Research Article
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Between Bound and Extremum: A Mathematical Reading of Odyssey 15.69-71
1
Department of Business Administration, Philips University, Nicosia 2001, Cyprus
* Corresponding Author:
Spyros Missiakoulis,
[email protected]
Volume 1, Issue 1
2025
Received: 17 August 2026
Revised: 27 August 2026
Accepted: 06 October 2026
Published: 24 October 2026
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Article Information
Published in
Journal of Mathematical Studies of Literature
Volume/Issue
Volume 1, Issue 1, 2025
Pages
21-27
Abstract
Odyssey 15.69-71 has Menelaus advise Telemachus that a host who loves or hates a guest to excess is worse than one who observes αἴσιμα (aisima; `due measure'), a word usually rendered as measure, balance or moderation. Read against the vocabulary of modern optimisation, the passage can look like an early statement of an optimisation principle: two extremes excluded, something better in between. We argue that this resemblance is misleading. The Greek text describes a tolerance interval, a set of acceptable conduct with no criterion for ranking one acceptable choice above another, rather than an interior extremum, a unique optimal point which, for a differentiable objective, is marked by a vanishing derivative. Aristotle's doctrine of the mean occupies an intermediate position. It introduces a selection criterion, the judgement of the φρόνιμος (phronimos; `person of practical wisdom'), while explicitly declining to express that criterion mathematically. A survey of thirty-four published English translations of the passage shows the same conflation recurring in practice. Three translators, writing between 1665 and 1932, render αἴσιμα as `the Golden Mean' or `the happy mean', importing the vocabulary of the later doctrine of the mean into a much earlier text. We conclude that distinguishing a qualitative bound from a quantitative extremum clarifies both the ancient text and a confusion about balance and moderation that persists in ordinary language today.
Keywords
Homeric ethics
Aristotelian mean
mathematical optimisation
classical translation reception
Data Availability Statement
Not applicable.
Funding
This work received no external funding.
Conflicts of Interest
The author declares no conflicts of interest.
AI Use Statement
During the preparation of this work, the author drafted the manuscript in his native language (Greek) and used ChatGPT and Claude to assist with the translation into English. The same tools were also used to improve the grammatical accuracy, syntax and fluency of the English text. The author subsequently reviewed, revised and edited the content to ensure academic rigour and accuracy, and takes full responsibility for the final content of the publication.
Ethical Approval and Consent to Participate
Not applicable.
References
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Missiakoulis, S. (2026). Between Bound and Extremum: A Mathematical Reading of Odyssey 15.69-71. Journal of Mathematical Studies of Literature, 1(1), 21-27. https://doi.org/10.62762/JMSL.2026.634016
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TY - JOUR AU - Missiakoulis, Spyros PY - 2026 DA - 2026/10/24 TI - Between Bound and Extremum: A Mathematical Reading of Odyssey 15.69-71 JO - Journal of Mathematical Studies of Literature T2 - Journal of Mathematical Studies of Literature JF - Journal of Mathematical Studies of Literature VL - 1 IS - 1 SP - 21 EP - 27 DO - 10.62762/JMSL.2026.634016 UR - https://www.icck.org/article/abs/JMSL.2026.634016 KW - Homeric ethics KW - Aristotelian mean KW - mathematical optimisation KW - classical translation reception AB - Odyssey 15.69-71 has Menelaus advise Telemachus that a host who loves or hates a guest to excess is worse than one who observes αἴσιμα (aisima; `due measure'), a word usually rendered as measure, balance or moderation. Read against the vocabulary of modern optimisation, the passage can look like an early statement of an optimisation principle: two extremes excluded, something better in between. We argue that this resemblance is misleading. The Greek text describes a tolerance interval, a set of acceptable conduct with no criterion for ranking one acceptable choice above another, rather than an interior extremum, a unique optimal point which, for a differentiable objective, is marked by a vanishing derivative. Aristotle's doctrine of the mean occupies an intermediate position. It introduces a selection criterion, the judgement of the φρόνιμος (phronimos; `person of practical wisdom'), while explicitly declining to express that criterion mathematically. A survey of thirty-four published English translations of the passage shows the same conflation recurring in practice. Three translators, writing between 1665 and 1932, render αἴσιμα as `the Golden Mean' or `the happy mean', importing the vocabulary of the later doctrine of the mean into a much earlier text. We conclude that distinguishing a qualitative bound from a quantitative extremum clarifies both the ancient text and a confusion about balance and moderation that persists in ordinary language today. SN - pending PB - Institute of Central Computation and Knowledge LA - English ER -
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@article{Missiakoulis2026Between,
author = {Spyros Missiakoulis},
title = {Between Bound and Extremum: A Mathematical Reading of Odyssey 15.69-71},
journal = {Journal of Mathematical Studies of Literature},
year = {2026},
volume = {1},
number = {1},
pages = {21-27},
doi = {10.62762/JMSL.2026.634016},
url = {https://www.icck.org/article/abs/JMSL.2026.634016},
abstract = {Odyssey 15.69-71 has Menelaus advise Telemachus that a host who loves or hates a guest to excess is worse than one who observes αἴσιμα (aisima; `due measure'), a word usually rendered as measure, balance or moderation. Read against the vocabulary of modern optimisation, the passage can look like an early statement of an optimisation principle: two extremes excluded, something better in between. We argue that this resemblance is misleading. The Greek text describes a tolerance interval, a set of acceptable conduct with no criterion for ranking one acceptable choice above another, rather than an interior extremum, a unique optimal point which, for a differentiable objective, is marked by a vanishing derivative. Aristotle's doctrine of the mean occupies an intermediate position. It introduces a selection criterion, the judgement of the φρόνιμος (phronimos; `person of practical wisdom'), while explicitly declining to express that criterion mathematically. A survey of thirty-four published English translations of the passage shows the same conflation recurring in practice. Three translators, writing between 1665 and 1932, render αἴσιμα as `the Golden Mean' or `the happy mean', importing the vocabulary of the later doctrine of the mean into a much earlier text. We conclude that distinguishing a qualitative bound from a quantitative extremum clarifies both the ancient text and a confusion about balance and moderation that persists in ordinary language today.},
keywords = {Homeric ethics, Aristotelian mean, mathematical optimisation, classical translation reception},
issn = {pending},
publisher = {Institute of Central Computation and Knowledge}
}
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Copyright © 2026 by the Author(s). Published by Institute of Central Computation and Knowledge. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
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