Overview
Standard scientific beliefs are that when we move, say a finger through a small distance, it does so by moving through an infinite number of very small "infinitesimal" steps. This proof asks a very basic question: What is the electrical, chemical activity in the body that can account for, and control that infinitestep process?
Introduction
Proving the impossibility of physical movement,
using the assumptions of modern science
This proof, based on the assumptions of modern science and medicine, reveals how we are unable to move our bodies even for the simplest of tasks, such as blinking an eye, or lifting a finger. In view of our easy ability to blink, or move a finger, we may confidently conclude that standard scientific theories  reliant on the assumption of 'perfectly contiguous and continuous' movement  are inappropriate and incorrect at the microscaled dimensions of spacetime, but approximately correct in the macroscaled events of everyday life.
As is more fully explained in this proof, modern deterministic science (including and especially medical and biological science) requires that
This expectation (of perfect biological determinism) is unable to accommodate the quantum facts: the majority of contemporary science is based on incorrect assumptions. A new scientific paradigm is required.

Scientific Assumption #1: The standard, widelyaccepted scientific solution for explaining the paradox of physical movement (often referred to as Zeno's Paradoxes) is fully resolved by the mathematics of infinite series  that we are able to traverse each point in an infinite sequence of small 'infinitesimal' contiguous and continuous steps in finite time, thus enabling everyday movement of our bodies etc.
In particular, the assumption of, and reliance on a onetoone correspondence of mathematical values with actual physical quantities (e.g.. position, velocity) is required. It is never assumed or stated that the mathematical points (in whichever equations or formula) are entirely unrelated to physical reality: that would make the mathematical expressions a 'nonsense' exercise. The assumption is that we are able to traverse each point in an infinite sequence of 'infinitesimal' contiguous physical steps in finite time, thus enabling everyday movement of our bodies etc.
 Scientific Assumption #2: Neurological activity (namely, electrical activity in the brain, electrical signaling in the body) is the cause for all our thoughts and feelings (awareness).

Scientific Assumption #3: Physical movement of our bodies directly corresponds to, and results from neurological activity, and that 'subconscious' processes are still the result of neurological activity. Any movement of bodies, or parts of bodies is controlled by neurological processes that start, continue and stop such movements. That is to say
for each and every physical effect (i.e.. for each and every infinitesimal physical step) there MUST BE an identifiable physical (NEUROLOGICAL) cause 
Scientific Assumption #4: Each thought, choice and movement we initiate originates with some identifiable electrical activity in the brain (namely, with the firing of neurons) and/or within the body, in accord with Scientific Assumption #3.

Scientific Assumption 1 requires that for some arbitrary movement of our bodies, or of parts of our bodies such as a finger, it must move through an infinite number of small "infinitesimal" increments. Each of these increments must have an identifiable physical cause  Assumption No. 1 requires there to be some identifiable electrical or chemical process for each step. The firing of neurons in the brain is commonly accepted as being one of the processes involved in causing physical movement in our bodies.
However, we do not have infinite neurons in the brain. Nor do the limited number of neurons (although vast in number) fire infinitely many times in order to be responsible for the required infinite number of incremental movements.
In any event, the carriers of electrical signals (electrons, ions) required for muscular contraction and movement are quanta that, according to quantum theory, do not move continuously, thus do not provide the continuity of signal and muscular movement required by point 1*."
 Scientific Assumption 1 in conjunction with Assumption 3 requires that for each and every one of the infinite infinitesimal movements, including movements that must occur at and below the Planck length, there must be some identifiable physical, neurological cause. That is to say, the standard, widelyaccepted infinite series solutions to Zeno's Paradoxes requires that our physiology initiates movements shorter than the Planck length – well beyond any measurable limits of quantum theory, and well beyond any known neurological/physiological/quantumphysical processes. On this basis one or more of the above assumptions must be invalid. 1,2
 Physical movement of our bodies, when based on these Assumptions is categorically impossible since the neurological activity that necessarily causes infinite infinitesimal subPlanckscaled physical movements, has yet to occur, and cannot occur.
** For more indepth analysis, refer "The modern superstitions of science and religion"
Important footnote:
It is often suggested that what "carries" ions and quanta through the necessary subPlanck incremental positions is 'momentum'. Momentum is a property  it's related to velocity (momentum is velocity x mass of an object). Like velocity it is not a cause of the movement of mass. The question remains: what interrupts, interjects, or in some way 'tracks' that momentum through infinite subPlanck increments that (by necessity of the infiniteseries assumptions) exist well beyond any physically observable qualities? How does the finite track, follow, correspond to, and control an infiniteseries of subPlanck movements?
 1. Either that or the experimental evidence and the theoretical limits of quantum mechanics, together with the Heisenberg's Uncertainty Principle and Bell's Theorem are all incorrect or can be invalidated.
 2. In addition, and as stated Scientific Assumption 1 involves absolute determinism, in that for each point within the infinite sequence of points when traversing any arbitrary length, there exists an associated physicality (measurable, tangible, physical 'particles' or frames of particles). In effect, movement of one's finger requires that it is composed of not only quantum particles, such as quarks, but also 'subquantum' particles  'superquarks', and 'supersuperquarks' ... ad infinitum. Thus, string theories and other theories involving multidimensional solutions (that extend beyond our tangible 3dimensional physicality) are disallowed by the strict deterministic requirements of Assumption 1, again confirming that physical movement, when based on these assumptions, is impossible.