I found the paper rather difficult to sort out but in due course I think I see how it fits into other things.
He talks about an observer looking at a train going by.
The argument seems to be that if you look at the observer and the train as having relative motion; the observer can not precisely specify position of the train at an "instant" in time. As if he/she could, it would allegedly be a stationary train (in fact both parties would be stationary, frozen).
Well, a time-piece involves a movement (vibration of atom; swing of pendulum; etc.).
A movement has a beginning and ending.
An "instant of time" would be "an instant in movement". But "movement" has a beginning and an ending; what about what happens in between?
An "instant" in time could be any size?
So how spcify an "instant"; a beginning and ending?
By comparing with: another beginning or ending (or both). An "instant" would be an undefined region where say one beginning and ending meets another; for example the clock-hand on the clock held by an observer passes one second-space division: while a train moves past a certain amount of track.
So you have movement meets movement. This looks like Dr. Richard Stafford's idea of "data transmission as part of explanation" and of "partial differentiation"; and like Chris Langan's idea of "conspansive duality".
Peter Lynds seems to be noting that the definition of : "instant" in time, in this scenario; is not (allegedly) fixed precisely.
The definition of "instant of time" requires a movement in the clock-hand, so a beginning and ending; during which the train has movement.
The train is like a clock: so you have movement meets movement; or clock meets clock.
But how can they meet, if they do not have a common background, a meeting place?
The train is not the observer. They are obviously different. They have their meeting in common in meeting itself; any additional background might be constructed by a negotiated deal between them, you might say.
What is "precision"? A necessary match of patterns; a defined association?
What is precise about the observer meets the train is that they are defined as "meeting". What is precise is the very definition of the scenario, it seems.
In a broad sense one might say the scenario itself defines a "scenario instant" (beginning and ending of the thought experiment) which precisely identifies the train's position only as "it was in a position to be observed by the observer".
Any attempt to break down a more detailed definition of the train's position would require what looks like a process of assigning roles and definitions in mutual logical consistency. This looks like Chris Langan's "conspansive duality", and Dr. Richard Stafford's "assignment of definitions" idea; and the idea of negotiation space.
Given the boundary conditions of a thought experiment, "space-time" is complexified through mutual negotiation one might consider say.
Peter Lynds in the abstract of his paper says:
"It is postulated there is not a precise static instant in time underlying a dynamical physical process at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined."
Another way to look at what Peter Lynds says is to say:
There is not a 2 in a 3 underlying where you place the brackets (how order the ones) in (1 + 1) + 1 at which the selected bracketing would necessarily be the only option.
This whole idea leads directly to the idea of "eternal life"; where everything is constructed by mutual consideration (Christianity: God is Love).
The question of division:
the parties in the scenario are already divided: they are separate and distinguishable (train; track; observer; clock held by observer) and have a common backgound (they meet).
Why would further dividing the movement of the
clock or the train be "more precise" re: train's position on track?
Such dividing generates a "directional" aspect; the whole directional structure of this meeting appears to be constructed by the self-referential aspects of "dividing". Each division of a previous division refers to that previous division.
An ordered sequence is constructed, giving directionality. The very definition of "time" and "space" it looks can be seen as potentially constructed along with the directional definition structure of the items in this meeting.
It looks like space-time complexity may be constructed by mutual agreement between the train, the observer, the track, the clock.
How is "one" defined? A beginning and ending...
How is "two" defined? A beginning and ending, a beginning and ending; the size of the "two" units is not stated; where the division of the whole into two is made is not considered relevant as only the division itself is considered...
How is "three" defined? A beginning and ending; a beginning and ending; a beginning and ending....
Back in time the old "two" division of the whole is shifted to make space say for the new (relatively future) "three" division of the whole so that the divisions are allegedly equal spaced.
The assumption of equal sized and equal spaced units in numbers appears to be constructed from a "Zeno's Arrow" -like self-referential defining process.