Draft Chapter 2 for SI Brochure
Epiphany
http://www.bipm.org/utils/common/pdf/si_brochure_draft_ch2.pdf and had
some thoughts I wanted to ask the readers here about.
The proposed redefinition of the ampere is:
> The ampere, A, is the unit of electric current; its magnitude is set by
> fixing the numerical value of the elementary charge to be equal to
> exactly 1.602 17X *10^−19 when it is expressed in the unit s A, which is
> equal to C.
First of all, why not make the coulomb the base unit if we are basing
the the definition on the constant unit of elementary charge? The
ampere can become a derived unit. And then we ought to define the
coulomb as an *integer* number of those charges, not as some reciprocal
of some value in scientific notation that isn't likely to be an integer.
Sure, we can *have* a coulomb that isn't an integer multiple of e, but
if we preferred to make the cesium frequency an integer number of hertz
and the speed of light an integer number of meters per second surely we
would feel happiest with a coulomb that is an integer number of basic
charges, particularly given the difficulty we would have actually
assembling a fractional number of elementary charges to be measured.
Next, the mole is proposed to become:
> The mole, mol, is the unit of amount of substance of a specified
> elementary entity, which may be an atom, molecule, ion, electron, any
> other particle or a specified group of such particles; its magnitude is
> set by fixing the numerical value of the Avogadro constant to be equal
> to exactly 6.022 14X *10^23 when it is expressed in the unit mol^-1.
I ask, why is Avogadro's number to include any sort of unit (like
reciprocal mole)? Surely it is just the quotient of (based on the
current definition of the mole) 0.012 kg divided by the *mass* of a
single carbon-12 atom, a *dimensionless* number resulting. Including a
reciprocal of the mole would be like saying "The number of sides
possessed by a dodecagon is 12 per dozen." No, that number of sides is
just 12, not "per anything". Isn't a mole just a number like a dozen is
a number? One can have a dozen of anything (one dozen cans, two dozen
boxes) and likewise one could have moles of whatever substances (one
mole of ammonia, half a mole of calcium carbonate), right?
Finally, about the candela's new redefinition:
> The candela, cd, is the unit of luminous intensity in a given direction;
> its magnitude is set by fixing the numerical value of the luminous
> efficacy of monochromatic radiation of frequency 540 *10^12 Hz to be
> equal to exactly 683 when it is expressed in the unit s^3 m^-2 kg^-1 cd
> sr, or cd sr W^-1, which is equal to lm W^-1.
Again, why not make the *lumen* the base unit and the candela a derived
unit, or even, noting the deep dependence of these units on the *watt*,
make both the lumen and the candela derived units?
I further ask, given even the current definition of the candela, why is
it not clear from the definition whether or not *only* the intensity of
light of 540*10^12 Hz from a given source counts toward the luminous
intensity of that source? In other words, when we have a light source
radiating at a variety of frequencies and different intensities for
every frequency, I can't tell from the definition whether I would
compare the overall light intensity with the standard lamp or just
compare the sample's 540*10^12 Hz intensity and ignore all other
frequencies.
And beyond the draft document I ask, why is there a base unit for light
intensity yet no analogous base unit for sound intensity? Did the
framers of SI consider sound a phenomenon of less relevance to the human
condition than light? Was sound just harder to quantify in days of
yore? Why no base acoustic SI unit? (Of course, I would withdraw this
objection were the luminous units to be *wholly* relegated to derived
status.)
\ | /
-Epiphany-
/ | \
Erik Max Francis
> I was reading
> http://www.bipm.org/utils/common/pdf/si_brochure_draft_ch2.pdf and had
> some thoughts I wanted to ask the readers here about.
>
> The proposed redefinition of the ampere is:
>> The ampere, A, is the unit of electric current; its magnitude is set by
>> fixing the numerical value of the elementary charge to be equal to
>> exactly 1.602 17X *10^−19 when it is expressed in the unit s A, which is
>> equal to C.
>
> First of all, why not make the coulomb the base unit if we are basing
> the the definition on the constant unit of elementary charge? The
> ampere can become a derived unit. And then we ought to define the
> coulomb as an *integer* number of those charges, not as some reciprocal
> of some value in scientific notation that isn't likely to be an integer.
Why?
> Next, the mole is proposed to become:
>> The mole, mol, is the unit of amount of substance of a specified
>> elementary entity, which may be an atom, molecule, ion, electron, any
>> other particle or a specified group of such particles; its magnitude is
>> set by fixing the numerical value of the Avogadro constant to be equal
>> to exactly 6.022 14X *10^23 when it is expressed in the unit mol^-1.
>
> I ask, why is Avogadro's number to include any sort of unit (like
> reciprocal mole)? Surely it is just the quotient of (based on the
> current definition of the mole) 0.012 kg divided by the *mass* of a
> single carbon-12 atom, a *dimensionless* number resulting.
It's just a rejiggering of the way it's defined, so it's in terms of
something other than a particular isotope of C. It doesn't really
matter how it's defined. Are you asking why we have the unit mol in the
first place?
> Finally, about the candela's new redefinition:
>> The candela, cd, is the unit of luminous intensity in a given direction;
>> its magnitude is set by fixing the numerical value of the luminous
>> efficacy of monochromatic radiation of frequency 540 *10^12 Hz to be
>> equal to exactly 683 when it is expressed in the unit s^3 m^-2 kg^-1 cd
>> sr, or cd sr W^-1, which is equal to lm W^-1.
>
> Again, why not make the *lumen* the base unit and the candela a derived
> unit, or even, noting the deep dependence of these units on the *watt*,
> make both the lumen and the candela derived units?
Again, why?
> I further ask, given even the current definition of the candela, why is
> it not clear from the definition whether or not *only* the intensity of
> light of 540*10^12 Hz from a given source counts toward the luminous
> intensity of that source? In other words, when we have a light source
> radiating at a variety of frequencies and different intensities for
> every frequency, I can't tell from the definition whether I would
> compare the overall light intensity with the standard lamp or just
> compare the sample's 540*10^12 Hz intensity and ignore all other
> frequencies.
>
> And beyond the draft document I ask, why is there a base unit for light
> intensity yet no analogous base unit for sound intensity? Did the
> framers of SI consider sound a phenomenon of less relevance to the human
> condition than light? Was sound just harder to quantify in days of
> yore? Why no base acoustic SI unit? (Of course, I would withdraw this
> objection were the luminous units to be *wholly* relegated to derived
> status.)
It's because the human response of the ear to sound is not as complex as
that to light. The luminosity units are designed to take into account
the varying sensitivity of the human eye to different frequencies. The
human ear has varying sensitivity, sure, but it's much simpler and more
of the form, "You can hear fine in this range; right at the edges of it,
not so good; and outside of it, you can't hear anything."
--
Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
Liberty is the right to do whatever the law permits.
-- Charles Louis Montesquieu
Epiphany
> Epiphany wrote:
>> First of all, why not make the coulomb the base unit if we are basing
>> the the definition on the constant unit of elementary charge? The
>> ampere can become a derived unit. And then we ought to define the
>> coulomb as an *integer* number of those charges, not as some
>> reciprocal of some value in scientific notation that isn't likely to
>> be an integer.
>
> Why?
Because by basing the ampere on the elementary charge we are essentially
defining the coulomb more simply than we are defining the ampere. So
for the sake of simplicity, why not make the coulomb the base unit?
> It's just a rejiggering of the way it's defined, so it's in terms of
> something other than a particular isotope of C. It doesn't really matter
> how it's defined. Are you asking why we have the unit mol in the first
> place?
No, I am not asking why we have the mole. And you didn't answer the
question I asked. But I see that one can define things in two different
ways. Avogadro's constant can be a pure number or it can be the
conversion factor from moles to a pure number. I'm just used to
thinking of a mole like I think of a dozen, just a *number*. Doesn't it
seem simpler to say the mole is just a number like a googol is just a
number?
>> Again, why not make the *lumen* the base unit and the candela a
>> derived unit, or even, noting the deep dependence of these units on
>> the *watt*, make both the lumen and the candela derived units?
>
> Again, why?
For the same reason I asked about the coulomb above: simplicity. If
luminous efficacy is to be defined as 683 lumens/watt, why not state
things simply and directly that it is 683 lumens/watt? It seems more
concise than candela*steradian/watt, doesn't it?
For future aid to me, when you ask 'why?' again, could you write a
complete thought (sentence) so that I have the most help in knowing what
to address in my response?
>> And beyond the draft document I ask, why is there a base unit for
>> light intensity yet no analogous base unit for sound intensity? Did
>> the framers of SI consider sound a phenomenon of less relevance to the
>> human condition than light? Was sound just harder to quantify in days
>> of yore? Why no base acoustic SI unit? (Of course, I would withdraw
>> this objection were the luminous units to be *wholly* relegated to
>> derived status.)
>
> It's because the human response of the ear to sound is not as complex as
> that to light. The luminosity units are designed to take into account
> the varying sensitivity of the human eye to different frequencies. The
> human ear has varying sensitivity, sure, but it's much simpler and more
> of the form, "You can hear fine in this range; right at the edges of it,
> not so good; and outside of it, you can't hear anything."
So those proposing units just thought watts or watts/steradian were good
enough for the measurement of sound and thus no need for a
specially-named acoustic unit? It does seem like the decibel has been
designated "friendly" to SI even though SI hasn't seen the need for a
specific SI sound unit. But I see where you are coming from, E.M.F.
\ | /
-Epiphany-
/ | \
Julian Bradfield
> On 30-Mar-11 16:12, Erik Max Francis wrote:
>> Epiphany wrote:
>>> First of all, why not make the coulomb the base unit if we are basing
>>> the the definition on the constant unit of elementary charge? The
>>> ampere can become a derived unit. And then we ought to define the
>>> coulomb as an *integer* number of those charges, not as some
>>> reciprocal of some value in scientific notation that isn't likely to
>>> be an integer.
>>
>> Why?
>
> Because by basing the ampere on the elementary charge we are essentially
> defining the coulomb more simply than we are defining the ampere. So
> for the sake of simplicity, why not make the coulomb the base unit?
Just history, I would imagine. Sure, if you were designing SI now,
you'd make the coulomb the base unit. But SI changes with reluctance,
and a change that is purely aesthetic is unlikely to be considered
worth the effort.
> No, I am not asking why we have the mole. And you didn't answer the
> question I asked. But I see that one can define things in two different
> ways. Avogadro's constant can be a pure number or it can be the
> conversion factor from moles to a pure number. I'm just used to
> thinking of a mole like I think of a dozen, just a *number*. Doesn't it
> seem simpler to say the mole is just a number like a googol is just a
> number?
This confused me for a long while. But then I realized that dimensions
are arbitrary (after all, the ampere is defined in terms of a force
per unit length, so it could be given those dimensions; mass is the
same as energy, so velocity is dimensionless; time and space have the
same dimensions (which is why velocity is dimensionless); and so
on). It's just a convenience for doing dimensional analysis of your
equations if you decide that "amount of substance" is a dimension,
which might be measured in units, or moles.
>>> Again, why not make the *lumen* the base unit and the candela a
>>> derived unit, or even, noting the deep dependence of these units on
>>> the *watt*, make both the lumen and the candela derived units?
Also historical. The candela came first, and then a need for the lumen
was felt. Again, the reason for making them base rather than derived
is for convenience of dimensional analysis. Light is conceptually
different from power, just as length is different from time, even
though we could make the metre a derived unit from the second.
> For the same reason I asked about the coulomb above: simplicity. If
> luminous efficacy is to be defined as 683 lumens/watt, why not state
> things simply and directly that it is 683 lumens/watt? It seems more
> concise than candela*steradian/watt, doesn't it?
History.
>>> And beyond the draft document I ask, why is there a base unit for
>>> light intensity yet no analogous base unit for sound intensity? Did
>>> the framers of SI consider sound a phenomenon of less relevance to the
>>> human condition than light? Was sound just harder to quantify in days
>>> of yore? Why no base acoustic SI unit? (Of course, I would withdraw
>>> this objection were the luminous units to be *wholly* relegated to
>>> derived status.)
>>
>> It's because the human response of the ear to sound is not as complex as
>> that to light. The luminosity units are designed to take into account
>> the varying sensitivity of the human eye to different frequencies. The
>> human ear has varying sensitivity, sure, but it's much simpler and more
>> of the form, "You can hear fine in this range; right at the edges of it,
>> not so good; and outside of it, you can't hear anything."
>
> So those proposing units just thought watts or watts/steradian were good
> enough for the measurement of sound and thus no need for a
> specially-named acoustic unit? It does seem like the decibel has been
> designated "friendly" to SI even though SI hasn't seen the need for a
> specific SI sound unit. But I see where you are coming from, E.M.F.
I don't entirely agree with E.M.F. The response of the human ear is
quite complex (a fact of importance for phonetics).
Perhaps a better explanation might be that by the time a unit of
loudness was required, we knew what sound was, so there was already a
unit available: the unit of pressure. When we first started defining
units of luminous intensity, we didn't know what light was.
Epiphany
> Just history, I would imagine. Sure, if you were designing SI now,
> you'd make the coulomb the base unit. But SI changes with reluctance,
> and a change that is purely aesthetic is unlikely to be considered
> worth the effort.
I didn't realize that whether a unit is base or derived was so pointedly
a conceit.
> This confused me for a long while. But then I realized that dimensions
> are arbitrary (after all, the ampere is defined in terms of a force
> per unit length, so it could be given those dimensions; mass is the
> same as energy, so velocity is dimensionless; time and space have the
> same dimensions (which is why velocity is dimensionless); and so
> on). It's just a convenience for doing dimensional analysis of your
> equations if you decide that "amount of substance" is a dimension,
> which might be measured in units, or moles.
You aren't the first to suggest such dimensional thoughts to me. But I
am not entirely comfortable with rendering quantities that way. I know
that this could be that I am merely not sufficiently enlightened. But,
take torque and energy. Don't they have the same dimensionality? Yet
it would be a mistake to do 4 joules of work to make a bolt tight when
what was needed was torquing to 4 N•m rotational resistance, right?
Are you saying "a dozen" can be a dimension too? The thing about the
mole is that you can't just have a quantity of 3.76 moles like you can
have a length of 3.76 meters; you really have to specify moles *of
what*, right? Or could I, if I had 5.3 moles of water and 1.1 moles of
ammonia, usefully say I had a total of 6.4 moles of stuff?
> Also historical. The candela came first, and then a need for the lumen
> was felt. Again, the reason for making them base rather than derived
> is for convenience of dimensional analysis. Light is conceptually
> different from power, just as length is different from time, even
> though we could make the metre a derived unit from the second.
But don't we want to keep things up to date? If we always pled
"history" or "tradition" wouldn't we be saddled with anachronisms like
non-SI units?
I wouldn't be against making the meter a derived unit, as you point
out, except I point out that we could just as rationally make the second
a derived unit based on the meter, so there does not seem to be a
physical *hierarchy* of meter more fundamental or second more
fundamental. Meter and second seem of equal degree of derivation.
> I don't entirely agree with E.M.F. The response of the human ear is
> quite complex (a fact of importance for phonetics).
>
> Perhaps a better explanation might be that by the time a unit of
> loudness was required, we knew what sound was, so there was already a
> unit available: the unit of pressure. When we first started defining
> units of luminous intensity, we didn't know what light was.
So it was just a double accident of the when of scientific
investigation? The first accident was not beginning to analyze sound
early, before it was understood to be pressure waves, yet (the second
accident) analyzing light before it was understood to be electromagnetic
waves? Interesting, and thank you.
\ | /
-Epiphany-
/ | \
Julian Bradfield
> You aren't the first to suggest such dimensional thoughts to me. But I
> am not entirely comfortable with rendering quantities that way. I know
> that this could be that I am merely not sufficiently enlightened. But,
> take torque and energy. Don't they have the same dimensionality? Yet
> it would be a mistake to do 4 joules of work to make a bolt tight when
> what was needed was torquing to 4 N•m rotational resistance, right?
Yes, that's a good example. We happen to use dimensions where these
quantities have the same dimension - though there is an important
difference, in that energy is a scalar, and torque is a
vector, or rather a pseudovector. Similarly, angular momentum,
which is a fundamental physical quantity, has the same dimensions as
energy · time, which is not, but again one is pseudovector and the
other scalar.
However, if you took the radian as a base unit, you could define the
units of angular momentum to be kg·m²·rad/s (using the equation in
terms of moment of inertia and angular momentum), and then they would
be distinct. Likewise torque would then be kg·m²·rad/s² (unit torque
causes unit rate of change of angular momentum), which would
distinguish it from energy dimensionally.
Then any pseudovector like torque or "distance from an axis of
rotation" or would be dimensionally distinct from a scalar or vector
quantity like energy or distance. (So the cross product would have to
be defined to introduce a dimension of radians - which is reasonable,
as it's a fluke of having 3 spatial dimensions that the cross product
of two vectors "looks like" a vector, not a universal. Really,
pseudovectors live in a different world from vectors.)
Hm. I hope this makes sense and is correct.
> Are you saying "a dozen" can be a dimension too? The thing about the
> mole is that you can't just have a quantity of 3.76 moles like you can
> have a length of 3.76 meters; you really have to specify moles *of
> what*, right? Or could I, if I had 5.3 moles of water and 1.1 moles of
> ammonia, usefully say I had a total of 6.4 moles of stuff?
Usefully? I don't know. I don't think there's any principled reason
why you can't say "a mole of assorted molecules", any more than
there's reason you can't say "a mole of carbon atoms (of any mix of
isotopes)". I'm not sure when it would be useful.
> But don't we want to keep things up to date? If we always pled
> "history" or "tradition" wouldn't we be saddled with anachronisms like
> non-SI units?
The definitions do change, as you know. But they only change when
there's a clear improvement, such as removing a source of error, or
removing an unnecessary independent measurement.
> I wouldn't be against making the meter a derived unit, as you point
> out, except I point out that we could just as rationally make the second
> a derived unit based on the meter, so there does not seem to be a
> physical *hierarchy* of meter more fundamental or second more
> fundamental. Meter and second seem of equal degree of derivation.
Is mass more fundamental than energy? Why?
> So it was just a double accident of the when of scientific
> investigation? The first accident was not beginning to analyze sound
> early, before it was understood to be pressure waves, yet (the second
> accident) analyzing light before it was understood to be electromagnetic
> waves? Interesting, and thank you.
I don't know whether that's really the explanation - I'm not a
historian. But I put it forward as a plausible explanation, based on
what I can remember of the history of physics.
Erik Max Francis
There's a simpler way of looking at it. Torque and energy have the same
units (at least at first glance), but that's because we use a coherent
unit system.
More concretely, in linear kinematics, work equals force times
displacement (dW = F dot ds). In rotational kinematics, torque is the
analog of force, and angular displacement is the analog of linear
displacement, so not surprisingly, work equals torque times angular
displacement (dW = tau dot dtheta).
Energy has units of J, torque has units of N m. The reason we don't
write those the same is because to get from one to the other you have to
multiply (or divide) by an angle. Since SI is coherent, we use the
radian to represent this angle, which is strictly dimensionless.
So this subthread is in essence yet another example of why we use
radians as our unit of angular measure. It's because they help make up
a coherent unit system, and coherent unit systems keep everyone from
going batty.
--
Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
In the fight between you and the world, back the world.
-- Frank Zappa
Erik Max Francis
> On 30-Mar-11 16:12, Erik Max Francis wrote:
>> Epiphany wrote:
>>> First of all, why not make the coulomb the base unit if we are basing
>>> the the definition on the constant unit of elementary charge? The
>>> ampere can become a derived unit. And then we ought to define the
>>> coulomb as an *integer* number of those charges, not as some
>>> reciprocal of some value in scientific notation that isn't likely to
>>> be an integer.
>>
>> Why?
>
> Because by basing the ampere on the elementary charge we are essentially
> defining the coulomb more simply than we are defining the ampere. So
> for the sake of simplicity, why not make the coulomb the base unit?
What makes you think one is more simple than the other?
In a system of units, the unit of charge and current differ by a unit of
time. To make a system of units, you need a base set of fundamental
units that are enough to span the vector space of all the units you care
about, but other than that, it's arbitrary which ones are fundamental
and which ones are derived. Which ones you choose are a matter of
history, convention, convenience, and accident.
>> It's just a rejiggering of the way it's defined, so it's in terms of
>> something other than a particular isotope of C. It doesn't really matter
>> how it's defined. Are you asking why we have the unit mol in the first
>> place?
>
> No, I am not asking why we have the mole. And you didn't answer the
> question I asked. But I see that one can define things in two different
> ways. Avogadro's constant can be a pure number or it can be the
> conversion factor from moles to a pure number. I'm just used to
> thinking of a mole like I think of a dozen, just a *number*. Doesn't it
> seem simpler to say the mole is just a number like a googol is just a
> number?
Because it's useful for chemists to talk about the amount of substance
in fixed batches of atoms. Yes, they're really just like dozens. Are
you _sure_ you're not asking why we have the unit mol?
>>> Again, why not make the *lumen* the base unit and the candela a
>>> derived unit, or even, noting the deep dependence of these units on
>>> the *watt*, make both the lumen and the candela derived units?
>>
>> Again, why?
>
> For the same reason I asked about the coulomb above: simplicity. If
> luminous efficacy is to be defined as 683 lumens/watt, why not state
> things simply and directly that it is 683 lumens/watt? It seems more
> concise than candela*steradian/watt, doesn't it?
Same answer as above.
> For future aid to me, when you ask 'why?' again, could you write a
> complete thought (sentence) so that I have the most help in knowing what
> to address in my response?
Well, you're the one suggesting that we change the fundamental basis of
our system of units, so it really seems like you're the one who ought to
be explaining your reasoning, not me.
But since you point it out, okay, I'll ask a clearer question: What
difference does you think it would make? Why would it be "simpler"?
(That's usually what "Why?" questions mean, for the record. When you
say something, and someone asks why, they're asking why you think what
you just said is a good idea. Just helping.)
>> It's because the human response of the ear to sound is not as complex as
>> that to light. The luminosity units are designed to take into account
>> the varying sensitivity of the human eye to different frequencies. The
>> human ear has varying sensitivity, sure, but it's much simpler and more
>> of the form, "You can hear fine in this range; right at the edges of it,
>> not so good; and outside of it, you can't hear anything."
>
> So those proposing units just thought watts or watts/steradian were good
> enough for the measurement of sound and thus no need for a
> specially-named acoustic unit?
No, but it would be helpful if you actually read what I answered.
> It does seem like the decibel has been
> designated "friendly" to SI even though SI hasn't seen the need for a
> specific SI sound unit.
And the reason it hasn't is the reason I gave. Would you like me to
repeat it? It's written above where you quoted it.
--
Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
Some people see things as they are and say why. I dream things that
never were and say why not. -- George Bernard Shaw
Erik Max Francis
I didn't say it wasn't "complex," or "quite complex." I said it was
"not as complex as that to light."
The big difference is that we hear sounds with frequencies over a vastly
greater range of frequencies of light that we can see. That means that
we tend to measure sound levels with a logarithmic scale (B or Np,
depending on how hardcore you want to be with SI). With a logarithmic
scale, the sensitivities to intermediate frequencies are much less
important than with light and it's much easier to model it as pretty
much the same response except for the cutoffs. It's wrong, but it's not
wrong enough to have warranted its own SI unit, which was precisely my
point.
--
Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
Out from his breast / his soul went to seek / the doom of the just.
-- Beowulf
Epiphany
> Epiphany wrote:
>> Because by basing the ampere on the elementary charge we are
>> essentially defining the coulomb more simply than we are defining the
>> ampere. So for the sake of simplicity, why not make the coulomb the
>> base unit?
>
> What makes you think one is more simple than the other?
My understanding is that the current definition of the ampere is the way
it is, with the coulomb being a derived unit, because we didn't have the
*technology* to count out individual fundamental charges. So,
if we have gotten to the technological level where we can count out
those charges, I was thinking switching "back" to the coulomb being the
base unit would be called for. That's my thrust here, that if we could
have counted those charges from day 1, so to say, we would have derived
the ampere from the coulomb all along. The fundamental charge is a unit
of charge, right, not a unit of current, right? That's why I see the
coulomb (the SI unit of charge) as being more simple when we redefine
the ampere to X number of charges per second.
> In a system of units, the unit of charge and current differ by a unit of
> time. To make a system of units, you need a base set of fundamental
> units that are enough to span the vector space of all the units you care
> about, but other than that, it's arbitrary which ones are fundamental
> and which ones are derived. Which ones you choose are a matter of
> history, convention, convenience, and accident.
And if you are emphasizing things like tradition and history, you win.
I emphasize conciseness in practical definitions, so I guess I lose.
>> No, I am not asking why we have the mole. And you didn't answer the
>> question I asked. But I see that one can define things in two
>> different ways. Avogadro's constant can be a pure number or it can be
>> the conversion factor from moles to a pure number. I'm just used to
>> thinking of a mole like I think of a dozen, just a *number*. Doesn't
>> it seem simpler to say the mole is just a number like a googol is just
>> a number?
> Because it's useful for chemists to talk about the amount of substance
> in fixed batches of atoms. Yes, they're really just like dozens. Are you
> _sure_ you're not asking why we have the unit mol?
Sure I'm sure. You answered my question by agreeing with me: "Yes,
they're really just like dozens." My original trouble here was why they
wanted to make the *Avogadro constant* to be a [large number] per mol,
essentially a conversion factor, and not simply the *large number*, as
even my Merriam-Webster dictionary happens to define "Avogadro's
number". In my dictionary it's just the number, and not "per anything".
It's just a very small objection hinging on their proposed use of
"mol^-1" in their definition of Avogadro's number, not anything deeper
about the utility of the mole.
> Well, you're the one suggesting that we change the fundamental basis of
> our system of units, so it really seems like you're the one who ought to
> be explaining your reasoning, not me.
Well, then I apologize for not explaining well enough when I started the
thread. I newsposted with the most glorious hopes that I had stated my
take on the situation as fully and concisely as possible.
> But since you point it out, okay, I'll ask a clearer question: What
> difference does you think it would make? Why would it be "simpler"?
> (That's usually what "Why?" questions mean, for the record. When you say
> something, and someone asks why, they're asking why you think what you
> just said is a good idea. Just helping.)
That's a very helpful answer. I thank you very much! Again I have the
most glorious hopes that my replies in this newspost are clear.
>>> It's because the human response of the ear to sound is not as complex as
>>> that to light. The luminosity units are designed to take into account
>>> the varying sensitivity of the human eye to different frequencies. The
>>> human ear has varying sensitivity, sure, but it's much simpler and more
>>> of the form, "You can hear fine in this range; right at the edges of it,
>>> not so good; and outside of it, you can't hear anything."
>>
>> So those proposing units just thought watts or watts/steradian were
>> good enough for the measurement of sound and thus no need for a
>> specially-named acoustic unit?
>
> No, but it would be helpful if you actually read what I answered.
I did read what you answered, and asked the question to help clarify my
understanding of the *plan* behind SI based on what you answered. I am
sorry if your answer lacked some clarity with respect to my views. Now
I am worried that my answers won't be clear enough for you because I
cannot emulate your thinking sufficiently to understand fully your
responses.
I ask again, if "the human response of the ear to sound is not as
complex as that to light," what was the view of those framing SI on this
matter of sound? Was measuring sound therefore not even something that
concerned them?
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-Epiphany-
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