User talk:KBlott

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 * --Your friendly ProofWiki WelcomeBot 22:15, 7 January 2012 (EST)

Subpages
Hey, I've moved some of the pages you've made to be subpages of your user page. --Joe (talk) 16:21, 8 January 2012 (EST)

Your strategy
I've been watching some of your edits from a distance for a while, and I'm interested: what is your strategy? Are you planning on either (a) incorporating it into our general house structure at any stage, and (b) linking it all up with the existing work? Or is all this being designed as a completely independent body of knowledge? --prime mover 01:30, 17 January 2012 (EST)
 * I have no particular strategy really. I just go where the evidence takes me and all work is essentially derivative.
 * Notice that this page is incompatible with standard set theory.  I would not dream of attempting to integrate it into work that is based on standard set theory as it would quickly lead to problems.  There is evidence, however, that the Cardinality of sets can be relative.   Consider the set of all locations of a particle at a given time.  It is generally assumed that such sets are necessarily singleton.  (A particle is assumed to have only one location at a given time.)  However, the double slit experiment refutes this assumption.  This suggests that inclusion in a given set ($\in$) may be relative to the observer and, of course, the time the observation is made ($\in_t$).
 * Class algebra is mentioned on this web site but seems not to be treated with a great deal of reverence. Although mappings obviously operate on classes, their definition on this web site is restricted to sets.
 * The same is true of the definition of lattices on this web site. Notice that the definition of a lattice given by these authors is not equivalent.  While all lattices of sets are lattices of classes, the converse is not true.  Consider, for example the class $U$ of all sets.  This is a class lattice (with $\vee = \cup$ and $\wedge = \cap$) but it is not a set lattice because $U$ is not a set.  --KBlott 16:18, 17 January 2012 (EST)
 * I can see separate interest for what you are developing on referenced page for $\in$. It appears that this yields a rigorous (possibly extendible) definition of $\in$ when considering non-standard set theory and logic (where eg. a lattice of truth values is used; though I don't know if something like that is viable). --Lord_Farin 16:45, 17 January 2012 (EST)
 * Several authors have attempted to reformulate propositional calculus in terms of lattice theory. Two such attempts are cited by Sudbery on page 209.  Though as Sudbury himself pointed out “it would involve reconstructing the whole of mathematics” (p 223).  Who has that much time?  I sure don’t.
 * I do believe that such a reconstruction is necessary. Einstein believed that the laws of physics are invariant under all possible co-ordinate transformations.  However, he restricted his attention to one-to-one co-ordinate transformations and failed to unify his theory of gravity with quantum mechanics.
 * Consider a co-ordinate transformation of the world line of an electron from its own frame of reference to an observer's frame of reference. In the electron's frame of reference, the electron's location is fixed.  So, the mechanics of its motion is very simple.  Now consider the motion of the electron in an observer’s frame of reference.  Let $t$ be the time on the observer’s clock.  Let $S$ be the set of all points in space from the observers point of view.  Let $L \in$ $\mathcal P(S)$ be the set of all points in $S$ at which the electron happens to be located.  Since, the co-ordinate transformation from the electron’s frame of reference to the observer's frame of reference may not be one-to-one, the electron’s world line may map onto a particular point in $S$ more than once.  Worse still, the electron may be moving either forward in time or backward in time, with respect to the observer, at any given instance.  So, we need two sets of natural numbers: $n_+$ to describe the number of times it maps to a point $\underline x  \in S$ while traveling forward in time and $n_-$ to describe the number of times it maps to a point $\underline x  \in S$ while traveling backward in time.  So, rather than having two truth values (true or false), $\underline x \in_t L$ maps to  infinitely many truth values $(n_+, n_-)$.  So, $\in_t: S \times \mathcal P(S) \to \mathbb N \times \mathbb N$.  I was thinking about this when I wrote this page. --KBlott 20:03, 17 January 2012 (EST)