Re: [ccp4bb] units of f0, f', f''

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CCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999

Previous message:
Subject: Re: units of f0, f', f''
From: Dale Tronrud det102 {- at -} UOXRAY {- dot -} UOREGON {- dot -} EDU
Date: 2010-02-26

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Subject: Re: units of f0, f', f''
From: Lijun Liu lijun {- dot -} liu {- at -} UCSF {- dot -} EDU
Date: 2010-02-26

Subject: Re: units of f0, f', f''
From: Ian Tickle I {- dot -} Tickle {- at -} ASTEX-THERAPEUTICS {- dot -} COM
Date: 2010-02-26

> For maps it is important for people to know if their map is
> in e/Å^3 or sigma/Å^3. Both maps are commonly encountered in
> this field and both are called electron density maps. I could
> put a note on my home page stating that whenever I talk about
> a map I give numbers in e/Å^3 but it is more convenient for the
> reader if I just put the convention next to the number.

The problem obviously arises here because of the ambiguity of using the same name ('electron density') to define two different quantities simultaneously. You'll recall I pointed out that "Problems with units often stem from an ambiguous definition"! Let's suppose you were writing equations involving both of these quantities, and let's say 'electron density' = 'rho'. Then you might write in a computer program the perfectly valid statement:

rho = rho/sigma

where the 'rho' on each side means different things. However this is certainly not valid as an algebraic statement as it stands (where sigma may take any value). Note that it is not the usual practice to carry the units with the variables in the equations in the way you suggest in order to allow you to distinguish them (it would make the equations pretty unreadable!), so the units are actually irrelevant are far as equations are concerned. So you would have to write something like:

rho' = rho/sigma

then the ambiguity is resolved. Moreover you would now need to define rho and rho' in a way that the reader would be able to distinguish them, for example you might say "rho = electron density = number of electrons/Angstroem^3" and "rho' = electron density Z-score = rho/sigma(rho)". So now you have not only been forced to distinguish the variable names, you also have had to distinguish them in their definitions, hence it should no longer be necessary to distinguish them by labelling their units.

Now of course labelling things in a computer output in order to distinguish things that might be confused is quite a different issue from distinguishing things in equations, for one thing you're free to write anything you want in your own program, but equations have to obey the rules of algebra. I don't know what was the context that gave rise to the original question but I think it's quite likely to have been the equation f = f0 + f' + if", in which case one needs to be careful to avoid ambiguous definitions.

Cheers

-- Ian

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CCP4bb navigation

CCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999

Previous message:
Subject: Re: units of f0, f', f''
From: Dale Tronrud det102 {- at -} UOXRAY {- dot -} UOREGON {- dot -} EDU
Date: 2010-02-26

Next message:
Subject: Re: units of f0, f', f''
From: Lijun Liu lijun {- dot -} liu {- at -} UCSF {- dot -} EDU
Date: 2010-02-26