Formally, a complex number (e.g. a structure factor) is not a vector. Just because the addition & subtraction rules (i.e. 'a+b' & 'a-b') are defined for real numbers, complex numbers and vectors doesn't make a complex number a vector, any more than it makes a real number a vector (or vice versa). Entities are defined according to the rules of algebra that they obey, thus real and complex numbers obey the same rules, i.e. the familiar addition, subtraction, multiplication, division & raising to a power. Hence real and complex numbers are both scalars: a real number is a special case of a complex scalar with zero imaginary part (one could program an algorithm for reals using only complex variables & functions and still get the right answer). This also means that the transcendental functions (sin, cos, tan, exp, log etc) are all defined equally well for both real and complex scalars, but not for vectors, a property that programmers in Fortran, C & C++ (and probably others) will be familiar with. Of the addition, subtraction, multiplication, division & power rules, vectors only obey the first two, but unlike real & complex scalars they also obey the scalar product and exterior product rules.
The general rule is that "if and only if it looks like a duck, waddles like a duck and quacks like a duck, then it is a duck" - complex numbers might look like vectors but they neither waddle nor quack like them! Cheers -- Ian On Wed, Oct 13, 2010 at 9:57 PM, Yong Y Wang <wang_yon...@lilly.com> wrote: > It is already vertical, relative to the real part of Fa (in red), i.e. the > blue vector is always vertical to the red vector in this picture (and > counter-clockwise). > > Yong > > > > > William Scott <wgsc...@chemistry.ucsc.edu> > Sent by: CCP4 bulletin board <CCP4BB@JISCMAIL.AC.UK> > 10/13/2010 01:48 PM > Please respond to > William Scott <wgsc...@chemistry.ucsc.edu> > > > To > CCP4BB@JISCMAIL.AC.UK > cc > > Subject > [ccp4bb] embarrassingly simple MAD phasing question > > > > > > > Hi Citizens: > > Try not to laugh. > > I have an embarrassingly simple MAD phasing question: > > Why is it that F" in this picture isn't required to be vertical (purely > imaginary)? > > http://www.doe-mbi.ucla.edu/~sawaya/tutorials/Phasing/phase.gif > > (Similarly in the Harker diagram of the intersection of phase circles, one > sees this.) > > I had a student ask me and I realized that there is this fundamental gap > in my understanding. > > Many thanks in advance. > > -- Bill > > > > > William G. Scott > Professor > Department of Chemistry and Biochemistry > and The Center for the Molecular Biology of RNA > 228 Sinsheimer Laboratories > University of California at Santa Cruz > Santa Cruz, California 95064 > USA > > phone: +1-831-459-5367 (office) > +1-831-459-5292 (lab) > fax: +1-831-4593139 (fax) >
