[extropy-chat] Possible Worlds Semantics

[spike]

> bounces at lists.extropy.org] On Behalf Of Chris Hibbert
> Subject: Re: [extropy-chat] Possible Worlds Semantics
> 
> > Both sons say yes.
> 
> The possible combinations are as follows:
...
> 
> An involuntary trade?  Now I think you have to make the trade if you
> think the draws were random.  In any case but the 10M, you gain more
> than you lose in the long run by trading.  The asymmetry at the top
> makes it possible. Chris...


Chris remember what messed us up on this last time around?  Modify the
question only slightly by saying the envelopes contain 10^x, the other
contains 10^(X+1).  X need not be an integer for this to work: one envelope
contains ten times the amount in the other, with no hard limits.  By the
line of reasoning presented, one would trade.  But with the given
information one might be tempted to trade even without looking in one's own
envelope.  What have you actually learned by looking?  

Even if there is a one dollar charge to trade, one would still want to
trade.  But after paying a buck and trading, the same line of reasoning
would still apply.  So one would pay another buck to trade back.  The smirky
gift giver is up four dollars so far and the receivers are back where they
started, at which time the original line of reasoning still applies.  Do the
silly proles keep paying a dollar and trading themselves into chapter 11?
That sounds too much like playing the stock market.

Since we are in puzzle mode, consider this one:

For a plane to fly around the world without landing, its tank would need to
hold sufficient fuel to go all the way around.  But what if you had two
identical planes, with fuel transfer capability.  They could take off
together, fly some distance, one transfers a quantity of fuel into the other
plane and immediately turns back, returning to the point of origin.  The
other plane, which received the fuel, flies on around.  

1.  What is the necessary minimum range of the two planes such that the two
could fly a ways, do a transfer, one plane turn around and go back to the
start and the other go around?

2.  What is the necessary minimum range capability if one had three such
planes?

3.  What is the necessary range capability if one has N planes?  (This one
is cool).

spike