Because mathematics is infinite, the field of cybersecurity can never be truly closed. The space of vulnerabilities is unbounded, each patch or solution only ever an approximation against the open horizon of possible attacks. Risk is permanent, not as a flaw but as a structural consequence: a system that protects itself must also endlessly expose […]
Context: Gödel’s Incompleteness Theorem, The Inherent Limitation Of Mathematics The discontinuous boundary condition at the edge of (as much as being that around which we built) logic, physics and mathematics is a global property, distributed across and as the complex hypersurface of a self-propagating, soliton-like hybrid matter/energy/information system. It is as though a logical vacuum, […]
Context: Paradox at the heart of mathematics makes physics problem unanswerable What happens if we are to assert this reflexive tesseract of indefinitely-extensible symbolic information as abstraction at (and as) the beating heart of autonomously self-propagating, soliton-like logical vacuum and necessity that compels this Universe forwards? What might it mean to engage with uncertainty, incompleteness, […]
“Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an ‘intelligence explosion,’ and the intelligence of man would […]
Context: Could We Force the Universe to Crash? If we were to take seriously the implications of much-maligned and misunderstood general principles of endemic incompleteness and uncertainty that occur both in and as distributed (“Global”) hyper-surfaces across logic, physics and mathematics, we might consider that such a cosmological “Entscheidungsproblem” is not so much fantasy as […]
Context: Truth Beyond Logic and Time Beyond Clocks: Janna Levin on the Vienna Circle and How Mathematician Kurt Gödel Shaped the Modern Mind Gödel is interesting in many ways. While acknowledging that his logical and mathematical foundation-shaking Incompleteness proofs have a very specific context and meaning, the extent to which a broader reading (and thinking) […]
Some truths are only known by inversion, by negation and through a proof by contradiction. Alan Turing’s proof of the undecidability of non-trivially complex algorithms, that is – the impossibility of analysis to arrive at certainty concerning whether a given computer program will terminate or continue forever, was just such a proof. Kurt Gödel’s proof […]
It is only an immature psychological and cultural status which seeks certainty and completion in all things and in so doing, generates endless entropy and confusion. Science has no logical endpoint.
There is no “best” theory, there are only progressively “better” ones.
If you know who Kurt Gödel was and understand what a Constitution represents in regards to the logical axioms (i.e. assumptions) made in the formulation of a rules-set (i.e. legal system) and their theorems (i.e. formal legal consequences) underpinning governance and political power, you already know where this is heading…
The idea that Gödel’s logical insights might reflect deeply upon physics is fascinating…
Daedelus Kite 