> Incidentally, why is the degree immune to disappearance in division unlike all other units?
I understand why one could say that, but I’d say it’s more misleading than helpful. (And the reason why is directly connected to the problem TFA discusses.)
Instead of temperature, let’s look at time first.
If you’re measuring the temporal extent of an event, then it absolutely makes sense to divide 30s by 15s or 6 days by 3 days and obtain a dimensionless 2: one thing takes twice as long as another, and the factor 2 that doesn’t depend on the choice of units, so it’s dimensionless.
Now consider dates. The year AD 2022 denotes (not very precisely) a point in time by specifiying its distance from a fixed reference in years; as another example, astronomers use the “Julian day”, which is a (possibly non-integer) number of days from a different reference point.
And you could technically divide AD 2022 by AD 1011—the ratio between the distances to the reference point is indeed a dimensionless 2, and if you counted days from it instead of years it’d still be the same. But it’s just not a very useful statement. And if you divide the Julian days instead, you’ll get a different number, because the reference point has moved 4712 years. So you can divide the time coordinates as long as the chosen origin stays in place, but you can’t really divide points in time.
Similarly, when you’re talking about differences in temperature, degrees work like any other unit, but temperatures themselves cannot be divided in the standard scales (without tying yourself to the scale): you’ll get the same result in Celsius and Réaumur (using the same origin) but a different result in Fahrenheit (using a different origin).
Of course, the silly part is that there is a natural origin for temperature, it’s just that the usual scales don’t use it. But then there’s a natural origin for time as well (and you’ll occasionally see it used in cosmology), it’s just that it’s metrologically inconvenient (being known only very approximately) in addition to being very far away.
(Library assignment: what defines a coordinate system on an affine line?)