but if we

*stipulate* that, alone
among such co-planar, meeting lines,

**mutually parallel lines**

are those that meet

at the same point “at infinity”

**then we seem to secure the match**

to the real ruler above right

—which **carries the implication**

that the above left picture,

while not of an *actual* ruler.....

**
**
- properly
*represents* pictures of actual rulers generally
- and that the
*stipulation* above agrees with reality.

## **We stress that this is ***strictly* empirical,

### in that

we __ observe__ a “good” match.

We do __not__ have absolute, first-principle
certitude here,

concerning the infinite;

**we instead have ***an hypothesis*,

which needs to be tested .

**Clearly, we need to** detect **these points-at-infinity**

as __absolute, natural objects__,

**because, as will now perhaps be appreciated,**

we are currently in an *intellectual* loop,

from which there is no *intellectual* exit:

“Where will we find infinity?”

“Where parallels meet.”

“How will we know they are parallel?”

“They will meet at infinity.”

“How will we know that they do that?”

“They will be parallel.”

“How will we know they are parallel?”

“They will meet at infinity.”

**We need an** experimental **way out. **