What is a valid unit of measurement?
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Ok, so this is a bit of an odd question. It is sort of a physics question, but I felt it was more appropriate here. Feel free to suggest another venue.
Let's just look at a simple example. We'll use kilograms as an example unit of measurement. Let's say we have three objects, A, B, and C with masses 11 kg, 12 kg, and 23 kg. It is clear there is an additive relationship here that has a real physical meaning. The third object really does have the equivalent amount of matter as the first two combined. This real relationship is played out with how physical laws play out. We can go down the philosophical rabbit hole here, but I don't think it is productive.
From the wikipedia article, a measurement in a given unit must be equivalent to that number times the unit, i.e. $11 kg = 11 times (1 kg)$. Of course, multiplication can be defined in terms of addition. So we actually require that
$$11 kg = underset{text{11 terms}}{underbrace{1 kg + 1 kg + cdots 1 kg}}.$$
In a real physical sense, the amount of stuff in eleven objects each with 1 kg mass really is equivalent to the amount of stuff in one object with 11 kg of mass.
So here is the main question: Is number of kilograms beyond 10 kilograms a valid unit of measurement? Let us denote it $kg_{10}$
Now our objects have "masses" $1 kg_{10}$, $2 kg_{10}$, and $13 kg_{10}$. These aren't actually masses, they are "masses beyond 10kg". The additive relationship from our original unit of kg does not carry over to our new "unit" of kg$_{10}$.
Can we even say that $1 kg_{10}$ + $1 kg_{10}$ = $2 kg_{10}$? What are we actually adding here? We are not adding kilograms! If I have an object that has mass 11 kg ($1 kg_{10}$) and I increase its mass by 1 kg, it now has mass 12 kg ($2 kg_{10}$) so it would seem that $1 kg_{10}$ + $1 kg$ = $2 kg_{10}$.
So, maybe this is a stupid thing to worry about, but it just seems that we should have rigorous set of rules about what constitutes a valid unit of measurement. Those rules would include something about additivity and the relation to the thing being measured and not being able to just arbitrarily set zero anywhere.
I would argue that kg$_{10}$ is not technically a valid unit of measurement, and that this is reasonable since the unit of measurement is actually kilograms, which is a true unit of measurement (arithmetic operations on it make sense in terms of the physical thing it is actually measuring), but for whatever reason, we might be interested only in kilograms beyond 10.
definition unit-of-measure
asked Jan 21 at 0:52
jdodsjdods
3,66011234
$endgroup$
add a comment |
$begingroup$
Ok, so this is a bit of an odd question. It is sort of a physics question, but I felt it was more appropriate here. Feel free to suggest another venue.
Let's just look at a simple example. We'll use kilograms as an example unit of measurement. Let's say we have three objects, A, B, and C with masses 11 kg, 12 kg, and 23 kg. It is clear there is an additive relationship here that has a real physical meaning. The third object really does have the equivalent amount of matter as the first two combined. This real relationship is played out with how physical laws play out. We can go down the philosophical rabbit hole here, but I don't think it is productive.
From the wikipedia article, a measurement in a given unit must be equivalent to that number times the unit, i.e. $11 kg = 11 times (1 kg)$. Of course, multiplication can be defined in terms of addition. So we actually require that
$$11 kg = underset{text{11 terms}}{underbrace{1 kg + 1 kg + cdots 1 kg}}.$$
In a real physical sense, the amount of stuff in eleven objects each with 1 kg mass really is equivalent to the amount of stuff in one object with 11 kg of mass.
So here is the main question: Is number of kilograms beyond 10 kilograms a valid unit of measurement? Let us denote it $kg_{10}$
Now our objects have "masses" $1 kg_{10}$, $2 kg_{10}$, and $13 kg_{10}$. These aren't actually masses, they are "masses beyond 10kg". The additive relationship from our original unit of kg does not carry over to our new "unit" of kg$_{10}$.
Can we even say that $1 kg_{10}$ + $1 kg_{10}$ = $2 kg_{10}$? What are we actually adding here? We are not adding kilograms! If I have an object that has mass 11 kg ($1 kg_{10}$) and I increase its mass by 1 kg, it now has mass 12 kg ($2 kg_{10}$) so it would seem that $1 kg_{10}$ + $1 kg$ = $2 kg_{10}$.
So, maybe this is a stupid thing to worry about, but it just seems that we should have rigorous set of rules about what constitutes a valid unit of measurement. Those rules would include something about additivity and the relation to the thing being measured and not being able to just arbitrarily set zero anywhere.
I would argue that kg$_{10}$ is not technically a valid unit of measurement, and that this is reasonable since the unit of measurement is actually kilograms, which is a true unit of measurement (arithmetic operations on it make sense in terms of the physical thing it is actually measuring), but for whatever reason, we might be interested only in kilograms beyond 10.
definition unit-of-measure
asked Jan 21 at 0:52
jdodsjdods
3,66011234
$endgroup$
$begingroup$
Are you familiar with modular arithmetic? What you're saying is similar to being in modulus $10$. As far as practical measurements go though, this becomes impractical.
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– Gnumbertester
Jan 21 at 1:15
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Yes, I'm familiar with modular arithmetic, but don't use it ever. That's a good point that this silly "unit" actually is just that.
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– jdods
Jan 21 at 2:04
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I'm not surprised this got a down vote. Can someone suggest a way to make the question better, or maybe a different venue where more people might have an interest?
$endgroup$
– jdods
Jan 21 at 2:07
$begingroup$
I do not see the reason for the downvote, it is a genuine query and not technically incorrect if you define it for a given scenario.
$endgroup$
– Gnumbertester
Jan 21 at 2:10
1
$begingroup$
What about degrees Celsius--does it count as a unit of measurement? It is a useful way of giving meaning to numeric temperature measurements in common use. For example, $25^circ C$ is the temperature of a warm day, whereas $25^circ F$ is freezing cold. But if you want temperature for various formulas in physics, you need to convert to an absolute scale such as Kelvins, either explicitly or implicitly.
$endgroup$
– David K
Jan 21 at 2:46
add a comment |
$begingroup$
Ok, so this is a bit of an odd question. It is sort of a physics question, but I felt it was more appropriate here. Feel free to suggest another venue.
Let's just look at a simple example. We'll use kilograms as an example unit of measurement. Let's say we have three objects, A, B, and C with masses 11 kg, 12 kg, and 23 kg. It is clear there is an additive relationship here that has a real physical meaning. The third object really does have the equivalent amount of matter as the first two combined. This real relationship is played out with how physical laws play out. We can go down the philosophical rabbit hole here, but I don't think it is productive.
From the wikipedia article, a measurement in a given unit must be equivalent to that number times the unit, i.e. $11 kg = 11 times (1 kg)$. Of course, multiplication can be defined in terms of addition. So we actually require that
$$11 kg = underset{text{11 terms}}{underbrace{1 kg + 1 kg + cdots 1 kg}}.$$
In a real physical sense, the amount of stuff in eleven objects each with 1 kg mass really is equivalent to the amount of stuff in one object with 11 kg of mass.
So here is the main question: Is number of kilograms beyond 10 kilograms a valid unit of measurement? Let us denote it $kg_{10}$
Now our objects have "masses" $1 kg_{10}$, $2 kg_{10}$, and $13 kg_{10}$. These aren't actually masses, they are "masses beyond 10kg". The additive relationship from our original unit of kg does not carry over to our new "unit" of kg$_{10}$.
Can we even say that $1 kg_{10}$ + $1 kg_{10}$ = $2 kg_{10}$? What are we actually adding here? We are not adding kilograms! If I have an object that has mass 11 kg ($1 kg_{10}$) and I increase its mass by 1 kg, it now has mass 12 kg ($2 kg_{10}$) so it would seem that $1 kg_{10}$ + $1 kg$ = $2 kg_{10}$.
So, maybe this is a stupid thing to worry about, but it just seems that we should have rigorous set of rules about what constitutes a valid unit of measurement. Those rules would include something about additivity and the relation to the thing being measured and not being able to just arbitrarily set zero anywhere.
I would argue that kg$_{10}$ is not technically a valid unit of measurement, and that this is reasonable since the unit of measurement is actually kilograms, which is a true unit of measurement (arithmetic operations on it make sense in terms of the physical thing it is actually measuring), but for whatever reason, we might be interested only in kilograms beyond 10.
definition unit-of-measure
asked Jan 21 at 0:52
jdodsjdods
3,66011234
$endgroup$
Ok, so this is a bit of an odd question. It is sort of a physics question, but I felt it was more appropriate here. Feel free to suggest another venue.
Let's just look at a simple example. We'll use kilograms as an example unit of measurement. Let's say we have three objects, A, B, and C with masses 11 kg, 12 kg, and 23 kg. It is clear there is an additive relationship here that has a real physical meaning. The third object really does have the equivalent amount of matter as the first two combined. This real relationship is played out with how physical laws play out. We can go down the philosophical rabbit hole here, but I don't think it is productive.
From the wikipedia article, a measurement in a given unit must be equivalent to that number times the unit, i.e. $11 kg = 11 times (1 kg)$. Of course, multiplication can be defined in terms of addition. So we actually require that
$$11 kg = underset{text{11 terms}}{underbrace{1 kg + 1 kg + cdots 1 kg}}.$$
In a real physical sense, the amount of stuff in eleven objects each with 1 kg mass really is equivalent to the amount of stuff in one object with 11 kg of mass.
So here is the main question: Is number of kilograms beyond 10 kilograms a valid unit of measurement? Let us denote it $kg_{10}$
Now our objects have "masses" $1 kg_{10}$, $2 kg_{10}$, and $13 kg_{10}$. These aren't actually masses, they are "masses beyond 10kg". The additive relationship from our original unit of kg does not carry over to our new "unit" of kg$_{10}$.
Can we even say that $1 kg_{10}$ + $1 kg_{10}$ = $2 kg_{10}$? What are we actually adding here? We are not adding kilograms! If I have an object that has mass 11 kg ($1 kg_{10}$) and I increase its mass by 1 kg, it now has mass 12 kg ($2 kg_{10}$) so it would seem that $1 kg_{10}$ + $1 kg$ = $2 kg_{10}$.
So, maybe this is a stupid thing to worry about, but it just seems that we should have rigorous set of rules about what constitutes a valid unit of measurement. Those rules would include something about additivity and the relation to the thing being measured and not being able to just arbitrarily set zero anywhere.
I would argue that kg$_{10}$ is not technically a valid unit of measurement, and that this is reasonable since the unit of measurement is actually kilograms, which is a true unit of measurement (arithmetic operations on it make sense in terms of the physical thing it is actually measuring), but for whatever reason, we might be interested only in kilograms beyond 10.
definition unit-of-measure
definition unit-of-measure
asked Jan 21 at 0:52
jdodsjdods
3,66011234
asked Jan 21 at 0:52
jdodsjdods
3,66011234
asked Jan 21 at 0:52
jdodsjdods
3,66011234
asked Jan 21 at 0:52
jdodsjdods
3,66011234
asked Jan 21 at 0:52
jdodsjdods
3,66011234
3,66011234
$begingroup$
Are you familiar with modular arithmetic? What you're saying is similar to being in modulus $10$. As far as practical measurements go though, this becomes impractical.
$endgroup$
– Gnumbertester
Jan 21 at 1:15
$begingroup$
Yes, I'm familiar with modular arithmetic, but don't use it ever. That's a good point that this silly "unit" actually is just that.
$endgroup$
– jdods
Jan 21 at 2:04
$begingroup$
I'm not surprised this got a down vote. Can someone suggest a way to make the question better, or maybe a different venue where more people might have an interest?
$endgroup$
– jdods
Jan 21 at 2:07
$begingroup$
I do not see the reason for the downvote, it is a genuine query and not technically incorrect if you define it for a given scenario.
$endgroup$
– Gnumbertester
Jan 21 at 2:10
1
$begingroup$
What about degrees Celsius--does it count as a unit of measurement? It is a useful way of giving meaning to numeric temperature measurements in common use. For example, $25^circ C$ is the temperature of a warm day, whereas $25^circ F$ is freezing cold. But if you want temperature for various formulas in physics, you need to convert to an absolute scale such as Kelvins, either explicitly or implicitly.
$endgroup$
– David K
Jan 21 at 2:46
add a comment |
$begingroup$
Are you familiar with modular arithmetic? What you're saying is similar to being in modulus $10$. As far as practical measurements go though, this becomes impractical.
$endgroup$
– Gnumbertester
Jan 21 at 1:15
$begingroup$
Yes, I'm familiar with modular arithmetic, but don't use it ever. That's a good point that this silly "unit" actually is just that.
$endgroup$
– jdods
Jan 21 at 2:04
$begingroup$
I'm not surprised this got a down vote. Can someone suggest a way to make the question better, or maybe a different venue where more people might have an interest?
$endgroup$
– jdods
Jan 21 at 2:07
$begingroup$
I do not see the reason for the downvote, it is a genuine query and not technically incorrect if you define it for a given scenario.
$endgroup$
– Gnumbertester
Jan 21 at 2:10
1
$begingroup$
What about degrees Celsius--does it count as a unit of measurement? It is a useful way of giving meaning to numeric temperature measurements in common use. For example, $25^circ C$ is the temperature of a warm day, whereas $25^circ F$ is freezing cold. But if you want temperature for various formulas in physics, you need to convert to an absolute scale such as Kelvins, either explicitly or implicitly.
$endgroup$
– David K
Jan 21 at 2:46
$begingroup$
Are you familiar with modular arithmetic? What you're saying is similar to being in modulus $10$. As far as practical measurements go though, this becomes impractical.
$endgroup$
– Gnumbertester
Jan 21 at 1:15
$begingroup$
Are you familiar with modular arithmetic? What you're saying is similar to being in modulus $10$. As far as practical measurements go though, this becomes impractical.
$endgroup$
– Gnumbertester
Jan 21 at 1:15
$begingroup$
Yes, I'm familiar with modular arithmetic, but don't use it ever. That's a good point that this silly "unit" actually is just that.
$endgroup$
– jdods
Jan 21 at 2:04
$begingroup$
Yes, I'm familiar with modular arithmetic, but don't use it ever. That's a good point that this silly "unit" actually is just that.
$endgroup$
– jdods
Jan 21 at 2:04
$begingroup$
I'm not surprised this got a down vote. Can someone suggest a way to make the question better, or maybe a different venue where more people might have an interest?
$endgroup$
– jdods
Jan 21 at 2:07
$begingroup$
I'm not surprised this got a down vote. Can someone suggest a way to make the question better, or maybe a different venue where more people might have an interest?
$endgroup$
– jdods
Jan 21 at 2:07
$begingroup$
I do not see the reason for the downvote, it is a genuine query and not technically incorrect if you define it for a given scenario.
$endgroup$
– Gnumbertester
Jan 21 at 2:10
$begingroup$
I do not see the reason for the downvote, it is a genuine query and not technically incorrect if you define it for a given scenario.
$endgroup$
– Gnumbertester
Jan 21 at 2:10
1
1
$begingroup$
What about degrees Celsius--does it count as a unit of measurement? It is a useful way of giving meaning to numeric temperature measurements in common use. For example, $25^circ C$ is the temperature of a warm day, whereas $25^circ F$ is freezing cold. But if you want temperature for various formulas in physics, you need to convert to an absolute scale such as Kelvins, either explicitly or implicitly.
$endgroup$
– David K
Jan 21 at 2:46
$begingroup$
What about degrees Celsius--does it count as a unit of measurement? It is a useful way of giving meaning to numeric temperature measurements in common use. For example, $25^circ C$ is the temperature of a warm day, whereas $25^circ F$ is freezing cold. But if you want temperature for various formulas in physics, you need to convert to an absolute scale such as Kelvins, either explicitly or implicitly.
$endgroup$
– David K
Jan 21 at 2:46
add a comment |
3 Answers
3
active
oldest
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$begingroup$
If I've understood your system correctly, we do this all the time with temperatures: absolute temperature is measured in kelvins but degrees Celsius are effectively "kelvins beyond 273.16". (Loosely, the freezing point of water.) We routinely use them all the time to compare temperaures, but things go awry if we want to say that one thing is twice as hot as another.
Note that 30°C isn't 20°C plus 10°C unless we use $x$°C to mean two different things, namely a temperature of $x$ temperature steps above freezing, and an increment of $x$ temperature steps.
You might argue that we do something similar (but inconsistently) with weights when we treat them like mass: we're neglecting the buoyancy effect in air so there's a slight offset. This actually has to be taken into account when dealing with very precise mass measurenents.
And decibels are in fact meaningless on their own as a unit: a decibel is a power ratio of $sqrt[10]{10}$ so the actual measurement unit is dBA, ie decibels above the threshold of hearing. On its own, a decibel is simply the number $sqrt[10]{10}$ treated as a multiplication factor.
answered Jan 21 at 2:59
timtfjtimtfj
2,448420
$endgroup$
$begingroup$
This is helpful! Very good examples. I didn't think of these and will have to let it churn on my mind a bit. This might prove my idea is too restrictive and ultimately incorrect.
$endgroup$
– jdods
Jan 21 at 12:17
add a comment |
$begingroup$
The International Vocabulary of Metrology (VIM) states that a measurement unit should be a
real scalar quantity, defined and adopted by convention, with
which any other quantity of the same kind can be compared to
express the ratio of the two quantities as a number
So by the BIPM ( International Bureau of Weights and Measures ) the number of kilograms beyond 10 kilograms cannot be defined to be a unit, since it's not a ratio.
And quantity is expressed by the VIM as
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.
So it has to be connected to nature itself. Like the meter which was first defined as as one ten-millionth of the distance from the equator to the North Pole. But changes between one unit and other are still aceptable and must be possible. In the VIM there is a table of all the principals quantities.
I think that occurs because of the way we do math, you have state $1 kg_{10} + 1 kg_{10} = 2 kg_{10}$ that wouldn't be true if we try to convert the numbers to kilograms, since $2 kg_{10} = 12 kg_{10} neq 22 kg = 1 kg_{10} + 1 kg_{10}$. So a unit should always respect our math principles and that would leave us only with ratio units, which are easily convertible, opposite to your created unit. But I guess any unit is possible to make, as long as you invent a different math to it.
answered Jan 21 at 1:35
Ellian CarlosEllian Carlos
215
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Wow, that's rather unsatisfying language. All it says is we must be able to express the ratio of two quantities as a number. But $2 mathrm{kg_{10}}$ is twice as much mass above $10$ kg as $1 mathrm{kg_{10}}$ is, and indeed the ratio computes as $2/1 = 2.$ This still seems like a very silly thing to do, but the VIM doesn't say why. (Maybe one has to read other parts of it to get that information.)
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– David K
Jan 21 at 2:39
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I think I didn't made it clear, my fault. Quantity in the VIM is a 'property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference ', so it's not any ratio, not even can be based on another unit, it has to come from nature. I'll add that to my answer.
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– Ellian Carlos
Jan 21 at 2:46
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I think I know what they mean, it's just that human language muddies the issue because we have too many habitual uses of terms that don't conform to the idea they're trying to get across. I suppose, by the way, that various temperature scales in use outside scientific applications (Celsius, sometimes Fahrenheit, even Reaumur) are not considered actual units of measurement according to the standard. Does the standard have another term for such scales of measurement, or does it ignore them completely?
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– David K
Jan 21 at 2:51
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At first I think all those scales were based on some experiment. The VIM as a vocabulary does not explicit classifies all units, but by the SI (International System) the system of units used by the BIPM, Kelvin is a base unit, Celsius is a derived unit, Fahrenheit and Reaumur are units from others system of units.
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– Ellian Carlos
Jan 21 at 3:04
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Historically, I think the general idea of the scales was to be able to describe how warm or cold a temperature is in a way that is precise and repeatable, without necessarily understanding what temperature actually is. For repeatability, the scales are based on measurements that can be made by repeatable experiment; for precision we place those measurements on a numeric interpolation/extrapolation scale. The scales persist because people never quite caught onto the idea that 300 Kelvin is fine weather for swimming but at 270 Kelvin you should beware of ice on the road.
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– David K
Jan 21 at 3:26
|
show 1 more comment
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I'm not sure what you mean by "valid" unit of measurement, but it is certainly impractical because, as you correctly identified, you cannot add properly. You could obviously define $1 kg_{10} + 1 kg_{10} = 12 kg_{10}$, but this gets clumsy at best...
answered Jan 21 at 1:01
KlausKlaus
1,7979
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add a comment |
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3 Answers
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3 Answers
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$begingroup$
If I've understood your system correctly, we do this all the time with temperatures: absolute temperature is measured in kelvins but degrees Celsius are effectively "kelvins beyond 273.16". (Loosely, the freezing point of water.) We routinely use them all the time to compare temperaures, but things go awry if we want to say that one thing is twice as hot as another.
Note that 30°C isn't 20°C plus 10°C unless we use $x$°C to mean two different things, namely a temperature of $x$ temperature steps above freezing, and an increment of $x$ temperature steps.
You might argue that we do something similar (but inconsistently) with weights when we treat them like mass: we're neglecting the buoyancy effect in air so there's a slight offset. This actually has to be taken into account when dealing with very precise mass measurenents.
And decibels are in fact meaningless on their own as a unit: a decibel is a power ratio of $sqrt[10]{10}$ so the actual measurement unit is dBA, ie decibels above the threshold of hearing. On its own, a decibel is simply the number $sqrt[10]{10}$ treated as a multiplication factor.
answered Jan 21 at 2:59
timtfjtimtfj
2,448420
$endgroup$
$begingroup$
This is helpful! Very good examples. I didn't think of these and will have to let it churn on my mind a bit. This might prove my idea is too restrictive and ultimately incorrect.
$endgroup$
– jdods
Jan 21 at 12:17
add a comment |
$begingroup$
If I've understood your system correctly, we do this all the time with temperatures: absolute temperature is measured in kelvins but degrees Celsius are effectively "kelvins beyond 273.16". (Loosely, the freezing point of water.) We routinely use them all the time to compare temperaures, but things go awry if we want to say that one thing is twice as hot as another.
Note that 30°C isn't 20°C plus 10°C unless we use $x$°C to mean two different things, namely a temperature of $x$ temperature steps above freezing, and an increment of $x$ temperature steps.
You might argue that we do something similar (but inconsistently) with weights when we treat them like mass: we're neglecting the buoyancy effect in air so there's a slight offset. This actually has to be taken into account when dealing with very precise mass measurenents.
And decibels are in fact meaningless on their own as a unit: a decibel is a power ratio of $sqrt[10]{10}$ so the actual measurement unit is dBA, ie decibels above the threshold of hearing. On its own, a decibel is simply the number $sqrt[10]{10}$ treated as a multiplication factor.
answered Jan 21 at 2:59
timtfjtimtfj
2,448420
$endgroup$
$begingroup$
This is helpful! Very good examples. I didn't think of these and will have to let it churn on my mind a bit. This might prove my idea is too restrictive and ultimately incorrect.
$endgroup$
– jdods
Jan 21 at 12:17
add a comment |
$begingroup$
If I've understood your system correctly, we do this all the time with temperatures: absolute temperature is measured in kelvins but degrees Celsius are effectively "kelvins beyond 273.16". (Loosely, the freezing point of water.) We routinely use them all the time to compare temperaures, but things go awry if we want to say that one thing is twice as hot as another.
Note that 30°C isn't 20°C plus 10°C unless we use $x$°C to mean two different things, namely a temperature of $x$ temperature steps above freezing, and an increment of $x$ temperature steps.
You might argue that we do something similar (but inconsistently) with weights when we treat them like mass: we're neglecting the buoyancy effect in air so there's a slight offset. This actually has to be taken into account when dealing with very precise mass measurenents.
And decibels are in fact meaningless on their own as a unit: a decibel is a power ratio of $sqrt[10]{10}$ so the actual measurement unit is dBA, ie decibels above the threshold of hearing. On its own, a decibel is simply the number $sqrt[10]{10}$ treated as a multiplication factor.
answered Jan 21 at 2:59
timtfjtimtfj
2,448420
$endgroup$
If I've understood your system correctly, we do this all the time with temperatures: absolute temperature is measured in kelvins but degrees Celsius are effectively "kelvins beyond 273.16". (Loosely, the freezing point of water.) We routinely use them all the time to compare temperaures, but things go awry if we want to say that one thing is twice as hot as another.
Note that 30°C isn't 20°C plus 10°C unless we use $x$°C to mean two different things, namely a temperature of $x$ temperature steps above freezing, and an increment of $x$ temperature steps.
You might argue that we do something similar (but inconsistently) with weights when we treat them like mass: we're neglecting the buoyancy effect in air so there's a slight offset. This actually has to be taken into account when dealing with very precise mass measurenents.
And decibels are in fact meaningless on their own as a unit: a decibel is a power ratio of $sqrt[10]{10}$ so the actual measurement unit is dBA, ie decibels above the threshold of hearing. On its own, a decibel is simply the number $sqrt[10]{10}$ treated as a multiplication factor.
answered Jan 21 at 2:59
timtfjtimtfj
2,448420
edited Jan 21 at 3:16
answered Jan 21 at 2:59
timtfjtimtfj
2,448420
answered Jan 21 at 2:59
timtfjtimtfj
2,448420
answered Jan 21 at 2:59
timtfjtimtfj
2,448420
2,448420
$begingroup$
This is helpful! Very good examples. I didn't think of these and will have to let it churn on my mind a bit. This might prove my idea is too restrictive and ultimately incorrect.
$endgroup$
– jdods
Jan 21 at 12:17
add a comment |
$begingroup$
This is helpful! Very good examples. I didn't think of these and will have to let it churn on my mind a bit. This might prove my idea is too restrictive and ultimately incorrect.
$endgroup$
– jdods
Jan 21 at 12:17
$begingroup$
This is helpful! Very good examples. I didn't think of these and will have to let it churn on my mind a bit. This might prove my idea is too restrictive and ultimately incorrect.
$endgroup$
– jdods
Jan 21 at 12:17
$begingroup$
This is helpful! Very good examples. I didn't think of these and will have to let it churn on my mind a bit. This might prove my idea is too restrictive and ultimately incorrect.
$endgroup$
– jdods
Jan 21 at 12:17
add a comment |
$begingroup$
The International Vocabulary of Metrology (VIM) states that a measurement unit should be a
real scalar quantity, defined and adopted by convention, with
which any other quantity of the same kind can be compared to
express the ratio of the two quantities as a number
So by the BIPM ( International Bureau of Weights and Measures ) the number of kilograms beyond 10 kilograms cannot be defined to be a unit, since it's not a ratio.
And quantity is expressed by the VIM as
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.
So it has to be connected to nature itself. Like the meter which was first defined as as one ten-millionth of the distance from the equator to the North Pole. But changes between one unit and other are still aceptable and must be possible. In the VIM there is a table of all the principals quantities.
I think that occurs because of the way we do math, you have state $1 kg_{10} + 1 kg_{10} = 2 kg_{10}$ that wouldn't be true if we try to convert the numbers to kilograms, since $2 kg_{10} = 12 kg_{10} neq 22 kg = 1 kg_{10} + 1 kg_{10}$. So a unit should always respect our math principles and that would leave us only with ratio units, which are easily convertible, opposite to your created unit. But I guess any unit is possible to make, as long as you invent a different math to it.
answered Jan 21 at 1:35
Ellian CarlosEllian Carlos
215
$endgroup$
$begingroup$
Wow, that's rather unsatisfying language. All it says is we must be able to express the ratio of two quantities as a number. But $2 mathrm{kg_{10}}$ is twice as much mass above $10$ kg as $1 mathrm{kg_{10}}$ is, and indeed the ratio computes as $2/1 = 2.$ This still seems like a very silly thing to do, but the VIM doesn't say why. (Maybe one has to read other parts of it to get that information.)
$endgroup$
– David K
Jan 21 at 2:39
$begingroup$
I think I didn't made it clear, my fault. Quantity in the VIM is a 'property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference ', so it's not any ratio, not even can be based on another unit, it has to come from nature. I'll add that to my answer.
$endgroup$
– Ellian Carlos
Jan 21 at 2:46
$begingroup$
I think I know what they mean, it's just that human language muddies the issue because we have too many habitual uses of terms that don't conform to the idea they're trying to get across. I suppose, by the way, that various temperature scales in use outside scientific applications (Celsius, sometimes Fahrenheit, even Reaumur) are not considered actual units of measurement according to the standard. Does the standard have another term for such scales of measurement, or does it ignore them completely?
$endgroup$
– David K
Jan 21 at 2:51
$begingroup$
At first I think all those scales were based on some experiment. The VIM as a vocabulary does not explicit classifies all units, but by the SI (International System) the system of units used by the BIPM, Kelvin is a base unit, Celsius is a derived unit, Fahrenheit and Reaumur are units from others system of units.
$endgroup$
– Ellian Carlos
Jan 21 at 3:04
$begingroup$
Historically, I think the general idea of the scales was to be able to describe how warm or cold a temperature is in a way that is precise and repeatable, without necessarily understanding what temperature actually is. For repeatability, the scales are based on measurements that can be made by repeatable experiment; for precision we place those measurements on a numeric interpolation/extrapolation scale. The scales persist because people never quite caught onto the idea that 300 Kelvin is fine weather for swimming but at 270 Kelvin you should beware of ice on the road.
$endgroup$
– David K
Jan 21 at 3:26
|
show 1 more comment
$begingroup$
The International Vocabulary of Metrology (VIM) states that a measurement unit should be a
real scalar quantity, defined and adopted by convention, with
which any other quantity of the same kind can be compared to
express the ratio of the two quantities as a number
So by the BIPM ( International Bureau of Weights and Measures ) the number of kilograms beyond 10 kilograms cannot be defined to be a unit, since it's not a ratio.
And quantity is expressed by the VIM as
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.
So it has to be connected to nature itself. Like the meter which was first defined as as one ten-millionth of the distance from the equator to the North Pole. But changes between one unit and other are still aceptable and must be possible. In the VIM there is a table of all the principals quantities.
I think that occurs because of the way we do math, you have state $1 kg_{10} + 1 kg_{10} = 2 kg_{10}$ that wouldn't be true if we try to convert the numbers to kilograms, since $2 kg_{10} = 12 kg_{10} neq 22 kg = 1 kg_{10} + 1 kg_{10}$. So a unit should always respect our math principles and that would leave us only with ratio units, which are easily convertible, opposite to your created unit. But I guess any unit is possible to make, as long as you invent a different math to it.
answered Jan 21 at 1:35
Ellian CarlosEllian Carlos
215
$endgroup$
$begingroup$
Wow, that's rather unsatisfying language. All it says is we must be able to express the ratio of two quantities as a number. But $2 mathrm{kg_{10}}$ is twice as much mass above $10$ kg as $1 mathrm{kg_{10}}$ is, and indeed the ratio computes as $2/1 = 2.$ This still seems like a very silly thing to do, but the VIM doesn't say why. (Maybe one has to read other parts of it to get that information.)
$endgroup$
– David K
Jan 21 at 2:39
$begingroup$
I think I didn't made it clear, my fault. Quantity in the VIM is a 'property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference ', so it's not any ratio, not even can be based on another unit, it has to come from nature. I'll add that to my answer.
$endgroup$
– Ellian Carlos
Jan 21 at 2:46
$begingroup$
I think I know what they mean, it's just that human language muddies the issue because we have too many habitual uses of terms that don't conform to the idea they're trying to get across. I suppose, by the way, that various temperature scales in use outside scientific applications (Celsius, sometimes Fahrenheit, even Reaumur) are not considered actual units of measurement according to the standard. Does the standard have another term for such scales of measurement, or does it ignore them completely?
$endgroup$
– David K
Jan 21 at 2:51
$begingroup$
At first I think all those scales were based on some experiment. The VIM as a vocabulary does not explicit classifies all units, but by the SI (International System) the system of units used by the BIPM, Kelvin is a base unit, Celsius is a derived unit, Fahrenheit and Reaumur are units from others system of units.
$endgroup$
– Ellian Carlos
Jan 21 at 3:04
$begingroup$
Historically, I think the general idea of the scales was to be able to describe how warm or cold a temperature is in a way that is precise and repeatable, without necessarily understanding what temperature actually is. For repeatability, the scales are based on measurements that can be made by repeatable experiment; for precision we place those measurements on a numeric interpolation/extrapolation scale. The scales persist because people never quite caught onto the idea that 300 Kelvin is fine weather for swimming but at 270 Kelvin you should beware of ice on the road.
$endgroup$
– David K
Jan 21 at 3:26
|
show 1 more comment
$begingroup$
The International Vocabulary of Metrology (VIM) states that a measurement unit should be a
real scalar quantity, defined and adopted by convention, with
which any other quantity of the same kind can be compared to
express the ratio of the two quantities as a number
So by the BIPM ( International Bureau of Weights and Measures ) the number of kilograms beyond 10 kilograms cannot be defined to be a unit, since it's not a ratio.
And quantity is expressed by the VIM as
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.
So it has to be connected to nature itself. Like the meter which was first defined as as one ten-millionth of the distance from the equator to the North Pole. But changes between one unit and other are still aceptable and must be possible. In the VIM there is a table of all the principals quantities.
I think that occurs because of the way we do math, you have state $1 kg_{10} + 1 kg_{10} = 2 kg_{10}$ that wouldn't be true if we try to convert the numbers to kilograms, since $2 kg_{10} = 12 kg_{10} neq 22 kg = 1 kg_{10} + 1 kg_{10}$. So a unit should always respect our math principles and that would leave us only with ratio units, which are easily convertible, opposite to your created unit. But I guess any unit is possible to make, as long as you invent a different math to it.
answered Jan 21 at 1:35
Ellian CarlosEllian Carlos
215
$endgroup$
The International Vocabulary of Metrology (VIM) states that a measurement unit should be a
real scalar quantity, defined and adopted by convention, with
which any other quantity of the same kind can be compared to
express the ratio of the two quantities as a number
So by the BIPM ( International Bureau of Weights and Measures ) the number of kilograms beyond 10 kilograms cannot be defined to be a unit, since it's not a ratio.
And quantity is expressed by the VIM as
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.
So it has to be connected to nature itself. Like the meter which was first defined as as one ten-millionth of the distance from the equator to the North Pole. But changes between one unit and other are still aceptable and must be possible. In the VIM there is a table of all the principals quantities.
I think that occurs because of the way we do math, you have state $1 kg_{10} + 1 kg_{10} = 2 kg_{10}$ that wouldn't be true if we try to convert the numbers to kilograms, since $2 kg_{10} = 12 kg_{10} neq 22 kg = 1 kg_{10} + 1 kg_{10}$. So a unit should always respect our math principles and that would leave us only with ratio units, which are easily convertible, opposite to your created unit. But I guess any unit is possible to make, as long as you invent a different math to it.
answered Jan 21 at 1:35
Ellian CarlosEllian Carlos
215
edited Jan 21 at 2:52
answered Jan 21 at 1:35
Ellian CarlosEllian Carlos
215
answered Jan 21 at 1:35
Ellian CarlosEllian Carlos
215
answered Jan 21 at 1:35
Ellian CarlosEllian Carlos
215
215
$begingroup$
Wow, that's rather unsatisfying language. All it says is we must be able to express the ratio of two quantities as a number. But $2 mathrm{kg_{10}}$ is twice as much mass above $10$ kg as $1 mathrm{kg_{10}}$ is, and indeed the ratio computes as $2/1 = 2.$ This still seems like a very silly thing to do, but the VIM doesn't say why. (Maybe one has to read other parts of it to get that information.)
$endgroup$
– David K
Jan 21 at 2:39
$begingroup$
I think I didn't made it clear, my fault. Quantity in the VIM is a 'property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference ', so it's not any ratio, not even can be based on another unit, it has to come from nature. I'll add that to my answer.
$endgroup$
– Ellian Carlos
Jan 21 at 2:46
$begingroup$
I think I know what they mean, it's just that human language muddies the issue because we have too many habitual uses of terms that don't conform to the idea they're trying to get across. I suppose, by the way, that various temperature scales in use outside scientific applications (Celsius, sometimes Fahrenheit, even Reaumur) are not considered actual units of measurement according to the standard. Does the standard have another term for such scales of measurement, or does it ignore them completely?
$endgroup$
– David K
Jan 21 at 2:51
$begingroup$
At first I think all those scales were based on some experiment. The VIM as a vocabulary does not explicit classifies all units, but by the SI (International System) the system of units used by the BIPM, Kelvin is a base unit, Celsius is a derived unit, Fahrenheit and Reaumur are units from others system of units.
$endgroup$
– Ellian Carlos
Jan 21 at 3:04
$begingroup$
Historically, I think the general idea of the scales was to be able to describe how warm or cold a temperature is in a way that is precise and repeatable, without necessarily understanding what temperature actually is. For repeatability, the scales are based on measurements that can be made by repeatable experiment; for precision we place those measurements on a numeric interpolation/extrapolation scale. The scales persist because people never quite caught onto the idea that 300 Kelvin is fine weather for swimming but at 270 Kelvin you should beware of ice on the road.
$endgroup$
– David K
Jan 21 at 3:26
|
show 1 more comment
$begingroup$
Wow, that's rather unsatisfying language. All it says is we must be able to express the ratio of two quantities as a number. But $2 mathrm{kg_{10}}$ is twice as much mass above $10$ kg as $1 mathrm{kg_{10}}$ is, and indeed the ratio computes as $2/1 = 2.$ This still seems like a very silly thing to do, but the VIM doesn't say why. (Maybe one has to read other parts of it to get that information.)
$endgroup$
– David K
Jan 21 at 2:39
$begingroup$
I think I didn't made it clear, my fault. Quantity in the VIM is a 'property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference ', so it's not any ratio, not even can be based on another unit, it has to come from nature. I'll add that to my answer.
$endgroup$
– Ellian Carlos
Jan 21 at 2:46
$begingroup$
I think I know what they mean, it's just that human language muddies the issue because we have too many habitual uses of terms that don't conform to the idea they're trying to get across. I suppose, by the way, that various temperature scales in use outside scientific applications (Celsius, sometimes Fahrenheit, even Reaumur) are not considered actual units of measurement according to the standard. Does the standard have another term for such scales of measurement, or does it ignore them completely?
$endgroup$
– David K
Jan 21 at 2:51
$begingroup$
At first I think all those scales were based on some experiment. The VIM as a vocabulary does not explicit classifies all units, but by the SI (International System) the system of units used by the BIPM, Kelvin is a base unit, Celsius is a derived unit, Fahrenheit and Reaumur are units from others system of units.
$endgroup$
– Ellian Carlos
Jan 21 at 3:04
$begingroup$
Historically, I think the general idea of the scales was to be able to describe how warm or cold a temperature is in a way that is precise and repeatable, without necessarily understanding what temperature actually is. For repeatability, the scales are based on measurements that can be made by repeatable experiment; for precision we place those measurements on a numeric interpolation/extrapolation scale. The scales persist because people never quite caught onto the idea that 300 Kelvin is fine weather for swimming but at 270 Kelvin you should beware of ice on the road.
$endgroup$
– David K
Jan 21 at 3:26
$begingroup$
Wow, that's rather unsatisfying language. All it says is we must be able to express the ratio of two quantities as a number. But $2 mathrm{kg_{10}}$ is twice as much mass above $10$ kg as $1 mathrm{kg_{10}}$ is, and indeed the ratio computes as $2/1 = 2.$ This still seems like a very silly thing to do, but the VIM doesn't say why. (Maybe one has to read other parts of it to get that information.)
$endgroup$
– David K
Jan 21 at 2:39
$begingroup$
Wow, that's rather unsatisfying language. All it says is we must be able to express the ratio of two quantities as a number. But $2 mathrm{kg_{10}}$ is twice as much mass above $10$ kg as $1 mathrm{kg_{10}}$ is, and indeed the ratio computes as $2/1 = 2.$ This still seems like a very silly thing to do, but the VIM doesn't say why. (Maybe one has to read other parts of it to get that information.)
$endgroup$
– David K
Jan 21 at 2:39
$begingroup$
I think I didn't made it clear, my fault. Quantity in the VIM is a 'property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference ', so it's not any ratio, not even can be based on another unit, it has to come from nature. I'll add that to my answer.
$endgroup$
– Ellian Carlos
Jan 21 at 2:46
$begingroup$
I think I didn't made it clear, my fault. Quantity in the VIM is a 'property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference ', so it's not any ratio, not even can be based on another unit, it has to come from nature. I'll add that to my answer.
$endgroup$
– Ellian Carlos
Jan 21 at 2:46
$begingroup$
I think I know what they mean, it's just that human language muddies the issue because we have too many habitual uses of terms that don't conform to the idea they're trying to get across. I suppose, by the way, that various temperature scales in use outside scientific applications (Celsius, sometimes Fahrenheit, even Reaumur) are not considered actual units of measurement according to the standard. Does the standard have another term for such scales of measurement, or does it ignore them completely?
$endgroup$
– David K
Jan 21 at 2:51
$begingroup$
I think I know what they mean, it's just that human language muddies the issue because we have too many habitual uses of terms that don't conform to the idea they're trying to get across. I suppose, by the way, that various temperature scales in use outside scientific applications (Celsius, sometimes Fahrenheit, even Reaumur) are not considered actual units of measurement according to the standard. Does the standard have another term for such scales of measurement, or does it ignore them completely?
$endgroup$
– David K
Jan 21 at 2:51
$begingroup$
At first I think all those scales were based on some experiment. The VIM as a vocabulary does not explicit classifies all units, but by the SI (International System) the system of units used by the BIPM, Kelvin is a base unit, Celsius is a derived unit, Fahrenheit and Reaumur are units from others system of units.
$endgroup$
– Ellian Carlos
Jan 21 at 3:04
$begingroup$
At first I think all those scales were based on some experiment. The VIM as a vocabulary does not explicit classifies all units, but by the SI (International System) the system of units used by the BIPM, Kelvin is a base unit, Celsius is a derived unit, Fahrenheit and Reaumur are units from others system of units.
$endgroup$
– Ellian Carlos
Jan 21 at 3:04
$begingroup$
Historically, I think the general idea of the scales was to be able to describe how warm or cold a temperature is in a way that is precise and repeatable, without necessarily understanding what temperature actually is. For repeatability, the scales are based on measurements that can be made by repeatable experiment; for precision we place those measurements on a numeric interpolation/extrapolation scale. The scales persist because people never quite caught onto the idea that 300 Kelvin is fine weather for swimming but at 270 Kelvin you should beware of ice on the road.
$endgroup$
– David K
Jan 21 at 3:26
$begingroup$
Historically, I think the general idea of the scales was to be able to describe how warm or cold a temperature is in a way that is precise and repeatable, without necessarily understanding what temperature actually is. For repeatability, the scales are based on measurements that can be made by repeatable experiment; for precision we place those measurements on a numeric interpolation/extrapolation scale. The scales persist because people never quite caught onto the idea that 300 Kelvin is fine weather for swimming but at 270 Kelvin you should beware of ice on the road.
$endgroup$
– David K
Jan 21 at 3:26
|
show 1 more comment
$begingroup$
I'm not sure what you mean by "valid" unit of measurement, but it is certainly impractical because, as you correctly identified, you cannot add properly. You could obviously define $1 kg_{10} + 1 kg_{10} = 12 kg_{10}$, but this gets clumsy at best...
answered Jan 21 at 1:01
KlausKlaus
1,7979
$endgroup$
add a comment |
$begingroup$
I'm not sure what you mean by "valid" unit of measurement, but it is certainly impractical because, as you correctly identified, you cannot add properly. You could obviously define $1 kg_{10} + 1 kg_{10} = 12 kg_{10}$, but this gets clumsy at best...
answered Jan 21 at 1:01
KlausKlaus
1,7979
$endgroup$
add a comment |
$begingroup$
I'm not sure what you mean by "valid" unit of measurement, but it is certainly impractical because, as you correctly identified, you cannot add properly. You could obviously define $1 kg_{10} + 1 kg_{10} = 12 kg_{10}$, but this gets clumsy at best...
answered Jan 21 at 1:01
KlausKlaus
1,7979
$endgroup$
I'm not sure what you mean by "valid" unit of measurement, but it is certainly impractical because, as you correctly identified, you cannot add properly. You could obviously define $1 kg_{10} + 1 kg_{10} = 12 kg_{10}$, but this gets clumsy at best...
answered Jan 21 at 1:01
KlausKlaus
1,7979
answered Jan 21 at 1:01
KlausKlaus
1,7979
answered Jan 21 at 1:01
KlausKlaus
1,7979
answered Jan 21 at 1:01
KlausKlaus
1,7979
1,7979
add a comment |
add a comment |
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$begingroup$
Are you familiar with modular arithmetic? What you're saying is similar to being in modulus $10$. As far as practical measurements go though, this becomes impractical.
$endgroup$
– Gnumbertester
Jan 21 at 1:15
$begingroup$
Yes, I'm familiar with modular arithmetic, but don't use it ever. That's a good point that this silly "unit" actually is just that.
$endgroup$
– jdods
Jan 21 at 2:04
$begingroup$
I'm not surprised this got a down vote. Can someone suggest a way to make the question better, or maybe a different venue where more people might have an interest?
$endgroup$
– jdods
Jan 21 at 2:07
$begingroup$
I do not see the reason for the downvote, it is a genuine query and not technically incorrect if you define it for a given scenario.
$endgroup$
– Gnumbertester
Jan 21 at 2:10
1
$begingroup$
What about degrees Celsius--does it count as a unit of measurement? It is a useful way of giving meaning to numeric temperature measurements in common use. For example, $25^circ C$ is the temperature of a warm day, whereas $25^circ F$ is freezing cold. But if you want temperature for various formulas in physics, you need to convert to an absolute scale such as Kelvins, either explicitly or implicitly.
$endgroup$
– David K
Jan 21 at 2:46