Re: Things we remember...

On Tue, 24 Nov 2009 08:57:35 -0800 (PST), Robert Carnegie
<rja.carnegie@xxxxxxxxxx> wrote:

On Nov 23, 5:28 pm, Mike Ash <m...@xxxxxxxxxxx> wrote:
In article
<2f786a11-3e24-4381-8086-fcaa16829...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
 Robert Carnegie <rja.carne...@xxxxxxxxxx> wrote:

I may as well take a guess... you're using satellites that are above
the horizon obviously, and in effect what you get from each is its
exact location in space and its distance from you?  Then, if all your
satellites are spaced round your terrestrial horizon then your
measurement will be specific as to map reference but inconclusive
about elevation, because whether you're high or low you'll get the
same signals.  Whereas if the satellites are nearer to overhead then
your north/south/east/west measurement will be fuzzier.

This sounds right to me!

An aeroplane flying on a course over your location spends a lot more
time on the horizon than appearing high overhead, the Sun doesn't (if
you're in the tropics)... I suppose these satellites are closer to the
aeroplane model?  Mostly seen near the horizon?

There are two factors at play. First is how the altitude compares to the
size of the Earth. Second is how close to overhead the paths are.

Take the first one: an airplane's angular speed is much higher when it's
overhead than when it's near the horizon, because it's much closer to
you when it's overhead. Thus, it spends much less time there. The Sun is
effectively infinitely distant, and has the same angular speed
regardless.

GPS satellites are at an altitude of about 20,000km. When they're on the
horizon, they're about 26,000km away (add the radius of the Earth).
Their angular speed there will be noticeably slower, although not hugely
so. Thus they'll spend less time overhead.

What I believe is the dominant factor is simply the paths they take.
Each satellite covers a big patch of the Earth at any given time, and is
far more likely to pass to the side of you than to pass straight
overhead.

On the other hand, a gambler knows that you can't do mathematics by
feel.  Or rather, a gambler who doesn't know that is an unsuccessful
gambler.

I disagree with this sentiment. What you can't do is do mathematics by
feel if you aren't already familiar with the problem at hand. But if you
know the math well, you can often get away with doing it by feel
(although you can't completely rely on it). I would wager (ha ha) that
an experienced and successful poker player can simply know the
approximate relative probabilities without needing to have the exact
numbers at hand.

Of course, I don't play poker....

I'm being careful because I found guessed wrong on a rather
complicated hypothetical gamble, in another forum, when I did the
figures (if I did that right).

Described in <http://en.wikipedia.org/wiki/Envelope_paradox>
I think the problem is that you can't calculate probabilities and odds
without knowing a probability distribution of the initial random or
unknown element, and the description of the problem appears to contain
sufficient information but doesn't really.

So at <http://www.bbc.co.uk/dna/mbradio4/F2766778?
thread=7070559&skip=40&show=20>
I propose: Two dice are thrown and a corresponding sum of British
money (x £1 pounds) is placed in an envelope. Dollars if you prefer.
Twice that sum is placed in another envelope. You get to take one
envelope, examine the contents, and then choose whether to swap with
the other envelope, which has more or less money. You discover that
your envelope contains £10 pounds. The other envelope therefore
contains either £5 pounds or £20 pounds. Should you swap?

I added the dice and maybe the exact figure, I think. Otherwise
you're left juggling numbers that are not probabilities.

You have discovered that the roll was either a 5 or a 10. Since
there are 4 ways to get a 5, and only 3 ways to get a 10, it
appears you should stick with what you have. (And BTW, even if
I'm wrong there, I can still sneer at the puzzle. The right
decision will be extremely easy to make if you discover an odd
number, or a number > 12, in the envelope.)


--
Bill Snyder [This space unintentionally left blank]
.

Relevant Pages

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  • Re: Things we remember...
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  • Re: Things we remember...
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