There are few things that really drive me nuts. Errors in number and bad data normalization are the big ones for me.
By number, I don't mean "numbers." I mean basically errors in singularity or plurality. When people can't tell the difference between 1 and not 1, wow... I go off on a rant. Not a small rant. A huge one. You would think that most people can tell the difference between a single thing, and not a single thing, but honestly, it's far more common than you would think. I see it daily. And that's not an exaggeration.
The stereotypical error comes in the form, "There is
." For example, "There is 8 paragraphs on the page." Turn that around a bit and you get, "8 paragraphs is on the page." Pretty easy to see. But you'd be surprised at just how many people do it. Watch TV or a movie and you'll hear it regularly.
There are other examples, but they're not as common. I ran across one from a non-native English speaker wanting to use "percents", which is entirely forgivable. I have no problem with non-native English speakers making mistakes. Their error is one of grammar or language, and not one of number. Native English speakers do not have an excuse though. They should be able to count in their own language.
That example was exacerbated when she (the non-native English speaker) got a native English speaker to help. The English speakers solution was to use "in percentages" as the unit instead of "in percent". Oh good grief... I flipped out! Here's why...
"Percent" is a unit of measure meaning "out of every one hundred." It is always singular. Never plural. And that's never as in 100% never. 
So, you can say, "We must measure the TEU container volume in percent." But you cannot say, "We must measure the TEU container volume in percentages." And you cannot say, "We must measure the TEU container volume in percents." (TEU means twenty-foot equivalent unit. It is for shipping containers. The other popular one is the 40' container, or FEU.)
"Percentage" can be used in the plural form, but these cases are generally very few. I'll go over one below, but first, what is "a percentage"?
A percentage is a relative unit that requires qualification. So you can say, "We must measure the TEU container volume as a percentage of ." But you can't say "We must measure the TEU container volume as a percentage." In the second example, there is no qualification. Expanding it out a bit makes it a bit clearer why this is so: "We must measure the TEU container volume as a unit in percentage." The question is, "a percentage of what?"
If there is any confusion still, consider the different ways to measure the volume:
- As a physical volume in m3.
- As the load capacity as a physical weight limit in kg. (volume meaning then the matter inside)
- As the load capacity as physical volume in m3.
- As the load capcity in terms of the occupied floor-space in m2.
- As the load capacity in terms of earning potential as a dollar value.
- As the load capacity in terms of the average earnings of a container:
- For the ship it is on.
- For the route the ship serves in.
- For the company as a whole.
- For the industry as a whole.
And that's just the beginning. There are many more ways to measure the "volume" of a TEU container.
So, if we are to measure that "as a percentage", what are we measuring it as a percentage of?
Now, someone will naturally say why does this not apply equally to "in percent." Going back to what a "percent" is, it is a measure "out of every 100." This we could say, "out of every 100 what?" However, that's not how percent is used. It is used to refer to the preceding object. In the above example, "volume" is the object, and this is taken to mean simple physical volume. "As a percentage" on the other hand, raises a question. It is used with a qualification to be more specific, or to add in an extra layer of information.
The above example naturally lends itself towards "as a percentage" instead of "in percent" because there are so many different possible meanings for "volume". "In percent" is better used when the scope is narrower, i.e. unambiguously singular.
Take for example rechargeable batteries. They are measured in terms of battery life, or when partially used, the remaining battery life. Measuring voltage doesn't really make much sense because the voltage is constant and batteries are separated into "types" of batteries by voltage and amperage. The only real thing to measure is battery life. This makes it much better to use "in percent." Consider the following two sentences:
- The info-panel shows the battery level in percent.
- The info-panel shows the battery level as a percentage of remaining battery life.
The second is simply wordy, while the first is nice and short.
Now, "percentages" in the plural form is used to talk about measurements (not about measures) when there are more than 1 distinct and sufficiently dis-similar measurements to be compared. For example, "TEU and FEU volumes here are expressed as percentages of their average earnings potential." This means that TEU volumes are measured "as a percentage of their average earnings potential" and "FEU" volumes are measured "as a percentage of their average earnings potential." Those two measurements are significantly different because the earnings potential of a TEU and the earnings potential of an FEU are significantly different.
That is, explicitly, we cannot distrubute "as a potential of earnings potential" equally on TEU and FEU, because the frame of reference is not the same and not similar to make a valid comparison. Contrast that to a situation where the frame of reference is the same.
"The solar years of planets in the solar system are expressed here as a percentage of an Earth solar day."
(A solar day is the length of time it takes a planet to have the sun rise and set once. This is called a "synodic period" or "day". The length of time it takes a planet to rotate once on its axis relative to the stars is a "sidereal" day.)
In this example, the frame of reference is exactly the same, that is, "an Earth solar day." We can convert that frame of reference to a dis-similar one like so:
"The solar years of planets in the solar system are expressed here as percentages of their solar days."
In there, each planet's year is expressed in terms of its own solar day, which may or may not be the same as an Earth solar day.
NOTE: The frames of reference in that example are actually dynamic as the length of a solar day changes due to decaying rotation rates. In the first example the frame of reference is absolute, but there is no requirement for the frame of reference to be absolute for the purposes of our topic of discussion here.
In our second solar system example, we could expand things out explicitly:
The solar years of Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune are expressed here as percentages of Mercury's solar day, Venus' solar day, Earth's solar day, Mars's solar day, Jupiter's solar day, Saturn's solar day, Uranus's solar day, and Neptune's solar day, respectively.
Or, stretching that out further for illustrative purposes to see "percentages" change to its singular form, "percentage":
The solar year of Mercury is expressed here as a percentage of Mercury's solar day.
The solar year of Venus is expressed here as a percentage of Venus' solar day.
The solar year of Earth is expressed here as a percentage of Earth's solar day.
The solar year of Mars is expressed here as a percentage of Mars's solar day.
The solar year of Jupiter is expressed here as a percentage of Jupiter's solar day.
The solar year of Saturn is expressed here as a percentage of Saturn's solar day.
The solar year of Uranus is expressed here as a percentage of Uranus's solar day.
The solar year of Neptune is expressed here as a percentage of Neptune's solar day.
That is all pretty verbose, but shows the principle. When the frame of reference is not the same and the unit of measure is percent, we need to use "percentage" in its plural form.
Now, we could say something like:
The solar year of Mercury is expressed here in percent.
However, were we to say this, we would be talking about "Mercury's solar year", which would be 100%. This is not particularly informative if we are interested in the number, but it tells us the unit of measure. And that is where the information stops. i.e. Are we talking about the number or are we talking about the unit?
Extend that to all of the planets, and funny enough, the number is always "100". It's always 100%. So obviously the information that we are getting is NOT about the number, but is about the unit. And that unit is, "percent".
Going back to this planet example:
"The solar years of planets in the solar system are expressed here as a percentage of an Earth solar day."
What will we find there? Well, first let's make the comparison a bit different and a bit more similar, but still sufficiently dis-similar.
"The solar days of planets in the solar system are expressed here as a percentage of an Earth solar day."
We find that a single thing (each planets' solar day) measures differently than 100%, except for Earth of course because that one is self-referential. We also find that our things being measured can be negative:
| Planet |
Solar Day Length in Earth Solar Days |
Solar Day Length as a Percentage of an Earth Solar Day |
| Mercury |
175.94 |
17,594.00% |
| Venus |
-116.75 |
-11,675.00% |
| Earth |
1.00 |
100.00% |
| Moon |
29.53 |
2,953.00% |
| Mars |
1.03 |
102.75% |
| Jupiter |
0.41 |
41.36% |
| Saturn |
0.44 |
43.93% |
| Uranus |
-0.72 |
-71.83% |
| Neptune |
0.67 |
67.13% |
| Pluto |
-6.39 |
-638.72% |
Here it is very clear that when we talk about '%', we are talking about something where a unit is not necessarily 100. i.e. One (1) day on Mercury is 17,594% the length of a day on Earth. We're not even limited to positive numbers as Venus, Uranus and Pluto show.
Hopefully this clarifies how "in percent" as a unit is used as a self-referential comparison of something with itself, where "as a percentage" with a qualification is used for non-self-referential comparisons.
BREATHE... That was long...
Now, back to how mistakes with number are made there...
The mistakes are:
- "Percents" is nothing. Correctly, "percent" is always singular. i.e. It is self-referential.
- "Percentage" is not a unit. "Percentage" is used with a qualifier to make a comparison, which involves 2 things, not one. i.e. It is not necessarily self-referential, and when it is self-referential, it is redundant.
Breaking it down to a more abstract and general level, "percent" compares to "percentage" as "singular and self-referential (involves a singularity)" compares to "singular, but not self-referential (involves a plurality)".
Now, it's time to complicate the singular, self-referential example for a moment in a non-trivial way...
Above, I went over how "as a percentage" becomes redundant for something that is self-referential and does not make a comparison to another specific measure. However, this doesn't need to be true if we complicate the matter by accepting that the totality of a thing does not necessarily equal 100% of itself under certain conditions.
Again, take the battery example. The life of a charged battery is 100% of the battery life when fully charged... right? Well, that is trivially true. BUT!!! Now consider the battery when you first purchase it. The battery life is 100% of the battery life when it is fully charged, and just for example purposes, we'll say that it is 1 solar Earth day (24 hours) . A few months later, the charged battery life is 100% of the charged battery life... or is it really? The charged life is probably more like 18 hours, which is 75% of the original, and not 100% of the original, but it's still 100% of the battery life... so 75% is 100%? Or 75 = 100? Well, that's obviously false and there must be an error in logic there.
What's going on is that the life decreases over time, and this is the comparison that we need to make. So, the following usage of "as a percentage" is non-trivial, even though it is "self-referential" (we'll get to this in a moment):
"The fully-charged battery life is expressed as a percentage of the original fully-charged battery life."
Here, "fully-charged" takes on two meanings: a) the original "new" full charge time, and b) the current full charge time. They are separated in time, and as such, there is no "self-referential" comparison going on, which makes the usage of "as a percentage" non-trivial.
This is actually a common issue where something is confused with itself by ignoring time. Sometimes time is an important consideration, and sometimes it is not.
Perhaps the most famous citation for this issue is when Heraclitus said, "You cannot step twice into the same river." This excuse was given in court by a contemporary saying that he was no longer the same man... It didn't fly very well and he was still beaten.
Abstracting this problem up one more level, it becomes a problem of context, and what context should be applied to a particular issue.
In the case of a man who has committed a crime, we are not willing to say that after some time has passed, he is different and cannot be punished for the crime. But, take a nice, ripe, juicy apple that you would gladly munch on, leave it for a month in the heat of the Sun, and would you say that you would gladly eat it? Obviously not. There is a difference in the apple that occurred over time that you are not willing to ignore.
But in both cases, there is some set of contextual rules going on. We apply one context to the first case, but a different context to the second case.
This contextual problem is best illustrated in Zeno's paradoxes. (But that, is another story.)
Anyways, that's enough for today. I'll save my ramblings on data normalization (and Zeno's paradoxes) for another day.
Cheers,
Ryan