On 2015-11-23 08:19, James Propp wrote:
I don't have time to record it and post the recording, but here's how it goes, IIRC:
Leader: A-bba! Group: I-ma!
Leader: I-ma! Group: A-bba!
Leader: Abba Ima! Group: Ima Abba!
Leader: Ima Abba! Group: Abba Ima!
Leader: Abba Ima Ima Abba! Group: Ima Abba Abba Ima!
Leader: Abba Ima Ima Abba Ima Abba Abba Ima! Group: Ima Abba Abba Ima Abba Ima Ima Abba!
(Actually, I'm not sure the last call-and-response pair is included outside of gatherings of especially nerdy Jews; most song-leaders probably fear over-taxing the short-term memories of the singers.)
Jim Propp
On Mon, Nov 23, 2015 at 10:13 AM, James Propp <jamespropp@gmail.com> wrote:
Does anyone know the background of the incursion of the Thue-Morse sequence into 20th century Jewish popular folk music?
There's a style of call-and-response mini-song often tucked into the middle of "David Melech Yisrael" dating back at least to the 1970s, in which two opposed Hebrew words or phrases, like mother/father and yes/no, are alternated in Thue-Morse style (see https://en.m.wikipedia.org/wiki/Thue–Morse_sequence).
Was there some particular musician who was responsible for this?
(Also, can anyone find a relevant clip on YouTube?)
Jim Propp
https://en.m.wikipedia.org/wiki/Thue–Morse_sequence is surprisingly good, but doesn't quite subsume http://www.inwap.com/pdp10/hbaker/hakmem/series.html Item 122 nor http://www.inwap.com/pdp10/hbaker/hakmem/topology.html Item 115
In particular, the non-regular continued fraction for t(1/2), In[284]:= 1/(3 - 1/(2 + ContinuedFractionK[1 - 2^2^k, 2^2^(k + 1), {k, 0, n}])) In[287]:= Table[%284, {n, 0, 4}] Out[287]= {7/17, 106/257, 27031/65537, 1771476586/4294967297, 7608434000728254871/18446744073709551617} is about twice as efficient as interpreting partial strings of T in binary: In[290]:= RealDigits[106/257, 2] Out[290]= {{{1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0}}, -1} (Remember to prefix a leading 0.) (The former is alternately mediant(x,x,1/1) and mediant(x,1/1), where x = the latter.) I got excited when the article mentioned fractals, but instead of Hilbert, named von Koch! In[302]:= hilbert /@ %287 Out[302]= {{2/5 + I}, {7/17 + I}, {106/257 + I}, {27031/65537 + I}, {1771476586/4294967297 + I}} I.e., the exact Hilbert function backs up one term, and adds i ! Likewise to the 1's complement: In[303]:= 1 - %287 Out[303]= {10/17, 151/257, 38506/65537, 2523490711/4294967297, 10838310072981296746/18446744073709551617} In[304]:= hilbert /@ % Out[304]= {{3/5 + I}, {10/17 + I}, {151/257 + I}, {38506/65537 + I}, {2523490711/4294967297 + I}} Thus bolstering the claim that x = t(1/2) and x = 1-t(1/2) are the only solutions to Hilbert(x) = x+i . I wonder if the wikisnobs will accept HAKMEM as unoriginal research. --rwg