Archive for alternating series

a journal of the chaos (en cuisine) year

Posted in Books, Kids, Mountains, pictures, Travel, Wines with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on June 12, 2025 by xi'an

 Read La Fille du Grand Hiver (The Daughter of the Great Winter) by Isabelle Autissier (also a sailor who was the first woman to complete a solo world race in 1991). This is a novelised version of the story of Arnarulunguaq, who accompanied Knud Rasmussen on the Fifth Thule Expedition over several years, all the way to the Bering Strait. She died of tuberculosis the year after. (And will appear on a Dane banknote soon.) The novel is told from Arnarulunguaq‘s perspective, as she opens to wider possibilities, cultural diversity, and traces back her Inuit lineage along Knud Rasmussen. It is a beautiful travel story (and then some more), in the fascinating Far North, which further reminded me of a catholic missionary visiting our primary school in the mid  1960’s and giving a conference on the Inuits and their culture. I pressed my parents until they bought his book and read it over and over, probably the seed of my fascination for the Far North!

Mis-made both a vat of rice pudding—presumably by first grinding the rice grains as the whey did not get absorbed—and a vat of chocolate mousse!—by not melting the chocolate long enough—and another of vegan mousse—by failing to notice the chickpea water was salted and that my MIL’s egg-beater was broken (but I salvaged it into a decent mole, if not with 49 ingredients)! I also grilled panned hot chilis I had found on a local market, but they were so hot they made me cough and open all windows; they are now resting in an olive oil jar, to be soon tested!!! Rhubarb is back in the stalls of my local market, providing me with my breakfast spread for the coming weeks. I again enjoyed Toukoul’s dora wat on the night of the privaCI workshopt—a workshop that focussed almost entirely on contextual integrity, if with very little overlap with the BIRS workshop in Kelowna. And harvested as many cherries as possible from our fruitful (!) cherry tree (#1) before the local birds are them all.

Watched Black Doves, with (Bend it Like Beckham) Keira Knightley as the only recognisable actress in the set, a very cartoony spies series taking place in London at Xmas time, with funny dialogues and too good vibes that should restrict a viewer to watching the show on 24 December and no other day.

Simulating a coin with irrational bias using rational arithmetic

Posted in Books, Statistics with tags , , , , , , on December 17, 2020 by xi'an

An arXived paper by Luis Mendo adresses the issue of simulating coins with irrational probabilities from a fair coin, somehow connected with one of the latest riddles. Where I realised only irrational coins could be simulated in a fixed and finite number of throws! The setting of the paper is however similar to the one of a Bernoulli factory in that an unlimited number of coins can be generated (but it relies on a  fair coin). And the starting point is a series representation of the irrational ζ as a sum of positive and rational terms. As well as an earlier paper by the Warwick team of Łatuszyński et al. (2011). The solution is somewhat anticlimactic in that the successive draws of the fair coin lead to a sequence of intervals with length divided by 2 at each step. And stopping when a certain condition is met, requiring some knowledge on the tail error of the series. The paper shows further that the number of inputs used by its algorithm has an exponential tail. The examples provided therein are Euler’s constant

\gamma =\frac{1}{2} + \sum_{i=1}^\infty \frac{B(i)}{2i(2i+1)(2i+2)}

where B(j) is the number of binary digits of j, and π/4 which can be written as an alternating series. An idle question that came to me while reading this paper is the influence of the series chosen to represent the irrational ζ as it seems that a faster decrease in the series should lead to fewer terms being used. However, the number of iterations is a geometric random variable with parameter 1/2, therefore the choice of the series curiously does not matter.