completely. There might be enough fragments to make Solar System dangerous place and destroy life on Earth.
Europa is the size of our Moon. Colliding it with Mars would be similar to the collision that formed our Moon.
Europa is the size of our Moon. Colliding it with Mars would be similar to the collision that formed our Moon.
But would it stay on Mars? I thought the issue was there was no dynamo in the core, which lets solar winds strip it away. How long would it stay?
At some point I saw a design for a machine you could park at the Lagrange point between Mars and the Sun that would collect solar power and spit out a magnetic field strong enough to deflect enough of the solar winds that we wouldn't need to worry about that.
There's probably a way to engineer it such that the spin of the planet is 24h, the core is spun up. We'd also like ~365 day years.
It would stay molten for millions of years.
Not sure if Europa's water would be flung into space, make atmosphere, or make a boiling ocean.
Not sure if Europa's water would be flung into space, make atmosphere, or make a boiling ocean.
And then we completely skew Mars's orbit until it crashes into the sun or is flung out of the solar system.
If we had the technology allowing us to move a full satellite through the solar system, we could probably do it in a way that would just make Mars a bit closer to the sun so that the weather gets nicer (sure, if it gets too close to earth it's going to mess up with both orbits, but we can as well correct it when it happens, right?)
It doesn't have to be near the sun to have heat or be warmed by the Sun. It is still currently in the goldilocks zone, same with Venus. The difference is how well each planet traps heat. No atmosphere no heat for mars, highest peak surface temperature is 70 fehrenheit or 20 celsius. Not much but enough green house gas and you could raise it by 20 degrees or more. Other thing to consider is that you don't need to move Mars, you could create artificial magnetospheres.
And then wait 160 million years for the planet to settle. I like your long term thinking.
Might have some "slight" orbital and shrapnel repercussions..
If we could crash Europa into Mars we'd have capability to terraform Mars in a more reasonable manner.
Ganymede having an ocean surprised me given that its surface appears rocky in photos. Apparently, it’s an internal ocean hidden under the surface.
If you could squeeze the Earth's atmosphere into a ball of similar density it would be more or less of size of the middle sphere (all the oceans only weigh 270 times as much as the atmosphere [1]).
So there you have it: the key ingredients all life depends on are but a tiny boundary layer of water and air, stretched thinly between solid rock and the hostile emptiness of outer space.
The grand challenge of our sustainability is, indeed, how much can we (humans) perturb this extraordinary complex boundary layer without inducing runaway dynamics that we (or rather, future generations of us) will not particularly like.
[1] https://www.sciencefocus.com/science/how-much-does-earths-at...
So there you have it: the key ingredients all life depends on are but a tiny boundary layer of water and air, stretched thinly between solid rock and the hostile emptiness of outer space.
The grand challenge of our sustainability is, indeed, how much can we (humans) perturb this extraordinary complex boundary layer without inducing runaway dynamics that we (or rather, future generations of us) will not particularly like.
[1] https://www.sciencefocus.com/science/how-much-does-earths-at...
Turn Randall Munroe loose on this idea and be prepared for unspeakable devastation as a tsunami of Lovecraftian proportions wreaks havoc on the planet...
Literally just posted today: the video version of his What If? analysis of what would happen if you took that ball of water and dropped it on Mars: https://www.youtube.com/watch?v=FkUNHhVbQ1Q
He already did it with a 1km diameter ball (https://what-if.xkcd.com/12/) and the destruction was terrifying. Please keep him away from these other bigger water balls.
It was just a friendly game of water balloons. We had no intent of destroying your planet.
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Just a few quick calculations to make it more relatable...
They say the smallest sphere of freshwater lakes and rivers amounts to 93,113 cu km. There are 1 bil cu m per cu km. With a global population of 8.2 bil people, that comes to 11,355 cu m per person. That's a 22.5 meter wide/deep/tall cube (or about 7 or 8 stories tall building).
If we use the sphere that includes groundwater, 10,633,450 cu km. Then we end up with 1,296,762 cu m or a 109m wide cube per person.
They say the smallest sphere of freshwater lakes and rivers amounts to 93,113 cu km. There are 1 bil cu m per cu km. With a global population of 8.2 bil people, that comes to 11,355 cu m per person. That's a 22.5 meter wide/deep/tall cube (or about 7 or 8 stories tall building).
If we use the sphere that includes groundwater, 10,633,450 cu km. Then we end up with 1,296,762 cu m or a 109m wide cube per person.
I'm having trouble picturing a 22.5 meter cube. So consider a 200 sq m house; with ceilings of 2.5 m that's 500 cu m. So "your" water fills 22 houses.
Also.. the largest sphere has a radius of about 92 miles. It reaches to the edge of the atmosphere, and about 1/3 of the way to low earth orbit.
> The largest sphere represents all of Earth's water. Its diameter is about 860 miles
Should be a radius of 430 miles, no?
The image is very non-intuitive, IMO, because it's making the water appear so small compared to the entire planet (which, duh, obviously the water is only part of earth), but also drawing the planet that small really hides how friggin big the earth is!
Should be a radius of 430 miles, no?
The image is very non-intuitive, IMO, because it's making the water appear so small compared to the entire planet (which, duh, obviously the water is only part of earth), but also drawing the planet that small really hides how friggin big the earth is!
Helped for me to compare to the moon. The water sphere has less than half the radius of the moon (~1080 miles). Think that’s roughly 7-8% of the moon’s volume if it were a perfect sphere.
Yes. The fresh-water lakes and rivers sphere definitely does not look like it could fill the Great Lakes next to it. I am not saying it doesn't, I'm just saying it doesn't look like it could.
Average depth of Lake Michigan is around 300 feet. Longest dimension is about 300 miles. If you drew a map of Lake Michigan on a sheet of letter-sized paper, the paper would be thicker than the average depth of water.
It does look very small in comparison to say Lake Michigan but most lakes are very thin. Lake Michigan is about 500km by 200km but only .085km(85m) average depth.
I thought the border with space is generally (and arbitrarily) said to be the Kármán Line, at 100 km / 62.1 mi. I'm not nitpicking, just curious about other definitions.
Also, I thought LEO typically begins around 180 km / 112 mi.
Also, I thought LEO typically begins around 180 km / 112 mi.
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It's interesting to consider that there's about 26,000,000 km^3 of ice in the Antarctic ice sheet, which would give you a much larger ~150 m^3 cube of ice per person. That's not including the Greenland ice sheet or any sea ice.
I think it’s important to keep in mind that if you did this same visualization on a planet with ten times Earth’s radius, but the same ocean depth and water distribution, then the water blobs would seem even smaller in comparison to the planet.
I’m just not sure it’s a particularly useful illustration to compare the volume of water on a planet to that of the planet itself.
I’m just not sure it’s a particularly useful illustration to compare the volume of water on a planet to that of the planet itself.
Why is this confusing? We aren't comparing planets by amount of water they have. I thought the goal of this visualization was just to make a point - the amount of fresh water in rivers and lakes appears to be the size of a large metropolis in radius. Seems like a cool way to show scale of water resources
Well, let me put it this way: that apparently little fresh water sphere? If the ISS passed over that spot, it would hit that.
This is the point: everything on the surface of the Earth is essentially two dimensional at this scale. Seeing a sphere with a 400 km radius placed on the Earth doesn’t give any better intuitions for the scale of water resources than simply reading the number “35 quintillion liters”. If you think it’s given you a better intuition, you’ve been misled.
This is the point: everything on the surface of the Earth is essentially two dimensional at this scale. Seeing a sphere with a 400 km radius placed on the Earth doesn’t give any better intuitions for the scale of water resources than simply reading the number “35 quintillion liters”. If you think it’s given you a better intuition, you’ve been misled.
Yes good point. This infographic doesn't scale properly.
Sounds like the water moon from Iain M Banks "The Algebraist", quote:
"I was born on a water moon.
Some people, especially its inhabitants, called it a planet, but as it was only a little over two hundred kilometers in diameter 'moon' seems the more accurate term. The moon was made entirely of water, by which I mean it was a globe that not only had no land, but no rock either, a sphere with no solid core at all, just water, all the way down to the very center of the globe.
If it had been much bigger the moon would have had a core of ice, for water, though supposedly incompressible, is not entirely so, and will change under extremes of pressure to become ice. (If you are used to living on a planet where ice floats on the surface of water, this seems odd and even wrong, but nevertheless it is the case.) This moon was not quite of a size for an ice core to form, and therefore one could, if one was sufficiently hardy, and adequately proof against the water pressure, make one's way down, through the increasing weight of water above, to the very center of the moon.
Where a strange thing happened.
For here, at the very center of this watery globe, there seemed to be no gravity. There was colossal pressure, certainly, pressing in from every side, but one was in effect weightless (on the outside of a planet, moon, or other body, watery or not, one is always being pulled towards its center; once at its center one is being pulled equally in all directions), and indeed the pressure around one was, for the same reason, not quite as great as one might have expected it to be, given the mass of the water that the moon was made up from."
"I was born on a water moon.
Some people, especially its inhabitants, called it a planet, but as it was only a little over two hundred kilometers in diameter 'moon' seems the more accurate term. The moon was made entirely of water, by which I mean it was a globe that not only had no land, but no rock either, a sphere with no solid core at all, just water, all the way down to the very center of the globe.
If it had been much bigger the moon would have had a core of ice, for water, though supposedly incompressible, is not entirely so, and will change under extremes of pressure to become ice. (If you are used to living on a planet where ice floats on the surface of water, this seems odd and even wrong, but nevertheless it is the case.) This moon was not quite of a size for an ice core to form, and therefore one could, if one was sufficiently hardy, and adequately proof against the water pressure, make one's way down, through the increasing weight of water above, to the very center of the moon.
Where a strange thing happened.
For here, at the very center of this watery globe, there seemed to be no gravity. There was colossal pressure, certainly, pressing in from every side, but one was in effect weightless (on the outside of a planet, moon, or other body, watery or not, one is always being pulled towards its center; once at its center one is being pulled equally in all directions), and indeed the pressure around one was, for the same reason, not quite as great as one might have expected it to be, given the mass of the water that the moon was made up from."
I think this is kind of useless information unless presented with other spheres for humans, structures, animals, plants, forests etc. for comparison. And ants.
This was my first thought too.
I had no idea where to start. ChatGPT had a rather impressive looking “proof of work” that put all living humans into a 976m-diameter sphere, compared to the ~1384km-diameter sphere. Ie ~1km human sphere and 1,384km water sphere.
I had no idea where to start. ChatGPT had a rather impressive looking “proof of work” that put all living humans into a 976m-diameter sphere, compared to the ~1384km-diameter sphere. Ie ~1km human sphere and 1,384km water sphere.
Wolfram Alpha had "us" making a 966 m sphere.
https://www.wolframalpha.com/input?i=estimated+total+volume+...
Which has a link that gives us the radius.
https://www.wolframalpha.com/input?i=4.73%C3%9710%5E8+cubic+...
https://www.wolframalpha.com/input?i=estimated+total+volume+...
Which has a link that gives us the radius.
https://www.wolframalpha.com/input?i=4.73%C3%9710%5E8+cubic+...
And Olympic sized pools.
Fun fact: If you did this, everyone would die.
Plus every other nation on the earth would be mad at the US for taking it all
Outside of Hawaii and maybe Alaska, everywhere in the US would be devastated by the ensuing flood
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Except for the Dutch. https://what-if.xkcd.com/53/
It would be nice to see the "carbon" version of this infography. How much carbon is in the atmosphere as CO_2, in the biosphere as part of living stuff, and buried kilometers underground as gas and oil. Also, how much of that carbon we are pumping per year from underground to the atmosphere+biosphere system, and vice-versa.
Not sure this is accurate as we've discovered that water can reside deeper in the Earth than previously imagined and in addition to that the density of water at the surface is different than at the bottom of the ocean. I suppose they are also accounting for the salt being removed too. But my argument is probably in the margin of error so what do I know?
https://www.technology.org/how-and-why/what-would-happen-if-....
So I feel like the USGS is exagerated.
https://www.technology.org/how-and-why/what-would-happen-if-....
So I feel like the USGS is exagerated.
The density of water at the bottom of the ocean is actually quite similar to the density on the surface; it differs by only a few percent. Gases compress proportionally to pressure, but liquids act more similar to solids and compress very little even under enormous pressures.
The oceans are only about 3.5% salt by weight, so that doesn't make a huge difference, either.
The oceans are only about 3.5% salt by weight, so that doesn't make a huge difference, either.
I figured it would be within 5% margin.
I find this pretty interesting, https://phys.org/news/2023-11-reveal-earth-surface-penetrate...
I find this pretty interesting, https://phys.org/news/2023-11-reveal-earth-surface-penetrate...
This is similar to the idea that if you scaled the Earth to the size of a standard size 5 football and dried it off, you would barely be able to feel the mountains or trenches on the surface. The water is therefore a very thin film over the land in those terms.
The water spheres look small but here's a fun back-of-the-envelope computation. The article states there is 22.3k mi^3 of water in lakes and rivers. One person in the USA (a high consumer) consumes 82 gallons of water every day (source: epa.gov) which is 7.4E-11 mi^3. Let's say each person does this for a long-lived 100 years, giving 7.4E-9 mi^3 per lifetime. So the 22.3k mi^3 of lake and river water can support 3 trillion lifetimes. That's not including the much larger amounts of ground water and ocean water. Those "small spheres" are huge!
Can’t help but want to build that.
Apparently all the mined gold in the world would fit inside a 5 m diameter sphere.
Spheres are suspicious in hiding weight.
Apparently all the mined gold in the world would fit inside a 5 m diameter sphere.
Spheres are suspicious in hiding weight.
The World Gold Council says:
> If every single ounce of this gold were placed next to each other, the resulting cube of pure gold would only measure around 22 metres on each side
So that can't possibly be right, you must be off by a factor of 10 or so at least—Wolfram Alpha says a 30m diameter sphere.
> If every single ounce of this gold were placed next to each other, the resulting cube of pure gold would only measure around 22 metres on each side
So that can't possibly be right, you must be off by a factor of 10 or so at least—Wolfram Alpha says a 30m diameter sphere.
27 meter diameter in fact. A 27-meter sphere is about 150 times as voluminous as a 5-meter sphere.
It's still a mind bogglingly small amount considering that humans have spared no toil, sweat and blood on industrial scale gold mining ever since the dawn of written history - and since gold is so valuable and hard to destroy, most of it should still exist to this day in form or another.
Yet, if you smelted it all to a single object it would fit on a typical single family housing plot.
It's still a mind bogglingly small amount considering that humans have spared no toil, sweat and blood on industrial scale gold mining ever since the dawn of written history - and since gold is so valuable and hard to destroy, most of it should still exist to this day in form or another.
Yet, if you smelted it all to a single object it would fit on a typical single family housing plot.
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I've heard something like this before, but 5m is too small. The gold council reckons it's a little larger than that: https://www.gold.org/goldhub/data/how-much-gold
Spheres/circles are definitely surprising in how a seemingly small increase in radius changes the volume/area much more drastically. The cubing/squaring exponent is easily taken for granted.
I was curious how much of this water we lose to space via evaporation. Looking around, apparently not much; only few molecules achieve escape velocity. But can't find a good calculation yet.
Over the life of Earth to date, about a quarter of its initial water bounty:
<https://www.sciencenordic.com/chemistry-climate-denmark/the-...>
<https://www.sciencenordic.com/chemistry-climate-denmark/the-...>
Pertinent video that came out 4 hours ago:
https://www.youtube.com/watch?v=FkUNHhVbQ1Q
https://www.youtube.com/watch?v=FkUNHhVbQ1Q
Does this include the water in all human made stuff like pools, tanks, etc and also water present in all organisms? Or is that negligible?
From TFA: "This sphere includes all of the water in the oceans, ice caps, lakes, rivers, groundwater, atmospheric water, and even the water in you, your dog, and your tomato plant."
thank you, you're doing real work with comments like that
> This sphere includes all of the water in the oceans, ice caps, lakes, rivers, groundwater, atmospheric water, and even the water in you, your dog, and your tomato plant.
Reminds me of the short story 'Sea of Dreams'[1] by Liu Cixin. It's in one of his anthologies but I can't remember which one
https://www.goodreads.com/book/show/61305943-sea-of-dreams
https://www.goodreads.com/book/show/61305943-sea-of-dreams
Helps one understand why pollution is such an insidious problem.
"in a single sphere"---- shows three spheres
I would like to have a zoomed-in picture of that 'tiny' freshwater lakes and rivers to see its height. From this perspective, it doesn’t add up. Just above it, the Great Lakes look far bigger, not to mention other lakes and rivers in the world.
The Great Lakes span across hundreds of miles, but the deepest point is less than a quarter mile, and most of it is much shallower than that. I.e., it's a super thin film over that big surface area.
"Yes, Lake Michigan looks way bigger than this sphere, but you have to try to imagine a bubble almost 35 miles high—whereas the average depth of Lake Michigan is less than 300 feet (91 meters)"
When you look at the image you can't help but think how it would look like if a giant ball of water was dropped like this on the surface. Apart from the flood / water destroying / reshaping the surface of the entire continent, anyone has an idea how it would the impact look like?
I am probably way off, but I imagine solid ice sinking deep into the ground with water starting to turn into vapor in the upper layers and the vapor generated inside exploding out from the ball as it gradually shrinks and deforms.
I am probably way off, but I imagine solid ice sinking deep into the ground with water starting to turn into vapor in the upper layers and the vapor generated inside exploding out from the ball as it gradually shrinks and deforms.
IIR, the Earth's mantle is understood to contain several times the total water content of the oceans, glaciers, lakes, etc.
Obviously that water would be somewhat less accessible and quantifiable, but...
Anyone familiar with the current geoscience on this?
Obviously that water would be somewhat less accessible and quantifiable, but...
Anyone familiar with the current geoscience on this?
Pretty interesting juxtaposition considering water makes up about 71% of the Earth's surface, while the other 29% consists of continents and islands!
Well, spill a glass of water on your kitchen counter and you'll find it suddenly makes up a large percentage of the counter's surface as well!
I'm aware, notice my comment specifically states "the Earth's *surface* " not just "the Earth". However, my kitchen counter is a flat surface, it's common knowledge the Earth isn't flat and the average ocean depth is 3,682 meters
The earth is smoother than a billiard ball when accounting for relative size. Highly likely the earth is actually flatter than your countertop when accounting for size.
I don't believe that's actually true, I looked that up myself and it appears to be a mistaken calculation that many pop sci articles ran with.
That was my point. The Earth isn't flat, but its surface is very smooth.
You give the average ocean depth at 3.7km, but the Earth's diameter is about 12,742km, making those bumps pretty insignificant. If you cover your countertop in sandpaper and spill water on it, the difference in coverage going to be almost negligible.
You give the average ocean depth at 3.7km, but the Earth's diameter is about 12,742km, making those bumps pretty insignificant. If you cover your countertop in sandpaper and spill water on it, the difference in coverage going to be almost negligible.
Yea, just to be clear, I'm not disputing the image at all, my original comment is only an observation on the stark contrast when you juxtapose those two representations
I think that part of what is surprising is that our brains cannot comprehend the scale of earth so we see the photo as a model of earth and wonder how it's possible that so little water can spread throughout. At model scale, the water wouldn't spread all the way around the globe because of viscosity and surface tension.
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The volume of humans is approximately 500B liters [1] and this would make a sphere just under 1km in diameter.
[1] https://www.wolframalpha.com/input?i=volume+of+all+humans
[1] https://www.wolframalpha.com/input?i=volume+of+all+humans
Spheres could be a more viable unit of measurement instead of "Millions of Gallons".
Imagine the headline:
Imagine the headline:
500 million gallons of water expected to melt this year
1.2 microspheres of seawater expected to melt this yearAs an aside, the smallest ball is a few hours travel by bicycle, or two days on foot. Planet Earth is large, but it brought home how it is not so large. I would have guessed that 35 miles was a lot smaller than is shown.
We always talk about how scarce freshwater is but this image reprenstation has made it difficult to imagine how much supply do we have for an ever growing human population, the growing demand for water and how long will it last.
Does water leave earth when used?
It's more extreme than that, it stops existing.
The comment you're replying to is about fresh water. Which becomes non-fresh when it mixes into seawater or waste or pollution. No need to leave the Earth.
Admittedly, it's probably better to talk about the cycle, since non-freshwater will be automatically converted back to freshwater via solar energy. But the rate can be slowed—eg, dump a bunch of toxic stuff in one place, it'll drain to a river, now everything from that point and downstream is no longer freshwater. Or pump up enough groundwater. Or inject toxic crap down where the groundwater lives.
We're quite good at reducing the total amount of freshwater available.
The comment you're replying to is about fresh water. Which becomes non-fresh when it mixes into seawater or waste or pollution. No need to leave the Earth.
Admittedly, it's probably better to talk about the cycle, since non-freshwater will be automatically converted back to freshwater via solar energy. But the rate can be slowed—eg, dump a bunch of toxic stuff in one place, it'll drain to a river, now everything from that point and downstream is no longer freshwater. Or pump up enough groundwater. Or inject toxic crap down where the groundwater lives.
We're quite good at reducing the total amount of freshwater available.
Only tiny amounts
I think this may have borrowed liberally from Corridor Crew’s video about the same topic earlier in 2019: https://youtu.be/b3_Abb2Vqnc
Anyone remember that Voyager episode where they find this exact thing floating in space, held together by some kind of gravity generator? The plot was forgettable but the concept was super interesting.
What a coincidence, One hour before reading this article I was thinking of it! I was imagining that how the sphere will look like if made of oceans and seas' water. Now I got to know it :D
Anyone see this and think “holy crap we better scale up desalination?”
Ok I don't mean to be pedanntic but a sphere is just the boundary of a ball. If we are trying to capture volume we should be talking about balls of water.
Counter pedant: a ball is indeed what you get when, as in TFA, you put water “in a sphere”
I agree. It's a volume of water bounded by a sphere. I'm just being pedantic about the common use of the word in this thread.
I'm also somewhat surprised no one else was being pedantic about this. I expect better from HN :)
I'm also somewhat surprised no one else was being pedantic about this. I expect better from HN :)
Let's find a large ice comet and direct it towards Mars!
That's actually a lot bigger than I thought - The largest asteroid Ceres would be 1/3 the diameter of this water sphere (860mi)
That's a LOT of water.
That's a LOT of water.
So what we're saying is, if there was less water then I could have really big back yard. Things may get a little crispy though.
also related they now believe earth's water is older than the sun by finding a similar pattern around another star
https://www.independent.co.uk/news/science/earth-scientists-...
https://www.independent.co.uk/news/science/earth-scientists-...
This freaks me out, and I have no idea why...
The height of the sphere isn’t easy to visualize, should over lay height of water over Americas area
Assuming you mean "the depth of this water, if confined to a cross-sectional area the size of the United States", this is one of those nice Fermi estimation problems:
- I know the US contains hundreds of millions of people, and the world contains a single-digit number of billions. So the US has about 10% of the world's people.
- The US probably isn't particularly dense or sparse relative to other populated areas, so 1/10 the population should be 1/10 the Earth's land area.
- The Earth has twice as much ocean as land, and
- The ocean is a few miles deep - let's say 5 - so there's about 10 miles of ocean depth per land area.
- So compressing that to 1/10th the land area suggests the oceans should cover the US to a depth of about 100 miles.
The exact answer, it turns out, is about 89 miles - really close, without looking up a single piece of information!
https://www.wolframalpha.com/input?i=%28332%2C500%2C000+cubi...
- I know the US contains hundreds of millions of people, and the world contains a single-digit number of billions. So the US has about 10% of the world's people.
- The US probably isn't particularly dense or sparse relative to other populated areas, so 1/10 the population should be 1/10 the Earth's land area.
- The Earth has twice as much ocean as land, and
- The ocean is a few miles deep - let's say 5 - so there's about 10 miles of ocean depth per land area.
- So compressing that to 1/10th the land area suggests the oceans should cover the US to a depth of about 100 miles.
The exact answer, it turns out, is about 89 miles - really close, without looking up a single piece of information!
https://www.wolframalpha.com/input?i=%28332%2C500%2C000+cubi...
I believe the US has about 350 million people out of about 7 billion people on Earth. That makes the US population equal to about 5% of the total, not 10%.
I'm trying to visualize the amount of water here, but it's hopeless unless an elementary student can calculate how many oil drums it would fill or football fields it would cover to a depth of one yard.
The beauty of a sphere is that ANY dimension is EVERY dimension! Height, length, width, depth, etc. are all the same.
It's a sphere, the height is equal to the diameter that you plainly see on the picture.
It's about 554.4 trillion Olympic-sized swimming pools, if you're interested.
I’ve alerted all my friends in Kentucky. That thing could blow any time.
Wow, imagine all the data centers you could cool with all that water
Does this include the water inside of living creatures?
Yes, from TFA:
> and even the water in you, your dog, and your tomato plant.
> and even the water in you, your dog, and your tomato plant.
I honestly find this extremely unsettling. There should definitely be more, though I don't really want our planet to look like Kamino
IIRC water in earth's mantle is magnitudes greater than the volume contained in our oceans. I think only part of Earth's H2O story is illustrated by this graphic.
Yes, see: <https://news.ycombinator.com/item?id=41240719>
The USGS visualisation is based on a 1993 work, discovery of mantle water is later (roughly 2017).
The USGS visualisation is based on a 1993 work, discovery of mantle water is later (roughly 2017).
[deleted]
I don't know why, but it scares me
Similarly, all of the gold we have mined could form a cube measuring 22 meters on each side [1] and would fit comfortably within a baseball infield [2].
[1]: https://www.visualcapitalist.com/sp/chart-how-much-gold-is-i...
[2]: https://www.berkshirehathaway.com/letters/2011ltr.pdf (p. 19)
[1]: https://www.visualcapitalist.com/sp/chart-how-much-gold-is-i...
[2]: https://www.berkshirehathaway.com/letters/2011ltr.pdf (p. 19)
An xkcd Drain the Oceans https://what-if.xkcd.com/53/ is highly entertaining on this vein.
Conspicuously near the Great Lakes (NA)
See, the water amount isn't that large. What if we crashed some comets that are mostly ice to Mars? Modern technology makes it easy to calculate some order of magnitude effects like what would be the average water coverage increase of Mars if Halley's comet (assuming it was completely water) was crashed there: 3 mm.
Calculation: https://www.wolframalpha.com/input?i=%28halley%27s+comet+vol...
Calculation: https://www.wolframalpha.com/input?i=%28halley%27s+comet+vol...
Shouldn’t this say “surface water”?
[deleted]
Jordan Peelems next movie, FLOAT
I'm sold. Let's do it!
How do we make more water
i want to se a Fluid simulation of this drop with an earth model
Yeah, but also if you took all humanity and compressed it into a "meat sphere", it would only be 1km wide [1].
[1] https://www.iflscience.com/blended-up-every-living-human-in-...
[1] https://www.iflscience.com/blended-up-every-living-human-in-...
mmm... meat sphere.
The problem with this sphere is that people are terrible at understanding the mind boggling scale represented by "height" here. It looks like a tiny drop that "fits on the US". Instead it has a diameter of 860 miles. That's a ball of water that reaches all the way to outer space...
...and then keeps going for another 800 miles.
...and then keeps going for another 800 miles.
156 x Mt. Everest
[deleted]
Where is liquid fresh water besides lakes and rivers?
> The blue sphere over Kentucky represents the world's liquid fresh water (groundwater, lakes, swamp water, and rivers).
So the medium blue sphere includes groundwater and swamp water while the tiny dot does not.
So the medium blue sphere includes groundwater and swamp water while the tiny dot does not.
Groundwater mostly, but also clouds (minuscule amount).
Groundwater, and swamp water, the post explains.
Underground
Do oil next!
... it's about as much water as this place
https://en.wikipedia.org/wiki/Ceres_(dwarf_planet)
https://en.wikipedia.org/wiki/Ceres_(dwarf_planet)
It would use up roughly the same volume, but it'd be a lot more water.
(Much heavier, I suspect, as well.)
(Much heavier, I suspect, as well.)
Much lighter, actually. Ceres isn't particularly dense as rocky bodies go (~2.2 g/cm^3, give or take), but it's still much denser than water (~1 g/cm^3).
So, crash Ceres into Mars, and we have made a huge step towards terraforming?
Ceres could be taken apart with solar energy and rebuilt into a habitat much bigger than the Earth, never mind Mars. Ceres leads to the stars, Mars is just a dead end.
Is there reason to believe the stars are less of a dead end than Mars? It's easy to imagine us making a huge bet on interstellar travel, and just dying in interstellar space. Surely there's untold abundance in the stars, but if you can't actually reach it, then it may as well be a mirage.
Whenever I consider the possibility of interplanetary colonization, I come back to the conclusion that the only way to make it feasible is to reorient our economy towards sustainability in order to survive on Earth indefinitely. It's going to take a long, long time to develop the required technology, there's no real reason to believe artificial terraforming is even possible (since our sample size is 0), and even if it is it may take thousands or millions of years to complete.
I'm not being facetious with that last part, in the absence of information to the contrary, we should expect technology that works via geologic processes to run on a geologic timescale. I personally think artificial terraforming is probably possible, and that we could accelerate it to be much faster than the natural terraforming of Earth. But accelerating a 2 billion year process to be 10000x faster still takes 200k years. (ETA: I suppose a lot of that was the planet forming and the rate of bombardment falling to something tolerable, which eg Mars was already subject to, so maybe call it 1B/100k years.)
Whenever I consider the possibility of interplanetary colonization, I come back to the conclusion that the only way to make it feasible is to reorient our economy towards sustainability in order to survive on Earth indefinitely. It's going to take a long, long time to develop the required technology, there's no real reason to believe artificial terraforming is even possible (since our sample size is 0), and even if it is it may take thousands or millions of years to complete.
I'm not being facetious with that last part, in the absence of information to the contrary, we should expect technology that works via geologic processes to run on a geologic timescale. I personally think artificial terraforming is probably possible, and that we could accelerate it to be much faster than the natural terraforming of Earth. But accelerating a 2 billion year process to be 10000x faster still takes 200k years. (ETA: I suppose a lot of that was the planet forming and the rate of bombardment falling to something tolerable, which eg Mars was already subject to, so maybe call it 1B/100k years.)
I did a lot of analysis for the problem of "build a solar sail factory on a carbonaceous chondrite asteroid that makes sunshades to deploy at the L1 point", particularly from a chemical engineering point of view.
One interesting thing was that a lot of the chemistry involved was similar to the chemistry of decarbonization and carbon capture, particularly when you get CO2 as a waste product it is too precious to vent so you are going to feed it back into your "petrochemical" line.
Objects like Ceres are the norm once you get out to the outer solar system, the difference is that Ceres is close enough to the sun for solar energy to be a good power source. Centaur objects, the moons of outer planets, and Kuiper belt objects like Pluto are similar but when you get far from the Sun you need to use a different power source such as D-D fusion.
If a species became independent of sunlight it could take advantage of very generic objects that exist throughout interstellar space (comets, rouge planets, etc.) and make the journey in hops of (say) 100 years from one object to another. At that rate it would be possible to visit another star system in 10,000 years with a comfortable lifestyle. People like that might as well keep comet hopping but if they came across a star system I'd imagine they start some project like a Ceres megastructure because it is generic you can find some object like that and be able to establish a huge industrial base and population larger than the Earth with the same head end you've used all this time and same comfortable lifestyle.
Earth would be priority two if that for those people. Grabby aliens might have disrupted Ceres but left the dinosaurs alone. But Ceres is here, so they were not. Ceres is such an attractive target that it should be a SETI goal to look for hardware left behind. Would be hilarious if they stole the Deuterium.
One interesting thing was that a lot of the chemistry involved was similar to the chemistry of decarbonization and carbon capture, particularly when you get CO2 as a waste product it is too precious to vent so you are going to feed it back into your "petrochemical" line.
Objects like Ceres are the norm once you get out to the outer solar system, the difference is that Ceres is close enough to the sun for solar energy to be a good power source. Centaur objects, the moons of outer planets, and Kuiper belt objects like Pluto are similar but when you get far from the Sun you need to use a different power source such as D-D fusion.
If a species became independent of sunlight it could take advantage of very generic objects that exist throughout interstellar space (comets, rouge planets, etc.) and make the journey in hops of (say) 100 years from one object to another. At that rate it would be possible to visit another star system in 10,000 years with a comfortable lifestyle. People like that might as well keep comet hopping but if they came across a star system I'd imagine they start some project like a Ceres megastructure because it is generic you can find some object like that and be able to establish a huge industrial base and population larger than the Earth with the same head end you've used all this time and same comfortable lifestyle.
Earth would be priority two if that for those people. Grabby aliens might have disrupted Ceres but left the dinosaurs alone. But Ceres is here, so they were not. Ceres is such an attractive target that it should be a SETI goal to look for hardware left behind. Would be hilarious if they stole the Deuterium.
It's interesting speculation. I just can't accept the existence of a spacecraft that can last 100 years without a catastrophic failure, or Ceres being reforged into a factory, or a nation of people who live entirely independent of Earth until I see it.
Sometimes people talk about these things as if they are inevitable, but I would say there's an extremely good chance we go extinct without ever leaving this solar system (Voyager 1 notwithstanding). I think this is a valuable and grounding perspective in planning for the long term future of humanity, because we have to accept that that future takes place here on Earth and largely with the technology we already have. Space colonization is seductive, but like all silver bullets, impossible to operationalize within the constraints imposed on us by our situation.
But it's probably not a useful one when picking SETI targets or generating other research ideas, and that stands on it's own merit.
Sometimes people talk about these things as if they are inevitable, but I would say there's an extremely good chance we go extinct without ever leaving this solar system (Voyager 1 notwithstanding). I think this is a valuable and grounding perspective in planning for the long term future of humanity, because we have to accept that that future takes place here on Earth and largely with the technology we already have. Space colonization is seductive, but like all silver bullets, impossible to operationalize within the constraints imposed on us by our situation.
But it's probably not a useful one when picking SETI targets or generating other research ideas, and that stands on it's own merit.
2019
"Consider a spherical ocean..."
"All the Earth's FRESH Water"
Nope. That's the small (not barely visible tiny) ball.
"all of Earth's water, Earth's liquid fresh water, and water in lakes and rivers"
Wouldn't a cube be a better choice for visualizing volume? A more complete version would do it alongside with minerals, biomass, etc
They're comparing the sphere of water to the Earth which is a sphere.
Also it's by the Water Science School, so it doesn't seem your definition of completeness was the intention.
Also it's by the Water Science School, so it doesn't seem your definition of completeness was the intention.
Spheres are much more efficient. You must not have had the soap bubble question in an interview! Not everything in life conveniently fits in a box.
Why?
Humans are notoriously terrible about estimating volumes when things are curved and volume functions are exponential.
A great example of this done in 8th grade science classes across the US is to put 100ml of water in a 100ml graduated cylinder, 150ml in a 1L beaker, and ask the class which has more. Humans are awful at estimating how much volume the increased radius adds, and usually will say the 100ml.
The problem only gets worse as we graduate from cylinders to spheres.
We can all visually see which sphere is bigger, but cannot come close to estimating how much bigger one is than another.
A great example of this done in 8th grade science classes across the US is to put 100ml of water in a 100ml graduated cylinder, 150ml in a 1L beaker, and ask the class which has more. Humans are awful at estimating how much volume the increased radius adds, and usually will say the 100ml.
The problem only gets worse as we graduate from cylinders to spheres.
We can all visually see which sphere is bigger, but cannot come close to estimating how much bigger one is than another.
Volume functions are not exponential. They are polynomial.
(Fair point that people are lousy at estimating even polynomial functions, though...)
(Fair point that people are lousy at estimating even polynomial functions, though...)
Already eight years ago, I complained that people were using "exponential" where it doesn't make any sense. (See these two data points? Clearly exponential growth happend there. They're so far apart!)
I believe the problem has increased exponentially since then. Now everyone is using exponentially in literally the same way as literally.
I believe the problem has increased exponentially since then. Now everyone is using exponentially in literally the same way as literally.
Thanks for adding the mathematical definition!
You might be interested to know that the first definition of "exponential" is "of or relating to an exponent". The second definition is, as you say, "involving a variable in an exponent". https://www.merriam-webster.com/dictionary/exponential
As this is an internet forum and not a rigorous mathematical setting, I assert that my use of "exponential" is correct in context and to claim otherwise is incorrect. :)
You might be interested to know that the first definition of "exponential" is "of or relating to an exponent". The second definition is, as you say, "involving a variable in an exponent". https://www.merriam-webster.com/dictionary/exponential
As this is an internet forum and not a rigorous mathematical setting, I assert that my use of "exponential" is correct in context and to claim otherwise is incorrect. :)
I'm not sure if you are kidding but just in case you are not this is very misleading and in fact misguided.
Refering to polynomials as exponential just results in confusion essentially removing any meaning from the word. Any function can be written as something involving exponents, so that statement becomes meaningless.
Refering to polynomials as exponential just results in confusion essentially removing any meaning from the word. Any function can be written as something involving exponents, so that statement becomes meaningless.
> They are polynomial
I don't think this word means what you think it does. Or I don't. Exponents are just the number the value is raised. Squaring a value just uses an exponent of 2 where cubing uses an exponent of 3. Polynomials are x^2 + x + 1 type of equations. But admittedly, it has been 30+ years since I've thought about them at that level, so maybe I'm the one with fuzzy groking
I don't think this word means what you think it does. Or I don't. Exponents are just the number the value is raised. Squaring a value just uses an exponent of 2 where cubing uses an exponent of 3. Polynomials are x^2 + x + 1 type of equations. But admittedly, it has been 30+ years since I've thought about them at that level, so maybe I'm the one with fuzzy groking
"Polynomial" meaning x^n. "Exponential" meaning e^x.
Exponentials eventually grow much faster than polynomials, no matter what the exponent is.
I mean, look, in v = x^3, the "3" is an exponent. But it's not an exponential function because the variable isn't in the exponent.
Exponentials eventually grow much faster than polynomials, no matter what the exponent is.
I mean, look, in v = x^3, the "3" is an exponent. But it's not an exponential function because the variable isn't in the exponent.
> Exponentials eventually grow much faster than polynomials, no matter what the exponent is.
Since we're being pedantic, that last clause should be: "as long as the exponent is greater than 1."
Since we're being pedantic, that last clause should be: "as long as the exponent is greater than 1."
We can go a step further with the pedantry, and say that the commenter above is using an unreasonably narrow definition of the work "exponential" and that there are others which allow x^2 to be described as "exponential".
https://www.merriam-webster.com/dictionary/exponential
https://www.merriam-webster.com/dictionary/exponential
We could, but I would describe it as "mathematically accurate". Which is not incompatible with "unreasonably narrow", given that the definition of "exponential" has recently gotten polluted enough that it is now often synonymous with "fast growing". But what's the point of arguing over definitions if we're going to start with a baseline of saying that there is no basis upon which to argue definitions other than recent conventional usage?
> there are others which allow x^2 to be described as "exponential".
Those same definitions allow x*1000 to be described as "exponential". (x*1000000 would be "more exponential"!)
If you're describing something as exponential, then either you're just saying "fast growing", or you're trying to describe the type of growth. If you're describing the type of growth, then neither x*1000 nor x^2 is exponential. The fact that x^2 has an exponent in it is no more relevant than saying that x*1000=x*10^3 and x*10^3 has an exponent in it.
(Again, I sadly accept that in today's world, "exponentially" is being used to mean "fast growing", or sometimes more specifically "faster than linear". If I'm trying to understand what someone means, then it doesn't matter whether I find that usage to be a good idea or not.)
> there are others which allow x^2 to be described as "exponential".
Those same definitions allow x*1000 to be described as "exponential". (x*1000000 would be "more exponential"!)
If you're describing something as exponential, then either you're just saying "fast growing", or you're trying to describe the type of growth. If you're describing the type of growth, then neither x*1000 nor x^2 is exponential. The fact that x^2 has an exponent in it is no more relevant than saying that x*1000=x*10^3 and x*10^3 has an exponent in it.
(Again, I sadly accept that in today's world, "exponentially" is being used to mean "fast growing", or sometimes more specifically "faster than linear". If I'm trying to understand what someone means, then it doesn't matter whether I find that usage to be a good idea or not.)
No; to characterize "exponential" as "fast-growing" is a misunderstanding of what I'm saying. "Faster than linear" would be a good descriptor.
> > there are others which allow x^2 to be described as "exponential".
> Those same definitions allow x1000 to be described as "exponential". (x1000000 would be "more exponential"!)
> If you're describing something as exponential, then either you're just saying "fast growing", or you're trying to describe the type of growth. If you're describing the type of growth, then neither x1000 nor x^2 is exponential. The fact that x^2 has an exponent in it is no more relevant than saying that x1000=x10^3 and x10^3 has an exponent in it.
I don't agree with this. These are categorically different.
In f(x)=x*1000, as x increases, the function's output increases linearly. The slope of the derivative is 0.
In f(x)=x^3, as x increases, the function's output increases more than linearly. The slope of the derivative is positive and linear.
In f(x)=3^x, as x increases, the function's output increases much more than linearly. The slope of the derivative is positive and is itself a function of x.
These are all categorically different, and refer to something different than "fast-growing". "Exponential" in the mathematical sense, means the derivative is a function of x. "Exponential" in the colloquial sense means that the derivative has a positive slope. "Fast growing" just means that the derivative is large, even if it is a constant.
> > there are others which allow x^2 to be described as "exponential".
> Those same definitions allow x1000 to be described as "exponential". (x1000000 would be "more exponential"!)
> If you're describing something as exponential, then either you're just saying "fast growing", or you're trying to describe the type of growth. If you're describing the type of growth, then neither x1000 nor x^2 is exponential. The fact that x^2 has an exponent in it is no more relevant than saying that x1000=x10^3 and x10^3 has an exponent in it.
I don't agree with this. These are categorically different.
In f(x)=x*1000, as x increases, the function's output increases linearly. The slope of the derivative is 0.
In f(x)=x^3, as x increases, the function's output increases more than linearly. The slope of the derivative is positive and linear.
In f(x)=3^x, as x increases, the function's output increases much more than linearly. The slope of the derivative is positive and is itself a function of x.
These are all categorically different, and refer to something different than "fast-growing". "Exponential" in the mathematical sense, means the derivative is a function of x. "Exponential" in the colloquial sense means that the derivative has a positive slope. "Fast growing" just means that the derivative is large, even if it is a constant.
Um, ok. Your position baffles me, because you clearly understand what exponential means mathematically, yet you insist that the word means something else colloquially. Specifically "faster than linear". Usually, people who (mathematically) misuse the term do so because they don't understand what it actually means, but that's not what is happening here.
If it's going to mean something precise, such as
> The slope of the derivative is positive and linear.
then why not pick the precise thing that the word already means?
Is x*log(x) also exponential to you? If so, then why not use the word that already exists: superlinear? If not... oh wait, the above definition I quoted wouldn't even cover x^2, since the slope of its derivative is constant, not linear. So I'm just completely confused; I can't figure out which (mathematically) non-exponential functions you would like to label as exponential. x*1000, no. x^3, yes. x^2, I don't know. x*log(x), I don't know. x^2*log(x), I don't know.
> "Exponential" in the colloquial sense means that the derivative has a positive slope.
"Exponential" in the colloquial sense means that the speaker isn't using a mathematical sense, and so isn't considering first or second derivatives. I don't buy the argument that the colloquial sense accepts x^3 and rejects x^2, and in fact I bet I could find someone using it for a linear relation ("My workload has gone up exponentially since you laid off half the team!")
> "Exponential" in the mathematical sense, means the derivative is a function of x.
No it doesn't. x^2 is not mathematically exponential, yet its derivative is a function of x. Exponential means the derivative is exponential. But that's just a detail that doesn't really change the core of your message.
The main purpose of the mathematical definition is to exclude polynomials. The main purpose of the colloquial definition seems to be something like an impressive or important increase.
If it's going to mean something precise, such as
> The slope of the derivative is positive and linear.
then why not pick the precise thing that the word already means?
Is x*log(x) also exponential to you? If so, then why not use the word that already exists: superlinear? If not... oh wait, the above definition I quoted wouldn't even cover x^2, since the slope of its derivative is constant, not linear. So I'm just completely confused; I can't figure out which (mathematically) non-exponential functions you would like to label as exponential. x*1000, no. x^3, yes. x^2, I don't know. x*log(x), I don't know. x^2*log(x), I don't know.
> "Exponential" in the colloquial sense means that the derivative has a positive slope.
"Exponential" in the colloquial sense means that the speaker isn't using a mathematical sense, and so isn't considering first or second derivatives. I don't buy the argument that the colloquial sense accepts x^3 and rejects x^2, and in fact I bet I could find someone using it for a linear relation ("My workload has gone up exponentially since you laid off half the team!")
> "Exponential" in the mathematical sense, means the derivative is a function of x.
No it doesn't. x^2 is not mathematically exponential, yet its derivative is a function of x. Exponential means the derivative is exponential. But that's just a detail that doesn't really change the core of your message.
The main purpose of the mathematical definition is to exclude polynomials. The main purpose of the colloquial definition seems to be something like an impressive or important increase.
Or one step further
https://www.merriam-webster.com/dictionary/exponent
which is how I was taught. I only went to CalIII back in the early 90s, so who knows what's being taught now???
https://www.merriam-webster.com/dictionary/exponent
which is how I was taught. I only went to CalIII back in the early 90s, so who knows what's being taught now???
Exponential is c^x=y
Polynomial is x^c=y
Logarithmic is c^y=x
Polynomial is x^c=y
Logarithmic is c^y=x
It looks too small, perhaps there's more water tied up in the core and mantle than that?
[1] https://www.bnl.gov/newsroom/news.php?a=111648
[2] https://www.space.com/water-in-earth-core-forms-crystal-laye...
[3] https://www.goethe-university-frankfurt.de/125691203/An_ocea...
[1] https://www.bnl.gov/newsroom/news.php?a=111648
[2] https://www.space.com/water-in-earth-core-forms-crystal-laye...
[3] https://www.goethe-university-frankfurt.de/125691203/An_ocea...
More recent research, from about 2017, suggests that there's about as much water in Earth's mantle as in all the oceans, so we either need another drop roughly the volume of the first, or the second drop should be greatly expanded.
See: "There’s as much water in Earth’s mantle as in all the oceans" (2017) <https://www.newscientist.com/article/2133963-theres-as-much-...>
The USGS is citing a 1993 publication, Igor Shiklomanov's chapter "World fresh water resources" in Peter H. Gleick (editor), Water in Crisis: A Guide to the World's Fresh Water Resources (Oxford University Press, New York) (see the detail links from the submitted article).
That said, water remains a precious resource, and fresh surface water all the more so.
Edit: /double the size/s/size/volume/ above, for clarity.