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Comment by SilasX | Hacker News Reader

>You may be surprised to learn that Everest is not the tallest mountain on Earth, either. That honor belongs to Mauna Kea, a volcano on the Big Island of Hawaii. Mauna Kea originates deep beneath the Pacific Ocean, and rises more than 33,500 feet from base to peak.

Can someone explain this? How do you differentiate "the mountain" from "the rest of the earth that it comes out of"?

(Side note: the issue of "tallest mountain", as discussed here, is a great example of dealing with an ambiguous concept and clarifying it by asking what you're trying to do with the answer.)

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The article is likely referring to the estimated dry prominence of Mauna Kea. Topographic prominence [1] measures the height of a peak relative to its lowest surrounding contour line (that doesn't also contain another, taller peak). Usually the ocean's surface is considered "flat ground" when computing this measure (called a "wet prominence"), but one can alternatively imagine the Earth to have no water, and compute a "dry prominence" that permits the lowest surrounding contour line to be below sea level.

[1]: https://en.wikipedia.org/wiki/Topographic_prominence

The above Wikipedia article specifically mentions the dry prominence of Mauna Kea, estimating it to be 9330m which is taller than Everest's conventional height of 8848m. However, an apples-to-apples comparison would use the dry prominence of Everest too, which is the distance from the bottom of the Challenger Deep (-10,911m) to the summit. This would make Mauna Kea the second tallest mountain by topographic prominence if the Earth had no oceans.

> The article is likely referring to the estimated dry prominence of Mauna Kea.

It's talking around a mountain's "surrounding base" which is a related concept but doesn't take you in the absurd direction of 'drawing a circle around yourself in the challenger deep and claiming everything else is part of Everest'.

There is no precise definition of surrounding base, but Denali, Mount Kilimanjaro and Nanga Parbat are possible candidates for the tallest mountain on land by this measure. The bases of mountain islands are below sea level, and given this consideration Mauna Kea (4,207 m (13,802 ft) above sea level) is the world's tallest mountain and volcano, rising about 10,203 m (33,474 ft) from the Pacific Ocean floor. Ojos del Salado has the greatest rise on Earth—13,420 m (44,029 ft) from the summit[citation needed] to the bottom of the Atacama Trench about 560 km (350 mi) away, though most of this rise is not part of the mountain.

https://en.wikipedia.org/wiki/List_of_highest_mountains_on_E...

From your link, the lower elevation of a dry prominence of Everest would be the lowest contour that encircles Everest. That won't be nearly as deep as Challenger Deep but a quick google search does not find the correct dry prominence for me.

The lowest bottom of the Challenger Deep encircles the Everest. Think of the "outside" of the circle being the deepest point, and the "inside" of the circle being all rest of the Earth.

Reminds me of the joke where the mathematician is told to use a fixed length of fencing to enclose the biggest area possible and builds a tiny corral and stands inside and says "I define myself as outside the corral".

(Legit point on your part, though.)

In Douglas Adams''So Long And Thanks For All The Fish', Wonko the Sane resided either outside or inside, depending on your point of view, an inside-out house that he had built as an asylum for the world, after reading the instructions on a packet of toothpicks.

Got me on that one.

Seems to me "topographic prominence" is useful for people talking about peaks in a mountain range. Not so much when the spherical shape of the Earth starts to be significant.

The correct dry prominence of everest is the same as the regular prominence of everest, because there are no bodies of water between it and the nearest peaks.

Incorrect. There are no higher peaks than everest, so it's prominence is the same as its summit. Dry prominence would be measured from sea level, wet prominence would be based on the lowest point in the ocean floor.

>However, an apples-to-apples comparison would use the dry prominence of Everest too, which is the distance from the bottom of the Challenger Deep (-10,911m) to the summit. This would make Mauna Kea the second tallest mountain by topographic prominence if the Earth had no oceans

What? This does not make sense, if I am not mistaken? Topographic prominence would place Mauna Kea as the tallest (highest peak from base contour line), but it would certainly not be the second highest above the Challenger Deep... And the Challenger Deep is not the base contour line of any mountain..?

Think about it this way: imagine standing at the bottom of the Challenger Deep. Draw a small circle around yourself on the ocean floor. Now step outside the circle. Because you're standing on a spherical object (Earth), the area outside your circle isn't infinite like it would be on a plane. It's another finite region, which covers almost the entire Earth, and contains both yourself (standing just beside the lowest point of the Challenger Deep) and also the peak of Mount Everest. Therefore the circle is a base contour line for Everest, and Everest's wet prominence can be measured from the circle.

However, this same contour line cannot be used for the wet prominence measure of Mauna Kea, since it contains every mountain on Earth, many of which are taller. Mauna Kea's lowest contour line that doesn't contain another taller mountain would probably enclose a sizeable portion of the floor of the Pacific Ocean, but wouldn't include the Andes, Japan, or the Sierra Nevada, since those peaks are taller. The contour line would therefore be deep below the ocean surface, but not as deep as the Challenger Deep.

Is this measurement conceptually useful, or is it completely arbitrary? I thought it was an attempt to rigorously define "surrounding terrain" for purposes of measuring a mountain's height above the surrounding terrain, but if it defines the Challenger Deep as "surrounding" Everest, that's topologically interesting but doesn't seem like a useful way of thinking about geology.

>Draw a small circle around yourself on the ocean floor.

That circle encloses two areas. One roughly a square metre, and the other one roughly 5e8 km². In geology only the smaller area is used, and the smaller area does not contain the peak of the Everest and thus is not considered a valid base contour line of the Everest.

Why not? You are looking for the lowest contour that can surround everest, at what would would you stop going lower because the countour is getting too big? 50% of the planet's surface? This seems like an arbitrary bound.

Thank you, that's the kind of concept I was looking for.

Yes, that is correct. At almost 20,000 km, the dry prominence of Everest is by definition the maximum possible on Earth. You only get to claim Kea more prominent if you use a different standard to measure it!

I'm not seeing why that is true. If one were to imagine a deep moat around Kea, wouldn't that increase its prominence w/out impacting that of Everest? Or are you suggesting that Everest's dry prominence would be measured from whatever the deepest point on Earth is? Or something else?

Everest dominates Mauna Kea in prominence. In fact, Everest dominates any peak on Earth in prominence, since it's the tallest peak. By the mathematical definition of prominence, the dry prominence of Everest is always measured from the deepest point on Earth, the Challenger Deep.

If you dug a moat around Mauna Kea, it would indeed increase its prominence, but would not affect the prominence of Everest. Until you dug the moat deeper than the Challenger Deep (about -11,000 m), at which point the dry prominence of Everest would start to be measured from the bottom of your moat and not Challenger Deep. At this point, digging the moat any deeper would increase the prominence of both Everest and Kea by equal amount, but Everest as the higher mountain would nevertheless always dominate Kea.

Yeah that has always seemed a bit jumbled to me. It's not clear to me why that point, 33,500 feet below the peak of Mauna Kea, is appropriate to use as a basis of measurement for the mountain. And why not a lower point? And why can that point not be used to measure the height of Mount Everest as well?

Anyway, I think what you're asking can usually be described by the concept of Topographic Prominence[1], one definition of which is "the height of the peak’s summit above the lowest contour line encircling it but containing no higher summit"

[1] https://en.wikipedia.org/wiki/Topographic_prominence

It's wet :) (under water surface)

The claim of the article that mount Everest is the tallest point from the earth's center happens because earth's surface, relative to its size, is as smooth as a billiard ball. Even the tallest mountains are nothing. So high mountains located at the equator can easily "outperform" higher mountains elsewhere.

Apparently it's not quite as smooth as a billiard ball. More like very fine sandpaper.

https://skeptics.stackexchange.com/questions/10763/is-earth-...

When comparing the actual height of a mountain, they're measured from their base (which is whatever elevation the ground they sit on is) to their peak, rather than just looking at their peak altitude. This is how you compare mountains on other planets, and why Mons Olympus on Mars is the tallest mountain in the solar system. For Mauna Kea, the mountain is taller than it looks because its base sits at the bottom of the ocean, whereas Everest sits on an already-lofty piece of continental plate.

I get the impression that the asker knows that but that their question is more like, is there any official way to define where the mountain starts? Could we keep tracking the side of Everest right down into a far-off ocean trench and say it's now the tallest again, it's just also really wide?

I guess you're looking for obvious local minima. If the land slopes back up a lot or stays mostly flat for a long time it's probably not part of the mountain anymore. Would a smaller mountain in the middle of Uluru be measured starting from ground level at the top of Uluru?

Edit: Asker has now confirmed in a separate comment that this is what they meant.

My definition would involve some definition of geological homogeny such that you could classify the terrain as mountain and not-mountain. Probably based on whether it was involved in the process that formed the mountain.

Yeah, that was what I was hoping/expecting the definition would use, that mountains come from some plate interaction involving lava which would provide a natural boundary between "mountain" and "rest of earth".

I think a lot of mountains don't involve lava at all, they're just the product of continental plates running into each other. I'm pretty sure Everest is an example of this. Hawaii is the opposite; those mountains don't involve plates at all, they're solely the product of lava.

I like your clarification better though!

Right, I got that much. I'm asking, how do you rigorously distinguish "the base" from the rest of the earth (or that earth from the mountain itself)?

Edit: IOW, if Kea's base were on some raised ocean floor, when do you count that as part of Kea too?

I had to look this up, but apparently "sea level" on Mars (called "topographic datum") is decided using the average elevation near the equator.

http://passporttoknowledge.com/lfm/ask/terrain-geo/Determini...

Why is "height from the solid matter base" more correct than "height from the non-gaseous matter base" though. From the perspective of humans, who generally live at the border of gaseous matter not the border of solid matter, I think the latter might make more sense.

Right, basically, in a different context accrding to this principle volcanoes at higher altitudes (say close to andes but not in the andes proper) are not as tall as more coastal/lower altitude volcanoes, if the cone’s rise isn't as high.

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