Tuesday, September 27, 2011

Part III.: Intimations of a faster than light Interstellar Drive

CONTINUED FROM IMMEDIATELY-PREVIOUS BLOG ENTRY, #52

Part III.Intimations of a faster-than-light Inter-Stellar Drive: "Side-Stepping" the V = c Singularity -- An F.E.D. Hypothesis.

[¿A "Non-Celeritarian" Pathway from the "Tardyonic Meta-Phase", through the "Luxonic Meta-Phase", to the "Tachyonic Meta-Phase" of "Matter-Energy", or "Energy-Matter", and back again?]


[Note: as usual in this blog, I use visible-light-spectrum color-ordinality to highlight categorial, or system, dialectical ordinalities -- "ROY G. BIV"].



Dear Readers,

. . .



SOURCE NOTE:  FYI, the title of this post, "Intimations of an Inter-Stellar Drive", comes from the overview "contents map" of F.E.D.'s treatise --

Dialectical Ideography: A Contribution to the Immanent Critique of Arithmetic

-- from Part III. of that treatise, entitled "The Arithmetics Of Meta-Evolution", from a section entitled --

"'Convolute' Re-Qualification of the Einstein Momentum Equation:   
Specimen of 'Quanto-Qualitative Computation'?; 
Intimations of an Inter-Stellar Drive?"'

-- in the Dialectical Ideography Table of Contents --

http://www.adventures-in-dialectics.org/Adventures-In-Dialectics/DiaRith/PrescriptsOverview/PrescriptsOverview.htm

-- only parts of Part I. of which have been web-published to-date, to my knowledge. The only part of the contents of the "Intimations of an Inter-Stellar Drive" section to be web-published so far, to my knowledge, were web-published in the old F.E.D. on-line forum, formerly attached to the www.dialectics.org web-site. That forum was taken down some years back, after a "hack-attack".



Two-by-Two Matrix Validations of the Hypernumber Computations Crucial to the Hypotheses Presented in Earlier Blog-Entries of this Sub-Series of Blog-Entries.

I noted, earlier in this sub-series of blog-entries, that the hypernumbers E and i can be represented as linear operators in the form of 2 x 2 arrays of numbers, or matrices, using only entries that come from the number-space, or number-set, denoted by Z, which is constituent of the "Standard" axioms-system of arithmetic denoted by Z, such that --

Z = { . . ., -3, -2, -1, ±0, +1, +2, +3, . . . }

-- although the hypernumbers E and i can be represented in richer, more complicated ways as well.


More specifically, the hypernumbers E and i can be interpreted ['(---)'] as two x two matrices, using only entries that come from the small -- "cardinality three" -- sub-set, { -1, ±0, +1}, of the set Z, as follows --

..........................___................___
.........................|.....+1......±0...|
+1.(---)..|..............................|
.........................|.....±0......+1...|
.........................|___..............___|

-- and --

.........................___..................___
........................|.....±0..........-1....|
...i....(---).|..................................|
........................|....+1........±0.....|
........................|___.................___|

-- and --

.........................___..................___
........................|.....+1.......±0....|
...E...(---).|................................|
........................|....±0..........-1...|
........................|___................___|

-- using the "Standard" product rule for such matrices, wherein the entries in the top row of the Left Hand matrix multiply the entries in the corresponding positions of the left-most column of the Right Hand matrix, placing the sum of those multiplications in the top-row left entry of the new, product matrix, and, next, wherein, again, the entries in the top row of the Left Hand matrix then multiply the entries in the corresponding positions in the right-most column of the Right Hand matrix, placing the sum of those multiplications in the top-row right entry of the new, product matrix, thus completing its top row, and, then, next, wherein the entries in the bottom row of the Left Hand matrix multiply the entries in the corresponding positions of the left-most column of the Right Hand matrix, placing the sum of those multiplications in the bottom-row left entry of the new, product matrix, and, next, wherein, again, the entries in the bottom row of the Left Hand matrix then multiply the entries in the corresponding positions in the right-most column of the Right Hand matrix, placing the sum of those multiplications in the bottom-row right entry of the new, product matrix, thus completing the bottom row of that new, product matrix, and, thereby, also completing the entire product matrix, viz. --





..___...........___..........___.........___.............___............................................___
.|.....a.......b......|.........|.....e...........f..|...........|.....ae.+.bg.......af.+.bh.......|
.|.........................|...x...|........................|...=....|............................................................|
.|.....c.......d......|.........|....g..........h...|...........|.....ce.+.dg.......cf.+.dh........|
.|___.........___|.........|___........___|...........|___...........................................___|

-- we obtain the following "calculative behaviors" for the "E"-interpreting and "i"-interpreting matrices, mirroring the defining "computative behaviors" that we have given earlier for the E and i hypernumbers, thus validating the hypernumber calculations included in the preceding blog-entries of this sub-series of blog-entries --
..___.................___.........___....................___............___..................___
.|.....±0........-1....|........|.....±0..........-1.....|..........|......-1.......±0......|
.|................................|..x..|...................................|...=...|..................................|....(---)....i...x...i....=....-1
.|....+1.......±0.....|.......|....+1........±0.......|..........|.....±0........-1......|
.|___................___|.......|___...................___|..........|___.................___|

-- and --
..___..................___...........___...................___...........___.................___
.|.....+1.......±0....|.........|.....+1.......±0.......|..........|.....+1.......±0...|
.|................................|...x...|...................................|...=...|................................|....(---)....E...x...E....=....+1
.|.....±0.........-1....|.........|.....±0.........-1......|..........|.....±0.......+1....|
.|___................___|.........|___...................___|.........|___.................___|

-- and --
..___.................___.........___..................___............___....................___
.|.....±0........-1....|.......|.....+1.......±0......|..........|.....±0.......+1.......|
.|...............................|..x..|..................................|...=...|....................................|....(---)....i...x...E.... =....-1...x...E...x...i
.|.....+1.......±0...|.......|....±0..........-1......|..........|.....+1.......±0.......|
.|___...............___|.......|___..................___|..........|___...................___|

-- and --
..___...................___...........___......................___...........___....................___
.|.....+1.......±0......|.........|.....±0........-1..........|.........|.....±0.......-1.........|
.|..................................|...x...|.....................................|...=...|...................................|....(---)....E...x...i.... =....-1...x...i...x...E
.|.....±0........-1......|.........|.....+1.......±0..........|.........|.....-1.......±0.........|
.|___.................___|.........|___......................___|.........|___....................___|






-- and, most crucial of all for the F.E.D. "inter-stellar drive" hypothesis --
..___....................___..........___..................___............___...................___
.|.....+1.......±0.......|.........|.....±0........-1.....|..........|.....+1.......-1........|
.|...................................|..+..|................................|...=...|...................................|....(---)....E...+...i....=....i...+...E
.|.....±0........-1........|.........|.....+1......±0.....|..........|.....+1.......-1........|
.|___...................___|.........|___................___|..........|___...................___|


-- and, finally, the "nilpotent" key to their hypothesis --

..___..................___...........___...................___...........___...................___
.|.....+1........-1.....|..........|.....+1.........-1.....|..........|.....±0.......±0.....|
.|.................................|...x...|..................................|...=...|.................................|...(---)..(E + i)...x...(E + i)..=.±0
.|.....+1........-1.....|..........|.....+1.........-1.....|..........|.....±0.......±0.....|
.|___.................___|.........|___..................___|..........|___.................___|




F.E.D. source-documents upon which this sub-section is based, from two F.E.D. web-sites --


http://www.dialectics.org/dialectics/Primer.html


1. F.E.D. Introductory Letter, Supplement A, pages A-9 through A-14 --
http://www.dialectics.org/dialectics/Primer_files/3_F.E.D.%20Intro.%20Letter,%20Supplement%20A-1_OCR.pdf

2. Generic Dialectical Interpretation of the NQ_ Ideography, pages 23 through 27 --
http://www.dialectics.org/dialectics/Primer_files/8_Fract1-1_OCR.pdf


3. Dialectical Pictography: A Pictorial Summary of Dialectical Ideography, Part III.,
Meta-Systematic Dialectics, slides 87 through 98 in www.adventures-in-dialectics.org version,
and slides 23 through 34 in www.dialectics.org version--



TO BE CONTINUED

NEXT TOPIC IN THIS SUB-SERIES: 

Parities between the Musèan Hypernumber Qualifier Resolution, & the F.E.D. Dimensional Units, Metrical Qualifier, Meta-Number Resolution, of the Einstein Momentum Equation's V = c  Singularity.




Regards,

Miguel

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