old

Nothing new aka choosing suggested "new" over perceivable "now" implies ones de-nial (Latin nihilo; nothing).

a number which binds

Aka ONE binding self to another when consenting to suggestions.

Time would appear to traverse faster and faster

Appearances can be deceiving...velocity (inception towards death) remains steady; while resistance (life) fluctuates.

There would not be one...

There can be only one...unless ONE ignores self by counting others.