Probvious - Revision history

MrSolis at 13:05, 14 April 2025

2025-04-14T13:05:56Z

← Older revision		Revision as of 13:05, 14 April 2025
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	"'''Probvious'''" (a portmanteau of the words ''probabilistic'' and ''obvious'') is an adjective used to express a high degree of confidence about a mathematical statement that is not known to be true. It was introduced by John Conway in an article discussing possibly unprovable statements.<ref>Conway, J. H. (2013). On Unsettleable Arithmetical Problems. The American Mathematical Monthly, 120(3), 192–198. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref> The term has been used by [https://www.bbchallenge.org bbchallenge] contributors to describe the solutions to halting problems for [[Cryptids]] such as [[Bigfoot]] and [[Hydra]].		"'''Probvious'''" (a portmanteau of the words ''probabilistic'' and ''obvious'') is an adjective used to express a high degree of confidence about a mathematical statement that is not known to be true. It was introduced by John Conway in an article discussing possibly unprovable statements.<ref>Conway, J. H. (2013). On Unsettleable Arithmetical Problems. The American Mathematical Monthly, 120(3), 192–198. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref> The term has been used by [https://www.bbchallenge.org bbchallenge] contributors to describe the solutions to halting problems for [[Cryptids]] such as [[Bigfoot]] and [[Hydra]].
	==Usage==		==Usage==
	[[File:ProbviousExcerpt.png\|right\|300px\|thumb\|The excerpt from ~~the article by~~ John Conway where "probvious" is introduced.]]		[[File:ProbviousExcerpt.png\|right\|300px\|thumb\|The excerpt from John Conway's article where "probvious" is introduced.]]
	The word appears in Conway's article a few times as a way of forming conjectures about a known [[Collatz-like]] function.<ref>Atkin, A. O. L. “Problem 63-13.” SIAM Review, vol. 8, no. 2, 1966, pp. 234–36. JSTOR, http://www.jstor.org/stable/2028281</ref><ref>Guy, R. K. (1983). Don’t Try to Solve These Problems! The American Mathematical Monthly, 90(1), 35–41. https://doi.org/10.1080/00029890.1983.11971148</ref> This function, denoted <math>\mu(n)</math>, is defined as:		The word appears in Conway's article a few times as a way of forming conjectures about a known [[Collatz-like]] function.<ref>Atkin, A. O. L. “Problem 63-13.” SIAM Review, vol. 8, no. 2, 1966, pp. 234–36. JSTOR, http://www.jstor.org/stable/2028281</ref><ref>Guy, R. K. (1983). Don’t Try to Solve These Problems! The American Mathematical Monthly, 90(1), 35–41. https://doi.org/10.1080/00029890.1983.11971148</ref> This function, denoted <math>\mu(n)</math>, is defined as:
	<math display="block">\begin{array}{lll}\mu(2n)&=&3n\\ \mu(4n+1)&=&3n+1\\ \mu(4n+3)&=&3n+2\end{array}\Rightarrow\begin{array}{lll}\mu^{-1}(3n)&=&2n\\ \mu^{-1}(3n+1)&=&4n+1\\ \mu^{-1}(3n+2)&=&4n+3\end{array}</math>		<math display="block">\begin{array}{lll}\mu(2n)&=&3n\\ \mu(4n+1)&=&3n+1\\ \mu(4n+3)&=&3n+2\end{array}\Rightarrow\begin{array}{lll}\mu^{-1}(3n)&=&2n\\ \mu^{-1}(3n+1)&=&4n+1\\ \mu^{-1}(3n+2)&=&4n+3\end{array}</math>

MrSolis at 13:03, 14 April 2025

2025-04-14T13:03:40Z

← Older revision		Revision as of 13:03, 14 April 2025
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	"'''Probvious'''" (a portmanteau of the words ''probabilistic'' and ''obvious'') is an adjective used to express a high degree of confidence about a mathematical ~~property or~~ statement that is not known to be true. It was introduced by John Conway in an article discussing ~~potentially~~ unprovable statements.<ref>~~John~~ Conway. "On Unsettleable Arithmetical Problems". ~~2017~~. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref> The term has been used by [https://www.bbchallenge.org bbchallenge] contributors to describe the solutions to halting problems for [[Cryptids]] such as [[Bigfoot]] and [[Hydra]].		"'''Probvious'''" (a portmanteau of the words ''probabilistic'' and ''obvious'') is an adjective used to express a high degree of confidence about a mathematical statement that is not known to be true. It was introduced by John Conway in an article discussing possibly unprovable statements.<ref>Conway, J. H. (2013). On Unsettleable Arithmetical Problems. The American Mathematical Monthly, 120(3), 192–198. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref> The term has been used by [https://www.bbchallenge.org bbchallenge] contributors to describe the solutions to halting problems for [[Cryptids]] such as [[Bigfoot]] and [[Hydra]].
	==Usage==		==Usage==
	[[File:ProbviousExcerpt.png\|right\|300px\|thumb\|The excerpt from the article by John Conway where "probvious" is introduced.]]		[[File:ProbviousExcerpt.png\|right\|300px\|thumb\|The excerpt from the article by John Conway where "probvious" is introduced.]]
	The word appears in Conway's article a few times as a way of forming conjectures about a [[Collatz-like]] function ~~that had already been investigated in the past~~.<ref>Atkin, A. O. L. ~~"Problem~~ 63-13.~~" <i>~~SIAM Review~~</i>~~ 8, no. 2 (1966): 234–36. JSTOR, http://www.jstor.org/stable/2028281</ref><ref>Guy, ~~Richard~~ K. "Don’t Try to Solve These Problems!~~" <i>~~The American Mathematical Monthly~~</i>~~ 90~~, no.~~ 1 ~~(1983~~): 35–41. ~~JSTOR,~~ https://doi.org/10.~~2307~~/~~2975688~~</ref> This function, denoted <math>\mu(n)</math>, is defined as:		The word appears in Conway's article a few times as a way of forming conjectures about a known [[Collatz-like]] function.<ref>Atkin, A. O. L. “Problem 63-13.” SIAM Review, vol. 8, no. 2, 1966, pp. 234–36. JSTOR, http://www.jstor.org/stable/2028281</ref><ref>Guy, R. K. (1983). Don’t Try to Solve These Problems! The American Mathematical Monthly, 90(1), 35–41. https://doi.org/10.1080/00029890.1983.11971148</ref> This function, denoted <math>\mu(n)</math>, is defined as:
	<math display="block">\begin{array}{lll}\mu(2n)&=&3n\\ \mu(4n+1)&=&3n+1\\ \mu(4n+3)&=&3n+2\end{array}\Rightarrow\begin{array}{lll}\mu^{-1}(3n)&=&2n\\ \mu^{-1}(3n+1)&=&4n+1\\ \mu^{-1}(3n+2)&=&4n+3\end{array}</math>		<math display="block">\begin{array}{lll}\mu(2n)&=&3n\\ \mu(4n+1)&=&3n+1\\ \mu(4n+3)&=&3n+2\end{array}\Rightarrow\begin{array}{lll}\mu^{-1}(3n)&=&2n\\ \mu^{-1}(3n+1)&=&4n+1\\ \mu^{-1}(3n+2)&=&4n+3\end{array}</math>
	Conway first uses "probvious" to describe the idea that the sequences of iterates <math>(\cdots,8,\mu(8),\mu^2(8),\cdots)</math> and <math>(\cdots,14,\mu(14),\mu^2(14),\cdots)</math> diverge to infinity.		Conway first uses "probvious" to describe the idea that the sequences of iterates <math>(\cdots,8,\mu(8),\mu^2(8),\cdots)</math> and <math>(\cdots,14,\mu(14),\mu^2(14),\cdots)</math> diverge to infinity.

	Likewise, there exist [[Turing machines]] for which determining whether they halt requires solving a mathematical problem believed to be difficult (oftentimes a [[Collatz-like]] problem) but using probabilistic ~~approximations~~ of their ~~functions suggests~~ a clear solution. For example, Bigfoot and Hydra are probviously ~~nonhalting~~ because they simulate biased ~~pseudo-~~random walks ~~which (when interpreted as random) leave vanishingly small probabilities of ever halting~~. ~~Similarly~~, ~~machines such as~~ [[Lucy's Moonlight]] ~~and [[Mother of Giants]] are~~ probviously halting because ~~they simulate~~ a sequence of ~~pseudo-~~random ~~coin flips, halting with~~ a fixed probability on each ~~trial~~.		Likewise, there exist Turing machines for which determining whether they halt requires solving a mathematical problem believed to be difficult, oftentimes a Collatz-like problem, but arguments using probabilistic versions of their behaviour suggest a clear solution. For example, Bigfoot and Hydra are probviously non-halting because they simulate biased random walks that drift towards infinity yet must reach zero for these machines to halt. Alternatively, [[Lucy's Moonlight]] is probviously halting because it simulates a sequence of independent random trials for which it has a fixed probability of halting each time.

	== References ==		== References ==
	<references />		<references />

Sligocki: Cleanup some confusing sentences

2025-03-08T00:42:26Z

Cleanup some confusing sentences

← Older revision		Revision as of 00:42, 8 March 2025
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	The word appears in Conway's article a few times as a way of forming conjectures about a [[Collatz-like]] function that had already been investigated in the past.<ref>Atkin, A. O. L. "Problem 63-13." <i>SIAM Review</i> 8, no. 2 (1966): 234–36. JSTOR, http://www.jstor.org/stable/2028281</ref><ref>Guy, Richard K. "Don’t Try to Solve These Problems!" <i>The American Mathematical Monthly</i> 90, no. 1 (1983): 35–41. JSTOR, https://doi.org/10.2307/2975688</ref> This function, denoted <math>\mu(n)</math>, is defined as:		The word appears in Conway's article a few times as a way of forming conjectures about a [[Collatz-like]] function that had already been investigated in the past.<ref>Atkin, A. O. L. "Problem 63-13." <i>SIAM Review</i> 8, no. 2 (1966): 234–36. JSTOR, http://www.jstor.org/stable/2028281</ref><ref>Guy, Richard K. "Don’t Try to Solve These Problems!" <i>The American Mathematical Monthly</i> 90, no. 1 (1983): 35–41. JSTOR, https://doi.org/10.2307/2975688</ref> This function, denoted <math>\mu(n)</math>, is defined as:
	<math display="block">\begin{array}{lll}\mu(2n)&=&3n\\ \mu(4n+1)&=&3n+1\\ \mu(4n+3)&=&3n+2\end{array}\Rightarrow\begin{array}{lll}\mu^{-1}(3n)&=&2n\\ \mu^{-1}(3n+1)&=&4n+1\\ \mu^{-1}(3n+2)&=&4n+3\end{array}</math>		<math display="block">\begin{array}{lll}\mu(2n)&=&3n\\ \mu(4n+1)&=&3n+1\\ \mu(4n+3)&=&3n+2\end{array}\Rightarrow\begin{array}{lll}\mu^{-1}(3n)&=&2n\\ \mu^{-1}(3n+1)&=&4n+1\\ \mu^{-1}(3n+2)&=&4n+3\end{array}</math>
	Conway first uses "probvious" to describe the idea that the sequences of iterates <math>(\cdots,8,\mu(8),\mu^2(8),\cdots)</math> and <math>(\cdots,14,\mu(14),\mu^2(14),\cdots)</math> diverge to infinity. Likewise, there exist [[Turing machines]] for which determining whether they halt requires solving a mathematical problem believed to be difficult, oftentimes a [[Collatz-like]] problem, but using probabilistic approximations of their functions suggests a clear solution. For example, Bigfoot, Hydra~~, and others function like~~ biased random walks ~~and treating them~~ as ~~such leads to the conclusion that they are probviously nonhalting~~. Similarly, machines such as [[Lucy's Moonlight]], [[Mother of Giants]]~~, and others function like very slow~~-~~running~~ random ~~number generators that halt once a specific value is reached~~, ~~which probviously happens~~ with ~~enough attempts~~.		Conway first uses "probvious" to describe the idea that the sequences of iterates <math>(\cdots,8,\mu(8),\mu^2(8),\cdots)</math> and <math>(\cdots,14,\mu(14),\mu^2(14),\cdots)</math> diverge to infinity.

			Likewise, there exist [[Turing machines]] for which determining whether they halt requires solving a mathematical problem believed to be difficult (oftentimes a [[Collatz-like]] problem) but using probabilistic approximations of their functions suggests a clear solution. For example, Bigfoot and Hydra are probviously nonhalting because they simulate biased pseudo-random walks which (when interpreted as random) leave vanishingly small probabilities of ever halting. Similarly, machines such as [[Lucy's Moonlight]] and [[Mother of Giants]] are probviously halting because they simulate a sequence of pseudo-random coin flips, halting with a fixed probability on each trial.

	== References ==		== References ==
	<references />		<references />

MrSolis at 22:53, 7 March 2025

2025-03-07T22:53:48Z

← Older revision		Revision as of 22:53, 7 March 2025
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	"'''Probvious'''" (a portmanteau of the words ''probabilistic'' and ''obvious'') is an adjective used to express a high degree of confidence about a mathematical property or statement that is not known to be true. It was introduced by John Conway in an article discussing potentially ~~unproveable~~ statements.<ref>John Conway. "On Unsettleable Arithmetical Problems". 2017. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref> The term has been used by [https://www.bbchallenge.org bbchallenge] contributors to describe the solutions to halting problems for [[Cryptids]] such as [[Bigfoot]] and [[Hydra]].		"'''Probvious'''" (a portmanteau of the words ''probabilistic'' and ''obvious'') is an adjective used to express a high degree of confidence about a mathematical property or statement that is not known to be true. It was introduced by John Conway in an article discussing potentially unprovable statements.<ref>John Conway. "On Unsettleable Arithmetical Problems". 2017. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref> The term has been used by [https://www.bbchallenge.org bbchallenge] contributors to describe the solutions to halting problems for [[Cryptids]] such as [[Bigfoot]] and [[Hydra]].
	==Usage==		==Usage==
	[[File:ProbviousExcerpt.png\|right\|300px\|thumb\|The excerpt from the article by John Conway where "probvious" is introduced.]]		[[File:ProbviousExcerpt.png\|right\|300px\|thumb\|The excerpt from the article by John Conway where "probvious" is introduced.]]

MrSolis at 22:51, 7 March 2025

2025-03-07T22:51:11Z

← Older revision		Revision as of 22:51, 7 March 2025
Line 1:		Line 1:
	"'''Probvious'''" (a portmanteau of the words ''probabilistic'' and ''obvious'') is an adjective used to express a high degree of confidence about a mathematical property or statement that is not known to be true. It was introduced by John Conway in an article discussing potentially unproveable statements.<ref>John Conway. "On Unsettleable Arithmetical Problems". 2017. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref> The term has been used by [https://www.bbchallenge.org bbchallenge] contributors to describe the solutions to halting problems for [[Cryptids]] such as [[Bigfoot]] and [[Hydra]].		"'''Probvious'''" (a portmanteau of the words ''probabilistic'' and ''obvious'') is an adjective used to express a high degree of confidence about a mathematical property or statement that is not known to be true. It was introduced by John Conway in an article discussing potentially unproveable statements.<ref>John Conway. "On Unsettleable Arithmetical Problems". 2017. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref> The term has been used by [https://www.bbchallenge.org bbchallenge] contributors to describe the solutions to halting problems for [[Cryptids]] such as [[Bigfoot]] and [[Hydra]].
	==Usage==		==Usage==
	[[File:ProbviousExcerpt.png\|right\|~~400px~~\|thumb\|The excerpt from the article by John Conway where "probvious" is introduced.]]		[[File:ProbviousExcerpt.png\|right\|300px\|thumb\|The excerpt from the article by John Conway where "probvious" is introduced.]]
	The word appears in Conway's article a few times as a way of forming conjectures about a [[Collatz-like]] function that had already been investigated in the past.<ref>Atkin, A. O. L. "Problem 63-13." <i>SIAM Review</i> 8, no. 2 (1966): 234–36. JSTOR, http://www.jstor.org/stable/2028281</ref><ref>Guy, Richard K. "Don’t Try to Solve These Problems!" <i>The American Mathematical Monthly</i> 90, no. 1 (1983): 35–41. JSTOR, https://doi.org/10.2307/2975688</ref> This function, denoted <math>\mu(n)</math>, is defined as:		The word appears in Conway's article a few times as a way of forming conjectures about a [[Collatz-like]] function that had already been investigated in the past.<ref>Atkin, A. O. L. "Problem 63-13." <i>SIAM Review</i> 8, no. 2 (1966): 234–36. JSTOR, http://www.jstor.org/stable/2028281</ref><ref>Guy, Richard K. "Don’t Try to Solve These Problems!" <i>The American Mathematical Monthly</i> 90, no. 1 (1983): 35–41. JSTOR, https://doi.org/10.2307/2975688</ref> This function, denoted <math>\mu(n)</math>, is defined as:
	<math display="block">\begin{array}{lll}\mu(2n)&=&3n\\ \mu(4n+1)&=&3n+1\\ \mu(4n+3)&=&3n+2\end{array}~~\qquad~~\Rightarrow~~\qquad~~\begin{array}{lll}\mu^{-1}(3n)&=&2n\\ \mu^{-1}(3n+1)&=&4n+1\\ \mu^{-1}(3n+2)&=&4n+3\end{array}</math>		<math display="block">\begin{array}{lll}\mu(2n)&=&3n\\ \mu(4n+1)&=&3n+1\\ \mu(4n+3)&=&3n+2\end{array}\Rightarrow\begin{array}{lll}\mu^{-1}(3n)&=&2n\\ \mu^{-1}(3n+1)&=&4n+1\\ \mu^{-1}(3n+2)&=&4n+3\end{array}</math>
	Conway first uses "probvious" to describe the idea that the sequences of iterates <math>(\cdots,8,\mu(8),\mu^2(8),\cdots)</math> and <math>(\cdots,14,\mu(14),\mu^2(14),\cdots)</math> diverge to infinity. Likewise, there exist [[Turing machines]] for which determining whether they halt requires solving a mathematical problem believed to be difficult, oftentimes a [[Collatz-like]] problem, but using probabilistic approximations of their functions suggests a clear solution. For example, Bigfoot, Hydra, and others function like biased random walks and treating them as such leads to the conclusion that they are probviously nonhalting. Similarly, machines such as [[Lucy's Moonlight]], [[Mother of Giants]], and others function like very slow-running random number generators that halt once a specific value is reached, which probviously happens with enough attempts.		Conway first uses "probvious" to describe the idea that the sequences of iterates <math>(\cdots,8,\mu(8),\mu^2(8),\cdots)</math> and <math>(\cdots,14,\mu(14),\mu^2(14),\cdots)</math> diverge to infinity. Likewise, there exist [[Turing machines]] for which determining whether they halt requires solving a mathematical problem believed to be difficult, oftentimes a [[Collatz-like]] problem, but using probabilistic approximations of their functions suggests a clear solution. For example, Bigfoot, Hydra, and others function like biased random walks and treating them as such leads to the conclusion that they are probviously nonhalting. Similarly, machines such as [[Lucy's Moonlight]], [[Mother of Giants]], and others function like very slow-running random number generators that halt once a specific value is reached, which probviously happens with enough attempts.
	== References ==		== References ==
	<references />		<references />

MrSolis at 22:45, 7 March 2025

2025-03-07T22:45:56Z

← Older revision		Revision as of 22:45, 7 March 2025
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	'''Probvious''' is a portmanteau of ~~"probabilistically~~ obvious~~" coined~~ by John Conway in ~~"On Unsettleable Arithmetical Problems"~~.<ref>John Conway. "On Unsettleable Arithmetical Problems". 2017. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref>		"'''Probvious'''" (a portmanteau of the words ''probabilistic'' and ''obvious'') is an adjective used to express a high degree of confidence about a mathematical property or statement that is not known to be true. It was introduced by John Conway in an article discussing potentially unproveable statements.<ref>John Conway. "On Unsettleable Arithmetical Problems". 2017. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref> The term has been used by [https://www.bbchallenge.org bbchallenge] contributors to describe the solutions to halting problems for [[Cryptids]] such as [[Bigfoot]] and [[Hydra]].
			==Usage==
	~~<blockquote>~~		[[File:ProbviousExcerpt.png\|right\|400px\|thumb\|The excerpt from the article by John Conway where "probvious" is introduced.]]
	~~However, the numbers~~ in ~~both~~ of ~~these cycles have~~ been ~~followed~~ in ~~each direction until they get larger than 10~~<~~sup~~>~~400~~</~~sup~~> ~~and it’s obvious that they will never again descend below 100~~. ~~We need a name for this kind of obviousness~~: ~~I suggest probvious~~, ~~abbreviating “probabilistically obvious~~.”		The word appears in Conway's article a few times as a way of forming conjectures about a [[Collatz-like]] function that had already been investigated in the past.<ref>Atkin, A. O. L. "Problem 63-13." <i>SIAM Review</i> 8, no. 2 (1966): 234–36. JSTOR, http://www.jstor.org/stable/2028281</ref><ref>Guy, Richard K. "Don’t Try to Solve These Problems!" <i>The American Mathematical Monthly</i> 90, no. 1 (1983): 35–41. JSTOR, https://doi.org/10.2307/2975688</ref> This function, denoted <math>\mu(n)</math>, is defined as:
	</~~blockquote~~>		<math display="block">\begin{array}{lll}\mu(2n)&=&3n\\ \mu(4n+1)&=&3n+1\\ \mu(4n+3)&=&3n+2\end{array}\qquad\Rightarrow\qquad\begin{array}{lll}\mu^{-1}(3n)&=&2n\\ \mu^{-1}(3n+1)&=&4n+1\\ \mu^{-1}(3n+2)&=&4n+3\end{array}</math>
			Conway first uses "probvious" to describe the idea that the sequences of iterates <math>(\cdots,8,\mu(8),\mu^2(8),\cdots)</math> and <math>(\cdots,14,\mu(14),\mu^2(14),\cdots)</math> diverge to infinity. Likewise, there exist [[Turing machines]] for which determining whether they halt requires solving a mathematical problem believed to be difficult, oftentimes a [[Collatz-like]] problem, but using probabilistic approximations of their functions suggests a clear solution. For example, Bigfoot, Hydra, and others function like biased random walks and treating them as such leads to the conclusion that they are probviously nonhalting. Similarly, machines such as [[Lucy's Moonlight]], [[Mother of Giants]], and others function like very slow-running random number generators that halt once a specific value is reached, which probviously happens with enough attempts.
	~~Probviousness is subjective~~, there ~~is no precise~~ mathematical ~~definition of what is or is not probvious. However~~, ~~it is~~ a ~~useful concept when thinking about~~ [[Collatz-like]] ~~problems where we generally do not think that we are anywhere near being able to solve them~~, but ~~by observing the behavior as if it were probabilistically random, there is an~~ clear solution. ~~This is especially useful for [[Cryptids]] where we can have Cryptids which probviously never halt (like [[~~Bigfoot]], [[Hydra]] and [[~~Antihydra~~]]~~) and ones that probviously halt (like~~ [[Mother of Giants]]).

	== References ==		== References ==
	<references />		<references />

Int-y1: unmath

2024-07-24T03:14:14Z

unmath

← Older revision		Revision as of 03:14, 24 July 2024
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	<blockquote>		<blockquote>
	However, the numbers in both of these cycles have been followed in each direction until they get larger than <~~math~~>~~10^{~~400}</~~math~~> and it’s obvious that they will never again descend below 100. We need a name for this kind of obviousness: I suggest probvious, abbreviating “probabilistically obvious.”		However, the numbers in both of these cycles have been followed in each direction until they get larger than 10<sup>400</sup> and it’s obvious that they will never again descend below 100. We need a name for this kind of obviousness: I suggest probvious, abbreviating “probabilistically obvious.”
	</blockquote>		</blockquote>

Sligocki: Probvious

2024-07-10T19:57:14Z

Probvious

New page

'''Probvious''' is a portmanteau of "probabilistically obvious" coined by John Conway in "On Unsettleable Arithmetical Problems".<ref>John Conway. "On Unsettleable Arithmetical Problems". 2017. https://doi.org/10.4169/amer.math.monthly.120.03.192</ref>

<blockquote>
However, the numbers in both of these cycles have been followed in each direction until they get larger than <math>10^{400}</math> and it’s obvious that they will never again descend below 100. We need a name for this kind of obviousness: I suggest probvious, abbreviating “probabilistically obvious.”
</blockquote>

Probviousness is subjective, there is no precise mathematical definition of what is or is not probvious. However, it is a useful concept when thinking about [[Collatz-like]] problems where we generally do not think that we are anywhere near being able to solve them, but by observing the behavior as if it were probabilistically random, there is an clear solution. This is especially useful for [[Cryptids]] where we can have Cryptids which probviously never halt (like [[Bigfoot]], [[Hydra]] and [[Antihydra]]) and ones that probviously halt (like [[Mother of Giants]]).

== References ==
<references />