Dale,
> Clearly you have a passion for the SI. After our last discussion of > this topic on the CCP4BB I downloaded "The International System of > Units: NIST Special Publication 330" and actually read it. > (https://dx.doi.org/10.6028/NIST.SP.330e2008) The SI is a fine system > of units and this document is well written and easy to follow. > I would say that 'passion' here is absolutely the wrong word: more like 'grudging acceptance' of a illogical, ill thought-out and messy set of rules. It was fine and logical with only the 7 base & the derived units. Then the committee agreed to accept into SI all those non-SI units such as 'e' (unit of electronic charge: SI obviously already had a derived unit of charge, the coulomb) and 'Å' (ångström). Note that 'e' and 'Å' are officially accepted SI units, on an equal footing to all intents and purposes as the base and derived units (not 'SI-ish' units as you say further down). I (and you) have no choice but to use them, like it or not. What I am passionate about is clear and unambiguous communication within the scientific community, and between scientists and others not fortunate to have been through a first-class scientific education, including the politicians and the wider public. Conventions on all aspects of scientific nomenclature play a big part in eliminating ambiguities from communications, that's for sure. In these days of science denial and ludicrous conspiracy theories (such a creationism, flat-earth theorists, moon-landing deniers and GW deniers), it is more important that ever that scientists do not allow these people to take advantage of insignificant disagreements within the scientific community. I was brought up on CGS (my year was the last to use it; the year after mine switched to MKS which then became SI). I understood and accepted that having the derived unit of length 'centimetre' with the 'centi' prefix as a base unit made no sense: the base unit of length had to be the 'metre'. Then they go and choose 'kilogram' as the base unit of mass - why on earth not the gram? A 'gram' in SI units should therefore really be a 'millikilogram' which is plain silly! (I agree that there's a SI exception to allow use of 'gram' in this case). It's kind of hard to be passionate about a convention since it's a completely cut-and-dried thing and there's nothing in it to argue about (at least I thought so until now!). A convention is just a totally arbitrary set of rules that can't be right or wrong: it just is. In contrast, hypotheses can be right or wrong and are worth being passionate about. Like all conventions on nomenclature SI is something made on our behalf by our scientific representative at the annual SI convention and we have no choice but to accept it (or try to persuade our rep otherwise). You said in your previous email, quote: 'The meaning of the term "e/A^3" as used in Coot has nothing to do with the charge of an electron. The intention of its authors is to indicate that the value being represented by the map is the density of electrons'. That is definitely not permitted under SI. The SI unit symbols are 'reserved symbols': they cannot be arbitrarily and unilaterally be redefined in 'units' context (i.e. wherever a 'units' expression is expected as defined in the SI guide, so definitely in the Coot expression above). So 'e' in 'units' context signifies 'charge on the electron', period. It's like you are saying 'the units are e/Å^3, oh and by the way those are not real units, they are what I mean by units'. You can't redefine what is meant by 'units'! How confusing is that? You may as well allow 'kg' to be redefined to mean 'metre': imagine the chaos that would cause! Obviously this doesn't prevent you from redefining those symbols in a different context, since the meaning is clear from the context (context is everything!). For example in 'equation' context in the same document 'e' might signify the transcendental number '2.71828 ...', and there's no possibility of confusion with 'e' the unit of electronic charge used in 'units' context. So if 'e/Å^3' is not to turn out as charge density you need to use an SI unit symbol other than 'e', if you're going to use a symbol at all. But which SI unit would that be? There is only one possible: the SI unit 'one', value = 1, so the unit of electron density is '1/Å^3' or 'Å^-3'. > I don't believe that you and I have any serious disagreements about > "units". I agree with pretty much everything you have written in your > letter. > I'm very pleased to hear that: we are definitely making progress! We do seem to have a difference of opinion about the style of writing > appropriate for an informal venue such as the CCP4BB. > I have to admit that I was rather taken aback by your response to my posting, where I was merely pointing out that the 'e/Å^3' unit displayed by Coot cannot possibly be the unit of electron density as claimed because as already pointed out 'e' is unequivocably an SI unit of electric charge, whereas electron density is a number density, not a charge density. The latter is uncontroversial from its derivation from the unitless form factor, as indicated in my previous email. I had assumed that this had been resolved long ago, when Marc Schiltz also pointed out in the previous thread on this subject that for a unit to be acceptable in SI it must be possible to give a numerical conversion factor between it and the corresponding SI unit. It must also obviously appear in the list of acceptable units as given in the Guide! That's clearly not possible for the 'electron' (or 'e-') unit, simply because it's not a unit, not in SI, not in any system of units (it's not even one of the obsolete units not accepted by SI!). Clearly it's meaningless to ask what is the SI unit corresponding to an electron (or indeed any hunk of matter) if it's not even a unit (much less what the conversion factor is!). See the 'Check List for Reviewing Manuscripts' in the Guide, p. v, item 1. So you are required also to give the value of your electron density 'x e/Å^3' in SI units: can you do that? While the SI units of a "quantity density" would be "inverse cubic > nanometers" the actual value would remain meaningless if the nature of > the "quantity" was left unspecified. The document mentioned above makes > this clear (page 22) and I'm sure you agree as well. > I'm sorry, I don't see what you mean here. Are you referring to the sentence (section 7.13, p. 22): 'although it is acceptable to say "an object of mass 1 kg was attached to a string ...", it is not acceptable to say "a mass of 1 kg was attached ..."'? If so then I certainly don't agree with what you say above, since that is not what the document is saying, in fact it says the exact opposite! It says that it is not acceptable to say that 'a mass of 1 kg was attached to a string'. It does _not_ say as you claim that the nature of the object must always be specified, it's saying simply that a 'mass' object simply does not possess the property of having the capability to be physically attached to anything (again a category mistake), rather that it's the matter object that is attached and the matter object has an attribute 'mass'. We can surely talk about a 'mass of 1kg' (or any other quantity) without referring to the nature of the object that has that mass attribute. That is far from meaningless, in fact that is the very essence and beauty and utility of units: by design they are completely separable from the objects that they measure (otherwise can you imagine how many units you would need?). Indeed the Guide makes it clear that it's a requirement of SI that such a separation occurs, and that it is _not_ acceptable to include the object as a component of the units as you are clearly doing (see the above 'Check List', item 6). Note that 'Inverse cubic Angstroms' (or more strictly Å^-3) is also perfectly acceptable in SI, indeed this is the form recommended for use in IUCr journals, and the use of 'nanometre' is there not recommended (though not prohibited since obviously 'nanometre' is an accepted SI unit). I think you believe that just saying "the map value is electron > density" is sufficient to lead the reader to understand that the > "quantity" with SI'ish units of "/Angstrom^3" is, indeed, "number of > electrons", but I disagree. 'Map value' is totally ambiguous since a 'map' is simply an arbitrary function and a function can be of anything you can think of. You must say 'electron density map value' ('ED map value' or just 'ED value' is also clear to everyone), in which case it is already clear that we are talking about electrons, it doesn't need to be repeated! My STARANISO server displays 3 types of map (in reciprocal, not real space): a redundancy map (distribution of reflexion redundancies), a mean local I/sd(I) map and a Debye-Waller factor map. I certainly don't say 'the redundancy of reflexion hkl is 3 redundancies' ('redundancy' is not a unit). I say 'the redundancy is 3'. The definition of electron density is universally accepted to be 'the number of electrons divided by volume', so that definition ought to be in anyone's head when looking at electron density! > After all, people commonly refer to the rms > normalized maps as "electron density" maps as well, so the term > "electron density" has been overloaded with several meanings and is now > ambiguous. A normalised electron density map is clearly not an electron density map. I have fallen for that one myself so please don't call it 'electron density', call it by what it is: 'normalised electron density'. It's not even commensurate with electron density, having SI unit 'one' (which doesn't need to be specified). > In a forum where people routinely use abbreviations such as > "IMHO", and "A" instead of "Angstrom", it seems to me ridiculous to say > "the number density of electrons in SI units of per Angstrom cubed" when > I could simply say "electrons/A^3" knowing that most readers would > understand my intent. > The fact that we're having this discussion at all indicates that informality leads to misunderstandings, so could we please stick to the formal SI-acceptable units? At no point did I suggest that one should say 'the number density of electrons in SI units of per Angstrom cubed', that's absurd. One would say simply 'the electron density is x Å^-3' (since we already know that electron density is a number density). Are you saying that if I say for example that 'the mass of an object is x kg' that's not enough and I must say ''the mass of an object is x kg/object': that's absurd! In your post you defined electron density (in quotes) as "... or the > number of electrons per unit volume". Those are pretty much exactly the > words the little voice in my head utters when I read the symbols > "electrons/A^3". I never said that "electrons" is an SI unit, or that I > was even trying to obey the formality of the SI conventions. > Formality is what I'm talking about because informalities have a way of getting into formal publications. In using the phrase 'electrons/A^3' in 'units' context you are already implying that 'electron' is a unit (and SI units are the only ones allowed in a scientific setting), because you agreed that in the expression 'quantity = number units', the 'units' part are units (how could they be anything else?). So the moment you say 'electron density = x electrons/Å^3' then by implication 'electron' in the RHS expression is a quantity containing a unit as its 2nd element. Note that this is not about the SI convention at all, it's about something much more fundamental in philosophy, maths and science, namely logic. Can one be logically informal? You are saying: 'Electron density = number of electrons / volume = x electrons / volume' Cancelling the volumes on each side we get: 'number of electrons = x electrons' This is a clear category mistake because you are equating one of the attributes ('x') of the object 'x electrons' with the entire object, and anyway the grammatically correct sentence would be 'number of electrons = x'. The object 'x electrons' has many other attributes (mass, charge, spin etc) so semantically assigning the entire object to only one of its attributes makes absolutely no sense in logic (one cannot equate a set to one of its proper subsets, otherwise dire things will happen, even worse than the Dept of Commerce calling on you!). By 'reductio ad absurdum' therefore the first statement above makes no sense in logic either. Note that I no point in the above argument did I refer to SI units, or indeed any units: it's a pure logical argument. But OK, now I understand the source of our difference, you are being informal, and I am talking about formalities and logic, i.e. what the journals have instructions to accept. Should what is displayed in Coot remain informal, or conform to the rules of convention and logic? I would say the latter since images of Coot maps are often displayed in papers. I take it therefore that you agree that _formally_ the correct units of electron density are 'Å^-3', even though in an informal discussion such as this you are permitted some embellishment, even though it is not semantically logical? I will argue with you about the idea that electron density and proton > density are commensurate. I don't really know of an application where > the sum of electron density and proton density makes any sense, much > less the sum of electron and rabbit density. I'm not talking about utility, I'm talking about semantics. Any quantities with the same units are by definition commensurate. The number density of any object has the same units regardless of the object, so is commensurate with the number density of any other object. In any case, I was following your lead here and assuming that 'rabbit' was meant as a term for an arbitrary object (including electron, proton and every other matter object making up the Universe). I'm not even talking specifically about electrons and protons, that was only an example (possibly a bad one). Are you saying that in all the Universe of possible objects there is not a single application of summing number densities? Or are you saying that your terminology applies only to electron density? Mathematica can do the necessary algebra on quantities with (and without) units, with no problem: In[1]:= nProtons = 10 In[2]:= nElectrons = 20 In[3]:= nRabbits = 30 In[4]:= nObjects = nProtons + nElectrons + nRabbits Out[4]= 60 In[5]:= volume = 50. A^3 In[6]:= protonDensity := nProtons / volume Out[6]= 0.2 / A^3 In[7]:= electronDensity := nElectrons / volume Out[7]= 0.4 / A^3 In[8]:= rabbitDensity := nRabbits / volume Out[8]= 0.6 / A^3 In[9]:= objectDensity = protonDensity + electronDensity + rabbitDensity Out[9]= 1.2 / A^3 > Any class library I would > write would throw an exception if you attempted to calculate such a thing. > Huh? I see no exceptions. How could adding 2 or more quantities with the same units possibly throw an exception? Also: In[10]:= atomAmpltude = 24. nm # Scattering amplitude units can be anything since they will cancel. In[11]:= electronAmplitude = 4. nm In[12]:= formFactor := atomAmplitude / electronAmplitude Out[12]= 6. In[13]:= electronDensity := formFactor / volume Out[13]= 0.12 / A^3 Are you saying that it's not possible to implement in a class library what Mathematica can do? (for all I know Mathematica is using a class library). I would find that very hard to swallow (and so would all the OO programmers I know!). I presume your calculation is stepping toward the calculation of > charge density. I would first calculate the charge density due to the > electron density, using the knowledge that there is one quantum of > negative charge for each electron, then calculate the charge density due > to the proton density, using knowledge of the charge of a proton, and > then sum the two charge densities, which are not only commensurate but > identical. My code would then be ready should I run into a Xi baryon > with +2 charge whereas your code would have to be completely refactored. > ;-) > Not if I'm using Mathematica ;-) Anyway, sorry, but I have no interest whatsoever in calculating charge density, since it's completely outside of the subject of the current discussion about electron density in particular and number density in general. P.S. Before the United States Department of Commerce comes knocking on > my door, I expect they would prosecute the RCSB. Do you realize that > this criminal organization uses taxpayer money to store and distribute > files containing calculated structure factors represented as the number > of electrons per unit cell?! > So? The structure factor _is_ defined as the number of electrons per unit cell, where's the problem in that? I think you are confusing the _definition_ of some quantity with its _value_ (again a category mistake). Looking at one of the data files I see: loop_ _refln.crystal_id _refln.wavelength_id _refln.scale_group_code _refln.index_h _refln.index_k _refln.index_l _refln.status _refln.intensity_meas _refln.intensity_sigma _refln.F_calc _refln.phase_calc 1 1 1 -26 0 4 o -21.14000 23.43000 0.7492451 171.8 1 1 1 -26 0 6 o -5.068000 22.06000 1.012408 4.8 1 1 1 -26 0 8 o 0.8860000E-01 23.83000 1.251611 178.1 1 1 1 -26 0 10 o 65.75000 28.18000 3.442811 -0.1 1 1 1 -26 0 12 o 103.4000 35.89000 4.347793 -179.5 1 1 1 -26 0 14 o 6.858000 21.99000 2.418568 -178.6 All quantities are correctly specified with an empty 'units' field, with the exception that the phases should have 'degree' units specified somewhere (maybe it's in the documentation? - that would be fine). Otherwise one is entitled to assume that the units of phases are radians (which requires no unit to be specified), so it appears to be (almost) all perfectly in order. Cheers -- Ian
