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Can you see further than the old chestnut?
I was reminded of this by the post below about lines of longitude.
There is an old riddle that says that if I walk a mile south, then a mile east (or west), then a mile north, I will be back where I started, perhaps having seen a bear on the way. So where am I?
The well-known answer is 'The North Pole'.
But the number of such points on the earth's surface is infinite (if we leave out the bear) of which the North Pole is only one. Explain.
(Those who already know the answer, please give time for others to work it out from scratch. Ta.)
There is an old riddle that says that if I walk a mile south, then a mile east (or west), then a mile north, I will be back where I started, perhaps having seen a bear on the way. So where am I?
The well-known answer is 'The North Pole'.
But the number of such points on the earth's surface is infinite (if we leave out the bear) of which the North Pole is only one. Explain.
(Those who already know the answer, please give time for others to work it out from scratch. Ta.)
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The riddle is slightly different, it is to ask what colour the bear was and become amused at the protests that one can not know. So 'fail' unfortunately on that one :-)
But yes, as d9 says, it is to do with definitions. One heads away from the north pole going south, and towards it going north so end up at the starting point regardless of how much east or west travelling we do between those 2 journeys.
But yes, as d9 says, it is to do with definitions. One heads away from the north pole going south, and towards it going north so end up at the starting point regardless of how much east or west travelling we do between those 2 journeys.
It doesn't matter whether one sees the bear, shoots it, photographs it or whatever. It is the bear's presence which makes the North Pole a unique answer.
Eliminate the bear and you have an infinite number of points from which you can walk a mile south, a mile east or west, a mile north and end up where you started.
All I ask is where they are, once you have eliminated the bear.
Eliminate the bear and you have an infinite number of points from which you can walk a mile south, a mile east or west, a mile north and end up where you started.
All I ask is where they are, once you have eliminated the bear.
I believe you need to rethink your description of the issue. The bear is irrelevant to the triangular (on a globe's surface) stroll. It is merely there to give someone a riddle to answer. It certainly is not there to make the north pole a unique place. The north pole is already a unique place by definition.
You do not have an infinite number of points on a single world from which you can walk a mile south, a mile east or west, then a mile north and end up where you started. Try a few examples and you will see this. Indeed if you are just half a mile north of the equator when you start your stroll you will find yourself a whole mile away from your starting point at the end.
You do not have an infinite number of points on a single world from which you can walk a mile south, a mile east or west, then a mile north and end up where you started. Try a few examples and you will see this. Indeed if you are just half a mile north of the equator when you start your stroll you will find yourself a whole mile away from your starting point at the end.
Old Geezer, you are quite wrong for once.
There is no trick to this; it is simple geography. And we are talking about the surface of our planet as we know it.
Forget the North Pole, just one point as identified by the bear, then start again to find the other, infinite, number of points.
Think, folks, think.
There is no trick to this; it is simple geography. And we are talking about the surface of our planet as we know it.
Forget the North Pole, just one point as identified by the bear, then start again to find the other, infinite, number of points.
Think, folks, think.
I think what Old Geezer is suggesting has nothing to do with this particular geographical conundrum. What he is saying is that there cannot be an infinite number of points on a finite area (unless the point itself occupies no space, in which case you could not start your journey there).
As for the riddle itself it only seemingly works when the starting point is one of the poles because the lines of longitude (on which we base the notion of “north” and “south”) converge there. If you tried the experiment starting from a point on the equator (or indeed any lower latitude) you most certainly would not return to your starting point.
But do tell us if you know differently, chakka, because I’m intrigued.
As for the riddle itself it only seemingly works when the starting point is one of the poles because the lines of longitude (on which we base the notion of “north” and “south”) converge there. If you tried the experiment starting from a point on the equator (or indeed any lower latitude) you most certainly would not return to your starting point.
But do tell us if you know differently, chakka, because I’m intrigued.
No, chakka using your terminology it only works at the poles. EG If I start at my house on the equator and walk a mile south then a mile east then a mile north I am slightly less than one mile to the east of my house, still on the equator. It can only work as you say if I designate my house as the north pole and all other compass points relative to that.
All right, I’ll put you all out of your misery. Here goes:
Forget the North Pole and polar bears and move to the other end of the world.
About one-sixth of a mile north of the South pole (actually 1/2π) there is a circle of latitude (A) exactly one mile in circumference.
Take another circle of latitude (B) one mile north of that.
You can start anywhere on B, walk a mile south until you meet A, walk once around A to get back to where you joined it, then retrace your steps to B. You have walked a mile south, a mile east or west and a mile north and got back to where you started.
What’s more, the number of points on B from which you could have started is infinite.
But stay! There is more!
Inside A is another circle which is exactly half a mile in circumference. Starting from a circle one mile north of that you repeat the procedure, this time going twice around the inner circle. You can repeat this for circle of one third of a mile in circumference, one quarter and so on until the circle becomes too small to walk around.
So in the end you have a large number of circles from which too start, each having an infinite number of starting points.
Rather dwarfs the North Pole answer, doesn’t it? But, of course, pace Old Geezer, you can make te North Pole unique by specifying a bear, since there are no bears in the Antarctic.
Forget the North Pole and polar bears and move to the other end of the world.
About one-sixth of a mile north of the South pole (actually 1/2π) there is a circle of latitude (A) exactly one mile in circumference.
Take another circle of latitude (B) one mile north of that.
You can start anywhere on B, walk a mile south until you meet A, walk once around A to get back to where you joined it, then retrace your steps to B. You have walked a mile south, a mile east or west and a mile north and got back to where you started.
What’s more, the number of points on B from which you could have started is infinite.
But stay! There is more!
Inside A is another circle which is exactly half a mile in circumference. Starting from a circle one mile north of that you repeat the procedure, this time going twice around the inner circle. You can repeat this for circle of one third of a mile in circumference, one quarter and so on until the circle becomes too small to walk around.
So in the end you have a large number of circles from which too start, each having an infinite number of starting points.
Rather dwarfs the North Pole answer, doesn’t it? But, of course, pace Old Geezer, you can make te North Pole unique by specifying a bear, since there are no bears in the Antarctic.
Surely the point about your original riddle is that you get back to the north pole if the distance travelled is 2 miles or 3 miles or whatever number of miles you choose as long as when you go south you don't go past the south pole.
This is only possible if you start at the north pole every time. In your argument, if I change the distance travelled then I have to also change the starting point if I always want to end up where I started.
I think that's where the difference lies.
This is only possible if you start at the north pole every time. In your argument, if I change the distance travelled then I have to also change the starting point if I always want to end up where I started.
I think that's where the difference lies.
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