On Mon, 30 Jun 1997 12:05:39 -0500 Richard Lawson wrote:
: There is, of course, a solution.  However, the teacher said it was 

also

: possible with just three lines:  Just draw a line from where you 

are to

: the north pole, then drop back down to the south pole, then back on 

up.

:
: I protested:  doing that was physically impossible.  The teacher 

said

: no, it was possible.  I argued strongly that it wasn't, that you'd 

never

: be able to draw a straight line for thousands of miles over water, 

snow,

: etc.  Since I was just a kid, of course, the teacher ignored my
: argument.

And well he did.  Richard, the man was just illustrating a *point*
there.  He was trying to teach you the wonder of lateral thinking;
that by rising above the limited mindset of the person who thought
up the riddle and using *three*-dimensional geometry instead of
two-dimensional, you could simplify the solution even beyond the
requirements.  But, alas, you were a kid and the lesson was lost
on you.  :)

Gee, I guess I was just dumb, huh?

: However, I still believe I was right:  the solution he proposed 

was

: physically impossible.

No, Richard, you're wrong!  (He hates that, people. Remember that
for later.)

Yes, I do.

You are committing here, what I consider one of the cardinal sins
of pseudo-scientific thinking:  You are confusing "It is
impossible" with "It can't be done".

So I'm pseudo-scientific, am I?  I guess the two years I spent at 
Caltech learning scientific methodology meant nothing.

The definition of "impossible" is "it can't be done", Bast.

If someone told you "Go lift that mountain over there", you would
say "That's impossible", but in fact it is perfectly possible, and
that can be proven.  I merely need to measure the volume of the
mountain, look up what kind of stone it is and it's specific
weight, multiply the two numbers and ask you how high you want it
lifted.  Then I can tell you accurately what amount of force you
need to lift this mountain.  In other words, *it* *is* *possible*!
There is a definite number that gives the required energy to do
it.  Neither you or I can do it, but isn't it the height of
arrogance to conclude from this fact that it is plain impossible?

Arrogant, am I?

It's this kind of woolly thinking that prompts hundreds of rookie
mathematics each year to try and square the circle.

Woolly, am I?

Every maths
book worth its salt will tell them that it's impossible, but they
think that just means "Nobody mananaged it yet" - because common
usage (and I know how much store you put in that) has given the
words "It's Impossible" this meaning.  They do not realize that
science does not work this way.  When a mathematician (or a
physicist or, for that matter, any serious scientist) says "It's
impossible", it means exactly that.  There is *proof* that the
circle *cannot* be squared.  No secret trick or ingenious method
can ever be found - it is plainly impossible.  Which does not go
for lifting a mountain or drawing a line from pole to pole.

Yes it *DOES*, Bast.  Ever hear of Chaos Theory?  Chaos Theory would 
blow your little theory that "it is possible to draw a line from pole 
to pole" to smithereens.  There would be a nigh-inifinite number of 
variables that would keep this feat from being accomplished.  I've 
always loved Chaos Theory because it takes "thought experiments" out 
into the real world and shows how "theoretically possible" can be 
mathematically proven to be impossible.  Or close enough to make no 
difference - it is just as likely that my molecules will spontaneously 
jump a meter to the right.  I'm going to call both instances 
"impossible" myself.

In conclusion, let me say that as far as I'm concerned, you can
say in your story that it's impossible, and I wouldn't raise a
brow, much less an objection.  Just don't claim that any laws of
physics are involved, and you are right as rain.

Math theory.  Chaos.  Physics is based on math.  Same thing.

(Incidentally, Richard, when I was in school, I always *hated*
those kids who turned down wonderfully sneaky solutions like
drawing a line from pole to pole with such boring arguments like
"But you can't *do* that!"  I bet they all grew up to be
accountants with no lives. ;)

Well gee, Bast, thanks.  Thanks a lot.

Sebastian

You probably meant all of your insults above to be teasing, but I 
think you went a little too far, especially with that last 
observation.