Is there a maximum attainable beard thickness?

Question

This other question asks if attuning to a Belt of Dwarvenkind grants the following benefit (and literally nothing else):

you have a 50 percent chance each day at dawn of growing a full beard if you're capable of growing one, or a visibly thicker beard if you already have one.

My question is about the latter part of that bonus (marked in bold). Say you attune to the belt and then wear it for a prolonged period of time. You never shave, so every other day (on average) your beard becomes "visibly thicker".

Are there any mechanics governing how this works? Like, is there a maximum attainable beard thickness? Could a player reasonably argue that their beard has become so thick and dense that it acts as natural armor and grants them an AC boost or damage resistance?

Would it eventually become an impediment, or even a hazard to the bearded character? For instance, does it become so dense that it's effectively solid and while possibly granting a defensive boost it also impedes movement and makes it difficult to breathe? Do the ever-thickening beard fibers ultimately become so dense that they form a singularity and the character dies? Or does it just do the boring thing, and fizzle out somewhere along the way?

This may all be GM fiat. However the rules as written seem to imply that the beard gets perceptibly thicker every other day without end. If you have a beard, it gets thicker. Each day at dawn (more or less).

If a player demands a strict interpretation, how far do (or can) you take it? What makes sense from a fairness standpoint if the player has gone to the effort of attuning an item just for this one particular benefit?

Answer 1

It's asymptotic.

There's a finite amount of mass available for the beard (based on how much the wearer eats, the weight their neck can support, etc.). Since the beard must continuously get thicker, it has to approach a limit, perhaps something like $$b(t) = b_{max}(1-e^{-t/\tau})$$

where t starts at the time one starts growing a beard (so, for a dwarf, at birth).

What's really interesting is that the beard must not just grow thicker, but grow visibly thicker. This implies that dwarves, at least, can perceive infinitesimal differences in beard thickness, which means they can actually see everyone's facial hair growing all the time. Science!

Answer 2

As you already guessed yourself, RAW this would be a GM fiat.

If I apply some kind of logic (and a bit of humor) in this magic item concept, the beard will grow as thick as the thickest dwarven beard in the multiverse because the Belt of Dwarvenkind should never betray its people giving a non-dwarf the thickest beard there is; Moradin wouldn't approve that.

In the case of a Dwarf user, the belt would elevate his beard to the glorious thickness of Moradin's beard; a great honor for every dwarf.

Answer 3

Hair sheds.

When I have long hair, I seem to lose hair at a greater rate. Even if the number of hairs I lose is constant, since the average length of hairs lost is greater, I lose a greater volume of hair.

What we experience with beard growth in normal life without a magical belt is: When I've recently shaved, my beard is, indeed, visibly thicker the next morning. However, once my beard reaches a critical length, it sheds at a rate so that the rate of growth and the rate of shed hit an equilibrium, and it is no longer visibly thicker the next morning.

Supposing that I have a magical belt that causes my beard to be visibly thicker the next morning, my beard length would have surpassed the rate at which it sheds. Therefore, my beard will no longer be at equilibrium, and will actually become less thick throughout the day.

Once the beard becomes so thick, the beard would shed at such a rate during the day, as to become visibly less thick by evening. By morning, the beard could become visibly thicker than the previous evening, without actually being any thicker than the previous morning. This circumvents the paradox, and is in-line with intuitive hair growth experience.

Answer 4

Since man, dwarves, orcs and other various species are mortal, then the thickness of the beard will be limited by the lifetime of the creature. This circumvents the "infinitesimal beard visibility" paradox. It would follow that long-lived creatures could grow thicker beards than short-lived creatures, so very old dwarves, attuned to the belt, might have sea-otter-esque beards. This would be especially problematic for elves, but, IIRC elves are incapable of beard growth.

Answer 5

Seems to me that the beard thickness must wane during the day. Perhaps beard thickness is related to testosterone levels that peak about 8am. Assume there is a maximum attainable bead. If morning beard growth is proportional to the remaining growth required to reach max beard. With a nightly decline proportional to the beard size at daily apogee, a regime of visible morning size change with maximum beard size converging to a limit. It is not just dwarves who have to perceive the change in beard thickness after all.