I've asked myself all day why I would want to respond to this thread.
I should know better.
Regarding the Zen thing, or, the religious aspect of riding a fixed gear bike...think of a fish.
If you talk to a fish about water he might laugh at you.
"Water?"
"What water?"
If you explain to the fish how he lives and swims in water, he will laugh at you.
Your words will not reveal the water to the fish.
The fish must discover the water for himself.
The young woman to whom the original poster referred, who said "the fixed gear did make me feel far more in control than did any other bike I have ridden," has discovered the water for herself.
Riding a fixed gear bike, for some people, reveals the relentless immediacy of reality...which in turn corresponds to a religious experience for some people.
The fixed gear bike, for some people, provides a physical, non-verbal analogy to our relationship with reality.
Sometimes a simple discipline, a constraint, can give us a greater freedom than we had without the constraint.
A kite needs the constraint of a string in order to fly.
No string, no constraint, no fly.
If a fish can't see the water, then the water doesn't exist for that particular fish.
However, for some other fish the water exists.