Unsolved Math Problems

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After decades of studying the curve and the procedure that generates it, the consensus explanation is "it's just like that."
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jlvanderzwan
1 day ago
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I genuinely can't tell if he made stuff up or if these are real problems
wffurr
1 day ago
#1 is gobbledegook. #2 is a real problem. #3 might also be made up. https://explainxkcd.com/wiki/index.php/2529:_Unsolved_Math_Problems
alexanglin
1 day ago
It is quite the curve.
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Saturday Morning Breakfast Cereal - Life of a Salesman

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Click here to go see the bonus panel!

Hovertext:
It's time for a play about how wait a minute middle class life was okay.


Today's News:
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jlvanderzwan
2 days ago
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acdha
3 days ago
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Washington, DC
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1 public comment
brennen
2 days ago
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I have always really hated _Death of a Salesman_.
Boulder, CO

When hope is a hindrance

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When hope is a hindrance | Aeon Essays

For Hannah Arendt, hope is a dangerous barrier to courageous action. In dark times, the miracle that saves the world is to act

- by Samantha Rose Hill

Read at Aeon

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jlvanderzwan
4 days ago
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The silent pulse of the Universe

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The silent pulse of the Universe | Aeon Videos

In 1967, when Jocelyn Bell was still a postgraduate, she discovered pulsars. But the Nobel Prize went to her supervisor

- by Aeon Video

Watch at Aeon

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jlvanderzwan
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Single Cells Evolve Large Multicellular Forms in Just Two Years

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To human eyes, the dominant form of life on Earth is multicellular. These cathedrals of flesh, cellulose or chitin usually take shape by following a sophisticated, endlessly iterated program of development: A single microscopic cell divides, then divides again, and again and again, with each cell taking its place in the emerging tissues, until there is an elephant or a redwood where there was none...

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jlvanderzwan
5 days ago
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> These cathedrals of flesh, cellulose or chitin

Ok, thanks for making me feel gross about my own body
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Irregular Webcomic! #4621

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Comic #4621

To research this strip, I went through the Tomb of Horrors adventure module and roughly added up the available treasure. I believe the true total value is somewhere in the hundreds of thousands of gold pieces, but I admit I did a very rough job and it's possible that I overlooked or miscounted something significant. This estimate does not include the infamous Valves of Mithril, described as:

THE VALVES OF MITHRIL: These doors are 14 feet wide and 28 feet tall. They are made of solid mithril, 3 feet thick, and impregnated with great magicks in order to make them absolutely spell and magic proof.
The adventurers in this dungeon are patently not supposed to take the doors as treasure. The module as written contains no text whatsoever addressing this possibility, not assigning any value to the doors. The writer of the adventure presumably never considered that a group of heroes might want to loot the doors. But mithril is incredibly valuable. There are many discussions about exactly how much those doors are worth, and various escapades of adventuring parties who tried to steal them. We're looking at 14×28×3 = 1176 cubic feet of mithril, per door, so 2352 cubic feet in total. The linked calculation goes on to estimate the density and value of the metal, and comes up with a total value of something over 2 billion gold pieces. This is assuming the value is 150 gp per pound. However, the Dungeons & Dragons 3.5 System Reference Document lists the value of mithril as 500 gp per pound. So we need to multiply that estimate by a bit over 3, giving us a total value of more than 6 billion gold pieces. Additionally, the Tomb features earlier on in the dungeon an adamantite door. The size is not quoted, so presumably it's a more normal door size, but it's made of the even more valuable metal adamantite, which seems to be valued at somewhere from 2 to 5 times as much as mithril. It's not going to be in the billions of gold pieces due to the smaller volume, but it's going to be several million.
Reader B. Jonas writes:
The calculation about the price of the mithril doors is off by at least an order of magnitude. The error seems to be present already in the post that you link to. That post assumes that mithril is as dense as gold (in reality it's only as light as aluminium, but leave that aside for now), which is 19,300 kg/m3. The door is 14×28×3 ft3 in size, and the post assumes that mithril is worth 150 gold piece/lb. The conversions for imperial units are 1 lb = 0.454 kg and 1 ft = 0.305 m. All that together would give a price for the door that's only 212,000,000 gold pieces, rather than over 2,000,000,000 as the post claims.
And William S. writes:
The part many forget about the Tomb of Horrors is the doors bleed if even nicked a small amount. And it's not even a small bleed, it's full on house-of-horrors-bleeding-via-wall-boards level blood. This means melting the doors/repurposing is next to impossible, but even if you somehow did manage that trick the smallest cut in day-to-day use becomes the ultimate horror show.
He's right: the module says:
If the door is attacked by force it will not budge, but if it is scratched or nicked it will show red and if cut by a sharp weapon it will begin to gush forth blood - the blood of all those who have died within the area of the Tomb! The red flow will cascade down the steps and fill the area to the top of the 1st step in 6 rounds, and each round thereafter it will rise higher by 1 step. In 20 rounds it will completely fill the foyer to the ceiling.
That's a lot of blood, and - being mathematically curious - it lets us now calculate the minimum number of people who have died in the Tomb! The floorplan of the room and corridor before the doors is shown on the dungeon map, so we can calculate the area to be 600 square feet. The ceiling height is not specified explicitly, but the doors are 28 feet tall and the room immediately before the current room is stated to have a ceiling height of 30 feet, so it seems sensible to assume that height, giving a total volume of 18,000 cubic feet. (There are some steps, but let's assume the ceiling slopes up to maintain the height.) That's 509.7 cubic metres, or 509,700 litres. An average person contains about 5 litres of blood, so that means we're looking at 101,900 people worth of blood. That's a lot of adventurers who have lost their lives in the Tomb. If we assume one adventuring party of 8 characters per day, every single day, tried and failed to loot the Tomb, that means it's been there for at least 35 years. The timespan is reasonable, but where have all those adventurers come from? That's the population of a small city, just in adventurers. If it's more like one adventuring party per month, then we're looking at the Tomb having been there for a bit over 1000 years.
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jlvanderzwan
5 days ago
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> so that means we're looking at 101,900 people worth of blood
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