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John Karl wrote-

"George’s irrelevance
A.  He measures triangles from a known location."

If, instead of simply accepting a predicted distribution, we wanted to TEST 
the matter in real life, to decide whether or not each triangle embraced 
the observer, we would indeed need to know the observer's exact position.

"B.  And then he counts the number of times (i.e., the percent of time) 
that the known location is outside of the triangle.  (So yes George, you do 
need to know the fix location in order to do this counting.)"

"C.  This is not navigation.  It’s not determining anything about George’s 
location – we already know that.  It’s determining information about the 
random distribution of the triangles."

From that test, the result we will find is that from that known position, 
the triangle will embrace the observer, on average, one quarter of the 
time. Does John Karl dispute that?

And if we then make another such test, from a different known location, we 
will find exactly the same thing. After a few such tests, we can quickly 
deduce that it's equally true from any point on the Earth's surface. It 
doesn't matter whether the location of the point is known or unknown;  it's 
a general truth that applies the whole World over. One out of four. QED.

If John Karl disputes any step in this argument, he can explain exactly 
what is wrong. The logic remains unshaken, so far. His questions about 
whether it is, or isn't, "relevant to navigation", are no more than a 
distraction.

What, exactly, does his 86% figure represent? If it's the probability of an 
observer being outside the observed triangle, then one of us has to be 
wrong, although some Navlist comments have tried to claim that we can both 
be right.

George.

contact George Huxtable, at  george{at}hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

   

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