Monday, August 14, 2017

UNIVERSAL DIALECTICAL SCIENTIFIC METHOD.







UNIVERSAL DIALECTICAL SCIENTIFIC METHOD.






 
Dear Readers,



For a paradox-busting, radical-dualisms-transcending, algorithmic-heuristic, ontologically-dynamical, qualo-quantitative, predictive UNIVERSAL DIALECTICAL SCIENTIFIC METHOD [‘solvably’ NONLINEAR] for new knowledge/hypothesis discovery, its intuitive organization, its compact representation, and its systematic presentation, see www.dialectics.org .


Regards,


Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.







Friday, August 11, 2017

2nd ‘Dialectogram’ -- ‘The Dialectic of the Seldonian Arithmetics for Dialectics’.



 




 2nd Dialectogram -- The Dialectic of the Seldonian Arithmetics for Dialectics.






Dear Readers,



FYI:  Foundation Encyclopedia Dialectica [F.E.D.] is set to post a second dialectogram diagram, summarizing the Seldonian ‘[meta-]systematic dialectical method of presentation [long-form] of the Seldonian arithmetics for dialectics, for presentation step s = 3, to the Application Page of the www.dialectics.org web site --


For your convenience, I have also posted this dialectogram below.


ENJOY!



Regards,


Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.























Monday, August 07, 2017

‘The Dialectic of the Seldonian Arithmetics for Dialectics’.








The Dialectic of the Seldonian Arithmetics for Dialectics.






Dear Readers,



FYI:  Foundation Encyclopedia Dialectica [F.E.D.] has just posted a dialectogram diagram, summarizing the Seldonian ‘[meta-]systematic dialectical method of presentation [long-form] of the Seldonian arithmetics for dialectics, for presentation step s = 3, to the Application Page of the www.dialectics.org web site --


For your convenience, I have also posted this dialectogram below.


ENJOY!


Regards,

Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.























 

Tuesday, August 01, 2017

Division by Zero in the 'Mu' Dialectical Arithmetic.









Dear Readers,




See www.dialectics.org :  division by 0 [renamed ‘empty zero’] is readily performed, and yields a finitary, ‘quanto-qualitative’ value [called ‘full zero’], in the axiomatic system of the ‘Mu’ dialectical arithmetic.  This arithmetic also enables a fully arithmetical, fully algorithmic, fully ideographical expression of “dimensional analysis”, instead of the historically retrograde, “syncopated”-algebraic form presently prevalent, e.g., (1)[gm.], (2)[cm.], (3)[sec.], etc.

In this ‘Mu’ dialectical arithmetic, ‘quanto-qualitative’ subscripts/denominators behave analogously to the conventional superscripts extracted by logarithm functions:  script-level multiplications translate to subscript-level, non-amalgamative additions; script-level divisions translate to subscript-level subtractions.

Dynamical system state variable and control parameter ‘arithmetical quantifiers’ can be expressed in forms fully ‘‘‘qualified’’’ by ‘metrical arithmetical qualifier meta-numerals’, and by ‘ontological arithmetical qualifier meta-numerals’, in this ‘Mu’ system of arithmetic.

As a consequence, dynamical “singularities”, arising in finite time, resulting from division by zero in the dynamical differential equation itself, and/or in its solution-function, can be ‘semantified’ -- rendered in their real, G√∂delian-like meaning -- in a way which naturally avoids ‘infinity residuals’, i.e., the ‘infinitely erroneous’ values that result from interpreting “singularities” as signifying physical “purely”-quantitative infinities.

Dynamical singularities typically signify a change in the physical ontology that the dynamical equation models -- a change that goes beyond what the language and ‘‘‘ontological commitments’’’ of the model specification, implicit or explicit, can encompass.  That is, they signify an ‘ontological revolution’. 

Thus, the arising of the ‘full zero’ value ‘meta-numeral’ is typically a sign-post that the dynamical trajectory has reached a point where such ontological incompleteness of the model specification becomes explicitly manifest.


‘Arithmetical qualifiers’ are not a new ‘ideo-phenomenon’ in the history of human cognitions regarding numbers, or «arithmoi».  In the prelude to cuneiform in ancient Mesopotamia, ideograms representing both ‘ontological qualifiers’ and ‘metrological qualifiers’, as well as their ‘‘‘quantifiers’’’, eventually emerged, as documented in the work of Dr. Denise Schmandt-Besserat. 

The circa 250 C.E. proto-algebraic text by Diophantus of Alexandria, entitled  “«Arithmetik√©»”, which pioneered the movement toward symbolic or ideographical algebra, featured a syncopated proto-symbol, ‘M^o’, short for «Monad», or “unit”, which denoted a qualitative unit of a given kind of object, or, indifferently, of a metrological unit -- i.e., of a “qualitative unit” in either case. 

In Western mathematics after the Renaissance, the presence of ‘arithmetical qualifier meta-numerals’ in mathematical expressions entered a long eclipse and elision, in favor of “purely quantitative” ideographies -- except for the unrecognized presence of ‘metrological unit qualifiers’ in “syncopated” form, e.g., units of measurement like “sec.”, “gm.”, and “cm.”, when expressing “physical quantities”.

Later, an immanent re-emergence of a new kind of ‘arithmetical qualifiers’ ensued, with the discovery that the square root of negative unity could be represented by the so-called “imaginary unit”, i, with rich mathematical consequences, and with the subsequent development of the “hypernumbers” involved in, e.g., the Hamilton Quaternions, the Cayley/Graves Octonions/Octaves, and the “Grassmann [hyper]numbers”, all of which involve “qualitative units”.  “Vector” symbols also represent something beyond the “purely quantitative”, combining “scalar” quantity with ‘directionality’, or orientation.

Likewise, the recent development of set theory, and of the various “orders” of predicate calculus in mathematical logic, all involve the ideographical symbolization of ‘‘‘idea-objects’’’ that are not “pure quantities”, e.g., that represent “qualities”.
 

starting with --


http://www.dialectics.org/dialectics/Applications_files/Glossary,E._D._Notation_Definition,'Full_Zero'_Sign,Sheet_2_of_7,19APR2015.jpg

http://www.dialectics.org/dialectics/Applications_files/Glossary,E._D._Notation_Definition,'Full_Zero'_Sign,Sheet_3_of_7,19APR2015.jpg

http://www.dialectics.org/dialectics/Applications_files/Glossary,E._D._Notation_Definition,'Full_Zero'_Sign,Sheet_4_of_7,19APR2015.jpg

http://www.dialectics.org/dialectics/Applications_files/Glossary,E._D._Notation_Definition,'Full_Zero'_Sign,Sheet_5_of_7,19APR2015.jpg

http://www.dialectics.org/dialectics/Applications_files/Glossary,E._D._Notation_Definition,'Full_Zero'_Sign,Sheet_7_of_8,22APR2015.jpg

http://www.dialectics.org/dialectics/Applications_files/Glossary,E._D._Notation_Definition,'Full_Zero'_Sign,Sheet_8_of_8,22APR2015.jpg


Regards,

Miguel

Wednesday, July 19, 2017

Part 09. of 09. Concluding Observations on our Whole-Cosmos 'Meta-Models'. ‘‘‘The Dialectic of Nature’’’.
















Part 09 of 09.  Concluding Observations on our Whole-Cosmos 'Meta-Models'The Dialectic of Nature.










Dear Readers,


Below is the ninth part of our new series about The Dialectic of Nature as a singular whole, and about the Seldonian dialectical meta-modeling of that overall, all-encompassing dialectic.


ENJOY!


Regards,

Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.







Monday, July 17, 2017

Part 08. 'Meta-Models' #s 2, 3, and 4. '''The Dialectic of Nature'''.





Part 08.  'Meta-Models' #s 2, 3, and 4The Dialectic of Nature.










Dear Readers,


Below is the eighth part of our new series about The Dialectic of Nature as a singular whole, and about the Seldonian dialectical meta-modeling of that overall, all-encompassing dialectic.

ENJOY!


Regards,

Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.
















































Friday, July 14, 2017

Part 07. Observations on Some Universal Principles Embodied in 'Meta-Model' #1. The Dialectic of Nature [continued].





Part 07.  Observations on Some Universal Principles Embodied in 'Meta-Model' #1.










Dear Readers,




Below is the seventh part of our new series about The Dialectic of Nature as a singular whole, and about the Seldonian dialectical meta-modeling of that overall, all-encompassing dialectic.

ENJOY!


Regards,

Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.













































Tuesday, July 11, 2017

Part 06. 'Meta-Model' #1 in Predictive Mode: The Coming Irruption of 'The Meta-Human' .





Part 06.  'Meta-Model' #1 in Predictive Mode:  The Coming Irruption of 'The Meta-Human' .










Dear Readers,



Below is the sixth part of our new series about The Dialectic of Nature as a singular whole, and about the Seldonian dialectical meta-modeling of that overall, all-encompassing dialectic.

ENJOY!


Regards,

Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.




































Saturday, July 08, 2017

Part 05. 'Meta-Model' #1: 'Categorial Expansion' of this 'Meta-Model' of ‘‘‘The Dialectic of Nature’’’ to Epoch 8, 'Humanitys' Emerging -- Historical Dialectic of Cosmological Natural History as THE Whole.





Part 05.  'Meta-Model' #1:  'Categorial Expansion' of this 'Meta-Model' of  ‘‘‘The Dialectic of Nature’’’ to Epoch 8, 'Humanitys' Emerging -- Historical Dialectic of Cosmological Natural History as THE Whole.  Two-Hundred Fifty-Six [256  =  2^8] Category-Symbol Terms in All.






Dear Readers,





Below is the fifth part of our new series about The Dialectic of Nature as a singular whole, and about the Seldonian dialectical meta-modeling of that overall, all-encompassing dialectic.

ENJOY!



Regards,

Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.

























Friday, July 07, 2017

Part 04. 'Meta-Model' #1: Syntactic Mechanisms and 'Semantic Organisms' of this 'Meta-Model' of ‘‘‘The Dialectic of Nature’’’ -- The Historical Dialectic of Cosmological Natural History as THE Whole.





Part 04.  'Meta-Model' #1:  Syntactic Mechanisms and 'Semantic Organisms' of this 'Meta-Model' of  ‘‘‘The Dialectic of Nature’’’ -- The Historical Dialectic of Cosmological Natural History as THE Whole.






Dear Readers,




Below is the fourth part of our new series about The Dialectic of Nature as a singular whole, and about the Seldonian dialectical meta-modeling of that overall, all-encompassing dialectic.

ENJOY!



Regards,

Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.