Part 04: Seldon Presents Series -- Moments of Maximal ‘Homeomorphic Defect’.
It is my pleasure, and my honor, as an officer of the Foundation Encyclopedia Dialectica [F.E.D.] Office of Public Liaison, 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.
The fourth such release in this new series is entered below [Some E.D. standard edits have been applied, in the version presented below, to the direct transcript of our co-founder’s discourse].
For more information regarding, and for [further] instantiations of, these Seldonian insights, please see --
-- and, in particular, please see --
Member, Foundation Encyclopedia Dialectica [F.E.D.],
Participant, F.E.D. Special Council for Public Liaison,
Officer, F.E.D. Office of Public Liaison.
“... The moments -- the finite time values -- at which “singularities” erupt in the nonlinear total differential equation models, and, especially, in the nonlinear partial differential equation models, that provide our so far best analogues for various aspects of our observed -- of our experientially and experimentally revealed -- physical reality -- are moments of absolutely maximal ‘homeomorphic defect’ for those models.”
“I say “absolutely maximal” because the modeled states of reality -- or, if you prefer, as I do, because the modeled ‘dynates’ of reality -- calculated for those moments, from those models, deviate egregiously from actual, physical reality, because they become of infinite magnitude, and therefore become infinitely erroneous, at, and, typically, also after, those moments. That is so because mathematical infinity is, to all observations to-date, aphysical, contra-empirical, in general, and because, in particular, the measured reality that those models supposedly model, remains finite throughout, before, during, and after those moments of “singularity”. Such models’ predictions, at their moments of “singularity”, are thus “infinitely” wrong.”
“However, and nevertheless, this is not to say that the realities so misleadingly modeled at such “singular” moments, and after those moments as well, are not, well, momentous.”
“We characterize the kinds of changes that do occur at and after such moments of “singularity” as never “infinite”, but, still, as ‘metafinite’.”
“Such changes include qualitative changes, as well as, and in coordination with, quantitative changes.”
“Indeed, such moments -- which the prevailing mathematical models describe as “infinite” singularities -- and their aftermaths, typically correspond, in physical actuality, to ‘ontological revolutions’ -- to irruptions of new and unprecedented ontology, at least locally unprecedented, if not globally, cosmologically unprecedented. They correspond to the emergence of new qualities -- of new kinds -- of being.”
“Unfortunately, some mathematicians and, even worse, some mathematical physicists, seem to “take their models for reality”, or, as we would be wont to say, take their mathematical ‘ideo-ontology’ for ‘physio-ontology’.”
‘They fail to recognize the “infinite singularities” in their mathematical equation models as symptoms of a reality, of a ‘‘‘real time’’’, progressing beyond a boundary at and after which their mathematical models lose validity, reach a limit of their ‘descriptivity’ with respect to physical reality, and break down as maps of real, physical, empirical, observational human experience, including of human experiment.”
“If we want to find a metaphor for such “breakdown”, while staying wholly within the ‘ideo-ontological’ realm of “pure” mathematics itself, we might consider an algebraic “diophantine equation”, in the context of the “Natural” numbers, of the form ‘2x - 1 = 0’, or, to make its “paradox” plain, of ‘2x = 1’. This is a “well-formed” diophantine equation within the “Natural” numbers algebra. But its solution cannot be expressed within the “language” of the “Natural” numbers -- within the axiomatic system, or within the number “space”, of the “Naturals”.”
“But instead of recognizing the dynamical ‘‘‘incompleteness’’’ of the ontological commitments of their implicit “model specification”, and the limits of the mathematical “language of description” that this specification and that these commitments allow for a given mathematical model, some mathematicians, and some mathematical physicists, project “purely”-mathematical constructs, which are mental fictions and ‘ideo-artifacts’ with respect to physicality, onto actuality. E.g., they start to faithfully believe that, at the hearts of the [cumula of] ultra-collapsed stars that they call “[“supermassive”] black holes”, there actually exists an “infinitesimal [mass-]point”, exhibiting “infinite [mass-]density”.”
“And, e.g., some start to believe that another such “point”, again of “infinitesimal” volume, and of “infinite” mass-density, formed the original state of our universe as a whole.”
“But, in practical truth, we have never experienced physical “infinities”, or physical “infinitesimals”, in all of our eons of recorded empirical, observational, including experimental, experience.”
“Such ‘infinitary’ beliefs constitute a kind of contra-factual, contra-empirical, contra-actual, and therefore contra-rational RELIGION, or, were no ‘deificatory’ intent to be operating in such beliefs, a contra-scientific IDEOLOGY, and a mystification and degeneration of science, into religion or ideology.”
“The real job, in relation to such “singularities”, is to craft new, descriptively richer, and more apt, mathematical models, and even to craft a new mathematical language in which to express such, richer, models. ... .”