explain xkcd - User contributions [en]

3181: Jumping Frog Radius

2025-12-16T07:18:04Z

Jmm: /* Explanation */ typo

{{comic
| number = 3181
| date = December 15, 2025
| title = Jumping Frog Radius
| image = jumping_frog_radius_2x.png
| imagesize = 339x243px
| noexpand = true
| titletext = Earth's r_jf is approximately 1.5 light-days, leading to general relativity's successful prediction that all the frogs in the Solar System should be found collected on the surface of the Earth.
}}

==Explanation==
{{incomplete|This page was created by an CHAMPION PLANET-JUMPING FROG. Can someone calculate the size and mass of the largest object from which a champion frog can achieve escape velocity? Are there some named asteroids that are of sow low a mass that it would be possible for frog to jump of? (Of course there are some small ennough but do they have names)? Don't remove this notice too soon.}}
The {{w|Schwarzchild radius}} is essentially the size of a {{w|black hole}} -- the maximum distance from the center where gravity is so strong that light can't escape.

It is part of a solution to {{w|Einstein's field equations}}. It is usually calculated as the following:
:r = (2*G*M)/(c2),
where G is the {{w|gravitational constant}}, M is the mass of the object, and c is the {{w|speed of light}}.

If M is the mass of the {{w|Earth}} it would give the Schwarzchild radius for the Earth which is about 9 mm. (If all of Earth mass was pressed into a sphere of a bit less than 2 cm in diameter, it would become a black hole.)

The comic suggests a more useful radius. The ''Jumping Frog radius'', rjf, which is the size of a "planet" so that its gravity keeps a champion {{w|Frog jumping contest|jumping frog}} from being able to achieve {{w|escape velocity}}. Thus [[Randall]] has instead of c, the 299,792,458 m/s speed of light, used a much smaller value of 4.5 m/s, to represent the maximum speed of a jumping frog. It is possible that Randall got that value from [https://www.researchgate.net/publication/5661154_Explosive_Jumping_Extreme_Morphological_and_Physiological_Specializations_of_Australian_Rocket_Frogs_Litoria_nasuta this paper], which on page 179 puts an upper limit on the maximum velocity of adult {{w|Striped_rocket_frog|Australian rocket frogs}} at 4.52 m/s.

The title text points out that the rjf of the Earth is about 1.5 light days (compared to the 9 mm Schwarzchild radius), which is about 3 times the distance to {{w|Pluto}}. Since Earth's surface is much smaller than this{{cn}}, no frogs will be able to escape, so they'll all collect here on Earth. As far as we know, all the frogs in the Solar System are on Earth, so the data apparently matches the theory.

==Transcript==
{{incomplete transcript|Don't remove this notice too soon.}}
:[The panel shows a formula and a drawing to its right.]
:rjf = 2GM/(4.5 m/s)2
:[A small planet with the radius marked as rjf and a frog jumping on the surface. The frog jumps about as high as the planet's radius, saying "ribbit" in midair and "plop" as it lands.]

:[Caption below the panel:]
:More practically useful than the Schwartzchild radius, the ''Jumping Frog Radius'' is the radius at which an object's gravitational pull is so strong that even a champion jumping frog can't escape.

{{comic discussion}}<noinclude>

3020: Infinite Armada Chess

2024-12-05T07:23:37Z

Jmm: /* Explanation */ better explanation of the error -- hoping someone is working on an actual solver for infinite armada chess

{{comic
| number = 3020
| date = December 4, 2024
| title = Infinite Armada Chess
| image = infinite_armada_chess_2x.png
| imagesize = 282x497px
| noexpand = true
| titletext = Stockfish 16 suggests the unconventional opening 1. RuntimeError: Out of bounds memory access
}}

==Explanation==
{{incomplete|Created by an infinite armada of stockfish BOTS - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

{{w|Chess}} is a board game played between two players on an 8x8 chessboard. In standard chess, each player has 8 pawns and 8 pieces: 2 rooks, 2 knights, 2 bishops, a queen, and a king. {{w|Chess variants}} are chess games in which the rules, board sizes, and/or piece behaviors are altered. In the chess game presented here, the standard chessboard is presented, however, the board extends vertically past the original 1st and 8th ranks off the page to infinity in both directions. Each square beyond the 8 standard ranks is filled by an additional queen. The {{w|Queen (chess)|queen}} is the most powerful piece on the chessboard, having the powers of a {{w|Bishop (chess)|bishop}} and a {{w|Rook (chess)|rook}} combined. With an {{tvtropes|TitleDrop|infinite armada}} of queens, each player will be much stronger.{{citation needed}} Sometimes having a bunch of queens [https://x.com/chesscom/status/1841540380363211164 doesn't go very well], however.

In {{w|algebraic chess notation}}, chess moves are represented by the move number, the piece moved, and the destination square. For example, the sequence 1. e4 Nf6 indicates that White opened the game by moving their e-pawn to the e4 square and Black replied by moving their kingside knight to f6, the {{w|Alekhine Defence}}. In the title text, {{w|Stockfish_(Chess)|Stockfish}} is a {{w|chess engine}} designed to evaluate a chessboard and find the best move. However, it is designed to handle finite boards, so it is likely that some problem will occur as it runs, and indeed it returns a {{w|RuntimeError}} as the first move for White, signalling it probably accessed an array outside of its bounds.

While Stockfish is limited by the processing power of the computer on which it runs {{citation needed}}, it does not really need to consider the infinitely many pieces to suggest a move. Indeed, all but a finite number of pieces are stuck at every step, so there is always a finite number of possible moves, and so it would be possible in theory for suggestions to be made using a finite amount of {{w|RAM|memory}}.

==Transcript==
:[A chess board in the starting position, except it extends further at the top and bottom, going beyond the panel. The extra squares are filled with queens of the sides' respective colors.]

:[Caption below the panel:]
:Infinite armada chess

{{comic discussion}}
[[Category:Chess]]

Talk:3020: Infinite Armada Chess

2024-12-05T07:01:10Z

Jmm: /* Out of bounds error */ out of bounds

== Did I do well? ==

Added a very very basic explanation.
[[Special:Contributions/172.68.147.132|172.68.147.132]] 04:25, 5 December 2024 (UTC)

Well, yes but I wonder if just one tiny fix is needed. If you replace the white side with a simplyfied artillery tower, you reinvented space invaders.

I was personally hoping for an explanation of the Infinite Armada thing, and I feel like a link to the TV Tropes page doesn't really. Explain that at all. So I would love a bit of an expansion on that part! Just want to be sure I didn't miss some reference or something. [[Special:Contributions/172.68.23.91|172.68.23.91]] 05:48, 5 December 2024 (UTC)

== Out of bounds error ==

I think that since the error was "out of bounds", not "out of memory", it's referring to indexing outside of the region of memory that the program allocated to deal with the board. This would happen since instead of addressing rank 1..8, you could address rank 9, 10, 0, or -1. Unless bounds checking is performed when converting the board coordinates into linear array indices, you'd get an out-of-bounds error (or worse, succeed in reading or modifying memory that you weren't intending to). --[[Special:Contributions/172.71.30.253|172.71.30.253]] 05:45, 5 December 2024 (UTC)
:It was "Out of Bounds memory access". That means it was trying to access a memory address that was out of the bounds of the computer, as if it were trying to access the ω-th index of the board array, which would put it out of the memory range of any computer [[User:Firestar233|guess who]] ([[User talk:Firestar233|if you want to]] | [[Special:Contributions/Firestar233|what i have done]]) 06:15, 5 December 2024 (UTC)
:: There is no hint that the bounds are those of the computer, the simplest explanation really is that the bounds are those of an array. The error message does come up. In addition, to try to access the memory at the ω-th index, you would need to construct the ω-th index itself first (which would fail or not terminate) [[User:Jmm|Jmm]] ([[User talk:Jmm|talk]]) 07:01, 5 December 2024 (UTC)