Dear jon, I think that this is the mathematical manifold. It's similar to trasform a sphere in a plane, create a map of the earth. But if you trasform B in N you obtain a series of Nat and a series of Nat with the distance of a unit is the time. I try to follow you but I'm not a mathematician. I'm more interesting. Regards Mauro
Il dom 21 mar 2021, 18:26 Jon Awbrey <[email protected]> ha scritto: > Dear Mauro, > > Here I think Helmut is describing the transition > from forms of enclosure on a plane sheet of paper, > such as those used by Peirce and Spencer Brown, to > their topological duals in the form of rooted trees. > I gave a brief discussion of this transformation in > the following couple of places. > > Logical Graphs • Introduction > https://inquiryintoinquiry.com/2008/07/29/logical-graphs-1/ > > Logical Graphs • Duality : Logical and Topological > https://oeis.org/wiki/Logical_Graphs#Duality:_logical_and_topological > > This is the first step we need to carry out in the process > of converting planar maps to graph-theoretic data structures. > > Further transformations will take us from trees to cactus graphs, > which implement a highly efficient family of logical primitives > called "minimal negation operators". > > Minimal Negation Operator > https://oeis.org/wiki/Minimal_negation_operator > > Regards, > > Jon > > On 3/21/2021 12:21 PM, Mauro Bertani wrote: > > So, if I want transform a circle in a line i have to use a function > > f:B_n -> B? This is the base of temporal logic? I'm using f:N_n -> N > > > > Regards > > Mauro > > > > > Il sab 20 mar 2021, 19:45 Jon Awbrey <[email protected]> ha scritto: > > > >> Cf: Differential Propositional Calculus • Discussion 4 > >> > >> > http://inquiryintoinquiry.com/2021/03/20/differential-propositional-calculus-discussion-4/ > >> > >> <QUOTE HR:> > >> > >> 1. I think I like very much your Cactus Graphs. Meaning that I > >> am in the process of understanding them, and finding it much > >> better not to have to draw circles, but lines. > >> > > > > So, if I want transform a circle in a line i have to use a function f:B_n > > -> B? This is the base of temporal logic? I'm using f:N_n -> N > > > > Regards > > Mauro > > > > > >> 2. Less easy for me is the differential calculus. > >> Where is the consistency between (x,y) and (x, y, z)? > >> (x, y) means that x and y are not equal and (x, y, z) > >> means that one of them is false. > >> Unequality and truth/falsity for me are two concepts > >> so different I cannot think them together or see > >> a consistency between them. > >> > >> 3. What about (w, x, y, z)? > >> > >> 4. Can you give a grammar, like, what does a comma mean, > >> what do brackets mean, what does writing letters following > >> each other with an empty space but no comma mean, and so on? > >> > >> 5. Same with Cactus Graphs, though I think, they might be > >> self-explaining for me — everything is self-explaining, > >> depending on intellectual capacity, but mine is limited. > >> > >> </QUOTE> > >> > >> Dear Helmut, > >> > >> Many thanks for your detailed comments and questions. They help me see > >> the places where more detailed explanations are needed. I added numbers > >> to your points above for ease of reference and possible future reference > >> in case I can't get to them all in one pass. > >> > >> Cactus Graphs > >> ============= > >> > >> I'm glad you found the cactus graphs to your liking. > >> It was a critical transition for me when I passed from > >> trees to cacti in my graphing and programming and it > >> came about by recursively applying a trick of thought > >> I learned from Peirce himself. These days I call it a > >> “Meta-Peircean Move” to apply one of Peirce's heuristics > >> of choice or standard operating procedures to the state > >> resulting from previous applications. All that makes for > >> a longer story I made a start at telling in the following > >> series of posts. > >> > >> Animated Logical Graphs > >> https://inquiryintoinquiry.com/2019/05/28/animated-logical-graphs-14/ > >> > >> [Links omitted for this email. See the blog post linked at the top for > >> the list.] > >> > >> https://inquiryintoinquiry.com/2019/07/31/animated-logical-graphs-27/ > >> > >> Well, the clock in the hall struck time for lunch some time ago, > >> so I think I'll answer its call, break here, and continue later … > >> > >> Regards, > >> > >> Jon > >> > >
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