Wikipedia:Reference desk/Archives/Science/2021 August 4

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August 4

If we take all water in the atmosphere and collect them together it'll be equall to how many percent of the water on the earth?

If we take all water of the atmosphere (~0.001%) and collect them together, then it'll be equal to how many percent of the water on the earth? Is there any rough information / estimation about it? --ThePupil (talk) 01:09, 4 August 2021 (UTC)

Actually, sources debunking Creationism may already have done this, as they've done calculations about the thermodynamics of condensing that much water vapor to liquid all at once. Spoiler alert: the amount of heat released by that much condensation would be a lot, as in all life gets cooked alive and dies a lot. I think it is talked about here https://www.youtube.com/watch?v=vWZtbZGtiGA and in this paper https://www.tandfonline.com/doi/abs/10.5408/0022-1368-31.2.134 --OuroborosCobra (talk) 01:19, 4 August 2021 (UTC)

I've found here that the atmosphere has 37.5 million-billion gallons. I don't know based on what this calculation is made on, but if we compare it to the estimated quantity on the earth, how many percent does it take compared to it? --ThePupil (talk) 01:57, 4 August 2021 (UTC)

According to Wikipedia, the atmosphere of Earth has a mass of 5.15×10¹⁸ kg and contains 0.4% water vapor on average. So there's just over 2×10¹⁸ kg of water vapor. 1 g of liquid water has a volume of 1 cm³, so 1 kg has a volume of 1 L, and so 2×10¹⁸ kg has a volume of 2×10¹⁸ L, which is 2,000,000 km³. Again according to Wikipedia, The total volume of water on Earth is estimated at 1,386,000,000 km³. So the water in the atmosphere is 2/1,386 or about 0.14% of all the water. --184.144.99.72 (talk) 02:24, 4 August 2021 (UTC)

According to the given data, there are 194040000 km of water in the atmosphare, right? Does it go together with Wisconsin university's statement that the Earth’s atmosphere contains 37.5 million-billion gallons of water?--ThePupil (talk) 02:42, 4 August 2021 (UTC)

No, since km is a unit of length and gallons is a unit of volume. --OuroborosCobra (talk) 03:20, 4 August 2021 (UTC)

I recall reading that if all the water in the atmosphere were to rain out, it would only be 1 inch/ 2cm deep on average. This is consistent with atmospheric pressure being 14.7 psi, and water being about 0.25% of that. Abductive (reasoning) 03:51, 4 August 2021 (UTC)

Ah, I found a USGS website for schoolchildren that says exactly that. Abductive (reasoning) 03:54, 4 August 2021 (UTC)

To the IP user above: 5.15×10¹⁸ kg × 0.4% = 2×10¹⁶ kg, not 2×10¹⁸ kg. I think you used 0.4 rather than 0.4%, resulting in an estimate that's too high by a factor of 100. The section Atmosphere_of_Earth#Density_and_mass gives this number explicitly as 1.27×10¹⁶ kg. --Amble (talk) 17:40, 4 August 2021 (UTC)

Blast, so I did. Which means that my conclusion that "the water in the atmosphere is... about 0.14% of all the water" was too large by the same factor. If there are no other errors, I should have said 0.0014%. "Thanks for the correction", he muttered angrily. --184.144.99.72 (talk) 21:39, 5 August 2021 (UTC)

1 km³ converts to about 264,000,000,000 US gallons. Therefore "37.5 million-billion gallons", i.e. 37,500,000,000,000,000,000 US gallons, converts to only about 142,000 km³. If the figures in Wikipedia are anywhere near correct, whoever wrote that item at the U of Wisc has gotten it wrong by several orders of magnitude. --184.144.99.72 (talk) 04:20, 4 August 2021 (UTC)

The USGS website above says that there is 12,900 km³ of water in the atmosphere. So they're only wrong by a bit over 1 order of magnitude. Abductive (reasoning) 07:54, 4 August 2021 (UTC)

The OP linked to the source [1], which says that the water in the atmosphere is "0.001 percent of the total Earth's water volume". That's 0.001% of the water on Earth, not 0.001% of the mass of the atmosphere. So the linked source already gives a direct answer to OP's question. --Amble (talk) 17:42, 4 August 2021 (UTC)

Dimensions

• File:Escher Waterfall.jpg modified per WP:NFCC #9, copyrighted images may only appear in the article namespace. If you wish to view the image to understand the discussion, click the link --Jayron32 13:45, 4 August 2021 (UTC)

The Dutch artist M. C. Escher produced drawings that contain (in many cases) visual paradoxes. For example, "Waterfall" depicts water running downhill in a continuous loop. This is a representation in two dimensions of something that could not be constructed in three dimensions.

Is it possible to construct an object in three dimensions that is a representation of an object that could not be constructed in four dimensions? Ionlywanttoknow (talk) 10:43, 4 August 2021 (UTC)

The fourth dimension is time. ←Baseball Bugs ^{What's up, Doc?} carrots→ 12:19, 4 August 2021 (UTC)

The question obviously refers to a hypothetical universe with a macroscopic fourth spatial dimension. (And your unhelpful snark means that I have to resolve an edit conflict, so thanks for that.) TenOfAllTrades(talk) 12:43, 4 August 2021 (UTC)

There's nothing "obviously" about it to me. Though I'm "obviously" a lot dumber than you are. ←Baseball Bugs ^{What's up, Doc?} carrots→ 12:48, 4 August 2021 (UTC)

Time is already implied in the question as posed, which speaks of "water running".

If someone handed you a photograph of a sphere and asked you to construct a three-dimensional object from it, would you hand the picture back and say "Done! It's a two-dimensional object persisting in time!"? (At least, would you do so without knowing you were being a smartass?) TenOfAllTrades(talk) 13:28, 4 August 2021 (UTC)

No, I'd construct a sphere. If they wanted a depiction of a four-dimensional sphere, I'd represent it by several spheres, each with a nearby clock showing a different time. ←Baseball Bugs ^{What's up, Doc?} carrots→ 14:01, 4 August 2021 (UTC)

That's only if we're dealing with "three spatial dimensions and one time dimension". We live in that now, it's called Minkowski spacetime, and it is NOT the same thing as "four spatial dimensions", which is something different entirely. We cannot directly observe four spatial dimensions to understand what a 4-sphere would look like, but we can visualize what the 3-dimensional projection of a 4-sphere would look like, in the same way that you can project the shadow of a 3-dimensional sphere onto a 2-D surface, you can project the 3-dimensional "shadow" of a 4-sphere into 3 dimensions. here are a plethora of videos that show you how that works. --Jayron32 18:11, 6 August 2021 (UTC)

(I've added an image of Escher's Waterfall for reference.)

It's an interesting question that's got a number of possible answers, depending on exactly what you choose the question to mean.

A drawing is a notional projection of a three-dimensional structure onto a two-dimensional plane. So one version of your question might be, can you create a three-dimensional figure that represents an implausible 4-D structure? I strongly suspect the answer is 'yes', but you might refer this question to the Mathematics reference desk to address some of the more technical aspects.

Of course, part of the implausibility lies in the apparent perpetual motion of the water--the apparent defiance of common-sense laws of physics. Addressing the question from that angle means considering how one might generalize our existing physics to a fourth spatial dimension; we can't break the rules in our hypothetical universe if we don't establish what they are to begin with.

But then there's the third aspect of the question, which is that a lower-dimensional representation or projection necessarily sacrifices information about the higher-dimensional structure. A two-dimensional portrait, no matter how detailed, doesn't display the back of the subject's head. Escher's lithograph seems paradoxical because our brains fill in a presumed structure and orientation and connectivity for the parts of the scene. Escher's Waterfall is an image of an entirely possible, constructible, three-dimensional structure--it just isn't put together the way that you thought it was: YouTube link. TenOfAllTrades(talk) 12:35, 4 August 2021 (UTC)

I had to change your image addition; as a copyrighted work it can only be added to article pages, per WP:NFCC #9. I have modified it to a link rather than a copy of the image, so readers can still open the link to view it. --Jayron32 13:45, 4 August 2021 (UTC)

Yes, we learn in calculus III, that the surface of n dimension is the n-1 dimension. So the surface of a cube, is a plane. The surface of an object in 4D, is a 3D object. The cube is therefore the surface of whatever 4D objects are called. 67.165.185.178 (talk) 12:54, 4 August 2021 (UTC).

Sort of. There are many perspectives on the surface of a 4-cube (aka a Tesseract), and some of them do indeed look rather cubish. But by changing the angles by which one observes the 4D object, you can get a variety of rather un-cube-like looking things. While it is true that the surface of a 4-D object is a 3-D object, it's far too simplified to say that the surface of a tesseract is a cube. --Jayron32 18:16, 6 August 2021 (UTC)

The reason the Escher drawing "works" is despite knowing we're looking at an impossible three-dimensional object, our minds insist on interpreting it as a 3-D object anyway. That's because our brains are very, very good at visualizing things in 3 dimensions. That's in large part due to the fact we live in a three-spacial-dimensional world.

We do not live in a four-dimensional world and thus we are very, very bad at visualizing four-dimensional objects. The trick becomes getting the mind visualize the fourth spacial dimension in the first place. Yes, we can create a three-dimensional figure that represents an impossible 4-D structure, it just won't look like anything. It's like being told a joke in a language you don't understand. DB1729 (talk) 13:11, 4 August 2021 (UTC)

To clarify more on what DB1729 is saying, the problem is not one of geometry or physics, it is one of psychology and neuroscience. The illusion of the third dimension is solely a product of the human brain interpreting the series of lines and shading in a certain way, Escher's drawings break your brain, they don't break geometry. It is still just a 2-D series of lines and shades of grey and whatnot, there is no "3Dness" to it except in the way your brain tries to make it so. It is an Optical illusion, caused by an unconscious inference according structuralist psychology; there is also Gestalt psychology, which would have different frameworks for understanding such illusions. Regardless, it's still not a geometry issue, it's a brain issue. --Jayron32 13:51, 4 August 2021 (UTC)

How about a Klein bottle? It's doesn't really intersect itself, but the best we can do in 3D is have the handle intersect the side where it passes through. DMacks (talk) 18:17, 4 August 2021 (UTC)

The question asked for a 3D representation of an impossible 4D object. A truly non-intersecting Klein bottle can be constructed in four dimensions, so it is not impossible. As explained above by DB1729 and Jayron32, the illusion of 3D impossible objects depends on the human visual system interpreting 2D images as representing 3D objects. We as humans have no system on board for interpreting a 3D shape as representing a 4D object, so I agree the answer to the question is, "no, it is not possible".  --Lambiam 20:42, 4 August 2021 (UTC)

Ah, I read the original backwards, after trying to follow the thread...conjured up only possible in 4D to avoid illusion of impossibility when represented in 3D. DMacks (talk) 21:59, 4 August 2021 (UTC)

A 3-D hologram of an apple falling out of a tree. The apple never hits the ground. In 4-D, it would.195.50.139.86 (talk) 06:38, 5 August 2021 (UTC)alien