# Re: On Causation with Mind and brain as apples and oranges

On 9/24/2012 8:12 AM, Roger Clough wrote:

Hi Stephen P. King
I have trouble conceiving an isomorphism (or anything comparative) between
something that is there and something that is not. The something
that is not there is not the absence of the thing that was,
since it has no shape, no location, and cannot be found by a physical
search.


Hi Roger,


I sympathize with you but must point out that one must be sure that one's idea and assumptions are correct. What I am proposing is that that Minds are, at the lowest level, a relational structure that can be well represented by Boolean Algebras. There is a duality between BAs and a type of topological space:

http://en.wikipedia.org/wiki/Stone%27s_representation_theorem_for_Boolean_algebras


"EachBoolean algebra <http://en.wikipedia.org/wiki/Boolean_algebra_%28structure%29>/B/has an associated topological space, denoted here/S/(/B/), called its*Stone space*. The points in/S/(/B/) are theultrafilters <http://en.wikipedia.org/wiki/Ultrafilter>on/B/, or equivalently the homomorphisms from/B/to thetwo-element Boolean algebra <http://en.wikipedia.org/wiki/Two-element_Boolean_algebra>. The topology on/S/(/B/) is generated by abasis <http://en.wikipedia.org/wiki/Basis_%28topology%29>consisting of all sets of the form

\{ x \in S(B) \mid b \in x\}, where/b/is an element of/B/.


For any Boolean algebra/B/,/S/(/B/) is acompact <http://en.wikipedia.org/wiki/Compact_space>totally disconnected <http://en.wikipedia.org/wiki/Totally_disconnected>Hausdorff <http://en.wikipedia.org/wiki/Hausdorff_space>space; such spaces are called*Stone spaces*(also /profinite spaces/). Conversely, given any topological space/X/, the collection of subsets of/X/that areclopen <http://en.wikipedia.org/wiki/Clopen_set>(both closed and open) is a Boolean algebra."



This made complete sense to me once I realized what the Stone spaces "look like": a collection of particles in an emptiness (frozen in time). (A Cantor dust <http://en.wikipedia.org/wiki/Cantor_set> is a Stone space.) A nice illustration of the physical universe once we strip away of the detail. When we take change into account we get a succession of Stone spaces and BAs. The direction of the "arrows" of evolution of these are in opposite directions. BAs evolve by "looking backwards" to be sure no new proposition contradicts a previously accepted proposition. This property alone makes this hypothesis very appealing as it leads naturally to a reason why there are no "White Rabbits" (spontaneous events that present contradictory information, like a "White Rabbit" popping out of nowhere).

--
Onward!

Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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