Since my first post in November 2006, there has been a consistent bias by editors of the Zeno's Paradoxes article towards unsubstantiated claims that are, in the main, contrary to Wikipedian policy.

Primarily, that bias of behaviour is one that could be defined as being 'deterministic' -- the idea that we may resolutely and precisely explain and detail, by way of mathematics, the actual movement of physical things (e.g. of arrows, runners and tortoises, as originally exampled by Zeno of Elea).

The assumptions, common to the vast majority of editors, is that mathematics (in various forms -- e.g. algebra, calculus, geometry) can account for the detail of physical movement, and thus be used to 'solve' the paradoxes.

However, while generally such treatments are useful in the field of engineering and various sciences, the minutia of movement (as is highlighted by the theoretical developments and experimental evidence of quantum mechanics) is not able to be meaningfully resolved by such mathematical methods. That is, the mathematical treatments cannot be substantiated as having direct and unambiguous correspondence with the actual movement of physical objects. In other words, the theories (frequently offered on the main article page) cannot be correlated with the facts (as has been repeatedly observed in the field of quantum mechanics).

The call for formal mediation was initiated to correct content on the main page that echoed the above bias - e.g. "mathematics can be used to calculate where and when the moving Achilles will overtake the Tortoise." While this statement is (sort of) true – in the sense that you can perform calculations that for practical purposes (taking into account the margin of error normally allowed for macroscopic objects), produce an apparent "where and when" in question – it doesn't follow, in light of evidence from quantum mechanics, that such calculations provide direct congruence with movement in all its minute details.

Reliable Sources have been routinely and repeatedly requested to be presented that support said 'deterministic' statements, but none have been provided. As a result biased statements and opinions on the main page have persisted, despite requests for Reliable Sources in support of them. In effect, a continued and persistent violation of Wikipedian policy has occurred.

This arbitration has been called to clarify the inappropriateness of such deterministic statements (e.g. as cited above, and one that is, at time of lodgement of this arbitration request, still resident on the main article page).

Despite the common and "almost ubiquitous" acceptance that the above-mentioned mathematical treatments "solve" the paradoxes, there is, to my knowledge, no competent physicist who will attest that such methods account for the actual minutia of movement of physical things.

The main article, in view of the intent of Wikipedia towards being a reputable encyclopaedia, would need to clearly limit, or contextualise any statements that infer or directly support deterministic (mathematical) solutions to Zeno's Paradoxes. That is, the encyclopaedia would need to contextualise the various (and widely accepted) theories as being unsubstantiated in fact, and thus are no more credible in real terms --despite appearances in favour-- than various other beliefs and superstitions.

Comment on arbitrators responses

Regarding the responses by Newyorkbrad, Riske and Steve Smith

The arbitration was called in light of the guidelines about behaviour, not content. Without going into detail ("content") statements have been, and continue to be made that are speculative, POV and not supported by Reliable Sources.

This is a matter of inappropriate process, not content.

Perhaps the arbitrators are biased in their approach and opinions on this deep philosophical matter, and thus should recuse themselves.

Please address the issues of inappropriate behaviour.

Reply to comment by Pohta ce-am pohtit

Are you meaning to infer or directly state that a period of time in excess of 3 years that still sees this dispute unresolved is "timely"? Could you indicate what you consider "timely" ... 5, 10 or perhaps 15 years?

In any event, the argument here is one of inappropriate process. Statements have been made that are not supported by Reliable Sources. Ignore the content. Stick to the issue of inappropriate behaviour, thank you.

I note, somewhat incredulously that you have provided a link to a mathematics page. Have you understood the arbitration request? -- that mathematics in ANY form cannot be used to precisely account for the minutia of movement. No competent physicist will assert that mathematics can do what you infer can be done.

You have indicated either lack of comprehension of the inappropriateness of behaviour, or a bias that would require you to recuse yourself.

Reply to response by Ansgarf (replicated on the Zeno's Paradox talk page)

I requested arbitration not because of the historical content about the paradoxes, but about claiming (or even inferring) that various beliefs, theories or literature, actually account for, or "solve" the paradox of physical movement. There's an important difference about reporting on the literature (and theories) and claiming that the theories "solve" the paradoxes.

This arbitration would not have been called IF the theories were put in their proper context -- that they remain unsubstantiated theories! and do not (at least not from the evidence I've seen) offer congruent, verifiable solutions to the paradoxes. Statements like "Using ordinary mathematics we can calculate, (or arrive) ..." are simply biased opinions with no basis in verifiable fact.

By all means report on those opinions, but to state that "using ordinary mathematics, we may ... " is wrong until proven and confirmed by a Reliable Source.

This arbitration is fundamentally NOT about content, but about the abuse of Wikipedian policy - in this case offering unsubstantiated theories that have no demonstrable basis in fact.

Statement by Ansgarf

On the topic:

Zeno's argues that movement is an illusion. To do this he describes the movement of a hypothetical tortoise and a hypothetical runner mathematically, to show that motion is in theory impossible. A mathematical treatment of Zeno's argument is therefore legitimate. And it is also legitimate to use Zeno's assumptions, like that the position of an object is defined as a point, that in between any two points there is another, and that motion is essentially the same at all scales.

The fact that these assumptions do not or may not hold for physical system is a separate issue. It doesn't invalidate any of the mathematics, it only invalidates the classical model Zeno assumed to describe motion. These issues are only tangentially relevant for Zeno's paradoxes, and are best discussed in the entries on Quantum Mechanics. To the limited extend that they are relevant, the current article does already mention them.

On Arbitration:

Mediation didn't fail, it was just never followed through.

Statement by JimWae

Statement by Pohta ce-am pohtit

The editors involved are much more likely to solve the content matter in a timely manner by raising the issue at WT:WPM. Pcap ping 16:29, 11 February 2010 (UTC)[reply]

Comment to NewYorkBrad: the argument here seems to be that the paradox cannot be "solved" in quantum mechanics due to the Planck length, which indirectly prohibits infinite-precision real numbers (see real computer). Of course, Zeno's paradoxes are usually envisaged in classical mechanics. Interesting discussion, but not an ArbCom matter. Pcap ping 16:56, 11 February 2010 (UTC)[reply]

Clerk notes

This area is used for notes by non-recused Clerks.

Arbitrators' opinion on hearing this matter (0/5/0/0)

Decline. This appears to be purely a content dispute. I see no arbitrable user-conduct issues at all. For what it is worth, I think that the weight of reliable sources supports the geometric-series resolution of the "paradox", despite the filing party's disagreement. Newyorkbrad (talk) 16:24, 11 February 2010 (UTC)[reply]
Decline per Newyorkbrad, although I have no opinion on resolving Zeno's paradox. Risker (talk) 16:28, 11 February 2010 (UTC)[reply]
Decline: ArbCom, much like the rest of Wikipedia, does not resolve content disputes. Steve Smith (talk) 16:59, 11 February 2010 (UTC)[reply]
Decline. I've noticed that mediation was accepted but not followed up, perhaps the parties may want to give it another try? - Mailer Diablo 12:43, 12 February 2010 (UTC)[reply]
Decline - if you didn't follow through with the mediation, it is your next obvious port of call Fritzpoll (talk) 13:57, 12 February 2010 (UTC)[reply]

@@ Line 105: / Line 105: @@
 :''This area is used for notes by non-recused Clerks.''
-=== Arbitrators' opinion on hearing this matter (0/4/0/0) ===
+=== Arbitrators' opinion on hearing this matter (0/5/0/0) ===
 *'''Decline'''. This appears to be purely a content dispute. I see no arbitrable user-conduct issues at all. For what it is worth, I think that the weight of reliable sources supports the geometric-series resolution of the "paradox", despite the filing party's disagreement. [[User:Newyorkbrad|Newyorkbrad]] ([[User talk:Newyorkbrad|talk]]) 16:24, 11 February 2010 (UTC)
 *'''Decline''' per Newyorkbrad, although I have no opinion on resolving Zeno's paradox. [[User:Risker|Risker]] ([[User talk:Risker|talk]]) 16:28, 11 February 2010 (UTC)
 *'''Decline''': ArbCom, much like the rest of Wikipedia, does not resolve content disputes. [[User:Steve Smith|Steve Smith]] ([[User talk:Steve Smith|talk]]) 16:59, 11 February 2010 (UTC)
 *'''Decline'''. I've noticed that mediation was accepted but not followed up, perhaps the parties may want to give it another try? - [[User:Mailer diablo|Mailer Diablo]] 12:43, 12 February 2010 (UTC)
+*'''Decline''' - if you didn't follow through with the mediation, it is your next obvious port of call [[User:Fritzpoll|Fritzpoll]] ([[User talk:Fritzpoll|talk]]) 13:57, 12 February 2010 (UTC)