# Term for calculated values that lose pertinence when changing scale

I'm trying to find the term for a type of calculations or values that cannot be simpply added or multiplied when zooming in or out from a temporal scale. I know it's not very clear, if it were I would just google the question.

Here's an example: say you're comparing 2014 vs 2015 sales of ice cream and temperature at day's level. If you want to do an analysis by week, you can just add the sales for seven days, and compare weeks between them, the information still makes sense: there's a fact (amount of money deposited in the bank that week) that is grounded in reality that relate to the new figure. You could also calculate an average by day from the total by week.

But, adding temperatures for a total would not make any sense in reality, you need to calculate an average for that kind of data.

So is there a term for this type of values that can only make sense as average and never be added or multiplied (except as an intermediate step for calculating an average)?

• You are thinking of intensive and extensive properties. Commented Dec 10, 2015 at 2:56
• @Biswajit Banerjee Could you put that as an answer? It's very close to what I'm looking for, I think. Enough that it add to the debate. I'll try to reread the article to understand better. thanks. Commented Dec 10, 2015 at 15:52

Let us think of sales ($S$) as a property of a system. You could imagine Week 1 to be a system and Week 2 to be another system. Call the Week 1 system $W_1$ and the Week 2 system $W_2$. Then, $$S(W_1) + S(W_2) = S(W_1 + W_2)$$ A property that has this additive character is called extensive.

Now consider the temperature ($T$) as the property with values $T(W_1)$ and $T(W_2)$ for weeks 1 and 2. Assume that the two $T$ values are identical. Merge the Week 1 and Week 2 systems together to get another system $W$ for the two weeks together. Then $$T(W) = T(W_1+W_2)$$ Properties that follow this rule are called intensive and cannot be added.

These definitions were invented for physical properties and systems and one has to be careful in applying the definitions to general situations. I'm not sure how much thought along these lines has gone into the social sciences.

I don't get the assertion that a sum of temperature loses pertinence
$$\text{avg}(T) = \frac{\text{sum}(T)}{n}$$ $$\frac{\text{avg}(\text{Revenue})}{\text{avg}(\text{Temp})} = \frac{\frac{\text{sum}(\text{Revenue})}{ n}}{\frac{\text{sum}(\text{Temp})}{n}} = \frac{\text{sum}(\text{Revenue})}{\text{sum}(\text{Temp}) }$$ Now multiply does lack meaning if the value is not 0 based
200 degrees °F (Fahrenheit) is not twice as hot 100 °F
As °F is not zero based
You need to translate to absolute - °R (Rankine)
(200 + 459.67) / (100 + 459.67) = 1.17867672

Not sure what term you want to call it but I think you are describing linear zero based properties

Like $\log$ is not linear $\frac{\log(a)}{\log(b)} \ne \frac{a}{b}$ (even if $a$ and $b$ are zero based)

Spacial data does not add, subtract, or average in a simple linear manner.

• As I mentionned, summing temp does not make sense except to calculate an average. I mean two days at 150 Ranking or two liters of water at don't make 4 at 300 R whereas two days of sales or two liters of wine at $150 do make 4 at$300. Commented Dec 9, 2015 at 21:26
• Does't may sense to YOU. Cook in 1 hour at 275 versus 45 minutes at 300. Heat exposure versus time. I have BS in chemical engineering and masters in math. Entropy is the integral heat / temp dt from 0 to t. That is summing temperature on steroids. A physical property or measure does not have artificial analytical bounds. Commented Dec 9, 2015 at 21:45
• Well, cooking a piece of meat at 150 for one hour or 300 for 30 minutes do not get the same results in real life. But buying two pieces at 20 each does make a 40 total. And no need for the agressive "YOU" or to make an exposé on surface vs volume, chemical composition, protein folding and heat exposure... I understand where you're coming from and thank you for your try at answering my question. What make sense in your field does not necessary translate into other pratical domains. Commented Dec 9, 2015 at 22:19
• Other practical domains? Work is is the integral f dot ds. YOU don't need to italic bold. You have no basis to assume a measure has limited analytics. One counter example does not dismiss. Here is social domain. If I am real loud in class I may get kicked out in one day. If I am semi loud for three day I may get kicked out. Acoustics are not physically additive but the social effects may be. In a ML environment where I am trying to identify relationships I would be stupid exclude summation as a possible correlation. Commented Dec 9, 2015 at 22:35