Overview
There is now ample theoretical and experimental evidence that ought to motivate serious thinkers towards adopting a new, expansive worldview  one that eclipses the standard scientific view that physical things (genes, viruses, physical forces) are the sole cause of physical effects (bodies, behaviours etc.)
The section Zeno's Paradoxes at this site provides a number of useful thoughtexperiments, and related blog posts that clearly demolish the standard scientific worldview.
A new holodynamic, "discontinuous space  continuous metareality" is now required. The social benefits of adopting such a worldview would be "revolutionary".
Details
This content is provided as a resource to clearly illustrate how mainstream scientific thinking (of there being physical causes for all physical effects) is now untenable in the face of the latest quantum physics (e.g. how plants use nonlocal, atonce energy pathways to photosynthesize light).
Modern science is largely based on a deterministic, Newtonian clockwork model of our universe.
Thoughtexperiments and laboratory experiments can be performed to reveal how those models are now, in the minutia of quantumscaled increments of movement, incorrect.
The idea that we can apply calculus (infiniteseries) to solve a vexing philosophical problem dating back to Ancient Greek times, is now confirmed wrong.
As the renowned physicist Prof. Richard Feynmann explained "the simple ideas of geometry extended down into infinitely small space is wrong."
The arguments (facts and supporting evidence that the deterministic basis upon which infinite series solutions to Zeno's Paradoxes are reliant is untenable) are:

[Reference article: An experimental test of nonlocal realism]:
"Most working scientists hold fast to the concept of 'realism'  a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affect by actions in spacelike separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of 'spooky' actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such nonlocal realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for nonlocal realistic theories. Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned."Conclusion: in particular "we show by both theory and experiment that a broad and rather reasonable class of such nonlocal realistic theories is incompatible with experimentally observable quantum correlations".
In light of this experimental evidence, there are insufficient grounds for assuming that infiniteseries solutions, reliant on localism ''and'' realism are valid or tenable. The application of infiniteseries to the movement of objects (Zeno's arrow, runner, tortoise etc) requires that at every position and point in time, those objects remain physically real and local. They necessarily must remain local due to the deterministic correlations of actual position with the calculated position. Similarly, by using infiniteseries the objects must remain entirely 'real' (tangible, measurable, observable) at any and every point.
The evidence and quantum theory has shown the assumptions of locality and realism to be invalid. For infiniteseries solutions to meaningfully resolve the paradoxes, experimental evidence would need to show how localism and realism (upon which infiniteseries are entirely reliant) can be substantiated. Based on the available evidence, infiniteseries solutions are not able to meaningfully resolve the paradoxes (not even as a "proposed solution").
This research demonstrates that the assumptions upon which modern deterministic science (e. g. belief in biological determinism, as evidenced by the expectation that understanding the human genome will enable "cures" of diseases) is based, are incorrect.
Readers may wish to review Fig. 3 (of the referenced article [http://arxiv.org/pdf/0704.2529v2) which displays the "Experimental violation of the inequalities for nonlocal hiddenvariable theories (NLHV) and for local realistic theories (CHSH)"
It should be evident that infiniteseries are based on a local realistic (CHSH) model, which according to the evidence is clearly not within any reasonable range of error, in regards to the data. In fact the CHSH (infiniteseries) model (flatline) reveals an almost complete lack of correlation with the data (strikingly, Fig.3.b. reveals an extraordinarily similar lack of correlation as would be typical of how little a flatearth view correlates with the curved/round earth).
For any reasonable thinker who reviews the data, infiniteseries solutions are untenable models that, even though they offer crude approximations sufficient for practical use by engineers, provide no credible resolution to Zeno's Paradoxes.

The de Broglie wavelength of an object (e.g. Zeno's arrow) is : λ = h/p (where p = momentum). The '''infinitesimal precision''' of the object's position or any part thereof ('''as required by infiniteseries solutions''') requires that λ$$ approaches zero (since the de Broglie wavelength of the object indicates the range of possible positions and momentums of the object).
From the Wikipedia entry on Matter_waves "given the enormous momentum of a person compared with the very tiny Planck constant, the wavelength of a person would be so small (on the order of 10^{−35} meter or smaller) as to be undetectable by any current measurement tools".
However, the infiniteseries solutions require that the precise and exact location and speed of Zeno's runner can be calculated.
For this to be applicable to a runner (even for a heavy runner, at considerable speed) λ$$ must approach zero (to ensure a short sharp pulse with infinite precision, exactly matching that of infiniteseries). However as λ$$ approaches zero, p (momentum = mass x velocity) approaches infinity. Thus, to precisely predict (calculate) a runner's location at some arbitrary point in time t (as is expected using Newtonian mechanics/infiniteseries), requires the object to have infinite mass, and/or infinite velocity.
Despite the fact that the calculated wavelength for a runner, tortoise or arrow might be immeasurably small (short), it is still some finite wavelength. This finitewavelength categorically conflicts with the necessarily infinitelyshort wavelength required by infiniteseries. This undeniably rules out infiniteprecision/infiniteseries predictions of when the runner will overtake the hare.
The inability to calculate (even in theory) when the runner will (precisely) overtake the hare is not due to clumsy scientists, with fat fingers using blunt measuring instruments.
Many respondents on the talk page confuse the inability to experimentally measure the speed and location of objects as being a limitation of technology. Quantum theory requires that in theory, the uncertainty is an aspect of deep reality, and unrelated to whatever apparatus or means is used to measure or observe the object.
Based on this simple analysis, infiniteseries cannot be meaningfully applied to Zeno's Paradoxes.