Re: Numerical accuracy/precision - this is a bug or a feature?
- To: mathgroup at smc.vnet.net
- Subject: [mg120133] Re: Numerical accuracy/precision - this is a bug or a feature?
- From: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
- Date: Sat, 9 Jul 2011 07:32:48 -0400 (EDT)
- References: <email@example.com> <firstname.lastname@example.org>
On Fri, 08 Jul 2011 09:51:53 +0100, Noqsi <noqsiaerospace at gmail.com> wrote: > On Jul 7, 5:40 am, "slawek" <sla... at host.pl> wrote: > >> The convention that 2.0 is less accurate than 2.00 is applied ONLY in >> Mathematica (the computer program). > > Not true. This is a long-standing convention in experimental science. > Unfortunately so, given that it is severely erroneous: see e.g. <http://www.av8n.com/physics/uncertainty.htm>. However, Mathematica's approximation of how these uncertainties propagate is first-order, not zeroth-order. This does not make it completely reliable, of course, but certainly it is not almost always wrong as is the significant digits convention. Within the bounds of its own applicability, Mathematica's approximation is reasonable, although it would still be a mistake to apply it to experimental uncertainty analysis given the much broader scope of the latter.