Wikipedia:Reference desk/Archives/Mathematics/2013 September 18

= September 18 =

Turing thesis
Does Turing thesis entail that every algorithm must have a "starting point", i.e. a first step starting that algorithm? 84.229.81.123 (talk) 06:40, 18 September 2013 (UTC)


 * Please don't cross post the same Q on multiple desks. Your post at the Computer Ref Desk already has a reply. StuRat (talk) 06:59, 18 September 2013 (UTC)

Inverse of gross tonnage
I'd like to modify Template:GT to include a parenthetical figure in cubic meters, at least as an option.

The calculation of gross tonnage is kind of crazy: you take the volume V times a fudge factor K.

K = 0.20 + 0.02 * log10 (V). So reputedly the range is around 0.20 to 0.32 - 0.28 for a ship of 10,000 cubic meters.

After playing around with V^V type expressions for a bit, I should admit, I don't think I ever learned how to deal with this kind of expression, or if I did, I forgot! Is there a closed form inverse for the formula?

Of course, I realize it can be done easily with a simple method of successive approximation in a Lua module, but I risk getting grief over "original research" as it is, and using those is only going to make it more problematic. Besides, I'm just curious how you do this. Wnt (talk) 23:08, 18 September 2013 (UTC)
 * The inverse of xx is $$\frac{\ln x}{W(\ln x)}$$, where W is the Lambert W function. Not sure if this counts as "closed form", but it's probably as good as it's going to get. Staecker (talk) 11:43, 19 September 2013 (UTC)
 * Sigh. I'm still chasing my tail with stuff like "10^GT = ((V ^ V) ^ 0.02) * (N ^ V)"...  What is not encouraging is that a search for "gross tonnage" and "lambert function" yielded zero results. Wnt (talk) 20:27, 19 September 2013 (UTC)
 * I'm pretty sure you're best off using Newton's method or creating a Taylor series for the inverse.--Jasper Deng (talk) 04:03, 20 September 2013 (UTC)

I know this is an archived discussion but I did succeed in deriving a solution to this in terms of the Lambert W function.--Jasper Deng (talk) 06:53, 16 April 2015 (UTC)