3 ms·

> That comes from the fact that they don't understand the data they are dealing with (as you said with dimensions). You cannot use the arithmetic mean on intere

by qsort 6y ago

> That comes from the fact that they don't understand the data they are dealing with (as you said with dimensions). You cannot use the arithmetic mean on interest rates because it does not make sense to add them up. If you're going down that route, which operations make sense and which don't boil down to the algebraic structure of the set of the possible values of the datatype. For example, you can't add dates but you can subtract dates, because dates have an affine structure, therefore the arithmetic mean of January 14 and October 13 is an operation that makes sense. Similarly with temperatures. The thing is that it's sometimes tricky and unintuitive to figure out what you're allowed to do: ratios are a good example because you can add them, it just doesn't mean what most people expect it to mean. I do agree that understanding your data goes a long way, but I believe making people more aware that tools other than "sum / n" exist is worthwhile, even though the article does have problems as I highlighted above.

ttoinou 6y ago
Yes, but no temperatures cannot be substracted (nor added). For dates I believe you're right because they are vectors (what you think is "an absolute date in the calendar" is in fact the time elapsed after 00h00 year=1 after christ, so it's in fact relative)
- qsort 6y ago
  Both temperatures and dates have affine structure. For dates it's really easy to see, because when you're talking about the calendar you're actually talking about two different types of objects, absolute time references (i.e. Thursday January 1, 1970 12:00 AM) and time durations (i.e. 45 minutes). (If you're familiar with Java, Instants and Durations). Time references cannot be added nor subtracted, but you can add a time duration to a time reference (midnight + 45 minutes = 12:45 AM of the same day) and the difference of two absolute time references is well-defined, unique and is a duration (1 AM - 12 AM = 1 hour). Furthermore, durations satisfy the axioms of a vector space (trivially, just pick a canonical unit, e.g. 1 second, and measure everything as a multiple/fraction of that). The same holds with temperatures, with the unfortunate difference that we use the same notation for differences in temperatures (vectors of the affine space) and temperature references (base set of the affine space). For example, you can't add 18 celsius and 20 celsius, but saying that the temperature of a room increased by 2 celsius is meaningful, because "+2 celsius" is actually a vector. You can also add vectors to points, if the temperature increased by 2 more celsius, it would be 22 celsius. This does even have a physical meaning, and is independent of the frame of reference you pick for temperatures: a difference of 2 celsius is the same as a difference of 2 kelvin. (the same reasoning holds when replacing "celsius" with "fahrenheit" and "kelvin" with "rankine"). It is equally easy to verify temperature differences satisfy the axioms of a vector space, with the same argument as before.
  - ttoinou 6y ago
    That's your interpretation but it doesn't change the fact that physically you cannot add temperatures. You can take the numerical value of one temperature, add something to it, and re interpret it as a temperature; But the '+' operation on temperature does not have any physical meaning. Replace "temperature" by "speed in kilometer/hour" in your sentence : "we cannot add 18 km/h and 20 km/h but I can add 2 km/h to 18 km/h because +2 km/h is a vector" it doesn't make sense to me
    - qsort 6y ago
      I don't follow your line of reasoning. You can add speeds (vector space), you can't add temperatures (points in an affine space cannot be added), but you can add temperatures and temperature differentials (points and vectors in an affine space). Speeds are vectors in the first place, that's why you get to add them, while "temperature" denotes, depending on context, either a point (not addable) or a vector (addable). This explains why you can't add temperatures, but the average temperature makes 100% sense and has a direct physical meaning.
      - ttoinou 6y ago
        Speed and temperature are intensive properties, they don't add up. You can remove the unit and do whatever you want mathematically and add back the physical unit, but it's not physics. Average temperature has no meaning it's a common fallacy, the only reason I ever got for that meaning is "my teacher told me it was OK !"
        qsort 6y ago
        I'm not following your train of thought. > Speed and temperature are intensive properties, they don't add up. You can add speeds by their very definition. They are vectors in R^3 (or some other coordinate system, you get the point). The fact that addition of vectors is allowed is literally baked into the axioms of a vector space. > Average temperature has no meaning it's a common fallacy Yes, average temperature does have unambiguous meaning: https://en.wikipedia.org/wiki/Boltzmann_constant https://en.wikipedia.org/wiki/Boltzmann_constant > You can remove the unit and do whatever you want mathematically and add back the physical unit, but it's not physics. You do realize math can handle units of measurements/dimensions just fine, do you?

by qsort 6y ago

ttoinou 6y ago

Yes, but no temperatures cannot be substracted (nor added). For dates I believe you're right because they are vectors (what you think is "an absolute date in the calendar" is in fact the time elapsed after 00h00 year=1 after christ, so it's in fact relative)

qsort 6y ago
Both temperatures and dates have affine structure. For dates it's really easy to see, because when you're talking about the calendar you're actually talking about two different types of objects, absolute time references (i.e. Thursday January 1, 1970 12:00 AM) and time durations (i.e. 45 minutes). (If you're familiar with Java, Instants and Durations). Time references cannot be added nor subtracted, but you can add a time duration to a time reference (midnight + 45 minutes = 12:45 AM of the same day) and the difference of two absolute time references is well-defined, unique and is a duration (1 AM - 12 AM = 1 hour). Furthermore, durations satisfy the axioms of a vector space (trivially, just pick a canonical unit, e.g. 1 second, and measure everything as a multiple/fraction of that). The same holds with temperatures, with the unfortunate difference that we use the same notation for differences in temperatures (vectors of the affine space) and temperature references (base set of the affine space). For example, you can't add 18 celsius and 20 celsius, but saying that the temperature of a room increased by 2 celsius is meaningful, because "+2 celsius" is actually a vector. You can also add vectors to points, if the temperature increased by 2 more celsius, it would be 22 celsius. This does even have a physical meaning, and is independent of the frame of reference you pick for temperatures: a difference of 2 celsius is the same as a difference of 2 kelvin. (the same reasoning holds when replacing "celsius" with "fahrenheit" and "kelvin" with "rankine"). It is equally easy to verify temperature differences satisfy the axioms of a vector space, with the same argument as before.
- ttoinou 6y ago
  That's your interpretation but it doesn't change the fact that physically you cannot add temperatures. You can take the numerical value of one temperature, add something to it, and re interpret it as a temperature; But the '+' operation on temperature does not have any physical meaning. Replace "temperature" by "speed in kilometer/hour" in your sentence : "we cannot add 18 km/h and 20 km/h but I can add 2 km/h to 18 km/h because +2 km/h is a vector" it doesn't make sense to me
  - qsort 6y ago
    I don't follow your line of reasoning. You can add speeds (vector space), you can't add temperatures (points in an affine space cannot be added), but you can add temperatures and temperature differentials (points and vectors in an affine space). Speeds are vectors in the first place, that's why you get to add them, while "temperature" denotes, depending on context, either a point (not addable) or a vector (addable). This explains why you can't add temperatures, but the average temperature makes 100% sense and has a direct physical meaning.
    - ttoinou 6y ago
      Speed and temperature are intensive properties, they don't add up. You can remove the unit and do whatever you want mathematically and add back the physical unit, but it's not physics. Average temperature has no meaning it's a common fallacy, the only reason I ever got for that meaning is "my teacher told me it was OK !"
      - qsort 6y ago
        I'm not following your train of thought. > Speed and temperature are intensive properties, they don't add up. You can add speeds by their very definition. They are vectors in R^3 (or some other coordinate system, you get the point). The fact that addition of vectors is allowed is literally baked into the axioms of a vector space. > Average temperature has no meaning it's a common fallacy Yes, average temperature does have unambiguous meaning: https://en.wikipedia.org/wiki/Boltzmann_constant https://en.wikipedia.org/wiki/Boltzmann_constant > You can remove the unit and do whatever you want mathematically and add back the physical unit, but it's not physics. You do realize math can handle units of measurements/dimensions just fine, do you?