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    Re: Cocked hats, again.
    From: Peter Fogg
    Date: 2007 Mar 18, 09:15 +1100
    Earlier Gary baulked when asked to provide evidence to back up his contention:
    > Regarding your other post today, I too learned that your position was
    > always inside the triangle with the most likely point being the center.
    >
    We now know that was bad information.

    George Huxtable contends:
    > Gary was referring to what he had been taught, not quoting from a
    > book, so none of us is in a position to question his recollection, or
    > demand evidence.

    This is factually incorrect, my dear sweet old chap. You really should check your sources before rushing into print with what you imagine that you remember that someone once wrote - and in this case not so long ago! This goes to the heart of this matter, does it not? This is why evidence is needed - because our minds play these little tricks upon us, do they not?  It is only too easy to convince ourselves (whether unconsciously or not) that what we would like to remember is the fact, rather than fancy.

    This is what Gary actually wrote:
    > No, it read it a number of times from a number sources over a large
    > number of years.

    Now George attempts to do as much; to provide Gary's evidence (a quixotic crusade if ever I heard of one) accompanied by a few snide comments, as is his merry way. Let's have a look at this evidence:

    Little Ship Navigation, Rantzen, 1961, page 122. "...The crossing
    lines define a triangle, known as a cocked hat. ...The position of the
    ship is somewhere in this triangle..."

    I agree that this could be worded better. The addition of 'assumed to be' inserted between "is" and "somewhere" would do the trick. But it fails the Gary test: no " position ... always inside the triangle".
    Next!

    Sea Navigation, Gates, 1968, page 51. "Rarely, of course, will the
    three position lines intersect at a common point, and more usually
    they will form a small triangle or 'cocked hat'.... The ship's
    position is then assumed to be at the centre of the triangle. If the
    triangle is a large one (even after checking the observations), then
    the position of the ship is taken as the apex of the triangle nearest
    to danger."

    Well put. No problems here, that I can see. "Assumed to be" gets it right.
    Fails the Gary test: does not state: "position ... always inside the triangle".
    Next!

    Learn to Navigate, Mosenthal, 1998, page 42. "Your are more likely to
    end up with a cocked hat like this [diagram shown here]. You normally
    take the middle of the cocked hat as your position. Unless you are
    near a danger, when you take the 'worst' position- the point nearest
    the danger."

    This also seems fine. You DO normally, etc. Well put. I might add that this advice to assume a position on a position line closest to danger is good simple common sense, based on the evidence of that position line. Fails the Gary test: does not state: " position ... always inside the triangle".
    Next!

    Navigation for yachtsmen, Blewitt, 1973, page 52. "When your cocked
    hat is small, you can put yourself in the middle of it. This is not
    necessarily logical, but in practice is the best you can do."

    I am not impressed by how Mary puts this (why is it not logical - does she go on to say?) but, again, it fails the Gary test: no " position ... always inside the triangle".
    Next!

    Dutton's navigation and pilotage, 1969, [highly reliable on most
    matters] art. 2016. Referring to LOPs, "In practice they will seldom
    intersect at a point but will produce a small polygon, which usually
    contains the position of the ship."

    This is the most damning so far, as it directly contradicts the 25% / 75% theory. However, and crucially, it DOES NOT say: "always inside" [the shape].

    Admiraly Manual of Navigation, vol 3, 1938, page 166, states- "...
    when a cocked hat is obtained, it is customary to place the ship's
    position in the most dangerous position that can be derived from the
    observations..."

    Good. Well drafted. I'm not sure how customary it is, although makes excellent common sense.

    However, in the previous paragraph, an interesting,
    and somewhat contradictory statement is made "... it can be seen that
    the chance of F's falling inside the cocked hat is only 1 in 4". Here
    then, is the first official backing for the 1 in 4 figure that I have
    come across.

    So this doesn't quite fit the Gary contention either.

    And here we should give credit to Cotter, better known for his
    "History of Nautical Astronomy". In "The complete Coastal Navigator",
    1964, page 187, he writes- "In the general case, where the errors e1,
    e2, and e3 are not known either in magnitude or sign, the possibility
    or chance of P lying within the cocked hat is only 1 in 4."

    No assistance towards the Gary crusade here either, it seems.

    On that evidence, perhaps Peter Fogg will retract.

    Or perhaps not. Based on this lack of evidence. The need for retractions would seem to lie firmly in your camp, George. We shall all await them with bated breath.

    So, putting behind us that tedious and useless exercise - these sources mostly got it right; NONE could support Gary - you will note the silence from George on my recent, and more relevant, posts on this issue. What George does not say is sometimes more telling than what he does (not difficult in light of the above example).

    Neither George nor anyone else, it seems, has found much to quibble about with the central thrust of my contention, argued now on many fronts with examples and diagrams galore: that this 25% / 75% brou-ha-ha really is futile and pointless ... literally!



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