The NM Metrological Arithmetics and Their Sequel.
Part 02: ‘Beyond the NQ’ Series.
Dear Reader,
It
is my pleasure,
and my honor, as an elected member
of the Foundation Encyclopedia
Dialectica [F.E.D.] General Council, and as a voting member of F.E.D., to share, with you, from time to time, as they are approved for public release by the F.E.D. General Council, key excerpts from the internal writings, and from the internal sayings, of our co-founder,
Karl Seldon.
This 2nd release of
this new such
series is posted below
[Some E.D.
standard edits have been applied, in the version presented below, by the editors
of the F.E.D. Special Council for the Encyclopedia,
to the direct transcript of our co-founder’s
discourse].
Seldon
–
“The name ‘The NM Arithmetics’ is short for ‘The N-based Metrological-Dialectical Arithmetics’, solving
N q M ¶|-= N q QQ.”
“The
sequel to the q4 (--] N M = N q M
Arithmetics are the q5 (--] N q MN,
q6 (--] N q MQ, and
q7 (--] N q MQN ¶|-= N q MU or “Mu” Arithmetics.”
“The --
q4 (--] N M = N q M,
q5 (--] N q MN, and
q6 (--] N q MQ Arithmetics --
the fourth, fifth and sixth axioms-systems/categories of Arithmetics
in this dialectical-categorial progression of such systems, have mainly
pedagogical uses.”
“The
seventh system, N q MN,
and its immediate sequel -- not to mention the first,
«arché»-system, N , and the second
system, N Q -- all have
uses in scientific applications.”
“As
to the pedagogical uses of the fourth,
fifth and sixth axioms-systems/categories
of Arithmetics, recall that the dialectical
categorial progression in which these systems-categories progress is a
step-by-step, [meta-]system-atic dialectic, a presentational dialectic,
progressing from the simplest axioms-systems category, N , to ever more complex axioms-systems categories with
each further presentational step.”
“As
each arithmetical systems category is a potential ideographical language for
describing Nature [including human Nature], each more complex arithmetical
systems category is that of a language increasingly ‘determinations-rich’;
increasingly richer and more detailed in its potential Nature-descriptive
power.”
“We
call this categorial-progressional dialectic a ‘meta-systematic dialectic’, and
not just a ‘‘‘systematic dialectic’’’, because, as a progression of systems
this progression, as a whole, forms a ‘meta-system’, made up out of the
heterogeneous multiplicity of systems represented by its categories, as a whole,
as a ‘qualitative superposition/‘‘‘sum’’’ of the entire ‘cumulum’ of categories
that results from this progression.”
“The
pedagogical value of the fourth, N M systems-category is to demonstrate that the metrological units of its NM space or set –
NM = {mn} = {m1, m2, m3, …}
-- demonstrate, equally as for the units of the second, NQ = {q1, q2, q3, …} space, the core-dialectical, ‘contra-Boolean’ characteristic of all of these algebraic dialectical logics: ‘x2 is qualitatively unequal to x’."
"Thus mn2 is qualitatively unequal to mn, for all n in N."
"Thus, for example, in the case of the standard metrological unit of length, the centimeter, in “syncopated” notation, "cm.", is qualitatively different from the new, higher unit formed as "cm. x cm."."
"That is, a “square centimeter” is qualitatively different from a linear centimeter, or cm.2 is qualitatively unequal to cm.1."
"Thus, per our fourth systems category in this dialectical categorial progression, metrological units are established as belonging to our progression of dialectical systems of arithmetic.”
“The pedagogical value of the fifth systems category, as a partial dialectical synthesis category, synthesizing just the N q M and the N q N systems of arithmetic; their NM and N number-spaces – systems-category N q MN – is to demonstrate that the metrological unit qualifiers, from NM, can be quantified, by numbers drawn from N. That is, NqMN, the space or set of the units of the N q MN systems/languages category, looks like this –
NqMN =
{Nmn} = { n1m1, n2m2, n3m3, …}.”
“The pedagogical value of the sixth systems category, as a partial dialectical synthesis category, synthesizing just the N q MN and the N q Q systems of arithmetic; their NQ and N number-spaces – the systems-category
N q MQ – is to demonstrate that the Metrological unit qualifiers, from NM, can be “compound”
Metrological units, via “purely”-qualitative
division ‘denominatorization’ of various numbers of qualifiers drawn from NQ.”
“That is, NqMQ, the space or set of the generic unit of the
N q MQ systems/languages category, looks like this –
NqMQ = { Nmn/(qa,
…, qw) }, for a and w in N.”
“This
addresses the Metrological
need, in scientific and practical applications, for new metrological [meta-]units,
which are “compounds” of more basic metrological units, or “units of measure”.”
“For example, the velocity unit is defined, e.g., as cm./sec.;
the momentum unit, e.g., as gm. x cm./sec.;
the acceleration unit as that of cm./sec.2;
the force unit as that of gm. x cm./sec.2, and
the [kinetic] energy unit as (1/2)[gm. x cm.2/sec.2].”
The
seventh systems-category is usable in scientific and practical applications as outlined in the textual JPG image pasted-in below.”
For more
information regarding these
Seldonian insights, please see --
For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights -- specimens of ‘dialectical art’ – as well as dialectically-illustrated books
published by the
F.E.D. Press, see –
https://www.etsy.com/shop/DialecticsMATH
¡ENJOY!
Regards,
Miguel Detonacciones,
Voting Member, Foundation Encyclopedia Dialectica [F.E.D.];
Elected Member, F.E.D. General Council;
Participant, F.E.D. Special Council for Public Liaison;
Officer, F.E.D. Office of Public Liaison.
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