EPISODE · Jun 17, 2022 · 3 MIN
A Halting Problem
from The 21st Century Monads · host The 21st Century Monads
Will I ever stop? I guess that's the point. Lyrics written by Carrie Jenkins and Kris McDaniel Kris McDaniel: vocals, edrums, electric guitar, 8-string ukulele, keyboards Carrie Jenkins: vocals Ben Bradley: bass guitar, cello, electric guitar, acoustic guitar Cover art by Carrie Jenkins A Turing machine is a simple device that calculates a mathematical function. For any given function f and input i, a Turing machine that calculates f will, if fed the input i, halt on the output f(i) in the event that such an output exists (i.e. if f is defined for input i). A Halting Problem is the problem of specifying, for a given machine-input pair, whether the machine will halt (i.e. deliver an output) when fed that input, or keep calculating forever (in the event that the function is undefined for that input). Alan Turing, for whom the Turing machine is named, proved that there can be no universal algorithm which decides, for every machine-input pair, whether or not the machine halts when fed that input. This undecidability result helps philosophers understand the scope and limitations of formal mathematical systems. However, for robots it is a source of stress. Copyright 2022 © The 21st Century Monads
What this episode covers
Will I ever stop? I guess that's the point. Lyrics written by Carrie Jenkins and Kris McDaniel Kris McDaniel: vocals, edrums, electric guitar, 8-string ukulele, keyboards Carrie Jenkins: vocals Ben Bradley: bass guitar, cello, electric guitar, acoustic guitar Cover art by Carrie Jenkins A Turing machine is a simple device that calculates a mathematical function. For any given function f and input i, a Turing machine that calculates f will, if fed the input i, halt on the output f(i) in the event that such an output exists (i.e. if f is defined for input i). A Halting Problem is the problem of specifying, for a given machine-input pair, whether the machine will halt (i.e. deliver an output) when fed that input, or keep calculating forever (in the event that the function is undefined for that input). Alan Turing, for whom the Turing machine is named, proved that there can be no universal algorithm which decides, for every machine-input pair, whether or not the machine halts when fed that input. This undecidability result helps philosophers understand the scope and limitations of formal mathematical systems. However, for robots it is a source of stress. Copyright 2022 © The 21st Century Monads
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A Halting Problem
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