NHacker Next

- new
- past
- show
- ask
- show
- jobs
- submit

login

Rendered at 13:38:50 GMT+0000 (Coordinated Universal Time) with Vercel.

NHacker Next

- new
- past
- show
- ask
- show
- jobs
- submit

login

Rendered at 13:38:50 GMT+0000 (Coordinated Universal Time) with Vercel.

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.Specifically: given that the volume of a sphere is 4/3πR^3, doubling the volume is equivalent to increasing the radius by ~26%.

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...

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.

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.

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.

If we want to talk about the total amount of H2O

around, on, or in the Earththen 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

doesmake it to the surface over time is a good question. I've no idea though I'd suspect thatsomedoes 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.

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.

[0] https://en.wikipedia.org/wiki/Kola_Superdeep_Borehole

The breakout is for comparison: surface freshwater (total) and surface freshwater (lakes and rivers) relatively.

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).

Is the water pumped from beneath the crust in the Netherlands poisoned too or have you guys got the last of the good stuff?

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.

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.

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.

Radius of said sphere would only increase by ∛2. ;)

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.

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.

Adding in how far of a drive is it to X place or how far of a walk is it, is also fun.

https://en.wikipedia.org/wiki/Origin_of_water_on_Earth#Aster...

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.

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.

It's a ball of iron covered with rocks (i.e. metal oxides) cover with water (i.e. hydrogen oxide).

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).

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".

By mass, iron (32.1%) is still a minority constituent of the Earth.

<https://en.wikipedia.org/wiki/Abundance_of_the_chemical_elem...>

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.

Earth as a whole has a density about 5.5x that of water.

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.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.

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..

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

lol it's funny when you put it that way

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.

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)

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...>

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.

intothe mantle.https://lightsinthedark.com/wp-content/uploads/2013/06/ceres...

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...

lighterwhen 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).overand not freezethrough, 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.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).

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.

Water dissolving and removing There is water at the bottom of the 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-...

Ganymede vs. Earth is indeed very surprising!

[1]: https://science.nasa.gov/jupiter/jupiter-facts/ (Under "Structure")

Ganymede’s ocean is even bigger than Europa’sEuropa 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 is the size of our Moon. Colliding it with Mars would be similar to the collision that formed our Moon.

Not sure if Europa's water would be flung into space, make atmosphere, or make a boiling ocean.

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...

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.

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!

Also, I thought LEO typically begins around 180 km / 112 mi.

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.

This is the point:

everythingon 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 youthinkit’s given you a better intuition, you’ve been misled."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 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.

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.technology.org/how-and-why/what-would-happen-if-....

So I feel like the USGS is exagerated.

The oceans are only about 3.5% salt by weight, so that doesn't make a huge difference, either.

I find this pretty interesting, https://phys.org/news/2023-11-reveal-earth-surface-penetrate...

Apparently all the mined gold in the world would fit inside a 5 m diameter sphere.

Spheres are suspicious in hiding weight.

> 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.

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.

<https://www.sciencenordic.com/chemistry-climate-denmark/the-...>

https://www.youtube.com/watch?v=FkUNHhVbQ1Q

https://www.goodreads.com/book/show/61305943-sea-of-dreams

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.

Obviously that water would be somewhat less accessible and quantifiable, but...

Anyone familiar with the current geoscience on this?

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.

[1] https://www.wolframalpha.com/input?i=volume+of+all+humans

Imagine the headline:

VSThe comment you're replying to is about

freshwater. 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.

I'm also somewhat surprised no one else was being pedantic about this. I expect better from HN :)

That's a LOT of water.

https://www.independent.co.uk/news/science/earth-scientists-...

- 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...

> and even the water in you, your dog, and your tomato plant.

The USGS visualisation is based on a 1993 work, discovery of mantle water is later (roughly 2017).

[1]: https://www.visualcapitalist.com/sp/chart-how-much-gold-is-i...

[2]: https://www.berkshirehathaway.com/letters/2011ltr.pdf (p. 19)

thatlarge. 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...

[1] https://www.iflscience.com/blended-up-every-living-human-in-...

...and then keeps going for another 800 miles.

So the medium blue sphere includes groundwater and swamp water while the tiny dot does not.

https://en.wikipedia.org/wiki/Ceres_(dwarf_planet)

volume, but it'd be a lot morewater.(Much heavier, I suspect, as well.)

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).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.)

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.

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.

Also it's by the Water Science School, so it doesn't seem your definition of completeness was the intention.

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

awfulat 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

whichsphere is bigger, but cannot come close to estimating how much bigger one is than another.notexponential. They are polynomial.(Fair point that people are lousy at estimating even polynomial functions, though...)

I believe the problem has increased exponentially since then. Now everyone is using exponentially in literally the same way as literally.

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. :)

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.

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

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

functionbecause the variable isn't in the exponent.Since we're being pedantic, that last clause should be: "as long as the exponent is greater than 1."

https://www.merriam-webster.com/dictionary/exponential

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???

> 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". (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 x

1000 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.

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.

Polynomial is x^c=y

Logarithmic is c^y=x

[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...