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The Detection of Absolutes (1)

An ‘Absolute’ Cannot be Changed by Anything, and is Independent of Everything.

Interpunctual Intervals: the Ruler.
ruler_in_perspect

Projective Geometry cannot measure

But, by tolerating a somewhat less-than-pure geometry, absolute, unit-summing, Eucliean-style measurement can be rescued—at least, so say some mathematicians*.


It entails the importation of
“ideal points at infinity”.

Now, for pure geometry, there are no such points (all points are ordinary points), so these ideal points, along with infinity itself and, for that matter, absoluteness, are foreign incursions.

The pictures above

illustrate how the ‘foreign incursions’ take effect.

The left picture has a geometric construction (in blue)—of a notional ruler.

You may click and drag various elements to see if you can secure a better match to the inch markings on the actual ruler

The right picture is that same construction again, annotated.

Lines that are not skew must meet,

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.

 

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