Wikipedia:Reference desk/Archives/Mathematics/2018 June 2

= June 2 =

UK Passport
On one of the pages of the new style UK passports, there is a page that is an homage to Ada Lovelace and Charles Babbage. On that page, there are twelve equations, each with two v-like symbols, each one having a superscipt number to the top left and a subscript number to the bottom right. Does anyone know what these equations are in reference to? thanks for your help. 212.250.79.220 (talk) 19:45, 2 June 2018 (UTC)
 * Can you point us to an image? Ruslik_ Zero 19:51, 2 June 2018 (UTC)
 * Google  → first hit:
 * https://www.theguardian.com/uk-news/gallery/2015/nov/03/new-uk-passport-design-in-pictures
 * By way of a factual correction to that newspaper article, neither Babbage nor anyone else ever built the Analytical Engine. He invented it, he designed it, he built a component that could have gone into it, and that was all. (This machine should not be confused with the Difference Engine, his previous invention, which he also did not complete but other people did.) --76.69.118.94 (talk) 23:44, 2 June 2018 (UTC)
 * HTH. --CiaPan (talk) 20:07, 2 June 2018 (UTC)
 * See Ada_Lovelace, in particular the diagram. --Wrongfilter (talk) 20:37, 2 June 2018 (UTC)
 * "The diagram" being File:Diagram_for_the_computation_of_Bernoulli_numbers.jpg. Tigraan Click here to contact me 08:23, 4 June 2018 (UTC)


 * In Lovelace's notation for the Analytical Engine, the V-symbols represent variables. The subscript is an identifier for the variable - thus Lovelace's variables are V0, V1, V2 etc. The superscript shows the sequence of updates to the value held in each variable. Thus when variable Vn is initialised with a value of 0, this is represented by 0Vn. After it is updated from input or from the results of a calculation it is represented by 1Vn. After a second update it is represented by 2Vn etc. This notation is explained in Note D of her translation of Menabrea's Sketch of the Analytical Engine.


 * In Lovelace's notation each step combines the values held in two variables with a single operation of +, -, x or ÷ and stores the result in one or more "receiving" variables. Thus the calculation of $$-\frac{1}{2}\frac{2n-1}{2n+1}$$, which would take one line in a high-level programming language, requires 6 steps and several intermediate "working" variables in Lovelace's notation. Lovelace's notation resembles what we call assembly language. Gandalf61 (talk) 10:50, 4 June 2018 (UTC)