[ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor
Eh? m and Å are related by the dimensionless quantity 10,000,000,000. Vive la révolution! Marc SCHILTZ wrote: Frank von Delft wrote: Hi Marc Not at all, one uses units that are convenient. By your reasoning we should get rid of Å, atmospheres, AU, light years... They exist not to be obnoxious, but because they're handy for a large number of people in their specific situations. Hi Frank, I think that you misunderstood me. Å and atmospheres are units which really refer to physical quantities of different dimensions. So, of course, there must be different units for them (by the way: atmosphere is not an accepted unit in the SI system - not even a tolerated non SI unit, so a conscientious editor of an IUCr journal would not let it go through. On the other hand, the Å is a tolerated non SI unit). But in the case of B and U, the situation is different. These two quantities have the same dimension (square of a length). They are related by the dimensionless factor 8*pi^2. Why would one want to incorporate this factor into the unit ? What advantage would it have ? The physics literature is full of quantities that are related by multiples of pi. The frequency f of an oscillation (e.g. a sound wave) can be expressed in s^-1 (or Hz). The same oscillation can also be charcterized by its angular frequency \omega, which is related to the former by a factor 2*pi. Yet, no one has ever come up to suggest that this quantity should be given a new unit. Planck's constant h can be expressed in J*s. The related (and often more useful) constant h-bar = h/(2*pi) is also expressed in J*s. No one has ever suggested that this should be given a different unit. The SI system (and other systems as well) has been specially crafted to avoid the proliferation of units. So I don't think that we can (should) invent new units whenever it appears convenient. It would bring us back to times anterior to the French revolution. Please note: I am not saying that the SI system is the definite choice for every purpose. The nautical system of units (nautical mile, knot, etc.) is used for navigation on sea and in the air and it works fine for this purpose. However, within a system of units (whichever is adopted), the number of different units should be kept reasonably small. Cheers Marc Sounds familiar... phx Marc SCHILTZ wrote: Hi James, James Holton wrote: Many textbooks describe the B factor as having units of square Angstrom (A^2), but then again, so does the mean square atomic displacement u^2, and B = 8*pi^2*u^2. This can become confusing if one starts to look at derived units that have started to come out of the radiation damage field like A^2/MGy, which relates how much the B factor of a crystal changes after absorbing a given dose. Or is it the atomic displacement after a given dose? Depends on which paper you are looking at. There is nothing wrong with this. In the case of derived units, there is almost never a univocal relation between the unit and the physical quantity that it refers to. As an example: from the unit kg/m^3, you can not tell what the physical quantity is that it refers to: it could be the density of a material, but it could also be the mass concentration of a compound in a solution. Therefore, one always has to specify exactly what physical quantity one is talking about, i.e. B/dose or u^2/dose, but this is not something that should be packed into the unit (otherwise, we will need hundreds of different units) It simply has to be made clear by the author of a paper whether the quantity he is referring to is B or u^2. It seems to me that the units of B and u^2 cannot both be A^2 any more than 1 radian can be equated to 1 degree. You need a scale factor. Kind of like trying to express something in terms of 1/100 cm^2 without the benefit of mm^2. Yes, mm^2 have the dimensions of cm^2, but you can't just say 1 cm^2 when you really mean 1 mm^2! That would be silly. However, we often say B = 80 A^2, when we really mean is 1 A^2 of square atomic displacements. This is like claiming that the radius and the circumference of a circle would need different units because they are related by the scale factor 2*pi. What matters is the dimension. Both radius and circumference have the dimension of a length, and therefore have the same unit. Both B and u^2 have the dimension of the square of a length and therefoire have the same unit. The scalefactor 8*pi^2 is a dimensionless quantity and does not change the unit. The B units, which are ~1/80th of a A^2, do not have a name. So, I think we have a new unit? It is A^2/(8pi^2) and it is the units of the B factor that we all know and love. What should we call it? I nominate the Born after Max Born who did so much fundamental and far-reaching work on the nature of disorder in crystal lattices. The unit then has the symbol B, which will make it easy to say that the B
Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor
But in this case you are no longer defining distances but some other arbitrary
quantity, like vendors do when they convert a small computer speaker into a
rockband PA by using PMPO instead of music power.
Herman
-Original Message-
From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of Frank von
Delft
Sent: Friday, November 20, 2009 1:11 PM
To: CCP4BB@JISCMAIL.AC.UK
Subject: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re:
[ccp4bb] units of the B factor
Eh? m and Å are related by the dimensionless quantity 10,000,000,000.
Vive la révolution!
Marc SCHILTZ wrote:
Frank von Delft wrote:
Hi Marc
Not at all, one uses units that are convenient. By your reasoning we
should get rid of Å, atmospheres, AU, light years... They exist not
to be obnoxious, but because they're handy for a large number of
people in their specific situations.
Hi Frank,
I think that you misunderstood me. Å and atmospheres are units which
really refer to physical quantities of different dimensions. So, of
course, there must be different units for them (by the way: atmosphere
is not an accepted unit in the SI system - not even a tolerated non SI
unit, so a conscientious editor of an IUCr journal would not let it go
through. On the other hand, the Å is a tolerated non SI unit).
But in the case of B and U, the situation is different. These two
quantities have the same dimension (square of a length). They are
related by the dimensionless factor 8*pi^2. Why would one want to
incorporate this factor into the unit ? What advantage would it have ?
The physics literature is full of quantities that are related by
multiples of pi. The frequency f of an oscillation (e.g. a sound wave)
can be expressed in s^-1 (or Hz). The same oscillation can also be
charcterized by its angular frequency \omega, which is related to the
former by a factor 2*pi. Yet, no one has ever come up to suggest that
this quantity should be given a new unit. Planck's constant h can be
expressed in J*s. The related (and often more useful) constant h-bar =
h/(2*pi) is also expressed in J*s. No one has ever suggested that this
should be given a different unit.
The SI system (and other systems as well) has been specially crafted
to avoid the proliferation of units. So I don't think that we can
(should) invent new units whenever it appears convenient. It would
bring us back to times anterior to the French revolution.
Please note: I am not saying that the SI system is the definite choice
for every purpose. The nautical system of units (nautical mile, knot,
etc.) is used for navigation on sea and in the air and it works fine
for this purpose. However, within a system of units (whichever is
adopted), the number of different units should be kept reasonably small.
Cheers
Marc
Sounds familiar...
phx
Marc SCHILTZ wrote:
Hi James,
James Holton wrote:
Many textbooks describe the B factor as having units of square
Angstrom (A^2), but then again, so does the mean square atomic
displacement u^2, and B = 8*pi^2*u^2. This can become confusing if
one starts to look at derived units that have started to come out
of the radiation damage field like A^2/MGy, which relates how much
the B factor of a crystal changes after absorbing a given dose. Or
is it the atomic displacement after a given dose? Depends on which
paper you are looking at.
There is nothing wrong with this. In the case of derived units,
there is almost never a univocal relation between the unit and the
physical quantity that it refers to. As an example: from the unit
kg/m^3, you can not tell what the physical quantity is that it
refers to: it could be the density of a material, but it could also
be the mass concentration of a compound in a solution. Therefore,
one always has to specify exactly what physical quantity one is
talking about, i.e. B/dose or u^2/dose, but this is not something
that should be packed into the unit (otherwise, we will need
hundreds of different units)
It simply has to be made clear by the author of a paper whether the
quantity he is referring to is B or u^2.
It seems to me that the units of B and u^2 cannot both be A^2
any more than 1 radian can be equated to 1 degree. You need a
scale factor. Kind of like trying to express something in terms of
1/100 cm^2 without the benefit of mm^2. Yes, mm^2 have the
dimensions of cm^2, but you can't just say 1 cm^2 when you really
mean 1 mm^2! That would be silly. However, we often say B = 80
A^2, when we really mean is 1 A^2 of square atomic displacements.
This is like claiming that the radius and the circumference of a
circle would need different units because they are related by the
scale factor 2*pi.
What matters is the dimension. Both radius and circumference have
the dimension of a length, and therefore have the same unit. Both B
and u^2 have the dimension
Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor
Yes, but Å is really only just tolerated. It has evaded the Guillotine - for the time being ;-) Frank von Delft wrote: Eh? m and Å are related by the dimensionless quantity 10,000,000,000. Vive la révolution! Marc SCHILTZ wrote: Frank von Delft wrote: Hi Marc Not at all, one uses units that are convenient. By your reasoning we should get rid of Å, atmospheres, AU, light years... They exist not to be obnoxious, but because they're handy for a large number of people in their specific situations. Hi Frank, I think that you misunderstood me. Å and atmospheres are units which really refer to physical quantities of different dimensions. So, of course, there must be different units for them (by the way: atmosphere is not an accepted unit in the SI system - not even a tolerated non SI unit, so a conscientious editor of an IUCr journal would not let it go through. On the other hand, the Å is a tolerated non SI unit). But in the case of B and U, the situation is different. These two quantities have the same dimension (square of a length). They are related by the dimensionless factor 8*pi^2. Why would one want to incorporate this factor into the unit ? What advantage would it have ? The physics literature is full of quantities that are related by multiples of pi. The frequency f of an oscillation (e.g. a sound wave) can be expressed in s^-1 (or Hz). The same oscillation can also be charcterized by its angular frequency \omega, which is related to the former by a factor 2*pi. Yet, no one has ever come up to suggest that this quantity should be given a new unit. Planck's constant h can be expressed in J*s. The related (and often more useful) constant h-bar = h/(2*pi) is also expressed in J*s. No one has ever suggested that this should be given a different unit. The SI system (and other systems as well) has been specially crafted to avoid the proliferation of units. So I don't think that we can (should) invent new units whenever it appears convenient. It would bring us back to times anterior to the French revolution. Please note: I am not saying that the SI system is the definite choice for every purpose. The nautical system of units (nautical mile, knot, etc.) is used for navigation on sea and in the air and it works fine for this purpose. However, within a system of units (whichever is adopted), the number of different units should be kept reasonably small. Cheers Marc Sounds familiar... phx Marc SCHILTZ wrote: Hi James, James Holton wrote: Many textbooks describe the B factor as having units of square Angstrom (A^2), but then again, so does the mean square atomic displacement u^2, and B = 8*pi^2*u^2. This can become confusing if one starts to look at derived units that have started to come out of the radiation damage field like A^2/MGy, which relates how much the B factor of a crystal changes after absorbing a given dose. Or is it the atomic displacement after a given dose? Depends on which paper you are looking at. There is nothing wrong with this. In the case of derived units, there is almost never a univocal relation between the unit and the physical quantity that it refers to. As an example: from the unit kg/m^3, you can not tell what the physical quantity is that it refers to: it could be the density of a material, but it could also be the mass concentration of a compound in a solution. Therefore, one always has to specify exactly what physical quantity one is talking about, i.e. B/dose or u^2/dose, but this is not something that should be packed into the unit (otherwise, we will need hundreds of different units) It simply has to be made clear by the author of a paper whether the quantity he is referring to is B or u^2. It seems to me that the units of B and u^2 cannot both be A^2 any more than 1 radian can be equated to 1 degree. You need a scale factor. Kind of like trying to express something in terms of 1/100 cm^2 without the benefit of mm^2. Yes, mm^2 have the dimensions of cm^2, but you can't just say 1 cm^2 when you really mean 1 mm^2! That would be silly. However, we often say B = 80 A^2, when we really mean is 1 A^2 of square atomic displacements. This is like claiming that the radius and the circumference of a circle would need different units because they are related by the scale factor 2*pi. What matters is the dimension. Both radius and circumference have the dimension of a length, and therefore have the same unit. Both B and u^2 have the dimension of the square of a length and therefoire have the same unit. The scalefactor 8*pi^2 is a dimensionless quantity and does not change the unit. The B units, which are ~1/80th of a A^2, do not have a name. So, I think we have a new unit? It is A^2/(8pi^2) and it is the units of the B factor that we all know and love. What should we call it? I nominate the Born after Max Born who did so much fundamental and far-reaching work on the nature
Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor
What a funny pleasant piece of discussion ! Given any physical quantity Something, having any kind of dimension (even as awful as inches^2*gallons*pounds^-3) Would it exist any room for a discussion about the dimension of 2*Something ? And what about 1*Something ? Philippe Dumas attachment: p_dumas.vcf
Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor
What a funny pleasant piece of discussion ! Given any physical quantity Something, having any kind of dimension (even as awful as inches^2*gallons*pounds^-3) Would it exist any room for a discussion about the dimension of 2*Something ? And what about 1*Something ? (1) You can always convert anything into anything else (related to it by a scale factor) using Google, e.g.: http://www.google.com/search?hl=enq=2+fortnights+in+msec http://www.google.com/search?hl=enq=7+furlongs+in+mm http://www.google.com/search?hl=enq=7+square+angstrom+in+cm%5E2 To answer your question: http://www.google.com/search?hl=enq=1+inches%5E2*gallons*pounds%5E-3 So: 1 inches^2*gallons*pounds^-3 = 2.61687719 10^-5 m^5 / kg^3 (assuming US gallons! If you meant imperial gallons, the answer is 3.14273976 10^-5 m^5 / kg^3). (2) With respect to the subject of this thread, can I have my spam, spam, spam, spam and units with eggs, please? (http://www.youtube.com/watch?v=cFrtpT1mKy8) --dvd ** Gerard J. Kleywegt Dept. of Cell Molecular Biology University of Uppsala Biomedical Centre Box 596 SE-751 24 Uppsala SWEDEN http://xray.bmc.uu.se/gerard/ mailto:ger...@xray.bmc.uu.se ** The opinions in this message are fictional. Any similarity to actual opinions, living or dead, is purely coincidental. **
