I've used the phrase more than once, but in this answer I wrote:

closing thoughts: Realistic orbits are not perfect conics, and so they and their Keplerian elements do not represent realistic orbits. They are only approximations to reality, and so are not right even though they are close.

Keplerian elements were used when people were writing with feathers using light from burning animal fat (if they were not busy being burned at the stake themselves). They are a mixed blessing in the 21st century when everything has so many more digits.

I understand that I am probably jumbling a few different centuries together there, but I am wondering about the hardware more than the politics.

In the fields of mathematics and orbital mechanics, say from Kepler to Lagrange, were mathematical derivations and computations done with pens made from feathers, and if an inspiration came after sundown, was light often as not produced by animal fat, whale oil, or the like?

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    $\begingroup$ The name for such pen is "quill", and yes Bernoulli and Euler were using them. Metal pens only spread in early 1800-s. $\endgroup$
    – Conifold
    Jul 27 '17 at 6:02
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    $\begingroup$ There is an evidence that Euler used pencil. $\endgroup$ Jul 27 '17 at 9:04
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    $\begingroup$ @uhoh: It is from a statement of Euler himself which is frequently reproduced (for example, in Boyer's History of Mathematics): " He is supposed to have said that his pencil seemed to surpass him in intelligence, so easily did memoirs flow." $\endgroup$ Jul 27 '17 at 9:33
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    $\begingroup$ @uhoh: Wikipedia says that graphite pencil was invented in 1560, but it does not discuss how common was it in 18th century. $\endgroup$ Jul 27 '17 at 9:37
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    $\begingroup$ @AlexandreEremenko ... Euler was not speaking in English. Presumably in Latin. So what was the Latin word for "pencil"? We had another question around here (about "pencil" in geometry), where it turned out that "pencil" refered to the fibers of a brush that meet in a point... $\endgroup$ Jul 27 '17 at 13:58

Quick Internet search says that feather quills were mainly used in 600-1800 AD. After that people gradually switched to steel.

First true mathematicians (Babylonians) wrote on clay tablets. In the Greek/Roman Antiquity they wrote on papyrus, presumably with reed pens or brushes. Apparently they switched from brushes to pens in Ptolemaic Egypt, that is exactly when serious mathematics started:


Papyrus was used for "publication", for books and perhaps for letters, not for the actual work. The work was done on wax tablets, since the Roman times, and on sand before that. Even in 18th century, paper was not cheap enough for use as "scratch paper".

The data on when pencil became common diverge by 200 years, some say in 16th century, others in 18th.

Speaking of light sources, it does not have to be animal fat. The most common lamps used all kinds of vegetable oil. These lamps of various shapes were commonly used since Paleolith till 20th century in many places. In many locations, vegetable oil is cheaper than animal fat or wax candles.

  • $\begingroup$ Thank you very much for taking time to add a very nice answer to my question, I appreciate you taking it seriously. It seems my crude quote given in the question is not necessarily true throughout the period specified, although it is roughly the right idea in spirit. I'm glad I asked! $\endgroup$
    – uhoh
    Jul 27 '17 at 11:22
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    $\begingroup$ @udoh: I find your present question somewhat interesting indeed, but totally disagree with your quote from which the question arose. $\endgroup$ Jul 27 '17 at 15:48
  • $\begingroup$ In the context in which it was used, I don't think many readers thought that it was meant to be taken literally; the part about feathers and fat at least. If you disagree with my point that to gigaFLOP laptops with 20 digits of precision Keplerian elements are no longer the way to go, then please leave a comment at its point of origin and context. Thanks! $\endgroup$
    – uhoh
    Jul 27 '17 at 15:57
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    $\begingroup$ @uhoh: I do not participate in Space Travel exchange. $\endgroup$ Jul 27 '17 at 16:04
  • $\begingroup$ okay, well I appreciate your help with my trying to participate in HSM none the less :) $\endgroup$
    – uhoh
    Jul 27 '17 at 16:13

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