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This answer writes

You describe an imaginary measurement which could not be performed at the time of Columbus or before. There are several reasons for this. 1. Atmospheric refraction at the horizon is about 30' but it is not constant (depends of the weather conditions), and the knowledge of refraction at that time was very rudimentary. It is discussed by Ptolemy, but he could not really measure it, and I am not aware of any reliable measurement until 17 century. 2. One needs a devise to measure small angles with sufficient accuracy. We are talking of angles of less than 1 degree. There is no evidence that such devises existed until 17 century. (If you read how Archimedes tried to measure the diameter of the Sun directly, you get the idea of the difficulties involved. There was certainly no progress in this since Archimedes to the time of Columbus). 3. "You sail until you see 1/2 of the mountain". How do you measure what distance you sailed? Read the book of Morrison about how they measured sailing distances at the time of Columbus, and see how crude the methods were.

  1. So it incorrectly claims that the atmospheric refraction at the horizon of 30' applies to mountains (rather than just celestial bodies, for which this number is calculated). The refraction is actually caused by differences in air density, so light coming in from outer space will experience very different total refraction than light coming from a 1000m mountain.

  2. Another clear mistake in this answer was claiming that the simple method I described in the question required explicitly measuring the distance one has sailed. That is incorrect. I even gave a formula: $$ h \over {2 \alpha ^2} $$ It does not need this distance measurement.

I pointed out these mistakes in the comments, but they were deleted by someone. Who deleted these comments and why?

There were other mistakes in the answer BTW, but I guess I won't bother, if this SE would rather lap up nonsense.

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I am the one that deleted your comments. Deleting comments does not imply a value judgement: It simply reflects the fact that, on Stack Exchange, comments are not the right place for extended discussions. See here for more information. Moreover, in this case, some of the comments that constituted the discussion were already deleted, making (part of) the discussion hard to understand and adding to the sense of cluttering.

As a sign of goodwill, I've now created a chat room where your discussion can be viewed for those interested; you can find the link below the answer.

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  • $\begingroup$ "in this case, some of the comments that constituted the discussion were already deleted" -- Incorrect. The two comments I'm talking about stood on their own and referred only to the question, not any previous comments. Your actions are pure censorship followed by intentional muddying of the waters. $\endgroup$
    – MWB
    Jan 18, 2022 at 19:14
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    $\begingroup$ I stated clearly that I did delete your comments, and I think that it is clear from the page that I linked in my answer that this is completely standard procedure. I have also clearly stated that I created a chat room that contains them for your sake (against standard procedure). When I deleted the comments, you had already deleted a couple of comments, the responses to which did remain, which made the discussion hard to understand without access to the deleted comments. Anyone can check this in the chat room. I'm not sure why you think this is 'intentional muddying' of the waters in any way. $\endgroup$
    – Danu Mod
    Jan 19, 2022 at 8:56
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These are the two comments I am talking about:

"Atmospheric refraction at the horizon is about 30'" This is for celestial bodies, not 1000m mountains.

and

"How do you measure what distance you sailed?" The method I described does not require it.


As you can plainly see, they were quoting the flawed answer, and were not referring to any preceding comments. They were not part of any "extended discussion" and were aimed at improving the answer, which is precisely what comments are for.

  1. The moderator who deleted these two comments was wrong to do so on the main site.
  2. Further, he continues falsely claiming here in meta, that they were part of an "extended discussion", even after I pointed out his mistake.
  3. He also falsely claims that simply deleting "extended discussions" without a trace (as opposed to moving them to chat) is standard procedure on SE:

I stated clearly that I did delete your comments, and I think that it is clear from the page that I linked in my answer that this is completely standard procedure.

But this certainly isn't standard procedure:

  • If a user is prompted by the system to continue an extended conversation in chat (see below) and chooses to do so, an automatic comment will be posted with a link to the relevant chat room.
  • When a moderator moves a post's comments to chat, an automatic comment will be posted with a link to the chat room
  1. Contradicting SE's policy, he claims that the fact that earlier comments were deleted is justification to delete further comments:

Moreover, in this case, some of the comments that constituted the discussion were already deleted, making (part of) the discussion hard to understand and adding to the sense of cluttering.

But SE's policy is that comments aren't for extended discussions! Why would he have an expectation of being able to read a coherent discussion in the comment section?! I deleted some of my earlier comments, because they were no longer necessary after I updated the question with step-by-step instructions for estimating the Earth's diameter without traveling too far.

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