The connection between: One, Two and Old, New

QUESTION: I just noticed a very interesting phenomenon in the Hebrew Language:

New חדש — one חד

Old ישן — two שנ

Why is this? Is it because when something is old, it’s secondary? And when it’s new, it’s exclusive? Or because when it’s old, it has seen been around the corner (repetitive), or has seen many years (שנים)? And when it’s new, it’s sharp (חד)? (But on the other hand, שנ can mean sharp too, as in שנן!)

I understand why month is חדש, as moon gets renewed, while year is שנה because sun’s cycle just repeats.

But why is sleep ישן? Because it’s a secondary part of your day? Or because you’re changing? But when you rise, after sleeping, you’re renewed, חדש, as in חדשים לבקרים.