The Nonlinear Library: LessWrong LW - Quick look: applications of chaos theory by Elizabeth
Aug 19, 2024
12:57
Link to original article
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Quick look: applications of chaos theory, published by Elizabeth on August 19, 2024 on LessWrong.
Introduction
Recently we (Elizabeth Van Nostrand and Alex Altair) started a project investigating chaos theory as an example of field formation.[1] The number one question you get when you tell people you are studying the history of chaos theory is "does that matter in any way?".[2] Books and articles will list applications, but the same few seem to come up a lot, and when you dig in, application often means "wrote some papers about it" rather than "achieved commercial success".
In this post we checked a few commonly cited applications to see if they pan out. We didn't do deep dives to prove the mathematical dependencies, just sanity checks.
Our findings: Big Chaos has a very good PR team, but the hype isn't unmerited either. Most of the commonly touted applications never received wide usage, but chaos was at least instrumental in several important applications that are barely mentioned on wikipedia. And it was as important for weather as you think it is.
Applications
Cryptography and random number generators- Strong No (Alex)
The wikipedia page for Chaos theory has a prominent section on cryptography. This sounds plausible; you certainly want your encryption algorithm to display sensitive dependence on initial conditions in the sense that changing a bit of your input randomizes the bits of your output. Similarly, one could imagine using the sequence of states of a chaotic system as a random number generator. However a quick google search makes me (Alex) think this is not a serious application.
I've seen it claimed[3] that one of the earliest pseudo-random number generators used the logistic map, but I was unable to find a primary reference to this from a quick search.
Some random number generators use physical entropy from outside the computer (rather than a pseudo-random mathematical computation). There are some proposals to do this by taking measurements from a physical chaotic system, such as an electronic circuit or lasers. This seems to be backward, and not actually used in practice.
The idea is somewhat roasted in the Springer volume "Open Problems in Mathematics and Computational Science" 2014, chapter "True Random Number Generators" by Mario Stipčević and Çetin Kaya Koç.
Other sources that caused me to doubt the genuine application of chaos to crypto include this Crypto StackExchange question, and my friend who has done done cryptography research professionally.
As a final false positive example, a use of lava lamps as a source of randomness once gained some publicity. Though this was patented under an explicit reference to chaotic systems, it was only used to generate a random seed, which doesn't really make use of the chaotic dynamics. It sounds to me like it's just a novelty, and off-the-shelf crypto libraries would have been just fine.
Anesthesia, Fetal Monitoring, and Approximate Entropy- No (Elizabeth)
Approximate Entropy (ApEn) is a measurement designed to assess how regular and predictable a system is, a simplification of Kolmogorov-Sinai entropy. ApEn was originally invented for analyzing medical data, such as brain waves under anesthesia or fetal heart rate. It has several descendents, including Sample Entropy; for purposes of this article I'm going to refer to them all as ApEn.
Researchers have since applied the hammer of ApEn and its children to many nails, but as far as I (Elizabeth) can tell it has never reached widespread usage.
ApEn's original application was real time fetal heart monitoring; however as far as I can tell it never achieved commercial success and modern doctors use simpler algorithms to evaluate fetal monitoring data.
ApEn has also been extensively investigated for monitoring brain waves under anesthesia. However commercially avail...
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Quick look: applications of chaos theory, published by Elizabeth on August 19, 2024 on LessWrong.
Introduction
Recently we (Elizabeth Van Nostrand and Alex Altair) started a project investigating chaos theory as an example of field formation.[1] The number one question you get when you tell people you are studying the history of chaos theory is "does that matter in any way?".[2] Books and articles will list applications, but the same few seem to come up a lot, and when you dig in, application often means "wrote some papers about it" rather than "achieved commercial success".
In this post we checked a few commonly cited applications to see if they pan out. We didn't do deep dives to prove the mathematical dependencies, just sanity checks.
Our findings: Big Chaos has a very good PR team, but the hype isn't unmerited either. Most of the commonly touted applications never received wide usage, but chaos was at least instrumental in several important applications that are barely mentioned on wikipedia. And it was as important for weather as you think it is.
Applications
Cryptography and random number generators- Strong No (Alex)
The wikipedia page for Chaos theory has a prominent section on cryptography. This sounds plausible; you certainly want your encryption algorithm to display sensitive dependence on initial conditions in the sense that changing a bit of your input randomizes the bits of your output. Similarly, one could imagine using the sequence of states of a chaotic system as a random number generator. However a quick google search makes me (Alex) think this is not a serious application.
I've seen it claimed[3] that one of the earliest pseudo-random number generators used the logistic map, but I was unable to find a primary reference to this from a quick search.
Some random number generators use physical entropy from outside the computer (rather than a pseudo-random mathematical computation). There are some proposals to do this by taking measurements from a physical chaotic system, such as an electronic circuit or lasers. This seems to be backward, and not actually used in practice.
The idea is somewhat roasted in the Springer volume "Open Problems in Mathematics and Computational Science" 2014, chapter "True Random Number Generators" by Mario Stipčević and Çetin Kaya Koç.
Other sources that caused me to doubt the genuine application of chaos to crypto include this Crypto StackExchange question, and my friend who has done done cryptography research professionally.
As a final false positive example, a use of lava lamps as a source of randomness once gained some publicity. Though this was patented under an explicit reference to chaotic systems, it was only used to generate a random seed, which doesn't really make use of the chaotic dynamics. It sounds to me like it's just a novelty, and off-the-shelf crypto libraries would have been just fine.
Anesthesia, Fetal Monitoring, and Approximate Entropy- No (Elizabeth)
Approximate Entropy (ApEn) is a measurement designed to assess how regular and predictable a system is, a simplification of Kolmogorov-Sinai entropy. ApEn was originally invented for analyzing medical data, such as brain waves under anesthesia or fetal heart rate. It has several descendents, including Sample Entropy; for purposes of this article I'm going to refer to them all as ApEn.
Researchers have since applied the hammer of ApEn and its children to many nails, but as far as I (Elizabeth) can tell it has never reached widespread usage.
ApEn's original application was real time fetal heart monitoring; however as far as I can tell it never achieved commercial success and modern doctors use simpler algorithms to evaluate fetal monitoring data.
ApEn has also been extensively investigated for monitoring brain waves under anesthesia. However commercially avail...