‘EXCESSION’.
F.E.D. ‘Neologia’ Series.
Dear Reader,
We have used the term – and evoked the concept – of ‘excession’ so far
mainly in the context our ‘Regenerist’ Cosmological Hypothesis, regarding the possible limits of
the early self-expansion rate of physical space, before that, ‘anti-gravitic’,
self-expansion was opposed by “Matter”, either “Dark” or ‘Bright’. This limit is
one whose ‘excession’ – the “exceeding” of which – was, per hypothesis, the
genesis of ‘anti-anti-gravitic’ “Dark Matter”.
However, numerous dialectical
processes within our cosmos – especially processes of the transition from mere,
quantitative, “evolution” to ‘onto-dynamical meta-evolution’, are driven by the
‘excession’ of specific immanent limits within their formations of Nature.
‘Excession’ is the process or
the fact of a dynamic growing, until it crosses a critical threshold of one [or
more] of its dynamical parameter-values, whose ‘excession’ precipitates a
relatively sudden qualitative, ontological change. This kind of change is often signaled, in “purely-quantitative”,
e.g., differential equation, models, by a division-by-zero “singularity” – a spurious
“infinite” purely-quantitative value.
The classic Marxian example of such ‘excession’ is that of Marx’s “law” of the tendency of the rate of profit to fall.
Per that “law”, as the [value-]percentage of the relative “organic [“living[-labor], v], composition of capital, (c/v),
diminishes, due to the faster rise in c, denoting the value of raw & auxiliary
materials consumed, plus of plant and equipment consumed, in the process of production, rising faster than the rise in v, so that the (c/v) ratio’s value as a whole grows, in each given round of
production, for industrial capitalist society as a whole, the Marxian rate of profit on the total social capital, e.g., s’/((c/v) + 1), is
predicted to fall, leading ultimately to the demise of capitalism, as its
profit-rate main motive gradually wanes, unleashing socio-economic cataclysms all
along the way in that process.
Of course, this would only involve, per this ratio-model, an “infinite singularity” in the case of a rise in the ‘human-societal self-reproductive self-force’ that achieved complete automation of social production, i.e., v = 0: s’/((c/0) + 1) = “s’/oo” = 0. I regard that as possible only as an asymptotic limit, within the Domain of human-social ontology.
We also encounter ‘excession’-born
finite time singularities, for example, in modern physics.
The Newtonian 2-body gravitic
equation predicts -- with “infinite” error -- an “infinite” gravitic force if the “point-masses” by which
it represents, e.g., the two mutually-gravitating planetary bodies, reach an ‘excession’
of the physical-spatial mutual separation that maintains their ontological identities as
distinct, i.e., when they “collide”, say at the finite time-value named ‘t*’, so that, then, the distance between them, r12(t*), becomes 0 –
GM1M2/r12(t*)2 = GM1M2/02.
The Einstein
special-relativistic momentum (p) equation, for bodies of ‘Bright Matter’,
predicts a “infinite singularity” if such a body were to attain the velocity of
light, c, and an “imaginary”
value of momentum were an ‘excession’ of light’s vacuum-velocity to occur –
p = mv/( 1 – (v/c)2 )1/2
– so that, if v = c, the
model predicts –
p = mc/( 1 – (c/c)2 )1/2 = mc/01/2
– and, if V > c –
p = mV/( 1 – (V/c)2 )1/2 =
-imc/( (V/c)2 – 1 )1/2
-- wherein ‘i’ denotes the square-root of –1.
Quite generally, ‘excessions’
mark the transitions wherein apparent, mere, relatively-gradual, “purely”-quantitative
change irrupts, with relative sudden-ness, into “qualitative change”, into “change(s)
of kind” – into ‘ontological, onto-dynamical revolution’.
Regards,
Miguel
¡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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