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To the Teacher

Published online by Cambridge University Press:  05 June 2012

Oded Goldreich
Affiliation:
Weizmann Institute of Science, Israel
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Summary

According to a common opinion, the most important aspect of a scientific work is the technical result that it achieves, whereas explanations and motivations are merely redundancy introduced for the sake of “error correction” and/or comfort. It is further believed that, as with a work of art, the interpretation of the work should be left to the reader.

The author strongly disagrees with the aforementioned opinions, and argues that there is a fundamental difference between art and science, and that this difference refers exactly to the meaning of a piece of work. Science is concerned with meaning (and not with form), and in its quest for truth and/or understanding, science follows philosophy (and not art). The author holds the opinion that the most important aspects of a scientific work are the intuitive question that it addresses, the reason that it addresses this question, the way it phrases the question, the approach that underlies its answer, and the ideas that are embedded in the answer. Following this view, it is important to communicate these aspects of the work.

The foregoing issues are even more acute when it comes to Complexity Theory, firstly because conceptual considerations seem to play an even more central role in Complexity Theory than in other scientific fields. Secondly (and even more importantly), Complexity Theory is extremely rich in conceptual content. Thus, communicating this content is of primary importance, and failing to do so misses the most important aspects of Complexity Theory.

Type
Chapter
Information
P, NP, and NP-Completeness
The Basics of Computational Complexity
, pp. xxi - xxiv
Publisher: Cambridge University Press
Print publication year: 2010

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  • To the Teacher
  • Oded Goldreich, Weizmann Institute of Science, Israel
  • Book: P, NP, and NP-Completeness
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511761355.003
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  • To the Teacher
  • Oded Goldreich, Weizmann Institute of Science, Israel
  • Book: P, NP, and NP-Completeness
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511761355.003
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • To the Teacher
  • Oded Goldreich, Weizmann Institute of Science, Israel
  • Book: P, NP, and NP-Completeness
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511761355.003
Available formats
×