Well the strict mathematical term doesn't even make sense because a scalar can't be perpendicular. Unless you're claiming the moisture is imaginary, I guess...
This is not consistent with the data presented in the article, which shows that the "percent of Europe's area that is dryer than normal" is historically between 5% and 25%.
An anomaly in this case is defined as outside one standard deviation[1], so in a perfectly normal year you would expect ~15.9% of soil to be dryer than normal.
You're the one who's defining normal badly. If you are told someone, or even all the people in a country, is/are "taller than normal", would you think they were all above 1.853 meters or whatever, or that they were all outside the range of normal heights? Because that's what anyone else would assume.
The Dutch, as a country, are "taller than normal", and this is a fairly common point to make about them. I've always taken it to mean that their population average is somewhere above 1.852 meters or whatever, not that they are alarmingly, abnormally tall (which they are not).
So I think this example fails, at least. The original article is trying to make the point that Europe's soil is alarmingly, abnormally dry.
Dryer than the 'average' dryness of all the soil, perhaps, but if normal is an expected range of values - the soil in this place is typically somewhere from here to here in dryness - then it's not that case.
Even if we are looking at the mean average, it's still not necessarily the case that half the soil will be on one side of the mean average; long tails tugs that mean average above and below the median.
But if what's meant here is the median, then yes, half will always be below.
Excuse me now while I go and beat myself up in the car park for being that person on HN.
You mean mean, not average. Mean, median and mode are all averages. Only median splits into equal groups.
The point I was trying to make though is that "normal" is not in any way equivalent to any kind of average. It always refers to a range or distribution, even if that range is very small (eg if there is only one normal value, the normal range is the margin of error). 5'8" and 5'10" are both normal heights; you would not say they are taller or shorter than normal. They're shorter/taller than average.
Yao Ming is taller than normal. Dwarfism is by definition abnormally small size. Normal can't be the average, because there wouldn't be anything to describe the range of heights between abnormally short and normal height. Also, normally short and normally tall would be the same thing. Makes no sense.
The normal distribution does not define a mathematical meaning of the term "normal". Any distribution can define a normal range relative to that distribution.
Given an expected normal distribution of soil dryness you can compare a given year's distribution.
> Any distribution can define a normal range relative to that distribution.
Any particular sample will always have a corresponding probability in a normal distribution. So what you're saying is kind of right- values always fall within the range of a normal dostribution. That's not what it means to be outside the normal distribution, though. If you have another year that only partly overlaps with the expected distribution, you'll have an area that does not overlap despite being within the same range. That area is the fraction of values outside the normal range.
Log-normal is extremely common in hydrology. Turns out an anomaly in this case is defined as outside one standard deviation[1], so in a perfectly normal year you would expect ~15.9% of soil to be dryer than normal.
The term "normal" has to refer to a range - not a point - exactly for the reasons you gave. Then it does make sense to make a statement like 90% of some population is normal.
Both in mathematics as well as in colloquial language a term's definition must be such that it is useful. The term "normal" is grammatically an attribute (something is normal or is not normal). If "normal" is defined such that no object can be called "normal" - then the the term "normal" is useless.
This way of thinking about language is not just logical and economical but also conforming with a friendly approach on communication. Of course, this is something unattractive to many people who celebrate their incredible and superior intelligence for the purpose of grandstanding. And I fear this attitude is relatively more normal on HN.
In a "perfectly normal" year half of soil would be drier than normal, half would be wetter than normal, and none would be exactly normal.
The most reasonable way to interpret the headline would be to say soil is slightly wetter than normal, which is obviously not the intended message.