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17. The rise of symbolic notation in scientific communication: the case of mathematics

  • Michel Serfati
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Science Communication
This chapter is in the book Science Communication

Abstract

This article describes, in an epistemological analysis, the constitution of a specific language, namely mathematical symbolic writing. The framework of modern mathematics, physical sciences, and, generally speaking, of scientific communication, is today entirely organized around this language. Its initial constitution in the 17th century, with Descartes and Leibniz as main protagonists, constituted an unprecedented upheaval over previous designs - what I have called the “Symbolic Revolution”. This symbolic language has a very specific pattern: it is, in no way, the transcription in signs - a form of shorthand - of any natural language. I will show for example how, in its construction, it has undeniably relied on contradictions or ambiguities (see “The dialectic of indeterminacy”), and how much this apparently paradoxical organization has been fruitful. I will also highlight how much this language allowed, in mathematics, the invention of objects or concepts, in an unprecedented way in the construction of natural languages: see the “Invar-Ext” scheme; see also the ability of symbolic substitutability to construct new objects, in an unprecedented way, possibly without reference to the meanings. I also describe in detail how the need to dispel the ambiguity of order in the execution of the operations has led mathematicians to develop a new design that is common today, the so-called “arborescent thought”.

Abstract

This article describes, in an epistemological analysis, the constitution of a specific language, namely mathematical symbolic writing. The framework of modern mathematics, physical sciences, and, generally speaking, of scientific communication, is today entirely organized around this language. Its initial constitution in the 17th century, with Descartes and Leibniz as main protagonists, constituted an unprecedented upheaval over previous designs - what I have called the “Symbolic Revolution”. This symbolic language has a very specific pattern: it is, in no way, the transcription in signs - a form of shorthand - of any natural language. I will show for example how, in its construction, it has undeniably relied on contradictions or ambiguities (see “The dialectic of indeterminacy”), and how much this apparently paradoxical organization has been fruitful. I will also highlight how much this language allowed, in mathematics, the invention of objects or concepts, in an unprecedented way in the construction of natural languages: see the “Invar-Ext” scheme; see also the ability of symbolic substitutability to construct new objects, in an unprecedented way, possibly without reference to the meanings. I also describe in detail how the need to dispel the ambiguity of order in the execution of the operations has led mathematicians to develop a new design that is common today, the so-called “arborescent thought”.

Chapters in this book

  1. Frontmatter I
  2. Preface V
  3. Table of contents VII
  4. Introduction to the volume XI
  5. I. Perspectives of research on scholarly and science communication
  6. 1. Philosophy of science for science communication in twenty-two questions 3
  7. 2. Science understanding between scientific literacy and trust: contributions from psychological and educational research 29
  8. 3. The contribution of media studies to the understanding of science communication 51
  9. 4. Analyzing science communication through the lens of communication science: Reviewing the empirical evidence 77
  10. 5. Modeling science communication: from linear to more complex models 105
  11. 6. The contribution of laboratory studies, science studies and Science and Technology Studies (STS) to the understanding of scientific communication 123
  12. 7. The contribution of linguistics and semiotics to the understanding of science communication 143
  13. 8. The contribution of terminology research to the understanding of science communication 167
  14. 9. The study of student academic writing 187
  15. II. Text types, media, and practices of science communication
  16. 10. Epistemic genres 209
  17. 11. On the nature and role of visual representations in knowledge production and science communication 235
  18. 12. The lecture and the presentation – rhetorics and technology 257
  19. 13. Spoken language in science and the humanities 271
  20. 14. Scholarly reviewing 289
  21. 15. Scientific controversies 311
  22. 16. Symbolic notation in scientific communication: a panorama 335
  23. 17. The rise of symbolic notation in scientific communication: the case of mathematics 357
  24. 18. Grant proposal writing as a dialogic process 377
  25. III. Science, scientists, and the public
  26. 19. Communicative strategies of popularization of science (including science exhibitions, museums, magazines) 399
  27. 20. Science journalism 417
  28. 21. Teaching science journalism as a blueprint for future journalism education 439
  29. 22. Science communication and public relations: beyond borders 465
  30. 23. Science communication, advising, and advocacy in public debates 485
  31. 24. Forms of science presentations in public settings 515
  32. IV. Historical perspectives on science communication
  33. 25. Historical perspectives on internal scientific communication 547
  34. 26. Academic teaching: the lecture and the disputation in the history of erudition and science 569
  35. 27. Historical aspects of external science communication 585
  36. V. Science communication: present and future
  37. 28. Reconfigurations of science communication research in the digital age 603
  38. 29. The library in a changing world of scientific communication 625
  39. 30. Scholarly communication in social media 639
  40. 31. Current trends and future visions of (research on) science communication 657
  41. Contributors to this volume 689
  42. Index 697
https://doi.org/10.1515/9783110255522-017

Chapters in this book

  1. Frontmatter I
  2. Preface V
  3. Table of contents VII
  4. Introduction to the volume XI
  5. I. Perspectives of research on scholarly and science communication
  6. 1. Philosophy of science for science communication in twenty-two questions 3
  7. 2. Science understanding between scientific literacy and trust: contributions from psychological and educational research 29
  8. 3. The contribution of media studies to the understanding of science communication 51
  9. 4. Analyzing science communication through the lens of communication science: Reviewing the empirical evidence 77
  10. 5. Modeling science communication: from linear to more complex models 105
  11. 6. The contribution of laboratory studies, science studies and Science and Technology Studies (STS) to the understanding of scientific communication 123
  12. 7. The contribution of linguistics and semiotics to the understanding of science communication 143
  13. 8. The contribution of terminology research to the understanding of science communication 167
  14. 9. The study of student academic writing 187
  15. II. Text types, media, and practices of science communication
  16. 10. Epistemic genres 209
  17. 11. On the nature and role of visual representations in knowledge production and science communication 235
  18. 12. The lecture and the presentation – rhetorics and technology 257
  19. 13. Spoken language in science and the humanities 271
  20. 14. Scholarly reviewing 289
  21. 15. Scientific controversies 311
  22. 16. Symbolic notation in scientific communication: a panorama 335
  23. 17. The rise of symbolic notation in scientific communication: the case of mathematics 357
  24. 18. Grant proposal writing as a dialogic process 377
  25. III. Science, scientists, and the public
  26. 19. Communicative strategies of popularization of science (including science exhibitions, museums, magazines) 399
  27. 20. Science journalism 417
  28. 21. Teaching science journalism as a blueprint for future journalism education 439
  29. 22. Science communication and public relations: beyond borders 465
  30. 23. Science communication, advising, and advocacy in public debates 485
  31. 24. Forms of science presentations in public settings 515
  32. IV. Historical perspectives on science communication
  33. 25. Historical perspectives on internal scientific communication 547
  34. 26. Academic teaching: the lecture and the disputation in the history of erudition and science 569
  35. 27. Historical aspects of external science communication 585
  36. V. Science communication: present and future
  37. 28. Reconfigurations of science communication research in the digital age 603
  38. 29. The library in a changing world of scientific communication 625
  39. 30. Scholarly communication in social media 639
  40. 31. Current trends and future visions of (research on) science communication 657
  41. Contributors to this volume 689
  42. Index 697
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