How hard is it to get counting right?
desystemize.substack.com
desystemize.substack.com
Another way in which it’s very hard to get counting right is when the phenomenon being observed cannot be broken into discrete & fungible pieces — the essence of counting is that there is a meaningful fungible “unit” worth talking about.
One of my favorite illustrations of this is a beautiful excerpt [1] in an RK Narayan novel (Swami and friends) through the eyes of a child who can’t fathom the weird problems in his math homework — because he has a much richer sense of reality than his textbook can ever hope to convey.
Another example context (slightly more “high-brow”) in which fungibility clearly breaks down is fat-tailed distributions. In a thin-tailed distribution (like a bell curve) the fluctuations from “typical” can often be assumed small enough that any measurement/sample could be fungibly replaced by the typical (Eg: designing furniture for the typical person). Counting, averages, etc are only guaranteed to make sense in this situation. In a fat-tailed distribution, OTOH, it’s cumulative properties might be dominated by outliers — so trying to characterize the system based on counts might often be quite meaningless! (Eg: designing buildings for the typical earthquake or the typical tsunami)
(There’s a lot of nuance, but I’ll leave it at that)
[1] https://potterfiend.blogspot.com/2006/03/swami-and-friends-m...
If Rama has a transactional perspective on business and has the local monopoly on mangoes, and Krishna really needs mangoes right now and will accept no substitute, Krishna might have to pay fifteen annas for four mangoes. Or maybe one hundred annas per mango. Or one thousand. Is there any limit?
If there are competing mango vendors who are offering five mangoes for five annas, Rama may have difficulty convincing Krishna to pay more than four annas for four mangoes.
If Rama expects that competing mango vendors will run out of stock early, but some customers are likely to still come toward the end of the day, Rama's price per mango may depend upon the time of day - it may remain quite high throughout the day compared to other vendors and perhaps only drop if Rama fears ending the day without selling all the stock.
A local gas station changed gas prices to above a dollar and got a visit from the Sheriff's office. The demand was simple: you can either continue to charge ninety nine cents or you can close the pump. However, due to a chance of public unrest, you may not charge a dollar or more at this time.
What the professor didn't have to say is that in real life local authorities have incredible latitude and we must comply at least while we "work the courts". I think the morale was that free enterprise doesn't exist anywhere in real life and probably for good reason.
Whenever you take an average, you divide by some count. What you choose to count matters, and people can disagree about what belongs in this set. It's often a judgement call.
For example, just recently there was a study of vaccine effectiveness in Israel and it appears they made a mistake about the denominator. (Or did they?)
1. Those who can count.
2. Those who can't count.
3. Those who care what is counted and what isn't.
4. Those who like to read about why they should care what is counted and what isn't.
TFA is an informative ad aimed at recruiting #4 so as to increase the readership count of this blog.
Every measurement is a process of some imprecision - in experiment in itself lending itself to needing some sort of calibrating process or set of experiments.
Maybe though to give credit to the author, they’re looking for a focus on a place where one is just starting to form different concept of a particular estimate.
Problem: This include client side errors as well which the service owner has no control over.
Solution: Don't track client side errors.
Problem: Now all service owners are changing the error codes for most errors to be 4xx.