• Dean’s paradox highlights a core discrepancy between logical reasoning and lived reality. Logic insists that between two points lies an infinite set of divisions, making it "impossible" to traverse from start to end. Yet, in practice, the finger does move from the beginning to the end in finite time. This contradiction exposes a gap between the abstract constructs of logic and the observable truths of reality
Loop Quantum Gravity (LQG) says reality is discrete but this is contradicted by its own admission
Loop Quantum Gravity (LQG) says reality is discrete and at the Planck scale, you would witness a restless, unpredictable quantum foam—an ever-shifting landscape where space and time themselves are in constant, chaotic flux, and classical patterns or positions disappear
butLQG uses the real number line as its mathematical foundation, then any evolution or fluctuation in the quantum geometry—no matter how "chunky" or discrete it is physically—can be mathematically described as passing through an infinity of points between any two states
physics posits a discrete structure (like LQG's "chunks" of space), the mathematics used to describe these structures (real numbers, Hilbert spaces) remains infinitely divisible. Thus, the paradox of "infinity within the finite" endures at the formal level
thus the dean paradox applies
LQG uses continuum mathematics, so mathematically, the evolution of quantum geometry can be described as passing through an infinity of points. Physically, however, only discrete states are meaningful or observable—the continuum is a tool for calculation, not a direct reflection of physical reality
LQG uses continuum mathematics, so mathematically, the evolution of quantum geometry can be described as passing through an infinity of points. Physically, however, only discrete states are meaningful or observable—
Even with discrete models like LQG, the Zeno and Dean paradoxes persist at the mathematical level: the continuum of infinite divisibility remains in the formalism, even if physical measurement is fundamentally limited. This is a foundational tension between mathematics and physical reality that continues to challenge philosophers and physicists alike
thus
Physics’ discrete models (like LQG) still rely on infinite mathematics, so the dean paradox endures· Dean Paradox Endures:
This means that while LQG tries to "escape" the continuum and infinite divisibility at the level of physical interpretation, the mathematical foundation does not eliminate it. The "Dean Paradox" or related to Zeno's paradoxes—remains: the mathematics of infinity and continuity persists even in discrete models· .
· Philosophical Implication:
The hope for a "discrete escape" in physics is thus incomplete. The physical claim of indivisible quanta is not fully matched by the mathematical structure, which still allows for infinite division. This is a central open problem in the foundations of quantum gravity and the philosophy of logic and mathematicsConclusion:
Physics’ hope for a discrete escape (such as in LQG) is limited by theunderlying mathematics of infinite divisibility. The Dean paradox (and relatedlogical/mathematical paradoxes) endures at the formal level, even if physicalmeasurement is limited at the Planck scale
the dean dilemma
- If logic’s infinite divisibility is false, and reality (where motion or quantum processes occur) is true, LQG’s mathematical framework is falsified, as it relies on a logically incoherent continuum.
- Reality is Illusory: If logic’s infinity is true, and reality (discrete spacetime at the Planck scale) is illusory, LQG’s claims are logical constructs, not reality, undermining their validity, akin to Ptolemy’s epicycles.
the dean paradox
http://gamahucherpress.yellowgum.com/wp-content/uploads/The-dean-paradox.pdf
or
https://www.scribd.com/document/849019262/The-Dean-Paradox-science-mathematics-philosophy-Zeno
