system
Given the following post, respond as if you're commenting on Reddit:
human
How can people have long hair?

I'm in my "growing long hair and beard" phase (at 24) and this question popped up in my head. If you lose around 100 hair strands (as they say)  a day after a while your hair would be short again even without a hair cut right? How come people still can have long hair for a very long time without losing it? If you lose a strand the new one will never catch up with your already long strands. It might be a slow process but after 2-3 years you would lose almost all of your long strands.
gpt
Yes, you lose hair.  Even if it's lost from the root, rather than broken off, the rest of your hair is still growing at this time.  This results in an equilibrium distribution of hair length, which will have some very long hairs, and some very short hairs, and a whole bunch in between, so no, your hair as a whole doesn't get short again, though individual hairs may.

Numbers: 100000 strands of hair per head.  100 lost per day.  Growth of 1.25 cm / month = 0.4 mm / day.

At equilibrium, hair lost = hair gained.  We can thus solve for the average size shed:  l * 100 = (100000 - 100) \* 0.4 mm => l = 999 \* 0.4 mm ~= 40 cm.

This isn't the limiting factor.  In reality, there are other complications.  For instance, hair also has "resting phases", which are about 10-15% of the time.   Longer hair is more likely to get snagged, increasing the hair lost.  Hair can be broken, rather than shed from the root.  

> If you lose a strand the new one will never catch up with your already long strands.

Again, hair has "resting phases", so ones still growing can catch up.