Doctrine of Signatures
This is the idea, also prevalent on the Roundworld, that when the Creator devised all those helpful little plants that would be so useful to the human race for a variety of reasons, He or She built in a few hints to tell people where to look. Thus, a plant good for toothache might have little tooth-like leaves or petals; one for earache might have a vague semblence to a human ear; and Nobby Nobbs is attracted to a mushroom called Phallus Impudicus.
The Discworld has this folklore too; a world driven by Narrativium, however, takes it to extremes. witness the curious example of False Gentian. Or even the common walnut. which, if read by the light of a red cotton taper through a green filtered magnifying glass, carries the advisory legend printed on its shell May Contain Nuts.
It is possible that the Counting Pine has got the Doctrine completely wrong, in its ill-advised species decision to make itself useful to humanity by putting its age on the outside of its trunk, where it can be easily read, rather than have all that cutting-down-and-counting-the-rings business...