Comprehension of ignorance, nonsense and craziness

Mathematical Theology: Future Science of Confidence in Belief (Part #8)

Separately and together, mathematics and theology merit considerable attention in relation to:

infinity -- as the mysterious focus of a shared preoccupation of which many would readily claim ignorance, and others would variously assert to be "nonsense"
- as the primary characteristic of the divine with which theology is concerned
- as the underlying challenge to mathematics
ignorance -- of the subtle complexity with with they are variously preoccupied, a condition readily condemned as highly problematic by both theology and mathematics
- ignorance of mathematics on the part of others (including people of faith)
- ignorance of faith on the part of others is a matter of deep concern to the religious, specifically extending to those holding alternative beliefs (including those with a mathematical focus) -- and is clearly a primary trigger for many intractable conflicts
nonsense -- as a typical qualifier for those preoccupations raising issues for both as to how they might appropriately be rendered "sensible"
- as a characterization of mathematical subtleties beyond normal human ken, or as a descriptor of those using mathematics incompetently and inappropriately
- as a characterization of theological preoccupations by those focused on the mundane, or considered misguided in their understanding .

Given the intractable conflicts triggered by these factors, there is clearly a case for mathematical theology to address:

the implications for comprehension, learning and education of the nature of integrative and "meta" understanding
the nature of ignorance, nonsense and unbelief -- if only in terms of lack of credibility
the challenge of "everything" and "nothingness":
- as an aspiration of mathematics, given the focus on a Theory of Everything and the challenge of a Theory of Nothing (2006)
- as a preoccupation of theology, notably articulated in terms of "emptiness" as an outcome of meditation (Keiji Nishitani, Religion and Nothingness, 1983; James W. Heisig, Philosophers of Nothingness, 2001),

Efforts to render comprehensible the cognitive experience of these issues have been made in each case:

for mathematicians, the progression, and the interfaces, have been delightfully and insightfully explored in Flatland (1884), Sphereland (1965) or Flatterland (2001) and their associated animations.
for those of faith, the subtleties have characteristically been highlighted through parables, teaching stories (notably those of Nasreddin), and the Zen koan. Value has been attached by theology to "unsaying" and apophatic discourse (Being What You Want: problematic kataphatic identity vs. potential of apophatic identity? 2008). Notable significance has been attached to the nature of "unknowing"

Unforeseen cognitive challenges: The disturbing implications of Gödel's incompleteness theorems regarding undecidability have now been reinforced by the work of Harvey Friedman (Boolean Relation Theory and Incompleteness. 2010) through identification of entirely new forms of incompleteness. In his summary of such challenges, Richard Elwes (It doesn't add up, New Scientist, 14 August 2010) asks whether "a gaping hole has opened up in the foundations of mathematics". However, with respect to the above argument, perhaps even more challenging, is what this may imply for a "gaping hole" in the foundations of philosophical reflection on the development of consciousness and the governability of the planet. Curiously, as noted by Elwes:

With Friedman's work, it seems Gödel's delayed triumph has arrived: the final proof that if there is a universal grammar of numbers in which all facets of their behaviour can be expressed, it lies beyond our ken.... The only way that Friedman's undecidable statements can be tamed, and the integrity of arithmetic restored, is to expand Peano's rule book to include "large cardinals" -- monstrous infinite quantities whose existence can only ever be assumed rather than logically deduced.... We can deny the existence of infinity, a quantity that pervades modern mathematics, or we must resign ourselves to the idea that there are certain things about numbers we are destined never to know

Such large cardinals, notably understood to be "inaccessible", have yet to be fully admitted into the axioms of mainstream mathematics. Might they have been as readily named "angels" as "cardinals", as speculatively explored (Re-Emergence of the Language of the Birds through Twitter? 2010)?

Strategic implications: Current strategic significance has been given to the "unknown" through the notorious "poem" by Donald Rumsfeld as US Secretary of Defense in the midst of the intervention in Iraq. This has been separately discussed (Unknown Undoing: challenge of incomprehensibility of systemic neglect, 2008).

A matter of concern is the extent to which those in authority claim to "know" what is appropriate under conditions where there is both disagreement between authorities and between experts, and their track records suggest that it might be more fruitful to acknowledge ignorance. But this tendency is also shared between theology and mathematics in their quest for certainty and conviction and their discomfort with uncertainty. The need to believe then has an unfortunate quality of desperation.

This is to be contrasted with the much-cited reference to negative capability articulated by the poet John Keats as: when man is capable of being in uncertainties, Mysteries, doubts without any irritable reaching after fact and reason. It is now described as the resistance to a set of institutional arrangements or a system of knowledge about the world and human experience. It explains the capacity of human beings to reject the totalizing constraints of a closed context, and to both experience phenomena free from any epistemological bounds as well as to assert their own will and individuality upon their activity.

Craziness and creativity: Both theology and mathematics are considerably challenged by how to encompass what, as disciplines, they consider "crazy" -- but which may be evidence of creative insight for which they have no prepared explanation.

In the case of theology, craziness may well be used to characterize the behaviour of a person graced by some form of enlightenment -- perhaps a "holy fool". Various Eastern religions recognize "crazy wisdom", namely unconventional, outrageous, or unexpected behaviour having spiritual implications.

In the case of mathematics, the nature of the "requisite" cognitive surprise associated with creativity is well indicated by the much-quoted statement by physicist Niels Bohr in response to Wolfgang Pauli:

We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough.

To that Freeman Dyson added:

When a great innovation appears, it will almost certainly be in a muddled, incomplete and confusing form. To the discoverer, himself, it will be only half understood; to everyone else, it will be a mystery. For any speculation which does not at first glance look crazy, there is no hope! (Innovation in Physics, Scientific American, 199, 3, September 1958)

In response to intractable conflicts, it might be asked how mathematical theology could fruitfully frame the emergence of insights that were "crazy enough". What "systematic" provision might it make to encompass "muddled, incomplete and confusing" forms?