JF Ptak Science Books Post 2095

I am probably not understanding this wonderful effort^{1} by the dead Lewis Carroll, establishing a new algorithm for doing long division. It came into view while I was looking for a paper in *Nature* by A.A. Michelson on his analog computer, the harmonic analyzer, a fantastic device that he used to help measure the speed of light back in 1898. Carroll (as Dodgson) appeared just a few pages away^{2}; his obituary appears not much after the division article, thus making the paper the last of his career here on Earth.

It is a very interesting effort, and it perhaps is even brilliant and of a wonderful construct, but the bottom line is that it makes the process of division harder to do--perhaps it is mire understandable as a process, but the process itself is decidedly not a preferred one. Perhaps it is appropriate for his last work to have been on mathematics, since the majority of his 20 published books relate to mathematics or logic.

**Notes**

1. DODGSON, Charles Lutwidge ('Lewis Carroll'). "Abridged Long Division", in *Nature*, page 269, in the weekly issue for 20 January 1898, with the original outer wrappers removed from larger bound volume. Very good copy. It is here that Carroll announces (in a long 3pp letter to the editor) his implementation of a new algorithm for division--it makes the process longer and more difficult, unfortunately.

The article is abstracted here, a few weeks after publication:

*Article abstract: Nature* 57, 390-391 (24 February 1898), "Abridged Long Division" abstracted by ROBT. W. D. CHRISTI:

"HAVING been working on similar lines for some years, I was very much interested in the late Mr. Dodgson’s letter on abridged division in NATURE of January 20, and I should like to offer a few observations and to give a variation of the method which appears much simpler. It will be admitted that Mr. Dodgson’s plan is of limited application, and rather complicated for general use. There is nothing to hinder the method given below from being universally used, though it may not in all cases be the shortest. It also has the merit, I think, of directness and uniformity."

2. This is one of three publications of Carroll's mathematical works that appeared in Nature, being "Abridged long division", *Nature* 57, 269-271; "Brief method of dividing a given number by 9 or 11",* Nature* 56, 565-566; "Pillow problems. Curiosa mathematica. Part II", *Nature* XLVIII. 564.

The following list of Carroll's mathematical works is taken from the table of contents of *The mathematical pamphlets of Charles Lutwidge Dodgson and related piece*, compiled, with introductory essays, notes, and annotations, by Francine F. Abeles. (New York : Lewis Carroll Society of North America ; Charlottesville : Distributed by the University Press of Virginia, 1994.)

**Geometry**

- 1. Notes on the First Two Books of Euclid (1860)
- 2. Enunciations of Euclid, Books I and II (1863)
- 3. Fifth Book of Euclid (1868)
- 4. Enunciations of Euclid I-VI (1873)

**Trigonometry**

- 5. Formulae of Plane Trigonometry (1861)
- 6. Formulae (Group C) (undated)
- 7. Simple Facts about Circle-Squaring (1882)
- 8. Proof Sheets: Propositions I, II (undated)
- 9. Question 11530 (1893)

**Algebra**

- 10. Condensation of Determinants (1866)
- 11. Algebraical Formulae for the Use of Candidates for Responsions (1868)
- 12. Formulae in Algebra (1868?)
- 13. Algebraical Formulae and Rules for the Use of Candidates for Responsions (1870)
- 14. Algebra (1877)
- 15. Formulae (1878)
- 16. Question 9995 (1889)

**Probability**

- 17. Note on Question 7695 [including Question 7695 and its solution (1885)]
- 18. Response to "Infinitesimal or Zero?" (1886)
- 19. Something or Nothing? (1888)
- 20. Question 9588 (1889)

**Arithmetic Computation and Theory**

- 21. Arithmetical Formulae and Rules for the Use of Candidates for Responsions (1870)
- 22. Examples in Arithmetic (1874)
- 23. Arithmetic I (1870-74?)
- 24. Arithmetic II (1870-74?)
- 25. Arithmetic (undated)
- 26. Practical Hints on Teaching. Long Multiplication Worked with a Single Line of Figures (1879)
- 27. Divisibility by Seven (1884)
- 28. To Find the Day of the Week for Any Given Date (1887)
- 29. Question 9636 (1888)
- 30. Question 12650 (1895)
- 31. Number-Guessing (1896)
- 32. Question 13614 (1897)
- 33. Brief Method of Dividing a Given Number by 9 or 11 (1897)
- 34. Variant of Item 33 (same title, date)
- 35. Rule for Finding Easter-Day for Any Date till A.D. 2499 (1892-97?)
- 36. Abridged Long Division (1898)

**Cryptology**

- 37. Key-Vowel Cipher (1858)
- 38. Matrix Cipher (1858)
- 39. Alphabet Cipher (1868)
- 40. Telegraph Cipher (1868)

**Curriculum**

- 41. Circular to Mathematical Friends (1862)
- 42. Proof Sheets Accompanying the Circular (undated)
- 43. Guide to the Mathematical Student (1864).

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