Surprising
Examples
of
Quanto-Qualitative
Information
Conveyance.
GLOBAL STRATEGIC
HYPOTHESES.
Dear Reader,
The use of symbolic
arithmetical qualifiers was born, as far as we know, in North
African late Antiquity.
It was born in a papyrus multi-scroll
treatise, composed in ancient Alexandria, Egypt, then a pinnacular city-state for
mathematical, proto-scientific and engineering theory and practice – perhaps THE
pinnacular such city of the ancient world – circa 250 C.E.
This Greek scroll was titled,
per its English translation, “The Arithmetica”, and was written by
Diophantus of Alexandria.
This scroll was a prevenient
and protoic work of syncopated [word-abbreviating], quasi-ideographical-symbolic
arithmetic and algebra, which, after the long Dark Ages, was partially recovered,
translated and printed, then exercising a strong influence toward the rebirth
of mathematics in general, and of algebra in particular, to the North of
Alexandria, in Renaissance Europe.
A prominent feature of the Arithmetica
manuscript was the use of a proto-symbol standing for the ultimate unit of any «arithmos»,
or assemblage/«ensemble» of concrete qualitative – qualit(y)(ies)-bearing
– units, the «Monad», hence
its syncopated, proto-symbolic representation in that manuscript, Mo.
But the European development
of arithmetic, algebra, and beyond opted for abstract quantities, and ideographical
symbolizations of “pure”, unqualified quantities only,
reflecting, we think, the mostly unwitting psychohistorical
impact of the parallel development, to a more massive scale than ever before in
human history, of the money-mediated exchange of commodities, and of mercantile
and manufacturing capital.
For long centuries, arithmetic
and algebra exhibited an ‘Elision of the Arithmetical Qualifiers’, until
the discovery of the possible workability of, and then the widespread adoption
of, i, symbol for the +Ö(-1), later furthered by the less-widespread adoption of other
arithmetical qualifiers, such as the Grassmann qualitative units, not to
mention those of the Quaternions and Octonions.
Nonetheless, a ‘Re-Emergence
of the Arithmetical Qualifiers’ was underway, and the development of the
Seldonian axioms-systems of arithmetics/algebras for modeling dialectics is one
of the little-known latter-day culminations of that re-emergence.
But, apart from this more
macro psychohistorical trend, de facto arithmetical qualifiers,
typically not fully understood as such, have continued to
pop-up in practical and engineering applications of arithmetics and algebras.
Most all of us have
encountered the quantification of ‘metrological quasi-arithmetical unit qualifers’,
e.g., of the units-of-measure symbols – albeit still “syncopated”, much like
the proto-ideograms of the ancient Arithmetica manuscript, still after
all of these centuries! –
e.g., 8 hrs., 10 lbs., 20 cm.,
72 °F., 20$s, etc.
At last, these syncopations become fully
arithmetical – and fully ideographical – in the longform Seldon Dialectical Progression,
starting in its seventh arithmetic-system, that is, in the RqMQR º RqMU º Rm axioms-system.
In that, Seldonian, system,
the R-inherent quantifiers
quantify the M-inherent metrological-unit
qualifiers, and,
together, those two, as one, ‘quanto-qualify’ the ontological-qualifer
units of U.
But, far apart from these
Seldonian developments, surprising examples of arithmetical ‘quanto-qualities’
have emerged.
Consider the following standard
expression in the film-making world: 1920 ´ 1080p,
which, for example, AIs often write as “1920 ´ 1080p”, thus giving special emphasis to the “p”
via its italicization.
That “p” is an
arithmetical qualifier in its own right, because it is not
a quantity, an arithmetical quantifier.
It stands for the word “pixel”, which is a concrete, qualitative
unit, a unit of digital depiction.
The arithmetical quantifier,
(1920 ´
1080), will tell us explicitly, when the stated multiplication is carried out,
the number of pixels in a given “frame” of the digital film file: (2,073,600)p. This expression would tell us the “video resolution”
of the film. But something useful would
be lost thereby.
The carrying-out of even this,
“purely-quantitative”, multiplication operation would cause a loss of qualitative
information.
This is because the unmultiplied
expression, 1920 ´ 1080, tells us the shape of the
frame, by telling us the width versus the height, the “aspect ratio”, of each
frame in that, standard, digital film file.
Here quantitative information,
expressed in a certain way, also conveys qualitative information.
Evidently, then, ‘quanto-qualitative’
mathematics is not always a matter of the strict
separation of ‘arithmetical quantifiers’ from ‘arithmetical qualifiers’, asserted
by the expression –
(arithmetical
quantifiers)
“´” [arithmetical
qualifiers],
e.g.,
(1920 ´ 1080) Ä [p]
– where, herein, ‘Ä’ symbolizes a generalized concept of the “multiplication”
operation, that covers multiplication of quantifiers by quantifiers,
qualifiers by quantifiers, and qualifiers by qualifiers.
For more
information regarding these
Seldonian insights, and to read and/or download, free
of charge, PDFs and/or JPGs of Foundation books, other texts, and images, please see:
www.dialectics.info
and
https://independent.academia.edu/KarlSeldon
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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