17
$\begingroup$

I'm looking for some unpublished notes called "Eta Lore," which are apparently related to a talk Douglas Hofstadter first gave at the Stanford Math Club in 1963. I know these notes exist because they're cited in the following articles:

I've e-mailed the authors of the articles above, but I also thought I'd try asking around here, since none of the authors who've responded so far have been able to help. Any information on alternative references would also be appreciated.

Motivation and Background

I'm specifically interested in the definition of the function INT mentioned in Section I.33 of Gödel, Escher, Bach. The description there, in case it rings any bells, is: "The basic idea behind INT is that plus and minus signs are interchanged in a certain kind of continued fraction."

As far as I can tell, the notes I'm looking for are mostly about continued fractions and integer sequences---in particular, things called $\eta$-sequences and $\beta$-sequences (unfortunately, I have no idea what those are, and I haven't found any leads on OEIS).

Improve this question
$\endgroup$
7
  • 8
    $\begingroup$ Have you contacted Hofstadter? He is alive and working: cogs.indiana.edu/people/homepages/hofstadter.html $\endgroup$
    – David E Speyer
    Commented Jul 3, 2011 at 1:14
  • 1
    $\begingroup$ The link should be updated to cogs.indiana.edu/people/profile.php?u=dughof $\endgroup$
    – Andrés E. Caicedo
    Commented Dec 15, 2013 at 7:10
  • 3
    $\begingroup$ @DavidSpeyer, thanks for the suggestion! It should have been obvious, but wasn't to me at the time. I did get in touch with Hofstadter, and he send me a copy of the notes. (I'm sorry this thank-you was so long in coming, by the way---I completely forgot I'd asked this question, and was only reminded when it popped up on the front page again.) $\endgroup$
    – Vectornaut
    Commented Dec 15, 2013 at 7:28
  • $\begingroup$ @Vectornaut Can you send me his notes too? $\endgroup$
    – Alexey Ustinov
    Commented Dec 15, 2013 at 12:53
  • $\begingroup$ @Vectornaut (or Alexey) Could either of you forward it to me as well? $\endgroup$
    – Greg Zitelli
    Commented Dec 15, 2013 at 17:20

2 Answers 2

Reset to default
8
$\begingroup$

This graph is looks like a graf of the function which replaces partial quotient (in nearest integer continued fraction) in the following way: $$a_i+~\leftrightarrow~a_i+1-.$$ For example $$0+\cfrac{1}{3-\cfrac{1}{4+\cfrac{1}{5+0}}}\leftrightarrow 1-\cfrac{1}{2+\cfrac{1}{5-\cfrac{1}{6-0}}}. $$ \begin{align*} \frac{1}{2}=\frac{1}{2+0}&\leftrightarrow1-\frac{1}{3-0}=\frac{2}{3},&\frac{1}{3}=\frac{1}{3+0}&\leftrightarrow1-\frac{1}{4-0}=\frac{3}{4},\\ \frac{2}{5}=\frac{1}{2+\frac{1}{2+0}}&\leftrightarrow1-\frac{1}{3-\frac{1}{3-0}}=\frac{5}{8},&\frac{3}{5}=1-\frac{1}{2+\frac{1}{2+0}}&\leftrightarrow 0+\frac{1}{3-\frac{1}{3-0}}=\frac{3}{8}. \end{align*} The picture from the book: Picture

Improve this answer
$\endgroup$
11
$\begingroup$

A copy of Hofstadter's paper is on OEIS here: Link to Eta-Lore paper

It is also referenced on OEIS at A001468.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .