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Without rendering an opinion on the merits of the chosen date format, I at least want to defend it slightly in terms of consistency—it does follow a well-defined rule, however non-standard that rule might be. The rule it follows can be described as omitting the month for datapoints in the current month (and likewise for years.)
Again—no comment on whether or not that’s a reasonable rule to follow. But I feel the philosophical distinction between having a rule which one follows (however strange a rule it may be) and not following any rules at all is an important one.
You can imagine a hypothetical Beeminder Style Guide, which lists all sorts of rules for how Beeminder chooses to display stuff. How it formats dates, what punctuation it uses or doesn’t use, what gets capitalized and what doesn’t, etc. There are then two different types of argument you can make: you can point out that the Beeminder Style Guide is missing a rule for a certain bit of styling, or you can argue that the rule that the style guide chooses is can be improved upon.
Now, I prefer to use the word “inconsistency” specifically when making arguments of the first kind, as indeed I did. Arguments of the second kind of value too—and I don’t want to say that you shouldn’t use the same word, if you find it appropriate also in other cases. But this is why, despite the surface-level similarity reflected in the forum thread titles, I feel that there is an essential difference in the type of thing we’re talking about between the two threads.