That was very interesting.
Now this is getting somewhere; and Dick's recent post about acceleration clarifies the isues too.
You seem to recognise that so long as I am logically consistent between my definitions and my statements, that is O.K.
In argument, people imply a "set theory" approach; but at times a "category theory" approach is necessary. Langan acknowledges the need to move from "sets" to "categories".
(Incidentally; "categories" may be kind of "sets at right angles") (This could lead back to the "three way jump" theory I posted).
I do not claim that everything exists including "things that don't exist".
You say "if it is based on reality then it isn't abstract".
There is no such thing as something that does not exist. An abstract idea belongs to a different category as the non-abstract. It exists in the category "abstract".
What actually exists here is some person thinking abstract thoughts (playing musical chairs and imagining they can join the dots or collapse the wave functions). That doesn't make the moon actually made of cheese though (except postulated in someone's imagination).
One can "play musical chairs" with abstract ideas. One can play join the dots with reality.
To live is to "join the dots"; LINEAR superposition. "Apparant time-line" is thus generalised into an overall concept of 'linear'-superposition as "joining the dots".
Possibilities (uncollapsed wave-functions) are like "musical chairs fields" (quantum linear superposition?)
Actualities (collapsed wave functions) are like "join the dots fields"- actual linear superposition, you might say.
There is such a thing as a speculative, mistaken, or strategic, but erroneous; superposition.
I claim that maximum awareness of data is obtained by differentiating everything with respect to Existence.
There is a question of "category" and "superposition". Abstract thoughts exist,
but they must not be wrongly superposed.
Abstract thought: suppose the moon is made of cheese. "Moon" and "cheese" here are prevented from being superposed because the knowledge that this is "abstract" keeps these concepts apart.
Now you can play musical chairs with these concepts "moon" and "cheese" (abstract thinking); but don't fraudulently join the dots! (i.e. don't superpose them while denying the barrier (honest awareness of abstract-category differential) that keeps them separate).
Claims about reality: involve claims about joining the dots, about actual linear superpositions.
What Dick says about the physics definition of acceleration (and what you said about the way the game physics is played) is revealing.
You have a superposition between the physics-mathematical pattern and what is observed; Dick's claim appears to amount to "That physicists are just playing musical chairs". Are they joining the dots?
Considering the question: how do they succede in sending inter-planetary spacecraft without knowing more than the ancients knew? (Do they know more?)
Answer: because they know MORE CATEGORIES!
In so far as they differentiate categories from sets, they may be unravelling underlying logical-consistent structure. Like playing a Chess game but not knowing the rules, yet being bound by the rules.
You get more and more freedom (more advanced activity available to you), the more you differentiate "musical chairs" (optional moves of play) from "join the dots" (CATEGORIES of types of move). Important to know the difference between "I managed to move my knight to such-and-such specific square"
and "the pattern: 'knight' is superposed or joined to the pattern "general rule about how knights can move in Chess".
Compare patterns: musical chairs (partial differentiation) (Dick's equation?).
Match patterns: join the dots (integration)(effectively Schrodinger's equation?).
Know the difference: differentiate with respect to Existence.
Collapse of the wave function; quantum jump: make an actual Chess move.
When you say "both parties are assumed to know" that implies an agreement, as each party tacitly agrees that the other may be regarded as knowing something that allows them to operate with the proposed "definition". (That is, I ask: assumed by who?).
Physicists superpose mathematical systems (logical consistency) on reality. When they find such speculative superposition does not say back to them "category error"; they assume they have made progress in differentiating categories from sets.
Someone at the Langan website wanted to know Richard Stafford's website address and wondered who had alerted me to common ground between Dick's demonstration and the Langan CTMU- (I wrote them an e-mail)- as it was you I'll let them know (I guess that's O.K.)
I realise the above post is not as lucid as it could be!