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Idealised 'medium' in which the speed of light has its defined speed

I agree that there is an idealised 'medium' in which the speed of light has its defined speed and that this medium is practically unobtainable but, at the moment, BIPM refer to this medium just as 'vacuum'; so should we. Do you not agree? Martin Hogbin (talk) 11:07, 25 December 2011 (UTC)

I agree that any quote from BIPM or NIST should use their wording, which in the case of their definition of the speed of light refers to 'vacuum'. I don't think we have ever disagreed about this point.

I am happy that you agree that there is an idealized medium where c=c₀, which I would refer to a bit differently, maybe, as being "unobtainable in principle", rather than "practically unobtainable".

The unaddressed question, where we might have some residual disagreement, is as to the electromagnetic properties of this hypothetical (or maybe inaccessible is better) ideal medium, which I would take as the defined c, c₀, μ₀ and the subsidiary derived properties with the exact values ε₀ and Z₀. What is your view of this point? Brews ohare (talk) 21:08, 25 December 2011 (UTC)

I gather from the lack of any response to this query that your interest in this matter has lapsed? Brews ohare (talk) 15:57, 30 December 2011 (UTC)

Not quite, but I am trying not to argue unnecessarily. The relation between the EM constants and the speed of light is based on Maxwell's equations. These may not always be the appropriate equations to use. Martin Hogbin (talk) 17:05, 30 December 2011 (UTC)

Martin: While the speed of light in any medium can be determined from Maxwell's equations if the medium's permittivity and permeability are known, that fact is separate from the observation that the BIPM has defined c₀ and μ₀, and has also specified that ε₀ is given an exact value by the definition ε₀≡1 ⁄ (μ₀c₀²). Of course, this relation follows from classical electromagnetism, but the adoption of this formula by the BIPM is nowhere identified by them as a consequence of Maxwell's equations, and they have nowhere endorsed classical electromagnetism. Rather, the relations between the EM constants is a choice of definitions made by a standards committee based upon metrology, not upon a theory . Brews ohare (talk) 17:34, 30 December 2011 (UTC)

To follow up, the utility of the relation ε₀≡1 ⁄ (μ₀c₀²) as a property of a reference 'vacuum' depends upon many factors. Any philosophical stance regarding the "physical significance" of the standard is secondary. Brews ohare (talk) 17:52, 30 December 2011 (UTC)

BTW, the reference to the formula ε₀=1 ⁄ (μ₀c₀²) can be found in Table 1, p. 637 and following the equation for the fine structure constant here. Brews ohare (talk) 18:16, 30 December 2011 (UTC)

Metrology

Martin: Perhaps it would be interesting to explore the metrological aspect a bit. Why would the standards committee elect to choose a reference state with exactly defined properties, and why these particular properties?

My notion is that you and Steve Byrnes think this was done out of expediency on a provisional basis that will be abandoned should it evolve that we can measure the electromagnetic properties of vacuum more accurately. More than that, you both wish to read some deliberate ambiguity into the mention of 'vacuum' in the official definition of the metre and the speed of light, despite the posting of its exactly defined electromagnetic properties. You imagine that the goal is to avoid any change in wording as measurement advances, because 'vacuum' can be retained in these definitions, even though its meaning will have changed.

I'd suggest that when measurement evolves to the point that some very elaborate and expensive laboratory procedure allows very precise determination of the departure of a realizable vacuum from the reference 'vacuum' in a few highly specialized labs in a very few locations, it will have no effect whatsoever upon the adopted properties of the reference. There will be in fact absolutely no advantage in setting up a reference based upon a realizable vacuum and comparing against it, compared to comparing against the present unobtainable reference 'vacuum'. Just as there is no point today in comparing two wavelengths instead of two frequencies because wavelength comparisons are less accurate, comparison of a medium against a realizable vacuum only will introduce additional errors and expense. In contrast, by retaining the ideal reference, advances in measurement will find expression in a more accurate determination of the departure of any medium (including realizable vacuum) from the reference. Brews ohare (talk) 18:49, 30 December 2011 (UTC)

Sorry Brews but I do not know what to say because I cannot see what you are driving at. I think we should leave it and just stick to the wording used by BIPM. Martin Hogbin (talk) 18:35, 2 January 2012 (UTC)

Martin: I simply parroted your comments of 12 December and reasoned above that they are baseless from the view of metrology. Perhaps you could clarify what you do not understand? Brews ohare (talk) 15:18, 3 January 2012 (UTC)

Martin, are you unable to identify what statements of mine you are unable to follow? Brews ohare (talk) 15:24, 6 January 2012 (UTC)

Brews, I have no objection to the use of an unobtainable reference vacuum, it is your insistence of distinguishing between different kinds of ideal vacuum that I object to. Martin Hogbin (talk) 16:16, 6 January 2012 (UTC)

Martin: I have not referred to different kinds of ideal vacuum. Brews ohare (talk) 01:34, 7 January 2012 (UTC)

I have referred to an unobtainable reference vacuum as "an idealized medium with defined c, c₀, μ₀ and the subsidiary derived properties with the exact values ε₀ and Z₀." Brews ohare (talk) 01:57, 7 January 2012 (UTC)

This is a mere tautology. Of course c has its exact value in the medium in which the speed of light is exactly c. The same applies to the EM constants. Martin Hogbin (talk) 10:14, 7 January 2012 (UTC)

Yes, Martin, you have stated a tautology. I thought the question here was that you felt I had distinguished between multiple "ideal vacuums". Has that idea been put to rest? Brews ohare (talk) 15:36, 7 January 2012 (UTC)

You do not seem to be proposing anything that I disagree with. Martin Hogbin (talk) 00:03, 8 January 2012 (UTC)

Your recent answers

Hi Martin: I see you have replied to a query by a reader as to why the speed of light is an exact number. It seems to me another question is: If this is explained so clearly in the article, why are people asking questions about it? Of course, one can adopt the view that some readers can't read, or that the subject is basically beyond clear explanation. But it seems likely to me that the problem is not insoluble, it just has not been solved. The underlying difficulty is that the speed of light seems like a real thing, something measurable like the speed of a car, and a defined value seems to be something else. How will WP fix this problem? Brews ohare (talk) 04:27, 15 January 2012 (UTC)

I see the bee in your bonnet has started buzzing again. I do agree with you, however, that questions from readers can be taken as some indication that an article is not as good as it could be. I have the same view about the Centrifugal force article, where I think readers are confused by too much discussion of the historical usages of the word and the Monty Hall problem article, which I believe concentrates too much on a irrelevant complication, but let us leave those for the moment and concentrate on the Speed of light.

So far we have had just one 'complaint'. I often try to draw 'complainants' into discussion to try to find out exactly where there problem lies so that we can consider how the article might explain things better. Unfortunately may of them sense that they are being drawn into a hornets nest and do not respond.

What do you think of the replies given? Do you like the 'light-year' answer? Do you agree that the peed of light in light-years per year is exactly 1?

What would you suggest to improve the article? Not loads of stuff about EM constants and classical vacuums I hope. Martin Hogbin (talk) 10:05, 15 January 2012 (UTC)

Hi Martin: No, I don't think those things would be a clarification. It might help if it were pointed out that : Yes, the speed of light is a real speed and it can be measured, but not in SI units. So the discussion might take this form:

In SI units, the meter is not expressed as the length of some physical thing, but as the distance light travels in a given time of 1/299*** seconds. Consequently, the speed of light becomes 299*** m/s by definition. That opens the question of what can be done to determine the real speed of light? That has to be done using units of length that are not defined in terms of that speed, but are independent. For instance, it can be measured in wavelengths traveled per second for some particular wavelength of the light, as was once done, or in terms of electron wavelengths for a particular electron energy, or in terms of the spacing of atomic layers in a crystal. If it should happen by some as yet unknown mechanism that the speed of light actually changed in value, the speed we measured in wavelengths/s or atomic layers/s would change, but the speed in m/s, being defined, would not change but remain at 299*** m/s. Of course, this hypothetical change in the real speed of light would change how far the light traveled in 1/299*** s, so the real length of the metre would change too. One might reasonably ask why a unit of length is defined in terms of the speed of light this way, instead of the old-fashioned way. Those practical decisions made by standards organizations pertain to the field of metrology, and involve questions of reproducibility, measurement errors, availability, and utility of the standard. This particular decision on how to define the metre is discussed at length in the article metre.

Brews ohare (talk) 17:28, 15 January 2012 (UTC)

Oh dear, this really is the same bee. You ask '...what can be done to determine the real speed of light?' What do you mean by 'real speed'? Martin Hogbin (talk) 18:05, 15 January 2012 (UTC)

Martin: Methinks you are not trying too hard to understand. The 'real speed' is the speed that is measured in wavelengths/s or crystal layers/s that can (in principle) change if the second changes or if the speed of light changes, as opposed to the speed of 299***m/s which cannot change in principle even if the second changes or the speed of light changes. Brews ohare (talk) 18:16, 15 January 2012 (UTC)

What is not 'real' about the defined speed of light? We just accept that the length of the metre is subject to (very small) change. Martin Hogbin (talk) 18:23, 15 January 2012 (UTC)

Martin: This discussion is not about what 'real' means. It is about there being two different things: the speed of light in units where the speed of light can change in principle, and 299*** m/s that cannot change in principle. They have different behavior, so they are different from each other. Brews ohare (talk) 18:34, 15 January 2012 (UTC)

This matter is not resolved by noticing the metre can change (as is discussed in the sample paragraph); the changes that may occur in the metre do not affect the speed of light as 299***m/s. Brews ohare (talk) 18:47, 15 January 2012 (UTC)

Brews, you were the one who brought up the 'real speed' of light. Of course there are different ways of defining the speed of light with important differences in principle between them, but the way BIPM has chosen is to define the metre such that the speed in metres per second is a fixed constant. What is your objection to this? Why is it not the 'real' speed of light. Martin Hogbin (talk) 18:57, 15 January 2012 (UTC)

Martin: Again, you are changing the subject. First, I have no objection at all to the BIPM choice. It is based upon many practical matters that they are eminently qualified to weigh. That is not the subject here. The subject here is the clarification to the non-technical reader of a distinction between a system of units where the speed of light is defined as 299***m/s and the speed of light in other systems of units where length is not defined in terms of the speed of light. The present exposition of this difference at Speed of light is not clear to many readers. I've proposed what may be an improvement. You seemingly have not read it yet. Brews ohare (talk) 19:07, 15 January 2012 (UTC)

Brews, this is what you wrote just above, 'In SI units, the meter is not expressed as the length of some physical thing, but as the distance light travels in a given time of 1/299*** seconds. Consequently, the speed of light becomes 299*** m/s by definition'.

So far that is absolutely fine with me, although words to that effect already appear in the article, but perhaps it could be made clearer.

You follow with this with (my emphasis), 'That opens the question of what can be done to determine the real speed of light?'. What point are you trying to make here? Martin Hogbin (talk) 19:32, 15 January 2012 (UTC)

Martin, I see that this wording bothers you. So maybe a substitute is needed. Let me rewrite that phrase: 'That opens the question of the relation of the defined speed of light, which is exactly 299***m/s, to a measurement. That has to be done using units of length that are not defined in terms of the speed of light, but are independent.' ... and so forth. Brews ohare (talk) 19:55, 15 January 2012 (UTC)

I think that phrasing is better, so here is the proposal with this change:

In SI units, the meter is not expressed as the length of some physical thing, but as the distance light travels in a given time of 1/299*** seconds. Consequently, the speed of light becomes 299*** m/s by definition. That opens the question of the relation of the defined speed of light, which is exactly 299***m/s, to a measurement. That has to be done using units of length that are not defined in terms of the speed of light, but are independent. For instance, the speed of light can be measured in wavelengths traveled per second for some particular wavelength of the light, as was once done, or in terms of electron wavelengths for a particular electron energy, or in terms of the spacing of atomic layers in a crystal. If it should happen by some as yet unknown mechanism that the speed of light actually changed in value, the speed we measured in wavelengths/s or atomic layers/s would change, but the speed in m/s, being defined, would not change but remain at 299*** m/s. Of course, this hypothetical change in the speed of light would change how far the light traveled in 1/299*** s, so the length of the metre would change too. One might reasonably ask why a unit of length is defined in terms of the speed of light this way, instead of the old-fashioned way. Those decisions made by standards organizations pertain to the field of metrology, and involve practical questions about measurement errors, reproducibility, availability, and utility of the standard. This particular decision on how to define the metre is discussed at length in the article metre.

Brews ohare (talk) 20:04, 15 January 2012 (UTC)

Why not just say, 'The speed of light can be experimentally measured in units of length that are not defined in terms of the speed of light, but are independent, for example astronomical units. Martin Hogbin (talk) 20:07, 15 January 2012 (UTC)

Again I have no objection to, 'One might reasonably ask why a unit of length is defined in terms of the speed of light this way, instead of the old-fashioned way'. But, 'Those practical decisions made by standards organizations pertain to the field of metrology, and involve questions of reproducibility, measurement errors, availability, and utility of the standard' is only part of the story there are also good theoretical reasons why length is defined in this way. Martin Hogbin (talk) 20:11, 15 January 2012 (UTC)

Hi Martin: OK, you can add to the list of length units that don't depend upon the speed of light. One can argue why a.u.'s are a better example than the use of wavelengths of light as used today in interferometry, or electron wavelengths, used today in smaller dimensions, or crystal lattice spacings, used today to relate these two wavelengths. One can add to metrological considerations theoretical reasons (if you can think of any that can be explained in the context of an introductory exposition). But it appears that you accept the proposal, and are offering some suggestions for improving it? Brews ohare (talk) 20:19, 15 January 2012 (UTC)

The point about astronomical units is that they are a defined unit which I believe is still in current usage but any other unit that is actually used would be fine with me. Martin Hogbin (talk) 20:56, 15 January 2012 (UTC)

Wavelengths of light and of electrons are used extensively. For example, the BIPM maintains a listing on their site of recommended wavelengths, and the article length measurement provides some limited discussion. Brews ohare (talk) 21:06, 15 January 2012 (UTC)

I'd add that metrology is not above employing theoretical reasons in their decisions, but clearly the adoption of the definition is not primarily a theoretical matter, but one of commerce. Brews ohare (talk) 20:23, 15 January 2012 (UTC)

That is not my understanding so you would need a good secondary source for that. Martin Hogbin (talk) 20:56, 15 January 2012 (UTC)

We could discuss this later, but there is no need in the present context. My understanding as to the main impetus for this definition was the commercial need for a standard that was more reproducible and more precise than the old wavelength definition, and a definition independent of wavelength that wouldn't have to be changed every time a source with better frequency stability and narrower linewidth was invented. Brews ohare (talk) 21:06, 15 January 2012 (UTC)

Another factor was the need for a variety of measurements under very different circumstances, as in surveying vs. microchips, and practicality demanded use of different sources in different applications, and freedom from comparison of wavelengths with that of some standard source was achieved simply by relying upon their frequency. Brews ohare (talk) 21:25, 15 January 2012 (UTC)

Incidentally, the article astronomical unit is not written in a way that makes its independence from the SI units clear. It mentions the mean Earth-Sun distance, but abandons that as archaic and suggests that it is defined only as the theoretical orbital radius of an infinitesimal orbiting mass. It does say that the speed of light is 173.144 632 6847(69) AU/d, and suggests this was found by a comparison of ephemerides, a concept foreign to me, and to most people, I'd guess. I'd classify this choice of example as arcane, and this article as obscure. Brews ohare (talk) 20:47, 15 January 2012 (UTC)

I think they are still used by astronomers. Martin Hogbin (talk) 20:56, 15 January 2012 (UTC)

No doubt, but the quality of the article astronomical unit doesn't recommend its use here. Brews ohare (talk) 21:06, 15 January 2012 (UTC)

Maybe you know an intuitively simple and accepted definition of the astronomical unit of length that anyone can understand? Otherwise, it is hard to see that it is more understandable to the non-technical reader than, say, the spacing of atomic planes in crystal, or the wavelength of light? Brews ohare (talk) 21:33, 15 January 2012 (UTC)

Brews if you look at the article under the 'Astronomical measurements' you will see that it mentions that the speed of light can be measured in astronomical units and gives a very precise value for the result. I do not see the need to add any more. Martin Hogbin (talk) 23:46, 15 January 2012 (UTC)

Martin: The issue is not whether 173.144 632 6847(69) AU/d is a "precise" value or an "accurate" value, say compared to other values based upon interferometry, but whether stating the speed in AU/d is understandable to a non-technical person who has no idea what the AU is or whether it is based on the SI units or whatever. The article on AU isn't much help in figuring that out. Wavelengths of light or crystal lattice spacings are intuitively more obvious units for length, and are clearly not based upon SI units.

What strikes me more to the point, however, is whether you even would consider revising the speed of light article to make it clearer to the non-specialist how a defined speed differs from a measured speed? Maybe just by pointing out there is a difference? Brews ohare (talk) 00:20, 16 January 2012 (UTC)

One person has had trouble understanding why the speed of light is exact. There is therefore a case for making it clearer why this is so but I would suggest that one sentence is sufficient. On the other hand most people expect to be able to measure the speed of light in some independent units so I am not sure that an explanation for that is needed at all. I we had one we could just refer back to the earlier metal bar metre definition of the metre. Personally I would not want to devote more than a sentence or two to explaining all this succinctly. I am sure that the other regulars on the article will not support the addition of a long and rambling paragraph on the subject. Perhaps we should wait for some feedback from our original questioner. Martin Hogbin (talk) 00:48, 16 January 2012 (UTC)

Martin: Your remarks about the "other regulars" make me chuckle. The fact is that any attempt to change even a comma on that page will embroil one in a weeks-long battle over the way that added comma has completely altered the meaning of an absolutely perfect exposition arrived at only after painstaking negotiation among what should be acknowledged as world experts on the topic. However, I am gratified that we two have (in my view) managed to come to a pretty similar view of the subject. Thanks for the conversation. Brews ohare (talk) 01:17, 16 January 2012 (UTC)

Astronomical unit

Hi Martin: I've made some additions to the article Astronomical unit, mostly some added sources. It appears the AU is based upon setting a length scale so the measured positions of an assembly of solar system objects is best described theoretically using a very particular value for the gravitational constant. Because the measurements involve sensing light signals or echoing radar bounces the speed of light enters into the measurements. The article Astronomical unit makes no serious attempt to document what goes into the extraction of the speed of light from this comparison of theory and measurement, and the whole subject of where 173.144 632 6847(69) AU/d comes from is left to the imagination. Are you interested in fixing this discussion? Brews ohare (talk) 19:21, 16 January 2012 (UTC)

BTW, it appears that a wrinkle in this is that the metre is not well-defined for large distances because of unspecified (so far) relativity corrections, so the subject of converting an AU to metres could be interesting. Brews ohare (talk) 19:24, 16 January 2012 (UTC)

From this document (Chapter 1, Table 1.1 p. 18) it appears that the speed of light in IAU units is in fact defined to be c₀ of the SI units, and the error bar in the speed of light in AU/d is due to uncertainty in the AU, not due to any actual measurement of the speed of light itself. The AU is a length unit defined independently from the speed of light, but its length in meters is calibrated so the time of transit across an AU forces the speed of light to be exactly c₀ by definition. Brews ohare (talk) 22:33, 16 January 2012 (UTC)

That is, the transit time of light across 1 AU, τ_A, is set so that c₀τ_A = 1 AU. Brews ohare (talk) 22:38, 16 January 2012 (UTC)

Hi Martin: I'd thought that you felt the speed of light in AU was a measured value, and would be a bit surprised that in AU the speed of light is not measured at all, but defined to be the same c₀ used in SI units. Guess not, eh? Brews ohare (talk) 03:57, 25 January 2012 (UTC)

Your replies

Martin: I noticed with interest this exchange regarding the "exact speed" of light, and Blackburne's erroneous answer that it was a consequence of recondite implications of special relativity. I am unsure that your answer that you have to think quantum mechanically is a lot of help either.

One big problem here is trying so hard to be succinct in the intro that there is no explanation. The other problem is that some of those making the explanation don't understand the matter, always a bit of a tricky situation.

Is this an insoluble problem? If so, is it because of the contentious nature of revision on this page, or is it just hard to explain? Brews ohare (talk) 18:15, 14 February 2012 (UTC)

Kandahar massacre

Hi Martin,

Few days ago you expressed your concern about the use of the term 'shooting spree' as an appropriate title for the events in Kandahar on 11 March 2012, pointing out to "a serious and tragic matter" of this event. At the moment there is a discussion and a straw poll on this issue, with the suggestion to rename Panjwai shooting spree into Kandahar massacre. If you are still interested in this topic, you are very welcome to express your opinion there. --Potorochin (talk) 07:12, 16 March 2012 (UTC)

Your accusation

Martin, I don't like you making unsupported accusations, you have long history of doing this to me. Please explain how adding content like the section Plantings for the future is a promotional vehicle for Pooktre. Your unsupported comment of "the article ..... it has become the personal promotional vehicle for Blackash" I view as false, please back up your claim of my bad editing of tree shaping with diffs. Blackash have a chat 23:27, 27 March 2012 (UTC)

I have not accused you of anything, just pointed out how the article has, in my opinion, turned out. Qui s'excuse s'accuse. Martin Hogbin (talk) 21:31, 28 March 2012 (UTC)

So if I'm to understand correctly you where unaware that this comment of yours "I have left it alone just to see what would happen to it. Have a look yourself; it has become the personal promotional vehicle for Blackash"

throws a bad light on anyone who edited the article since you left it alone? Blackash have a chat 22:59, 28 March 2012 (UTC)

I might not phrase it as strongly, but, large parts of the article read as an advertisement for Pooktre. And I've never even heard of tree shaping before, nor do I have any knowledge of gardening. At first, I thought "Pooktre" had to be a French or pseudo-French work (like Le Parkour), as there was no way such advertising of specific financial or personal or artistic interests or methodology had gotten in to Wikipedia. St John Chrysostom ^Δόξα_{τω ^Θεώ} 15:44, 9 April 2012 (UTC)

I would be happy to save you a lot of time and effort and show you exactly what has happened at the 'Tree shaping' article. Of course, I would encourage you to thoroughly check out what I say but I think I can save you time. Martin Hogbin (talk) 21:15, 9 April 2012 (UTC)

St John Chrysostom by methodology I'm guessing you are referring to the methods/process section? I suggest you read a larger range of articles as there are various areas where techniques and process are outlined/explained in wiki articles. Wikipedia reflects what is in RS and if it's in RS then it ok to have in wikipedia. Also if you want to discuss the content of tree shaping, the correct place to do so is the at the talk page where there are up to 60 editors watching the page who may want to be part of the discussion. But please only discuss one point at a time, as most of the problems at the talk page have been caused by too many points discussed at the some time and it quickly becomes hard for editors to follow the discussions clearly. Blackash have a chat 07:11, 10 April 2012 (UTC)

Martin please answer my question to you above. Thanks Blackash have a chat 07:11, 10 April 2012 (UTC)

What question? Martin Hogbin (talk) 08:16, 10 April 2012 (UTC)

So if I'm to understand correctly you where unaware that this comment of yours "I have left it alone just to see what would happen to it. Have a look yourself; it has become the personal promotional vehicle for Blackash" throws a bad light on anyone who edited the article since you left it alone? Blackash have a chat 22:59, 28 March 2012 (UTC)

I have bolded my question within my earlier comment. Blackash have a chat 08:53, 10 April 2012 (UTC)

I believe that I have made my position quite clear above. Martin Hogbin (talk) 08:56, 10 April 2012 (UTC)

Dispute resolution survey

Dispute Resolution – Survey Invite Hello Martin Hogbin. I am currently conducting a study on the dispute resolution processes on the English Wikipedia, in the hope that the results will help improve these processes in the future. Whether you have used dispute resolution a little or a lot, now we need to know about your experience. The survey takes around five minutes, and the information you provide will not be shared with third parties other than to assist in analyzing the results of the survey. No personally identifiable information will be released. Please click HERE to participate. Many thanks in advance for your comments and thoughts. You are receiving this invitation because you have had some activity in dispute resolution over the past year. For more information, please see the associated research page. Steven Zhang DR goes to Wikimania! 11:21, 5 April 2012 (UTC)

regarding MHP RFC process

Regarding your question "In what way are you 'barred from trying to help'?"[1] This is my understanding of the sequence of events that led to the present situation:

1. Rick kicked the dispute up a level on 17 April at "Cutting to the chase" when he wrote (a) "Please indicate below who you'd rather keep this page on their watch list, me or Martin," making it a question not only of what content? but of which contributor?
2. Guy ran with this in his suggestion on 21 April at "Cutting DIRECTLY to the chase, minus the usual debates" when he wrote (b) "They disagree about something - something that we will not attempt to define," and (c) "Other editors are free to opine on the proposed method of resolution, but only Rick and Martin have to agree on it." That post also indicates the upshot would be that (d) "Whoever loses the vote will graciously step aside and let the winner have his way," which is consistent with quote (a).
3. Sunray formalized this on 27 April at "Proposed steps", including a provision known as point #3 that (e) "Input is requested from other regular editors on the proposed wording and parameters of the RfC." This is consistent with quote (c) above, but includes both the RFC wording and the decision process.
4. You objected on 28 April 2012 in that thread that (f) "point 3 is unnecessary and would go further and say that it is unhelpful."
5. Sunray accepted the objection later on 28 April 2012, writing (g) "As neither of them are in favour of point 3, I've struck that."

Thus, although things may not have been finalized, it is my understanding that, as things now stand, input from other regular editors on the proposed RfC is deprecated by the parties and the facilitator. This decision in quote (g) is consistent with the idea of quote (b) that it is up to the two of you to say for yourselves what you want to be decided; and the preference you expressed in quote (f) is very reasonable in light of quotes (a) and (d).

Frankly, although I agree with what I believe to be the general thrust of some of your ideas, the devil is in the details and it always seems to turn out more extreme than I can agree to. The exact same thing may be said about my impression of some of Rick's ideas. I feel that the choice before us, as expressed in quotes (a) and (d) although it is not currently incorporated in the terms of the draft RfC statement which does not yet have a preamble, is a sad state of affairs because you both have some good ideas. Unfortunately, even if the decision of quote (g) were reversed, I am not sure I could do much to turn the course of events. ~ Ningauble (talk) 20:30, 1 May 2012 (UTC)

As you will see, I struck out that statement.

What details of my proposal do you find too extreme? Martin Hogbin (talk) 23:01, 1 May 2012 (UTC)

Preparing an RfC statement

Would you be willing to begin discussion about an RfC statement? I've created a page for that purpose: User:Sunray/Discussion of Monty Hall RfC. Note that, although I roughed out some headings, and Rick has added to that, you would be welcome to modify (or suggest modifications to) the page. I simply wanted to create a space where the three of us could work on that task. We can modify it whatever way best achieves that aim. Sunray (talk) 05:21, 3 May 2012 (UTC)

I am happy to work in any way that fairly resolves this dispute. Martin Hogbin (talk) 08:47, 3 May 2012 (UTC)

editing

How can one tell this from the description above? Martin Hogbin (talk) 13:46, 4 May 2012 (UTC)

Pure formally you can't. However when cards are drawn, it is common in an not "overprecise" description, to make the obvious assumption, and make the necessary remarks when otherwise. Nijdam (talk) 16:24, 5 May 2012 (UTC)

That is my point, formally you cannot say which events are independent. So how does one formally set up a sample space when it is not possible formally to say which events are independent? Martin Hogbin (talk) 17:10, 5 May 2012 (UTC)

No, I guess you misinterprete what I say. I just meant that in a "common" description of an experiment, it is not done to be extreme precise. I.e. one does not say "I like to have precise two eggs for my breakfast" or "I'll draw precise one card from the complete deck of exactly 52 playing cards". Yet the description above of the game will be widely understood in only one way. Nijdam (talk) 10:08, 7 May 2012 (UTC)

Still following this. In the world of Patrick Jane, if the dealer always removed the same card at the start of the game, this introduces the possibility that the deck is rigged, as the dealer will have had to sort through for that card, and will therefore know the sequence of cards in the deck. I doubt that card sharping is what Nijdam has in mind though, so why otherwise would the draws not be independent? Or is it simply necessary to state this (the conditions thing), as it is necessary to state "an unbiased coin" in the coin toss problems. Where incidentally it should really also be necessary to state that the possibility of the coin landing on edge is excluded. Elen of the Roads (talk) 11:09, 28 April 2012 (UTC)

The rules of this type of discussion depend on the context and the participants. There are a number of conventions, such as urn problems where idealised concepts are understood. In this discussion I think Nijdam and I generally understand one another, so terms like 'a fair coin' and 'randomly drawn' are I think, understood by both. There are cases where we may have different conventions or understandings in mind and these sometimes lead to unnecessary argument. This is made worse by my tendency to be a little lax in my descriptions sometimes (I know what I mean).

The point where we seem to disagree is that I maintain that there is no mathematical or logical way to determine which events must be taken as conditions of a problem and that this decision can only be one of common sense or personal opinion. Attempts to give a mathematical answer just lead to a circular argument. Events which must be conditions are events which might reduce the sample space. The sample space must contain independent events. Independent events are not conditional on one another.

It seems to me that mathematicians have essentially thrown in the towel regarding the answers to this kind of question. If you look here you will see, 'The function f(x)\, mapping a point in the sample space to the "probability" value is called a probability mass function abbreviated as pmf. The modern definition does not try to answer how probability mass functions are obtained; instead it builds a theory that assumes their existence'. Martin Hogbin (talk) 13:55, 28 April 2012 (UTC)

They spring into existence fully formed? I kind of like that :) I guess I come at these problems more as a card sharper, and less as a mathematician, but I agree with you (I think). I cannot see how you can derive the conditions by mathematics - they must rather exist outside of the problem and drive the mathematics. Without the defined prerequisite "draw is random" the possibility always exists that the draw is not random for a variety of reasons - not just card sharping - but if such things as the way the dealer holds the cards, or returns a card to the deck affects the probability of the punter picking X card rather than Y card (as they do in magic - a good magician can guarantee the punter picks the 'right' card), this is psychology rather than mathematics. I think Nijdam really wants to be Mentor of Arisia - which would be pretty cool - but you can't really extrapolate the universe from a piece of fairy cake. Elen of the Roads (talk) 08:36, 2 May 2012 (UTC)

As Richard Gill pointed out, we are no nearer to knowing what probability means than we were 300 years ago. As you suggest in you card drawing example the only way we can guarantee to know the chances of drawing a specific card are is to essentially specify the answer. It is impossible to give the probability of drawing the ace of spaces from a standard pack of cards without specifying an infinite number of details or saying something like, 'drawn uniformly at random from a pack of 52 cards containing exactly 1 ace of spades' which effectively means, 'in a case where the probability of drawing the ace of spades is 1/52'. Many people may find this fact disappointing and believe that there should me some mathematical way of determining the probabilities of events but no one has succeeded in doing independently from a human state of knowledge.

Prof Seymann in his comment attached to the original Morgan paper sums things up perfectly, 'Without a clear understanding of the precise intent of the questioner, there can be no single correct solution to any problem. Thus, with respect to the three door problem, the answer is dependent on the assumptions one makes about the intent of the one who originally posed the question'. Martin Hogbin (talk) 11:29, 2 May 2012 (UTC)

On the ferry

I just returned from a visit to my son, and Monday night on the ferry a game was played (BTW I took part and won a 50 pound "eau de parfum" for my wife). The game is called 'Higher or lower'. Participants do have to choose whether the next drawn playing card will be higher or lower than the last one. The game starts with a complete deck of cards, and drawn cards are not replaced. The first card shown is just the 8 of clubs. What, Martin, will be your choice?Nijdam (talk) 10:15, 18 April 2012 (UTC)

Are aces high? What happens if they are the same value? Martin Hogbin (talk) 13:51, 18 April 2012 (UTC)

Aces are high, and by the same value, just a new card is drawn. Nijdam (talk) 21:25, 18 April 2012 (UTC)

OK, I am an optimist. I will go higher. Martin Hogbin (talk) 21:50, 18 April 2012 (UTC)

Why? Nijdam (talk) 09:55, 19 April 2012 (UTC)

I make it 24 cards higher and 24 lower than 8, so assuming the draw is random both should be equally likely. Martin Hogbin (talk) 15:29, 19 April 2012 (UTC)

Is it okay if I translate this into P(H1)=P(L1)=24/51, with "H1" meaning 1st draw is higher, and "L1" first draw is lower? Then suppose the 1st card drawn is 3 of spade. What would you decide (and of course: why)? Nijdam (talk) 20:41, 19 April 2012 (UTC)

That sounds like a definite 'higher' to me. Martin Hogbin (talk) 22:50, 19 April 2012 (UTC)

You're right of course, but you left out the why. Nijdam (talk) 14:29, 20 April 2012 (UTC)

4 cards lower, 44 higher? Martin Hogbin (talk) 14:38, 20 April 2012 (UTC)

Now in terms of probabilities. Nijdam (talk) 20:01, 20 April 2012 (UTC)

P(H2)=44/51 P(L2)=4/51 P(S2)=3/51 'S2' is the probability that the second draw will be of the same rank, I have slightly changed your terminology. Martin Hogbin (talk) 09:13, 21 April 2012 (UTC)

Which are the 51 cards? I.e. which card is not amongst the 51?Nijdam (talk) 20:12, 21 April 2012 (UTC)

3 of spades. Martin Hogbin (talk) 23:09, 21 April 2012 (UTC)

And what about the 8 of clubs?Nijdam (talk) 08:12, 22 April 2012 (UTC)

You said, 'Then suppose the 1st card drawn is 3 of spade', I thought you were suggesting an alternative start. Did you mean the next card? Martin Hogbin (talk) 09:14, 22 April 2012 (UTC)

The 8 of clubs is not part of the drawing, it is shown at the start as I mentioned, and as you reacted to. Nijdam (talk) 11:46, 22 April 2012 (UTC)

So, the 8 of clubs is removed from the pack and shown (draw 0) then on the first draw the 3 of spades is shown and removed from the pack. The question is what is the probability that the next card (draw 2) will be higher or lower than the 3 of spades.

On that basis P(H2)=43/50 P(L2)=4/50 P(S2)=3/50. Martin Hogbin (talk) 19:28, 22 April 2012 (UTC)

Is the P you use the same as my P?Nijdam (talk) 21:38, 22 April 2012 (UTC)

I think so. What am I missing? Martin Hogbin (talk) 22:00, 22 April 2012 (UTC)

The whole point! My P is the probability measure of a vase with 51 playing cards (no 8 of clubs) from which successively cards are drawn at random. Yours is clearly something different. Nijdam (talk) 22:22, 22 April 2012 (UTC)

The 8 of clubs is removed from the pack and shown (draw 0) then on the first draw the 3 of spades is shown and removed from the pack. The question is what is the probability that the next card (draw 2) will be higher or lower than the 3 of spades. Is this correct? Martin Hogbin (talk) 22:42, 22 April 2012 (UTC)

Yeah, yeah., but what about your "P"?Nijdam (talk) 05:33, 23 April 2012 (UTC)

It is not the 'C' word is it. Do you want me to write P(H2|D1=3S)=43/50 etc? Martin Hogbin (talk) 12:57, 23 April 2012 (UTC)

Or would you prefer P(H2|D1=3s,D0=8c)=43/50? Martin Hogbin (talk) 12:58, 23 April 2012 (UTC)

It is, and I do not want you to write anything, I hope you understand you have to write it. Your first choice is okay, as the 8 of clubs has not been drawn, hence is not part as an outcome of the random experiment. Do you agree about the need of the 'C' word? Nijdam (talk) 21:43, 23 April 2012 (UTC)

I would be interested to hear exactly why my second choice is unnecessary. Martin Hogbin (talk) 22:24, 23 April 2012 (UTC)

Nothing more than the experiment being the successive (random) drawings of a card from the deck without the 8 of clubs. Nijdam (talk) 09:02, 24 April 2012 (UTC)

Why is the removal of 8c not a condition? Suppose it had been 2c. Martin Hogbin (talk) 12:27, 24 April 2012 (UTC)

• I've been following this with fascination. Nijdam, it occurs to me that Martin has not realised that you are setting him up by using imprecise language (since I do not believe you would use such imprecise language accidentally). The first card "shown" is the 8 of clubs. You say nothing as to whether it was or was not removed from the deck. The dealer could simply have cut the cards and shown the 8 of clubs to the punter. Later you say that he game does not start until the first card is "drawn". I do think you were somewhat sneaky here as you asked him how he would bet after seeing the 8 of clubs - which guaranteed that he would think the game had started. So when you say "suppose the 3 of spades is the first drawn card", then he would be tricked into thinking a new game had started. However, knowing it was you he was talking to, Martin ought to have been suspicious as to why you were asking for what should have been the world's most obvious probabilities, and nailed down exactly what was going on. :)

• If one assumes that the shown card is discarded, and one card is then drawn as the betting card, then there are of course only 50 cards remaining in the deck. However, if the shown card is merely shown, and not discarded, then there are 51 cards remaining in the deck upon which to base one's bet after the first betting card is drawn.Elen of the Roads (talk) 13:27, 24 April 2012 (UTC)

Elen, it is a bit of a surprise to see you here but you are more than welcome to join in the discussion. I was sure that Nijdam had said that the first card shown was removed from the pack but on looking again it seems that this is indeed not clear. Nevertheless, I do not think that Nijdam is trying to trick me in the way that you think; the actual answer to this problem is not that important. The point that he was trying to make is that the required probability is a conditional one.

The point that we have been discussing is that of exactly which events must be considered as conditions in a probability calculation. So let us now assume that the 8c is replaced in the pack and the probabilities adjusted accordingly. Odd as you may find it, my question to Nijdam still stands as it was, 'Why is the showing of the 8c not a condition that must be included in the probability calculation?'. Martin Hogbin (talk) 16:57, 24 April 2012 (UTC)

Martin, you've got the right picture, be it I do not understand why you say the 8c is replaced? I clearly said it was not drawn, but just shown, and the first draw, which appears to be 3s came from a deck of 51 cards, the full deck without 8c. So where's the problem? I do not understand your question about the 8c being possibly a condition. I said, and I hope clearly, the 8c is not part of the experiment, hence it can't be a condition. [I forgot to repeat the question: Do you agree about the need of the 'C' word? Nijdam (talk) 20:29, 24 April 2012 (UTC)

What do you mean by 8c not being part of the experiment? Are you just saying that the 8c is always shown; no other card is possible?

Regarding conditions, supposing the 3s is drawn but returned to the pack. Must that be taken as condition? Martin Hogbin (talk) 22:11, 24 April 2012 (UTC)

The game always begins by showing the 8c, resulting in a random splitting of the participants. So yes, it is always shown at the start. The random part, the successive drawings are from the 51 remaining cards. Now your answer, please. Nijdam (talk) 06:49, 25 April 2012 (UTC)

My answer to your question is that I do agree that the problem is conditional and that the card drawn first should be taken as condition of the problem. The question is why?

And your answer to this question is?

That the removal of a specific card might affect the value of the probability of interest (which is the probability that the next car drawn will be higher than the last one)

Not just hat, but because the 'probability' of interest is defined on a restricted set of possibilities.

My question to you is, supposing the 3s is drawn but returned to the pack. Must that be taken as condition? What is the reason for your answer? Martin Hogbin (talk) 12:56, 25 April 2012 (UTC)

I come to your question shortly, Nijdam (talk) 21:45, 26 April 2012 (UTC) Drawing with replacement. Call Cn the card drawn the n-th time. The sample space consists of infinite sequences of the form: 2s7cAhKh.....

Of course I have to take 3s as a condition, as the decision depends on it. In the calculation of the desired probability, however, the condition disappears at some stage.

The event L2 ('second draw is lower than the first') consists of the outcomes: 3x2y..., 4x3y..., 4x2y..., ..., AxKy...,...,Ax2y... (x,y any suit)

P(L2)=P(H2)=(1-P(E2))/2=(1-12x16/51/51-9/51/51)/2=1/2-201/51/51/2 (E2: second same as first) but P(L2|C1=3s)=P(C2=2x)=4/51 Nijdam (talk) 22:27, 26 April 2012 (UTC)

Let me change the rules now. The question becomes always, 'Will the card drawn be greater or less then 8c?'.

Suppose that in one version the first card drawn is 3s. It is then removed from the pack. Must we describe the probability that the next card is >8c and conditional with (D1=3s) as a condition? In other words, do we require P(H2|D1=3c)?

Of course as the next draw is from a restricted set of cards.

Suppose that in another version the first card drawn is 3s but it is returned to the pack. Must we describe now the probability that the next card is >8c and conditional with (D1=3s) as a condition? In other words, do we still require P(H2|D1=3c)? Martin Hogbin (talk) 22:57, 26 April 2012 (UTC)

Formally yes, as the set of possible outcomes is also restricted, as only outcomes that start with 3s are allowed. Because of the independence one may easily calculate the answer. Nijdam (talk) 05:33, 27 April 2012 (UTC)

After a card has been drawn and returned to the pack the next card is always drawn at random from the complete pack. Do you still want to include the value of all previously drawn cards as a condition of the probability that the next card drawn will be >8c?

By, 'the set of possible outcomes is also restricted', you are saying the same thing as you have said before, that a condition reduces your sample space. This, of course, depends on what events you chose to include in your sample space, or what possible outcomes you consider.

To make clear what I am saying it is this:

In calculation of any probability the only way do decide which events must be taken as conditions is to consider whether they might affect the the value of the probability of interest.

This might sound terribly unscientific or non-mathematical but no one has given me any more definite answer to this question and I have not found one in any source anywhere. Martin Hogbin (talk) 09:12, 27 April 2012 (UTC)

As always ypu speak rather loosely about probabilities. The probability to get heads with a throw of a coin is something complete different from the probability to get a red coloured card from a complete deck. Yet we say in both cases for convenience 'probability'. If however there may be cause for confusion we have to clearly distinguish between the different probability. That's what our discussion is about. The probability measure used in our game with replacement to get >8c in the second draw is a different probability measure than the one used in the first draw. Nijdam (talk) 15:27, 27 April 2012 (UTC)

Am I made clear above I am using the phrase, 'what is the probability ...' to have its usual meaning of 'what is the value of the probability...?', not to mean, 'what conceptual entity am I referring to?'. With that meaning,the probability of randomly drawing a red card from a standard pack is 1/2 and is exactly the same as the probability of tossing a head with a fair coin.

No problem s long as you're aware of the difference. It is for instance nonsense to say that because the probability to draw a red card from a complete deck is 1/2, the probability for a fair coin to land twice heads up is 1/4. Or does this make sense to you?

I am sure that you must know that I do know the difference but how much difference is a difference? Is the probability that a coin tossed by a man wearing a red hat will be a head different from the probability that a coin tossed by a man wearing a blue hat will be a head. What about if the two tosses are by the same person but at different times? No two probabilities are are ever conceptually absolutely identical. Martin Hogbin (talk) 14:00, 28 April 2012 (UTC)

If you're just interested in the value, no. But if both persons are part of the same experiment, we have to distinguish them. Nijdam (talk) 10:53, 4 May 2012 (UTC)

So perhaps you can tell me, if a card has been drawn and returned to the pack and the next card is always drawn at random from the complete pack, do you still want to include the value of all previously drawn cards as a condition of the probability that the next card drawn will be >8c? Martin Hogbin (talk) 23:57, 27 April 2012 (UTC)

You need to argue that the successive draws are independent. Nijdam (talk) 10:12, 28 April 2012 (UTC)

But that leads us back to exactly what I have said above. 'Independent' means that the probability the next card drawn being >8c does not depend on the card previously drawn. Whether you consider the independence of events, events that must be in the sample space, or events that must be considered as conditions there is no mathematical or algorithmic may way to make a decision. If you disagree please tell me what it is. Martin Hogbin (talk) 13:30, 28 April 2012 (UTC)

No it does not. The problem is your loose way of formulating and not being aware of it. It means the conditional probability the next card drawn being >8c does not depend on the card previously drawn, hence equals (in value) the probability a card drawn being >8c.

So how is it possible to show that successive draws are independent? Martin Hogbin (talk) 10:43, 2 May 2012 (UTC)

Why would you like to show this? It's a property of this experiment.Nijdam (talk)

You say things like, "It's a property of this experiment" but you give no reasons for your statement. I am not complaining about that because that is exactly my point, you have to use common sense, judgement, and real world knowledge to decide which events are mutually independent.

In the MHP, my common sense, judgement, and real world knowledge tells me that the event that a player who swaps wins the car is independent of the legal door opened by the host. Martin Hogbin (talk) 11:05, 7 May 2012 (UTC)

Besides that one has to be careful with intuition and common sense - the MHP is exactly about the counterintuitive result - what is the implication of your intuitive idea about the independence?Nijdam (talk) 14:13, 7 May 2012 (UTC)

Yes I agree that the MHP is about a counterintuitive result but, in the standard formulation, this has nothing to do with the specific door opened by the host. In the standard formulation my intuition tells me that the probability that the player will win the car by swapping does not depend on the legal door opened by the host, and this proves to be correct.

You repeat this per and over, so it's time now you formulate in exact terms, best in formulas, what you mean by this. Nijdam (talk) 21:01, 7 May 2012 (UTC)

It's a property of this experiment. Martin Hogbin (talk) 21:59, 7 May 2012 (UTC)

Please formulate this property in exact terms. Nijdam (talk) 17:06, 8 May 2012 (UTC)

After you

Perhaps you could explain what you mean by that by formulating this property in exact terms for the same question that I asked you above about the card game. Martin Hogbin (talk) 17:38, 8 May 2012 (UTC)

No problem: the drawing of the cards is done in such a way that the second card is independent of the first card means: the simultaneous probability may be taken as the product of the marginal probabilities.

Now your turn. Nijdam (talk) 13:22, 9 May 2012 (UTC)

The MHP is set up in such a way that the event that the player has originally chosen the car is independent of the legal door opened by the host. Martin Hogbin (talk) 15:14, 9 May 2012 (UTC)

meaning?????( Your answer starts in a similar way as mine, but fails when it comes to the meaning of it) Nijdam (talk) 09:27, 10 May 2012 (UTC)

That, in the case that the player has initially chosen door 1, P(C=1 and H=2) = P(C=1) * P(H=2) = 1/6

Why do you mention: "in the case that the player has initially chosen door 1"? And BTW: P(C=1)=P(H=2)=1/3, hence P(C=1) * P(H=2) = 1/9????Nijdam (talk) 08:16, 11 May 2012 (UTC)

I am considering three possible cases as separate experiments, so in the experiment in which X=1 then P(H=1)=0 P(H=2)=P(H=3)=1/2.

If you prefer P(C=1 and H=2|X=1) = P(C=1|X=1) * P(H=2|X=1) = 1/6

Ultimately all probabilities are conditional. Martin Hogbin (talk) 11:12, 11 May 2012 (UTC)

I hope you do not mind I changed your P(layer) into X, as a mathematician doesn't like the same symbol for different things. Formally: P(C=1 and H=2|X=1) = P(H=2|C=1,X=1)P(C=1|X=1) = 1/6 = P(C=1|X=1) * P(H=2|X=1). What do you conclude from this?? Nijdam (talk) 19:45, 11 May 2012 (UTC)

I am not sure what you want me to conclude from what you have written but do you agree that P(C=1 and H=2|X=1) = P(C=1|X=1)P(H=2|X=1) = 1/6? Martin Hogbin (talk) 08:05, 12 May 2012 (UTC)

That "the probability the player will win the car by swapping does not depend on the legal door opened by the host" But how do you reach this conclusion?Nijdam (talk) 07:41, 13 May 2012 (UTC)

After you again. How did you reach your conclusion in the card example?

I can only explain further, if you didn't catch what I wrote, that the physical independance of the successive drawings give rise to the product measure of the probabilities, i.e. in the model the drawings are taken as independent. That's all. Now your turn. Nijdam (talk) 10:49, 13 May 2012 (UTC)

So in the end you resort to your assessment of physical reality to decide which events are independent. There is no mathematical or algorithmic way to decide, it is a matter of experience and common sense. I have no problem with that it is what I have been saying all along.

It may be my english, but I wouldn't call it 'resort'. Any mathematical model reflects the physical situation.

Regarding MHP, the physical independence of the event that the player has originally chosen the car is independent of the legal door opened by the host. In other words, the host choice of legal door is random and thus independent of all other events. Martin Hogbin (talk) 20:18, 16 May 2012 (UTC)

It's a nice try, but there is not such a similarity between my answer and yours. It will be best if you list the possible outcomes and formulate your answer in terms of these. Nijdam (talk) 12:46, 17 May 2012 (UTC)

Yes there is. It is quite obvious from the experiment setup that the event that the host (who follows the standard rules) opens door 2, for example is independent of the event that the player has chosen the car. The car is placed randomly and the host chooses randomly when he has a choice thus, given a particular choice of door by the player, the host's choice of legal door is random and therefore independent of all other events, including whether the player has originally chosen the car.

That may seem obvious for you, but it only is true, if the player chooses randomly. And for the MHP it is irrelevant whether the player chooses randomly or not.

P(X=C and H=2) = P(X=C=1 and H=2) +P(X=C=3 and H=2)= P(H=2|X=C=1)P(X=C=1) + ... = 1/2 P(X=1|C=1)/3 + ... = P(X=1|C=1)/6 + P(X=3|C=3)/6=

(P(X=1)+P(X=3))/6

P(X=C)P(H=2)=P(X=1|C=1)/9+...+... = 1/9

(X and C independent) Nijdam (talk) 23:14, 17 May 2012 (UTC)

To make this even clearer, if the player has originally chosen the car, the host is equally likely to choose each of the unchosen doors (because the host chooses randomly), if the player has not originally chosen the car, the host is also equally likely to choose each of the remaining doors (because the car is randomly placed). Do you disagree? If so please tell me in what way the host's door choice is dependent on whether the player has originally chosen the car.

How do I know all this without doing a calculation? The same way that I knew that Morgan's calculation was wrong before I made any calculations - symmetry. Martin Hogbin (talk) 13:52, 17 May 2012 (UTC)

Notice that I said host's choice of 'legal door', not just 'door'. Consider the case that the player always chooses door 1. My statement becomes that the host's choice between doors 2 and 3 (door 1 is not legal) is random.

To reformulate what I say above, if the car has been placed behind door 1, the host is equally likely to choose door 2 or door 3 (because the host chooses randomly), if the car has not been placed behind door 1, the host is also equally likely to choose door 2 or door 3 (because the car is randomly placed). Do you disagree? If so please tell me in what way the host's door choice is dependent on whether the car is behind door 1 or not. The same argument applies whatever door the player chooses. Martin Hogbin (talk) 08:07, 18 May 2012 (UTC)

Be so kind as to formulate this in an appropriate model. Nijdam (talk) 08:40, 18 May 2012 (UTC)

The model is described above. The car is placed randomly and host chooses a legal door randomly. That is sufficient for the two events that I described to be independent. It is obvious. Martin Hogbin (talk) 19:12, 18 May 2012 (UTC)

Meaning: C,H,X and P(C=c)=1/3; P(H=h|C=c,X=x)=1/2 if c=x<>h, P(H=h|C=c,X=x)=1 if {c,h,x}={1,2,3}? Then what: Nijdam (talk) 20:24, 18 May 2012 (UTC)

I am not quite sure what you are asking now.

Do you agree about the model? If not, formulate your own. And then formulate your statement in terms of this model. Nijdam (talk) 13:13, 19 May 2012 (UTC)

My model, if you insist would be {CG} representing the players original choice. I have no other events in my model because it is obvious from the setup that no other events are relevant. The host's choice of legal door, the host's choice of goat, the host's name or the day of the week are all obviously irrelevant under the standard assumptions. I know this not from a calculation involving a more complex model but from the symmetry of the problem. As with your card problem there have to be some things which are taken as being true without proof. Martin Hogbin (talk) 13:52, 19 May 2012 (UTC)

There you go again. As you already anticipated, I would ask you what it means when you said the car is placed randomly. As you know from former discussions, your model is inadequate to show the random placement of the car, the choice of the player, etc. etc. Nijdam (talk) 14:31, 19 May 2012 (UTC)

Ir simply means P(C)=1/3 P(G)=2/3. We need no model to say that. Martin Hogbin (talk) 15:49, 19 May 2012 (UTC)

Where is the randomness of the car placement, where the random opining of a door by the host???? Nijdam (talk) 20:10, 19 May 2012 (UTC)

The random car placement means that P(C)=1/3 P(G)=2/3. The random door choice by the host means that these probabilities do not change (in value) when the player makes their choice whether to swap or not. 22:16, 19 May 2012 (UTC)

For common people like me and most of the readers, the random placement of the car means something different. I do not quite understand your remark about the host. Please formulate this in terms of your sample space. And then give a formal proof of: "the probability the player will win the car by swapping does not depend on the legal door opened by the host". Nijdam (talk) 07:50, 20 May 2012 (UTC)

How do we know anything?

Surely to most people the random placement of the car means that the player will have a 1/3 chance of picking it, regardless how how the player chooses, hence P(C)=1/3. What is your understanding?

You must be surrounded by strange people. Everyone I asked said something like: the car will be with equal chances behind each of the doors. BTW as long as the first pick of door is independent of the placement of the car, the chance hitting the car is 1/3.

I cannot give you a formal proof of my statement because I am taking it as axiomatic. No information is revealed by a random choice that has a certain outcome thus no probability can change.

Tant pis.

Where is your formal proof that successive random draws (card replaced) from a pack of cards are independent? Martin Hogbin (talk) 08:52, 20 May 2012 (UTC)

Why should I prove this? I take them independent. Nijdam (talk) 19:52, 20 May 2012 (UTC)

Do you see my point then? You take the independence of successive card draws to be self-evident and thus not to require formal proof. I take it as self-evident that, in the case the player has originally chosen door 1, the event that the player has originally chosen the car is independent of the event that the host opens door 2. Do you assert that these two events are not independent? Martin Hogbin (talk) 07:51, 21 May 2012 (UTC)

No, as in my case my assumption is reflected in the model, that's the purpose of it. And your model does not show your assumption, i.e. your model is inadequate to show the conditional independence: P(C=1 and H=2|X=1)=P(C=1|X=1)P(H=2|X=1). That's why you do not have any point at all. Nijdam (talk) 09:16, 21 May 2012 (UTC)

Given the standard conditions, it is obvious. It is also obvious that P(C=1|X=1,H=2) = P(C=1|X=1,H=1) = P(C=1|X=1) = P(C=1)

You have yet to show exactly how your assumption is reflected in your model. Martin Hogbin (talk) 09:29, 21 May 2012 (UTC)

Is it obvious that P(C=1|X=1,H=2) = P(C=1|X=1,H=1) = P(C=1|X=1) = P(C=1)? Nijdam (talk) 20:42, 21 May 2012 (UTC)

Sorry, silly mistake. I meant, of course P(C=1|X=1,H=2) = P(C=1|X=1,H=3) = P(C=1|X=1) = P(C=1) Martin Hogbin (talk) 23:13, 21 May 2012 (UTC)

Okay, but then, what do you mean for instance by "X=1"?

I mean in the case where the player has originally chosen door 1. Equivalent statements apply in the case that the player has chosen doors 2 and 3. I am only mentioning door numbers at all to make clear what I mean in a notation that suits you.

Please indicate this event "X=1" in your model.Nijdam (talk)

It's important you answer this question.

I would rather say that it is obvious that the choice of goat that the host makes obviously does not affect the probability that the player has chosen the car. This means that we can sensibly use my sample space of {C,G}. Martin Hogbin (talk) 11:22, 22 May 2012 (UTC)

The probability the player picked the car is 1/3 (under the obvious assumptions). In what way could this be affected? Whatever might happen after the player made their first choice, this probability is, and will be forever, 1/3. What is it you have in mind?Nijdam (talk) 13:37, 22 May 2012 (UTC)

If you like, the choice of goat that the host makes obviously does not affect the conditional probability that the player has chosen the car under the condition that the game has proceeded according to the rules. Martin Hogbin (talk) 17:06, 22 May 2012 (UTC)

If I like?? It is what you like to claim. Please be more specific. Nijdam (talk) 17:14, 22 May 2012 (UTC)

I am not sure what you are getting at. Any probability is, in principle, conditional upon all other events that have occurred previously (unless they have been defined to be independent) so what we generally call the probability that the car is placed behind door 1 is in fact the conditional probability that the car has been placed behind door 1 given everything that has occurred up to that time. When referring to a probability later on in the game it is, strictly speaking, a conditional probability given all events that have occurred up to that point but it is not always necessary to refer to it that way. Also, as I have said before, when the word 'probability' is used it often is used to mean the numerical value of the probability. So when I say, 'probability that the player has chosen the car' I mean the numerical value of that probability given all events that have occurred up to that time.

So the probability that the player has initially chosen the car is 1/3 (given the standard rules). The probability that the player has chosen the car after the host has, under the standard rules, revealed a goat, is 1/3. This is the same value, thus these two probabilities are equal, although you may like to consider then conceptually different.

Under the rules contrived by Morgan however, the probability that the player has chosen the car after the host has revealed a goat may not be 1/3. Martin Hogbin (talk) 17:42, 22 May 2012 (UTC)

What happened, did you see the light? Let me put it straight, you defended Devlin's "solution", but apparently you must see now it is flawed. Loosely speaking I may say that two probabilities with the same value are "the same", although they might conceptually differ completely. However it is nonsense to say that some probability is the same as a conditional form of it, and hence conclude it should have the same value. This is what Devlin (and others) does.

This is what we all do all the time. You say that the conditional probability that the car is behind door 1 given that the host says the word 'pick' is the same as (has the same value as) the (nominally unconditional) probability that the car is behind door 1. You say this, not unreasonably, without mathematical proof or explanation. Martin Hogbin (talk) 08:05, 23 May 2012 (UTC)

Back to work: Describe in your model the event you mentioned: "X=1". And secondly: describe what it means that "the choice of goat that the host makes obviously does not affect the conditional probability that the player has chosen the car". Nijdam (talk) 22:11, 22 May 2012 (UTC)

The events 'X=1' and 'the choice of goat that the host makes' are not described in my model for the same reason 'the host says the word "pick"' is not included in yours. These events, although mentioned in the problem statement, do not affect the (value of the) probability of interest (which is the conditional probability that the player has chosen the car given all events which we take to have occurred when the player is asked to make their choice). Martin Hogbin (talk) 08:05, 23 May 2012 (UTC)

The events you mention play a complete different role than the host saying "shit" or what else. If you wish I incorporate in my model in every outcome all the aspects that happens for sure. Now again your turn. When you do not see the difference, start studying probability theory or logic. Nijdam (talk) 19:02, 30 May 2012 (UTC)

That is not a very good answer I am afraid. What exactly is the difference in role between the events that you wish to include in your model and those that I wish to include in mine? You have never told me that. I can tell you though. We must include all events which might affect the (numerical value of) the probability of interest (which is the conditional probability that the player has chosen the car given all events which we take to have occurred when the player is asked to make their choice). Now you give me a better definition of which events we must include in our calculation. Martin Hogbin (talk) 21:59, 30 May 2012 (UTC)

Orphan

Similar calculations apply if the player has initially chosen door 2 or door 3. Martin Hogbin (talk) 12:00, 10 May 2012 (UTC)

In non-standard formulations, intuition based on the standard formulation could lead one astray, as the host might turn out to have a door or a goat preference. Martin Hogbin (talk) 15:37, 7 May 2012 (UTC)