2626: d65536 - Revision history

Tromag at 17:09, 6 February 2026

2026-02-06T17:09:16Z

162.158.216.169: Undoing a right old mess of trying to put a link in, where there was already a preferable one there already.

2025-04-24T08:45:51Z

Undoing a right old mess of trying to put a link in, where there was already a preferable one there already.

172.70.115.216: /* Explanation */

2025-04-23T22:48:00Z

‎Explanation

108.162.241.84: /* Explanation */

2025-04-23T22:45:22Z

‎Explanation

108.162.241.84: /* Explanation */

2025-04-23T22:43:55Z

‎Explanation

108.162.241.84: /* Explanation */

2025-04-23T22:43:30Z

‎Explanation

Natg19: /* Trivia */ cat

2025-02-08T01:32:19Z

‎Trivia: cat

CalibansCreations: /* Explanation */

2025-02-06T13:33:53Z

‎Explanation

CalibansCreations: /* Explanation */

2025-01-21T14:22:27Z

‎Explanation

172.71.223.115: /* Explanation */ changed link type

2024-11-23T23:09:12Z

‎Explanation: changed link type

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 In binary computing, 16 bit unsigned numbers range from 0 to 65535, for a total of 65536 unique numbers, a number which is hence well-known to software engineers. Generating large numbers in a manner that is truly random is a recurring problem in cryptography, required to send private messages to another party. People today still use dierolls to generate private random numbers.
-In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges.  By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a {{w|Disdyakis triacontahedron|d120}} (excluding the bipyramids and trapezohedra, which can theoretically be made with arbitrarily many sides), so it is very likely that [[Cueball|Cueball's]] d65536 die is also biased.
+In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges.  By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. Consequently, numbers higher than 20 are usually generated by rolling multiple smaller dice. For example, rolling two d10s together will generate a number up to 100 (with one die providing each digit)
-Here, Cueball has constructed a d65536 for generating random 16 bit numbers. It may have solved the problem of generating large random numbers with fewer die rolls, but it magnifies all of the problems with large-numbered dice to ludicrous extremes. In order for the faces to be readable, the die is ridiculously huge, dwarfing the human standing next to it. Rolling such a die is not only physically challenging, but it would also need a huge space in which to roll if the result is to be random, and that space would need to have an extremely flat and rigid surface in order for the die to come to rest. And even if those problems were solved, simply getting to a vantage point to see the top of the die would be a major challenge, and determining which number was truly on top would be near impossible to do by eye. If one really wished to use dice, it would be much easier to simply use multiple dice rolls. For instance, one could roll eight d4 dice (or use 16 coin flips), and convert the result into binary. This has the same randomness as a single die roll,{{cn}} but can take much longer, so people do purchase d16s to simplify it and speed it up.
+Here, Cueball has constructed a d65536 for generating random 16 bit numbers. It may have solved the problem of generating large random numbers with fewer die rolls, but it magnifies all of the problems with large-numbered dice to ludicrous extremes. In order for the faces to be readable, the die is ridiculously huge, dwarfing the human standing next to it. Rolling such a die is not only physically challenging, but it would also need a huge space in which to roll if the result is to be random, and that space would need to have an extremely flat and rigid surface in order for the die to come to rest. And even if those problems were solved, simply getting to a vantage point to see the top of the die would be a major challenge, and determining which number was truly on top would be near impossible to do by eye. If one really wished to use dice, it would be much easier to simply use multiple dice rolls. For instance, one could roll eight d4 dice (or use 16 coin flips), and convert the result into binary.
 The closest regular shape similar to the depicted in the comic could be a {{w|Goldberg polyhedron}}. However, no such polyhedron exists with exactly 65536 hexagonal faces. The closest Goldberg Polyhedron has a mixture of 65520 hexagons and 12 pentagons, totaling 65532 faces. It is possible to construct a fair die without a matching regular shape by limiting the sides which it could land on and designing those sides to be fair (for instance, a prism with rectangular facets that extend its entire length, and rounded ends to ensure it doesn't balance on end).

@@ Line 10: / Line 10: @@
 In binary computing, 16 bit unsigned numbers range from 0 to 65535, for a total of 65536 unique numbers, a number which is hence well-known to software engineers. Generating large numbers in a manner that is truly random is a recurring problem in cryptography, required to send private messages to another party. People today still use dierolls to generate private random numbers.
-In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges.  By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a Disdyakis Tricontahedron (https://mathsgear.co.uk/collections/dice/products/d120-dice0
+In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges.  By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a {{w|Disdyakis triacontahedron|d120}} (excluding the bipyramids and trapezohedra, which can theoretically be made with arbitrarily many sides), so it is very likely that [[Cueball|Cueball's]] d65536 die is also biased.
 Here, Cueball has constructed a d65536 for generating random 16 bit numbers. It may have solved the problem of generating large random numbers with fewer die rolls, but it magnifies all of the problems with large-numbered dice to ludicrous extremes. In order for the faces to be readable, the die is ridiculously huge, dwarfing the human standing next to it. Rolling such a die is not only physically challenging, but it would also need a huge space in which to roll if the result is to be random, and that space would need to have an extremely flat and rigid surface in order for the die to come to rest. And even if those problems were solved, simply getting to a vantage point to see the top of the die would be a major challenge, and determining which number was truly on top would be near impossible to do by eye. If one really wished to use dice, it would be much easier to simply use multiple dice rolls. For instance, one could roll eight d4 dice (or use 16 coin flips), and convert the result into binary. This has the same randomness as a single die roll,{{cn}} but can take much longer, so people do purchase d16s to simplify it and speed it up.

@@ Line 10: / Line 10: @@
 In binary computing, 16 bit unsigned numbers range from 0 to 65535, for a total of 65536 unique numbers, a number which is hence well-known to software engineers. Generating large numbers in a manner that is truly random is a recurring problem in cryptography, required to send private messages to another party. People today still use dierolls to generate private random numbers.
-In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges.  By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a Disdyakis Tricontahedron. (https://mathsgear.co.uk/collections/dice/products/d120-dice0
+In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges.  By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a Disdyakis Tricontahedron (https://mathsgear.co.uk/collections/dice/products/d120-dice0
 ) (excluding the bipyramids and trapezohedra, which can theoretically be made with arbitrarily many sides), so it is very likely that [[Cueball|Cueball's]] d65536 die is also biased.

@@ Line 10: / Line 10: @@
 In binary computing, 16 bit unsigned numbers range from 0 to 65535, for a total of 65536 unique numbers, a number which is hence well-known to software engineers. Generating large numbers in a manner that is truly random is a recurring problem in cryptography, required to send private messages to another party. People today still use dierolls to generate private random numbers.
-In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges.  By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a {{https://mathsgear.co.uk/collections/dice/products/d120-dice|Disdyakis Tricontahedron}} (excluding the bipyramids and trapezohedra, which can theoretically be made with arbitrarily many sides), so it is very likely that [[Cueball|Cueball's]] d65536 die is also biased.
+In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges.  By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a Disdyakis Tricontahedron. (https://mathsgear.co.uk/collections/dice/products/d120-dice0
 Here, Cueball has constructed a d65536 for generating random 16 bit numbers. It may have solved the problem of generating large random numbers with fewer die rolls, but it magnifies all of the problems with large-numbered dice to ludicrous extremes. In order for the faces to be readable, the die is ridiculously huge, dwarfing the human standing next to it. Rolling such a die is not only physically challenging, but it would also need a huge space in which to roll if the result is to be random, and that space would need to have an extremely flat and rigid surface in order for the die to come to rest. And even if those problems were solved, simply getting to a vantage point to see the top of the die would be a major challenge, and determining which number was truly on top would be near impossible to do by eye. If one really wished to use dice, it would be much easier to simply use multiple dice rolls. For instance, one could roll eight d4 dice (or use 16 coin flips), and convert the result into binary. This has the same randomness as a single die roll,{{cn}} but can take much longer, so people do purchase d16s to simplify it and speed it up.

@@ Line 10: / Line 10: @@
 In binary computing, 16 bit unsigned numbers range from 0 to 65535, for a total of 65536 unique numbers, a number which is hence well-known to software engineers. Generating large numbers in a manner that is truly random is a recurring problem in cryptography, required to send private messages to another party. People today still use dierolls to generate private random numbers.
-In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges.  By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a {{| https://mathsgear.co.uk/collections/dice/products/d120-dice|Disdyakis Tricontahedron}} (excluding the bipyramids and trapezohedra, which can theoretically be made with arbitrarily many sides), so it is very likely that [[Cueball|Cueball's]] d65536 die is also biased.
+In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges.  By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a {{https://mathsgear.co.uk/collections/dice/products/d120-dice|Disdyakis Tricontahedron}} (excluding the bipyramids and trapezohedra, which can theoretically be made with arbitrarily many sides), so it is very likely that [[Cueball|Cueball's]] d65536 die is also biased.
 Here, Cueball has constructed a d65536 for generating random 16 bit numbers. It may have solved the problem of generating large random numbers with fewer die rolls, but it magnifies all of the problems with large-numbered dice to ludicrous extremes. In order for the faces to be readable, the die is ridiculously huge, dwarfing the human standing next to it. Rolling such a die is not only physically challenging, but it would also need a huge space in which to roll if the result is to be random, and that space would need to have an extremely flat and rigid surface in order for the die to come to rest. And even if those problems were solved, simply getting to a vantage point to see the top of the die would be a major challenge, and determining which number was truly on top would be near impossible to do by eye. If one really wished to use dice, it would be much easier to simply use multiple dice rolls. For instance, one could roll eight d4 dice (or use 16 coin flips), and convert the result into binary. This has the same randomness as a single die roll,{{cn}} but can take much longer, so people do purchase d16s to simplify it and speed it up.

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 The closest regular shape similar to the depicted in the comic could be a {{w|Goldberg polyhedron}}. However, no such polyhedron exists with exactly 65536 hexagonal faces. The closest Goldberg Polyhedron has a mixture of 65520 hexagons and 12 pentagons, totaling 65532 faces. It is possible to construct a fair die without a matching regular shape by limiting the sides which it could land on and designing those sides to be fair (for instance, a prism with rectangular facets that extend its entire length, and rounded ends to ensure it doesn't balance on end).
-The title text references how cryptographic systems (especially RSA and other factoring-is-hard based systems) are vulnerable to quantum attacks as quantum computing technology develops. The title text is essentially punning on the idea of a "large" quantum system. "Large" in the quantum computing sense would be on the order of 64 qubits each of which would be an atom or two at most. This would still be microscopic and will never be as large as the giant die the comic is centered on; but for a well-observed environment and human rolling without sufficient entropy (consider somebody obsessed with a certain number dropping the die on something soft), a conventional computer could predict some rolls. See also [[538]] for non-mathematical paths of cryptography.
+The title text references how cryptographic systems (especially RSA and other factoring-is-hard based systems) are vulnerable to quantum attacks as quantum computing technology develops. The title text is essentially punning on the idea of a "large" quantum system. "Large" in the quantum computing sense would be on the order of 64 qubits, each of which would be an atom or two at most. This would still be microscopic and will never be as large as the giant die the comic is centered on; but for a well-observed environment and human rolling without sufficient entropy (consider somebody obsessed with a certain number dropping the die on something soft), a conventional computer could predict some rolls. See also [[538: Security]] ([[Nate Silver|no, not that one]]) for non-mathematical paths of cryptography.
 Since 65536 is 2^16, if for some reason you must simulate a D65536 using nothing but D&D dice, the most efficient method is to roll a D8 4 times and roll a D4 twice (2^(3×4) · 2^(2×2)), or roll a D8 5 times and toss a coin (2^(3×5) × 2).