Riddle me this

[Andail]

Ok, so we were a group of people and someone told a riddle that went something like this:

A man walks up a hill one day, following a trekking route. He begins at the foot of the hill at 7 am and reaches the top at 7 pm. The next day, he descends the hill, walking the exact same route, beginning at 7 am and finishing at 7 pm.
The route is naturally uneven, with steep, slow parts and more level, fast parts.

While descending the hill, will there be a point, anywhere, at any time, where he can say "Exactly at this time yesterday, I was here"?
In other words - is there sure to be a point that he reaches the same time both days?

I see myself as moderately intelligent - I did take some math courses in university, with probability and shit, but am far from a logical mastermind - but I had no problems whatsoever understanding this riddle, saying "yeah of course." However, almost nobody there, and almost nobody I've spoken about the riddle with, could see this solution.

Now, you guys are genuinely clever, so I'm turning to you. Is this riddle really that hard? Isn't the answer quite obvious - yes, there must exist such a point, regardless of his pace, and regardless of the terrain?

[Snarky]

Yes.

Spoiler

If we imagine that instead of going up one day and down the next, you have two people, one who's going down and one who's going up on the same day, there has to be a point where they pass each other, i.e. they're at the same position at the same time. The same thing applies when he's comparing himself with the time and position from the day before.

[close]

But I don't think it's obvious. My intuition would have been to say no, and I'm not sure I'd have seen it if you hadn't insisted the answer is yes.

[NickyNyce]

Pretty easy one...

What has forests with no trees, mountains with no rocks and cities with no people


and another...

What word starts with E and ends with E but has only one letter

[ThreeOhFour]

What word starts with E and ends with E but has only one letter

Spoiler

Envelope

[close]

[NickyNyce]

Well done ThreeOhFour

[Anian]

What has forests with no trees, mountains with no rocks and cities with no people

Spoiler

A map.

[close]

[Andorxor]

The answers is no,because the earth moves around the sun.

[Radiant]

The answers is no,because the earth moves around the sun.

That's Newtonian physics, and is outdated. By contemporary physics, it depends on your frame of reference.

[Kweepa]

Huh.
Like Snarky, my intuition said no until I read his solution.
It's amazing how reframing exactly the same puzzle can make the answer so obvious!

[Ryan Timothy B]

Isn't the answer quite obvious - yes, there must exist such a point, regardless of his pace, and regardless of the terrain?

As I read it I also found the answer to be obvious (unless you factor in what Andorxor said).

To get a little side tracked, going by what Andorxor said, I sometimes like to pick apart time travel movies that somehow end up on the same spot of the planet no matter the rotation and such. Even with the Delorean just traveling one minute into the future on its first test, it would have returned thousand miles away from its origin (or inside the planet depending where they were on earth rotation). Unless Doc had somehow managed to calculate the exact location and rotation of the earth (and sun, since our solar system and galaxy is shifting along) with any given time and create the return warp hole there. Then there's the moon slowing or altering our rotation, asteroids, etc; but it shouldn't matter too much in a 20 year span.


So my riddle (or question - whatever you'd call it lol): What does a clock measure?

[Anian]

As I read it I also found the answer to be obvious (unless you factor in what Andorxor said).

To get a little side tracked, going by what Andorxor said, I sometimes like to pick apart time travel movies that somehow end up on the same spot of the planet no matter the rotation and such. Even with the Delorean just traveling one minute into the future on its first test, it would have returned thousand miles away from its origin (or inside the planet depending where they were on earth rotation). Unless Doc had somehow managed to calculate the exact location and rotation of the earth (and sun, since our solar system and galaxy is shifting along) with any given time and create the return warp hole there. Then there's the moon slowing or altering our rotation, asteroids, etc; but it shouldn't matter too much in a 20 year span.

1. Well it's obvious unless you have a different thought process. Because, while they will meet at one time, the percentage of their trip will almost certainly not be the same, since the path is pretty random and undefined. Ok, no need to get further into it, I thought Snarky's solution was pretty clear and obvious once I've read it.

2. About the time travel. I have often thought about this very restriction. While some time travelling devices are also space travelling devices, a lot of them I think are not. It's really hard to talk about this because I think we (not only personally but as humanity) don't know enough about time travel in practical form and usage.
BUT I think you could make an interesting story setting out if it, because you could say that in entire time line there's a limited number of times that you could travel to that same spot and not "teleport" into empty space. Btw I think there was even Xkcd comic about it. Though again if you take into account that the universe is expanding and shifting all the time, you wouldn't actually be able to time travel anywhere, though time travel space ship would hav some cool calculations to make, so they don't travel into a meteor or something. Then again, I found that time travel stories are often best when time travel is a mechanic that is set by it's limits and it's explained how it works in the simplest or most general way and then get on with the story as the main thing that should be paid attention to (stuff like Time traveller's wife etc.)
Oh, let's not forget that f-ing brain twister that is the movie Primer.

[EchosofNezhyt]

However, almost nobody there, and almost nobody I've spoken about the riddle with, could see this solution.

Thats wierd.

[Crimson Wizard]

...I sometimes like to pick apart time travel movies that somehow end up on the same spot of the planet no matter the rotation and such. Even with the Delorean just traveling one minute into the future on its first test, it would have returned thousand miles away from its origin (or inside the planet depending where they were on earth rotation). Unless Doc had somehow managed to calculate the exact location and rotation of the earth (and sun, since our solar system and galaxy is shifting along) with any given time and create the return warp hole there. Then there's the moon slowing or altering our rotation, asteroids, etc; but it shouldn't matter too much in a 20 year span.

Here's the simple semi-scientific explanation: time travel is being made inside the gravity field of the planet, the time machine and the planet are bound system of bodies.

What does a clock measure?

It measures the amount of changes inside itself.

[Ryan Timothy B]

It measures the amount of changes inside itself.

The answer I liked was from the movie The Man from Earth:

Dan: Time... you can't see it, you can hear it, you can't weigh it, you can't... measure it in a laboratory. It is a subjective sense of... becoming, what we... are, instead of what we were a nanosecond ago, becoming what we will be in another nanosecond. The whole piece of time's a landscape existing, we form behind us and we move, we move through it... slice by slice.
Linda Murphy: Clocks measure time.
Dan: No, they measure themselves, the objective referee of a clock is another clock.

[Khris]

Cool thread!
I was intuitively sure that there had to be a point as described, but I couldn't say why until I read Snarky's brilliant explanation.

Re the clock, I'd say it doesn't measure anything, it just moves.

One of my favorite riddles: a brick weighs 2 kilos + half of its weight. How much does it weigh?

[Crimson Wizard]

One of my favorite riddles: a brick weighs 2 kilos + half of its weight. How much does it weigh?

Spoiler

Since the brick's weight consist of two halves, then 2 kilos is another half, and total is 4 kilos.

[close]

That's actually difficult only for those who think too hard

[Andail]

I think the trekking route riddle is interesting because it's such an everyday scenario, not like many other far-fetched riddles about monkeys and lightbulbs and stacks of coins and whatnot, and yet it's so hard for some to visualize the solution.

Perhaps I was only lucky to see the solution as Snarky described it - or actually, I kind of mentally superimposed the two routes, and saw that no matter how they're laid out, they have to cross at some point.

PS:
I see that Snarky moved this to the Rumpus forum, which I don't completely agree with, but I still hope it can steer clear from nonsense riddles en masse, and stay somewhat serious. I really like the time-travelling discussion, though

[Snarky]

Incidentally, I'm pretty sure this is a particular case of Brouwer's fixed-point theorem.

[Stupot]

It's not much of a hill - it takes the same amount of time to go up as it does to come down?
The only way this is possible is if you are walking at the same constant speed going down as you did coming up, and completely disregarding the differences in terrain.
If both sets of people are walking at the same speed and disregarding the differences evenness, then they will meet at 1pm (because they will have both been walking for 6 hours and both have 6 hours remaining of their journey.
Of course, this is crap, though, because we ARE taking into account the unevenness of the hill, so the two sets of people will probably not meet at 1pm.
The steep, slow parts going up will become the fast parts going down... the level parts will remain level on the return journey.
This is a hill we're talking about, so I can't understand what the man is doing on his way down, to still finish at 7pm. Maybe he stops off for a long lunch, in which case, any maths involved in this riddle can go out of the window.

[Edit]
To be honest, I think all the talk of it being a hill, and of steep/level slow/fast parts is just to throw you out. What matters is the fact that both journey's take 12 hours. Snarky's solution is perfect, but would just as well be the answer to a question about a man walking to the shop and back on a level road. I think for this riddle (and Snarky's response) to work, you have to ignore all the 'hill' stuff.  Maybe that is the point :/

[Andail]

Sorry, stupot, but you're incorrect. Apart from the fact that most hills are easier to descend than ascend. But the rest is still valid, and is what makes this riddle special. Otherwise the point would simply be in the middle.