Talk:Perpetual motion
Of course, if it consumes it's own components, it will not move perpetually. WAFI--PalMD-If it looks like a donut, eat it 14:32, 26 November 2007 (EST)
- Yes, I just read that and thought the same thing.--Bobbing up 14:36, 26 November 2007 (EST)
- Joe Newman came up with that one off the top of his head, apparently, to avoid being told his energy machine was a perpetual motion device. Not too many people bought it because it didn't make any sense. But then again, for technical reasons, high-voltage electric motors don't either. EVDebs 14:50, 26 November 2007 (EST)
- One of the most common thinking errors made in this field is forgetting that solar energy is basically free and largely invisible/discounted. The answer to the question "Where did the energy come from?" is usually "The sun".--PalMD-If it looks like a donut, eat it 14:54, 26 November 2007 (EST)
- The case of a very heavy pendulum bob, is an interesting one, Max Planck re-formulated and restricted the third law of thermodynamics soon after Walther Nernst proposed it in 1910. There may exist 'priority' of energy consevation. Momentum such as linear and angular momentum may have first priority? A heavy boat in water may be moved with less effort than a similar weight truck, there is less friction. with magnetic or air levitation even less motive force is required. So also with a motionless heavy pendulum, let's say for example, a ten tonne wrecker ball. they even come as big as 25 tonnes! Just leaning nonchalantly against it, one will observe a slight oscillation, the ten ton wrecker will 'lean back' on you periodially! in 1686 In his treatise Brevis demonstratio erroris memorabilis Cartesii ("a short demonstration of Cartesius' remarkable errors") Gottfried Wilhelm Leibniz formulated the definition of potential energy as product of force by height. Mathematical analysis and actual experiment will reveal that the energy required to swing this gigantic pendulum bob, is equal(ignoring air frictional losses) to the amount of energy that would be required to lift that weight through a height which the subtended 'arc' of swing lifts the weight, normal triganomatory. Of note the angular velocity at the bottom of the swing also equals the linear achieved velocity of the same mass falling from a similar height. Leonard Euler formulated 'Euler Force' to describe the variable 'centrifugal forces' as such a pendulum oscillates through it's subtended arc of swing. This Euler Force, like Centrifugal force, is always perpendicular to the axis of rotation. At the bottom of the pendulum swing the effective 'weight' of the pendulum bob is increased by the Euler Force Component. Conversely if the subtended arc of swing is large, then say at 90 degrees of arc, the bob is momentarilly suspended weightless in mid air! So a full 180 degree subtended swing of a pendulum bob weighing ten or 25 tonnes, would impose very severe structural loading on both the suspension beam and the thrust pivot bearing! not to mention the breaking strain of the cable! Of extreme importance, is the de facto 'fact of life' observation that very little effort is required to 'maintain' a pre-swinging pendulum. Professor Walter Lewin in his now famous 'wrecker ball' demonstration at the MIT Classical Mechanics Lecture Series (also on YouTube) cautioned his startled undergraduate audience, that he had to be extremely! careful not to impart the slightest force to the large cannon ball he was letting go. his head was placed against a resiliant brick wall, and he did not want his skull crushed! The bob returned in accordance with the Laws of Consevation of Angular Momentum to within an inch of his nose! (a miss as good as a mile, phew!) The same would be perfectly true for a real wrecker ball, a slight shove and the wrecker ball could turn you into a casualty patient, if not strawberry jam! Now let's observe the beam and the pivot thrust bearing. The beam say, is a substantial steel girder, It can visibly be observed to flex with each maximum Euler Force. An intesting experiment is to incorporate a heavy goods vehicle suspension spring and shock absorber onto the pivotal thrust bearing, so that the 'axis perpendicular' Euler Forces are compressing that truck suspension mechanism at regular intervals. The wrecker ball still only requires a very gentle shove now and again, but now the shock absorber is heating up so hot it cant be touched and is in danger of exceeding it's design parameters. Vast amounts of heat are being generated for virtually no mechanical input. This experiment clearly demonstrates that just as Max Planck had to re-formulate and restrict Walther Nernst's third law of thermodynamics, the time is long overdue for the same much needed restrictions and reformulations to apply to the First Law of Thermodynamics and the resultant consevation laws as well...."How sad that so often funeral directors herald advances in scientific understanding!" Science is the most reliable map we have to guide us in our search for knowledge. Maps are of little use without signposts on the ground. "DANGER ERROR" would make one such useful signpost. (Alastair Carnegie, Chaplain, R.M.P.T.A., Visitor D.A.M.T.P Camb. 3450th Technical Training Group, 3400th Technical Training Wing, Lowry AFB. Stationed RAF Lakenheath, Feltwell & Mildenhall UK. 8th July 2008)— Unsigned, by: 195.93.21.106 / talk / contribs
- Very nice, thank you... ħuman
01:28, 9 July 2008 (EDT)
- Very nice, thank you... ħuman
- The case of a very heavy pendulum bob, is an interesting one, Max Planck re-formulated and restricted the third law of thermodynamics soon after Walther Nernst proposed it in 1910. There may exist 'priority' of energy consevation. Momentum such as linear and angular momentum may have first priority? A heavy boat in water may be moved with less effort than a similar weight truck, there is less friction. with magnetic or air levitation even less motive force is required. So also with a motionless heavy pendulum, let's say for example, a ten tonne wrecker ball. they even come as big as 25 tonnes! Just leaning nonchalantly against it, one will observe a slight oscillation, the ten ton wrecker will 'lean back' on you periodially! in 1686 In his treatise Brevis demonstratio erroris memorabilis Cartesii ("a short demonstration of Cartesius' remarkable errors") Gottfried Wilhelm Leibniz formulated the definition of potential energy as product of force by height. Mathematical analysis and actual experiment will reveal that the energy required to swing this gigantic pendulum bob, is equal(ignoring air frictional losses) to the amount of energy that would be required to lift that weight through a height which the subtended 'arc' of swing lifts the weight, normal triganomatory. Of note the angular velocity at the bottom of the swing also equals the linear achieved velocity of the same mass falling from a similar height. Leonard Euler formulated 'Euler Force' to describe the variable 'centrifugal forces' as such a pendulum oscillates through it's subtended arc of swing. This Euler Force, like Centrifugal force, is always perpendicular to the axis of rotation. At the bottom of the pendulum swing the effective 'weight' of the pendulum bob is increased by the Euler Force Component. Conversely if the subtended arc of swing is large, then say at 90 degrees of arc, the bob is momentarilly suspended weightless in mid air! So a full 180 degree subtended swing of a pendulum bob weighing ten or 25 tonnes, would impose very severe structural loading on both the suspension beam and the thrust pivot bearing! not to mention the breaking strain of the cable! Of extreme importance, is the de facto 'fact of life' observation that very little effort is required to 'maintain' a pre-swinging pendulum. Professor Walter Lewin in his now famous 'wrecker ball' demonstration at the MIT Classical Mechanics Lecture Series (also on YouTube) cautioned his startled undergraduate audience, that he had to be extremely! careful not to impart the slightest force to the large cannon ball he was letting go. his head was placed against a resiliant brick wall, and he did not want his skull crushed! The bob returned in accordance with the Laws of Consevation of Angular Momentum to within an inch of his nose! (a miss as good as a mile, phew!) The same would be perfectly true for a real wrecker ball, a slight shove and the wrecker ball could turn you into a casualty patient, if not strawberry jam! Now let's observe the beam and the pivot thrust bearing. The beam say, is a substantial steel girder, It can visibly be observed to flex with each maximum Euler Force. An intesting experiment is to incorporate a heavy goods vehicle suspension spring and shock absorber onto the pivotal thrust bearing, so that the 'axis perpendicular' Euler Forces are compressing that truck suspension mechanism at regular intervals. The wrecker ball still only requires a very gentle shove now and again, but now the shock absorber is heating up so hot it cant be touched and is in danger of exceeding it's design parameters. Vast amounts of heat are being generated for virtually no mechanical input. This experiment clearly demonstrates that just as Max Planck had to re-formulate and restrict Walther Nernst's third law of thermodynamics, the time is long overdue for the same much needed restrictions and reformulations to apply to the First Law of Thermodynamics and the resultant consevation laws as well...."How sad that so often funeral directors herald advances in scientific understanding!" Science is the most reliable map we have to guide us in our search for knowledge. Maps are of little use without signposts on the ground. "DANGER ERROR" would make one such useful signpost. (Alastair Carnegie, Chaplain, R.M.P.T.A., Visitor D.A.M.T.P Camb. 3450th Technical Training Group, 3400th Technical Training Wing, Lowry AFB. Stationed RAF Lakenheath, Feltwell & Mildenhall UK. 8th July 2008)— Unsigned, by: 195.93.21.106 / talk / contribs
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[edit] Fraudulent?
"Any claim of perpetual motion is fraudulent on its face". The Laws of Thermodynamics are a result of observation and experiment. They are "true" because everything that has been built or designed or observed seems to obey them. Apart from this overwhelming evidence, there is no "theorical" reason why they MUST be true (*). A perpetual machine would be nothing more and nothing less than an experiment falsifying one of the Laws, and as such it would be welcome by the scientific and technical community. Still, don't open if a self-identified perpetual machine designer knocks at your door. (Editor at) CP:no intelligence allowed 05:52, 9 July 2008 (EDT)
- (*)At least in mechanics, I don't know about the Laws in other more scientific fields.
- I agree, especially as I had read the article lately. The "assumption" that any such machine automatically voided "Laws" of physics that we have have never observed to be false, is obviously suspect. ħuman
06:40, 9 July 2008 (EDT)
- Actually, the first law of thermodynamics (and other laws) are a consequence of Noether's theorem. NightFlareStill doesn't have a (nonstub) RWW article. 15:09, 9 July 2008 (EDT)
- I agree, especially as I had read the article lately. The "assumption" that any such machine automatically voided "Laws" of physics that we have have never observed to be false, is obviously suspect. ħuman
[edit] Pseudo-Science?
>"Any claim of perpetual motion is fraudulent on its face".
That is an axiomatic claim, and only supported by heresay testimony. There is, as you correctly identify a very high probability that claims of over-unity devices are fraudulent. A confidence trickster's gold mine! We can speculate whether in 1100 C.E. when the indian astronomer and mathematician Bhaskara describes a perpetuum mobile made of a wheel with containers attached to its rim, partly filled with mercury, was also one of these con-artists. The Royal Executioner would know how to deal with him! if caught out. Gold, though massive, actually floats on mercury, so would be ideal for testing "The brachistochrone problem", which was posed by Johann Bernoulli in Acta Eruditorum in June 1696, and solved by both Gottfried Wilhelm Leibniz and Sir Issac Newton. If angular momentum is preserved. we have elegant proof that it is! then the brachistochrone curve allows the fastest route for the quicksilver to pass from one side to the other. This corrected Galileo Galilei's claim that a semi-circle was fastest.
It was Galileo Galilei who opposed the predominant aristotelian dogma (horror vacui) and introduced a combination of mathematical theory and experiment, today referred to as "scientific method". Horror vacui ca. 300 v.Chr. was the foundation stone of Hermann Helmholtz's 1848 proposition that underpins his "conservation of energy" principle. He was a Young Medical Doctor aged 26 at the time. He did not say "Because of the First Law of Thermodynamics, a Perpetual Motion Machine is impossible." as we do 'circulus in probando' today! His presentation to the Berlin Physical Society, reasoned that lack of success in constructing a PMM. persuaded him that some natural impediment prevented a PMM. and so consequently formulating his proposition as the 'Principle of Energy Conservation'.
The 'Bhaskara' quicksilver wheel, in my personal view probably works! A nice challenge for M.I.T. and D.A.M.T.P. (Dept. of Applied Mathematics and Theoretical Physics. Cambridge) I was their Visitor ca 1983/4 and later assisted Steven Hawking on his "Brief History of Time" (as the stand-in idiot!) Axioms, however persuasive, must always give way to fundamental laws. The physics of momentum and inertia have priority. we may not yet have discovered the 'Higgs' particle thought to explain 'inertia' but we are close! If a curve similar to the famous 'brachistochrone' curve can be calculated, such that a multiplicity of mercury filled glass tubes (bent into that curve's profile), might overbalance a wheel due to uneven Euler Forces, as the quicksilver pendulum-like oscillations flow through these bent glass tubes? i.e. in such a way that maximum Euler Force on one side coincides with minimum Euler Force on the other, and naturally "Vica-Versa" a stale mate! (The variable 'radius' of this hypothetical 'Bhaskara Curve' would periodically alter the angular velocity, allowing for a different frequency of oscillation on opposing sides of the 'Bhaskara Wheel'... then all that's needed is a length of velvet ribbon, borrowed from a bonnie straw hat, perhaps a pretty undergraduate punting with an escort under the Cam-bridge? and with a hot iron to smooth the velvet 'nap' in one direction, we can very easilly incorporate a velvet ratchet with a velvet uni-directional brake pad. or alternatively, dismantle a fishing real. (When the wheel wants to see-saw, tough luck! the ratchet stops it!;?) The great Bhaskara. may in time be entirely vindicated? I doubt a mathematician of his stature would swallow a circular 'circulus in probandum' logical fallacy "Hook Line & Sinker!"
Thanks for the prompt response, and sorry for my long reply!:?(... Fraud! GOOD POINT!;?) it happens too often!?! [Alastair Carnegie 9th July 2008]
- Um.... Gelileo would probably not be mentioning Newton's Laws of Thermodynamics. You do know Galileo died one year before Newton was even born, right?
- Also, please sign your posts with 4 tildes, like this: ~~~~ --Gulik 14:06, 9 July 2008 (EDT)
[edit] Silver
Nom for silver. ТyYarrr 21:04, 20 July 2011 (UTC)
- A bit more padding in the references first, perhaps. ADK...I'll bang your thumbtack! 11:03, 21 July 2011 (UTC)
- If anyone can find a decent answer to the question "would Boyle's Flask work with a superfluid?" they can win an internets. ADK...I'll receive your oak! 11:12, 21 July 2011 (UTC)
[edit] How about this.
I know that this doesn't really "create" free energy but I came across this idea the other day. My neighbour has installed an Air heat pump. Basically this takes ambient air heat, extracts it, concentrates it and expels cold air.
It is claimed to produce three units of energy for every unit used. This sounds suspiciously like "too good to be true". Especially if one considers the possibility of closing the system and using the output to power the input, although there would probably be some losses in the process.
But it still sounds like the closest thing to perpetual motion that I've heard of. Again, I understand that it's "just" moving energy from one place to another and no actually "creating" it but it surprised me. Thoughts?--Weirdstuff (talk) 19:54, 7 September 2012 (UTC)
- If you were to close the system, I highly doubt the output would be greater than the input. But I'm not a physicist. -- Seth Peck (talk) 20:04, 7 September 2012 (UTC)
- Well, claimed three out for every one in. If that's true you'd be able to tolerate some pretty big inefficiencies. But even if it's not presently practically possible it certainly sounds plausible in theory. But it's the whole concept that I find a bit doubtful - to close to "too good to be true" as I said before.--Weirdstuff (talk) 20:10, 7 September 2012 (UTC)
- You're basically talking about air conditioning in reverse. Yes, it consumes at least as much energy because the only way to "extract" heat from ambient air like that is through a compression/decompression cycle. The ratio talked about in the WP article is an efficiency ratio used for heat pumps - it's how much energy it can extract from the "hot" air per unit of electric that it consumes. That this is above 1 is obvious because otherwise the heat pump wouldn't be doing its job, and you may as well have used that electric to power a normal heater. It's not even close to perpetual motion.
sshole
20:34, 7 September 2012 (UTC)
- That was my feeling at first. I figured that, the best possible case, the output could only be equal to the input. But my neighbour has spent some three grand on the installation and claims it works. He also claims the same one in three out ratio. Though it's less efficient on colder days.
- This is really a cheap variant of the geothermal heat pump which takes the heat from low ground as its source (as opposed to using traditional "hot" rocks).
- Although they are more expensive systems to install they claim an efficiency of 3 to 6. But I'm still wondering about using the output to power the input. --Weirdstuff (talk) 10:04, 8 September 2012 (UTC)
- Though it's less efficient on colder days. Obviously, as it's ambient air where the energy is coming from.
narchist
11:08, 8 September 2012 (UTC)
- Well. Duh!--Weirdstuff (talk) 12:01, 8 September 2012 (UTC)
- Indeed.
pathetic
12:04, 8 September 2012 (UTC)
- Indeed.
- Well. Duh!--Weirdstuff (talk) 12:01, 8 September 2012 (UTC)
- Though it's less efficient on colder days. Obviously, as it's ambient air where the energy is coming from.
- You're basically talking about air conditioning in reverse. Yes, it consumes at least as much energy because the only way to "extract" heat from ambient air like that is through a compression/decompression cycle. The ratio talked about in the WP article is an efficiency ratio used for heat pumps - it's how much energy it can extract from the "hot" air per unit of electric that it consumes. That this is above 1 is obvious because otherwise the heat pump wouldn't be doing its job, and you may as well have used that electric to power a normal heater. It's not even close to perpetual motion.
- Well, claimed three out for every one in. If that's true you'd be able to tolerate some pretty big inefficiencies. But even if it's not presently practically possible it certainly sounds plausible in theory. But it's the whole concept that I find a bit doubtful - to close to "too good to be true" as I said before.--Weirdstuff (talk) 20:10, 7 September 2012 (UTC)
The point I am making is that this works (or claims to work) by taking in ambient air, cooling it, and in the process obtaining more energy than that which was input as electrical energy. It is (or is claimed to be, or is sold as providing) a method for heating water at a third of the cost which it would otherwise cost.
If this is true (and I'm saying if) then it would seem to be theoretically possible to power the thing off itself and thus get something which certainly would look like a perpetual motion machine in that it would withdraw ambient energy which could be used to continuously perform work with no input other than ambient air.
I was, and still am somewhat sceptical, of this; but the product is on sale in many places (though nowhere is it suggested that it could power itself, that's my own theoretical extension.)
I have not been able to find any site on the net which claims that the product is a fake. This site for example claims that they can provide "4 times the amount of energy they consume".
If RW feels that these claims are impossible then perhaps this technology needs its own article debunking it.--Weirdstuff (talk) 18:53, 8 September 2012 (UTC)
- It's analogous to saying that the energy required to transport coal from a mine to a power station is less than the output of the power station thanks to burning the coal, ergo it's like perpetual motion. The energy is derived from diabatic cooling of a unit of air. You require power to do this, and can gain more heat than you would simply by using that electricity to run a heater (you're effectively "fuelling" the system with warm air), but it's not a violation of conservation of energy and doesn't really require debunking. If anything requires debunking, it's the confusion between a heat pump's coefficient of efficiency and perpetual motion. These aren't the same thing.
theist
22:53, 8 September 2012 (UTC)
- I don't remember the exact efficiency but I have one of these things installed and it works fine. --83.84.137.22 (talk) 10:53, 9 September 2012 (UTC)
- Really? That's interesting. How much of an energy saving do you think you're getting?--Weirdstuff (talk) 12:24, 9 September 2012 (UTC)
[edit] An actual perpetual motion machine
The internet.
Get the right 'weird, oddball or nuts' memes therein and they will circulate round the tubes endlessly - and spawn 'new and improved memes' that are even more dingbat. 171.33.222.26 (talk) 18:02, 10 June 2013 (UTC)
bomination 21:55, 10 June 2013 (UTC)
[edit] Sources for Mr. Gravitational-Waves-Don't-Real
Just keeping it clean on the regular page. They aren't perfect as it took only a few minutes to find them, but they're something.
- Space is Near-Frictionless: http://helios.gsfc.nasa.gov/qa_sp_ms.html#friction
- Binary Neutron Stars and Collapsing orbits: http://iopscience.iop.org/2041-8205/757/2/L21
- Calcs showing Earth orbital decay won't outlast Sun's expansion: http://www.tapir.caltech.edu/~chirata/ph236/2011-12/lec15.pdf
Can some folks dig up some more reliable sources? Noir LeSable (talk) 19:14, 5 January 2015 (UTC)
[edit] Unlikely Theories
If there was ever confidence in perpetual motion, it has waned because of the number of fraudulent cases. Proving perpetual motion is now truly like winning the lottery. More than that, it is like winning all the lotteries that ever existed.
Nathan Coppedge is a hobbyist who theorizes that he does not need to discount Newtonian mechanics, but only thermodynamics.
He introduces an elaborate array of principles to defend the idea that simple perpetual motion is possible:
The Principle of Volitional Efficiency: combining an efficiency principle such as 0.5 with an advantageous principle such as 2 would result in a larger number. He calls this "volitional mathematics" [1]. The Principle of Momentum without Velocity: if an object can be tethered on a slope, there is such a thing as perpetually sustained tautness, which at least doesn't have to happen vertically, so perhaps it isn't a gravity force. The Principle of Equilibrization: two equal weights will move to equilibrize.
In addition, he provides "3 Proofs" of perpetual motion [2]: 1. Friction does not prevent motion where motion is permitted. 2. Dominoes can chain-react in a circle, wheels can turn. 3. Dominoes can chain-react using higher and higher altitudes. Energy can be created.
Collectively, these types of simple, combinatorial principles show the ultimate boundary of physical interactions.
The principle of the proofs was to demonstrate that thermodynamics was wrong. However, they do not disprove the universal function of thermodynamics on non-mechanical systems. They merely pose the possibility that interaction is of greater importance than previously thought.
Even if it is an ultimately flawed principle, it certainly contributes to the philosophy of perpetual motion. As far as physics is concerned, it remains a highly unlikely story.
- I don't know how exactly what is the relevance of this to the rest of the article.--ZooGuard (talk) 18:47, 14 March 2015 (UTC)
- I'm citing that the case similar to winning the lottery should be incorporated, for the sake of the scientific method. As long as proof depends on evidence, there remains a very small shadow of a doubt, which should be addressed. I'm not saying all things are possible, just that scientific theories are turned over now and then. For example, mathematics was considered very strong before Incoherence theory showed up. It's not that math is wrong, it's just that the new theory required a revision of the understanding. ---Veulm (talk) 19:17, 14 March 2015 (UTC)
- How do I get this part of the article reinstated? Should I revise? Relocate? Start a new article?---Veulm (talk) 19:30, 14 March 2015 (UTC)
- If there is genuine contradictory evidence of any kind, this means that there could be an exception, possibly. Even if it is only a theoretical exception. For example, Maxwell's Demon is considered an
exception. Veulm (talk) 19:45, 14 March 2015 (UTC)
- "IF". Maxwell's demon isn't an exception; it's a thought experiment. Sorry! Scream!! (talk) 19:58, 14 March 2015 (UTC)
- I did a lot of editing, but now the old article has been reinstated. Should I keep the content as it appears now?Veulm (talk) 21:03, 14 March 2015 (UTC)
- Don't edit things that have already been responded to. Start afresh if you must. Scream!! (talk) 21:15, 14 March 2015 (UTC)
- Personally I can't quite see what is going on. I there some element of the article you disagree with Veulm? What is your objective? Cheers. --Bob"I think you'll find it's more complicated than that." 21:19, 14 March 2015 (UTC)
- The point I'm making is that there are principles which are considered fringe science which actually work, only they haven't been used to build a perpetual motion machine yet. The theoretical importance seems significant, because science popularly is open to critical revisions. Veulm (talk) 21:33, 14 March 2015 (UTC)
- Ah. Then you are going to have a problem I'm afraid. We are only really interested in established tested science. If you have a "fringe" theory which you are trying to promote then I'm afraid this isn't the site for it. And you will have the same response in wikipedia. Sorry.--Bob"I think you'll find it's more complicated than that." 21:44, 14 March 2015 (UTC)
- I'm not even sure that it's fringe science, because it involves commonly understood principles, like equilibrizing. This is not stuff that's impossible to prove. It's stuff that could be modeled on a computer, or demonstrated with common objects. Thinking of these as principles of over-unity is banal but also exceptional. I don't think it's deceptive, nor does it involve string theory or ambient energy. It's not something that's hard to think about.Veulm (talk) 21:56, 14 March 2015 (UTC)
- Ah. Then you are going to have a problem I'm afraid. We are only really interested in established tested science. If you have a "fringe" theory which you are trying to promote then I'm afraid this isn't the site for it. And you will have the same response in wikipedia. Sorry.--Bob"I think you'll find it's more complicated than that." 21:44, 14 March 2015 (UTC)
- The point I'm making is that there are principles which are considered fringe science which actually work, only they haven't been used to build a perpetual motion machine yet. The theoretical importance seems significant, because science popularly is open to critical revisions. Veulm (talk) 21:33, 14 March 2015 (UTC)
- Personally I can't quite see what is going on. I there some element of the article you disagree with Veulm? What is your objective? Cheers. --Bob"I think you'll find it's more complicated than that." 21:19, 14 March 2015 (UTC)
- Don't edit things that have already been responded to. Start afresh if you must. Scream!! (talk) 21:15, 14 March 2015 (UTC)