Jack, Once again thank you for all your guidelines. You don't hear much from me but that's the sound of the work being done (as you said one your post = few weeks in a grad school). I dumped ninjatrader long ago and coded my own platform (NT records data incorrectly). I also focus on ES only now. Most importantly I dumped prediction and I dumped time. I am trying to nail granularity by moving as close as possible to origins of thought. Q. I feel that to be "like kind" I should be using only implication and parentheses. But in one of your posts I see: "The system uses operators called AND and OR and parentheses." From implication and ( ) no way to get AND. But perhaps from implication, ( ) and granularity I should be able to get that. Q. Does this look rightish or not right at all? h1: (0=>1) => (1=>0) [increasing => continuing] h2: (1=>0) => (0=>1) [decreasing => changing] I am trying to list the "possible combinations of two things taken two at a time". I am trying to be "like kind" and express everything in terms of PM. But I am not completely sure what PM is. Perhaps in the above "1" means (1=>0) in one context and means (0=>1) in another. Q. Is PM an algorithm that takes two algorithms as an input and outputs one algorithm? PM[A,B] = PM[C,D] PM: "Do the algorithm A with respect to algortihm B to get PM[C,D]" ? Q. I assume that PM follows the schema PM[PM[a,b], PM[c,d]] = PM[x,y] and it acts on arguments a,b,c,d to get x, y. It feels like making a counter out of JK flip-flops that counts both up and down. Q. Is the number of provable statements in the axiomatic system we are trying to design finite? Q. Is the number of provable statements arbitrary? Q. Will fixed point theorem be useful? Q. Since whatever we talk about has to be stated in relation to something else we need to start with a Paradigm. It seems that the Paradigm we should start with is already a defensibility hierarchy: HS_m, Q_m m = 1,..., alpha(Q,HS). HS_0 = HS = {h1, h2} Q_0 = Q = {{h1, h2}} (Initially h1 and h2 are totally Q symmetric) So for example we might have: HS_0 = {h1,h2} Q_0 = {{h1, h2}} HS_1 = {h1} Q_1 = ? HS_2 = {h2} Q_2 = ? HS_3 = {h1} Q_3 = ? HS_4 = {h2} Q_4 = ? HS_5 = {h1} Q_5 = ? HS_6 = {h1} Q_6 = ? HS_7 = {h1} Q_7 = ? and from this PM gives us HS_8 and Q_8. And at some event m: HS_m = HS_0 and Q_m = Q_0. I can't start only with HS_0, and QS_0 since there is no hypothesis there which can be non-arbitrarily referred to (there's no invariant hypothesis). So I need at least HS_1 and Q_1 which needs to be given to me by God. I feel that Q_(i+1) should somehow nest Q_i (perhaps as in von Neumann construction of natural numbers). Q. There's also a problem of how I "ground" (or attatch) this axiomatic system to reality to achieve synchronicity. But this is probably better to be dealt with once I have a better idea what PM is. Q. Jack does the picture I attatched trigger any thoughts in relation to PM? If so please annotate what your mind sees when you look at it. Where do you see variables? Where do you see events unfolding? Do you look at this picture from top to bottom, from left to right or perhaps diagonally? Or perhaps some other way? With red/blue lines I tried counting to 11 while looking at three rows only (I covered top six rows and two bottom rows).
The two Market (HS) are: IF and THEN,which resulting (PM),(PM) resulting Vector."In-Kind' is the Vector resulting the Pattern within parallelogramm.The complete paradigms is: If volume is increasing, then the price trend is continuing. If volume is decreasing, then the price trend is changing. This is pretty much it.