h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Sorry, correction -- the earth spins (its circling the sun is another matter).

Can I pop in again with another quick point? No? Tough

I've been wondering if this problem has any application in the real world? Is it something set for maths/physics students to work out, or does it have a useful application?

Either way it doesn't matter, but I think it needs a quick note at least as to its purpose.

Talking about purpose to a mathematician is like talking about money to an old-school aristocrat

You know what, Alex - a few of us would sort this out in 5 minutes in the pub.


Opening paragraph - good

The Problem section - good

To Circle or Not To Circle section -

I think "orbit" is ambiguous. I think you mean orbiting a stationary squirrel in this context.

Going Nowhere Fast section -

I think I follow your reasoning in the first two paragraphs, but it's quite an involved point - it's a kind of proof by contradiction. i.e. when we observe the motion relative to the tree, we see the man encircle the squirrel if the radius of his path is greater, but not if they are equal. But when we imagine the motion relative to the squirrel, the man encircles him no matter what his radius is. (He could even be running around inside a hollow tree trunk, for example)

The third paragraph lost me, I'm afraid. It's the "no motion relative to each other" which is the difficult (and arguable) concept. If you are keen to explore relative velocities then I think you would need to present this in a far more systematic way. It may be overkill for this entry.

Just thinking more about Trin's comments. I agree that Camp 2's view (if this is indeed what they see) has vague similarities with Zeno's paradoxes (A541937). I found them interesting to read after reviewing this, and I wonder if an informal mention might be worthwhile (maybe a footnote or something) For one thing, Zeno's paradoxes sparked a lot of philosophical and mathematical debate, which this appears to be doing too.


Finally, I just thought of an alternative way to present the article. You could do it as a conversation between two people (one of each camp) observing the scene. It may be one way to make it more accessible, if all else fails.

Hope this helps

Icy

This problem has little purpose other than to make people argue

I've made some changes should I just drop the last paragraph?

Entry: The Squirrel Dilemna - A Puzzle - A16967659
Author: Alex "Tufty" Ashman [!] - U566116

For ease, etc...

For ease of ridiculing me for all the crap I've dragged you lot through

To Circle or not to Circle section - better

Going Nowhere Fast section - A bit better, but yes I would consider dropping the final paragraph.

Let's see what others think...

Icy

I've decided to drop the last paragraph - it added to the confusion rather than exploring it

I think it's not bad at all now, Alex.

I wonder what others think...

I think you haven't dealt with my objection in post 139. I know, that's a whole page back, so here it is again:

If you argue that the man is not circling the squirrel, because he is not getting a 360-degree view of the squirrel -- head tail and both sides (or back, side, belly, other side), then you must accept the following:

If the squirrel sits on a rotating turntable and the man *stands still* then the man has circled the squirrel.

Well?

I myself haven't argued the various sides thing, and I don't think it quite works. I think the 'passing to the left' thing is easier to think about.

But to me the objection looks watertight. If you disallow one it can only be by allowing the other.

From the squirrel's point of view a stationary man will appear to circle him as he rotates on his turntable, just as from our point of view the sun appears to circle the earth. Mathematics may be impervious to changes of POV, but we must make special mention if we are to extend this neutrality to common language.

"Passing to one side" applies equally in the turntable example.

Maybe the notion of "circling" is dependent on a fixed background in which you can draw circles (in this case, the forest)? Which is why we say that Earth is orbiting the Sun and not the other way round, because we have the solar system in which we can (at least with the pencil of mind) draw circles (yeah, and ellipses).

Take for instance Recumbentman's experiment: the squirrel sits on a rotating turntable and the man *stands still*. I wouldn't say "the man has circled the squirrel". I could say, "from the squirrel's point of view everything happens as if the man was circling around him", and this model could be useful in solving some problems related to the man's position relative to the squirrel.

Now assume that everything, except squirrel and man is made of crystal-clear glass: you have no referential compared to which you can describe their movements. You have no idea who is moving and who is not. You couldn't distinguish the man moving around the squirrel or the squirrel moving on a turntable. Then who is circling who?

That's the way I imagine a mathematician isolating the two bodies.

Obviously the answer is to use a grenade and photograph the remains.

Been a fun read all this Alex - well done.

The flaw in that solution is you will go to jail....go directly to jail, do not pass go, do not collect £200 - the red squirrel is a protected species you beast.


I used to be in the Tufty Club.

I'll reproduce the link I posted on Lil's journal for you, Fizzy. Don't miss the video.
http://news.bbc.co.uk/1/hi/magazine/4690166.stm

Interesting motion as the squirrels follow the weasel around the ice cream van, but I found it a bit of a challenge to extrapolate it to Alex's scenario.