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The Traveler on a Bus

Posted by JG on May 17, 2011 – 5:03 am

If you are walking southbound on a northbound bus, in how many directions are you traveling at that moment in time, ignoring micromovements? You must explain your answer.

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1. 1. JB Said：

Assuming the bus is travelling faster than I, the simple answer would obviously be that I am heading north from a glaobal perspective. I assume that we are not looking for the simple solution. So,in addition, in relation to the bus I am heading south. I might also be headed in the up (or down) direction if the bus is on a hill. The earth is rotating from west to east, so that I am also traveling in an easterly direction as well. The earth is orbiting the sun so I am also traveling in that direction. The sun is orbiting the center of the Milky Way galaxy, dragging me along with it. Of course, all matter is travelling away from the point of the big bang.

2. 2. Chris Said：

I assume that ignoring micromovements means treat your body as if it were rigid e.g. ignore movement of the various parts of your heart. You can only be travelling in one direction at any given moment – ever, even on a roundabout (so you could be rotating as well).

No matter what co-ordinate system you use, the vector sum of the components of the velocity is a single value.

But I concur with JB as to the various contributions to your speed.

Of course as far as you are concerned you only ever have a velocity of 0, it’s everything else that’s moving.

3. 3. randy Said：

With the only two moveable variables provide, it depends on the speed of the bus and the speed you walk. If the bus is not moving or moving slower than you are walking, then your moving south only. If the bus and you are walking the same speed, then you are not moving north or south. If the bus is moving faster than you are walking, the you are moving north, only at a slower rate than you would be if your were sitting down.

4. 4. SP Said：

I was going to post along the same lines as JB. It depends on your frame of reference, or rather, how many frames of reference are allowed.

5. 5. John Said：

you are moving in 2 directions if you are on the northbound bus and walking south to the rear.

6. 6. Chris Said：

Hi John, if you were moving in two directions at the same time, you’d be ripped apart.

e.g. If you were suggest that I was travelling East and North, I’d say that’s wrong, I’m only travelling North-East.

7. 7. Jhuerta Said：

walking southbound on the northbound bus means the bus is sitting still and being loaded with people. in that case you are moving in one direction.

8. 8. John Said：

@Chris,

If the bus YOU are on is traveling northbound(Which the question states)Then therefore you are obviously on or(IN) the bus as being the passenger who is on his feet walking(down the aisle) southbound ON the bus as it’s traveling northward where your destination lies to take a seat in the back which is to the south of the bus.
Have I made myself anymore clearer as to what the question is asking?
The answer is obvious that you’re moving in 2 directions without being ripped in half.

9. 9. Chris Said：

Hi John. If you were right (and the bus was long enough etc.), you’d be going to the North pole and the South pole at the same time. When you get to them, you could send both of yourselves souvenir postcards.

10. 10. Chris Said：

Hi JB. I just re-read your post (#1). The point at which the big bang occurred is everywhere (the universe hasn’t got a centre, or if you prefer, every point is it’s centre). So you can’t travel away from it and your velocity with respect to it is 0 no matter how fast or what direction you are travelling – whatever either of those terms mean

11. 11. Karl Sharman Said：

Its all relative…. If only the question identified what it is relative to, as well as how fast the bus was going, as well as the person on the bus.
Overall, in the grand scheme of things, Northbound.
Relative to the bus, Southbound.
From a Hellraiser perspective – ripped apart!

12. 12. JB Said：

Hi Chris,

I did not intend for this to be a discourse in astrophysics. It has been a very long time since I studied this subject and my memory can be faulty, but I seem to remember that all matter was condensed into a single, incredibly small space, causing the big bang, sending all matter hurtling in all directs. Think in terms of a supernova, but on a much grander scale. The universe is expanding in all directions, everything moving away from everything else.

As for the question that was actually asked here, the fact that we are being asked how many directions we are going at a particular moment would seem to imply that we should be identifying multiple perspectives. From the bus driver’s perspective, I would be walking south, away from him, assuming the bus isn’t being driven backwards. From a bird’s eye view I would be moving north, but at a slower pace than the bus driver. To someone standing on the sun I would be moving generally along the earth’s orbit. And so on.

13. 13. Chris Said：

Hi JB. For the record I wasn’t criticising you, I was just going the extra mile and I’m aware that most people don’t realise the full meaning of what the big bang was about.

A supernova is an event in space-time. The big bang wasn’t merely an event involving an explosion of matter in a pre-existing (but empty/vacuus) universe – there was no universe before the big bang. Space and time did not exist before the big bang – they were created by it.

The idea that there is no centre is a consequence of the Cosmological Principle.

Fred Hoyle took it all the way (with the Perfect Cosmological Principle) and asserted that the universe always has been and always will be much the same as it is today (i.e. on average)- that led to his Steady State Theory. Funnily enough, he was a principle opponent of the big bang theory, yet the phrase “big bang” was coined by him.

14. 14. JB Said：

Chris,

I did not take your post as a criticism. This is an extremely fascinating subject that can be discussed at length, but I don’t think this is the proper forum for this.

15. 15. Chris Said：

Hi JB. My comment #10 was completely on topic and was a response/extension of the reasonable point you had made in your post #1. I’d be off-topic (not that I’m overly bothered by that) if I were to go on to say that because of the accelerating expansion of the universe, that it may have zero mass or even be made from nothing at all – so I won’t mention it. My post #13 was a response to your post #12. If you don’t want to dicuss those topics, then don’t bring them up. Also, don’t protest or slap me down when I elaborate on any comments – I’m usually trying to be helpful and/or informative.

To me the original question seems to be about recognising that you can only travel in one direction at a time, no matter what reference frame is used to determine that direction. The reference frame you use only affects the particular words that you’d use to describe the direction.

I find it strange to talk about moving South inside a bus – buses don’t have a North or South. North and South imply that the reference frame is the Earth.

16. 16. JB Said：

My intent definitely was not to slap you down. I apologize if that is the way you took my comments. This is a subject that I used to be very much into and always enjoyed talking, reading and learning about it. I am always interested in learning, which is one of the reasons I frequent this site. I have very high regards for you and the others who contribute. I simply did not think this was the venue for an in depth discussion of this topic. I stand corrected.

17. 17. Chris Said：

Hi JB. Of course I accept your apology. Thank you for offering it. Even if you hadn’t, I wouldn’t have held it against you; I realise that we all get a bit crotchety at times.

Obviously the extensions were just starting to get away from the real purpose of ths page, but I really do feel “so what?” as long as it’s interesting.

I expect that a lot of the stuff I know isn’t familiar to most of the visitors here, and that they might be interested in it and may even do a spot of Googling to find out more. I read a very good book (just for interest) many years ago: “Relativity: Special, General and Cosmological”, by Wolfgang Rindler. That’s where I learnt most of what I know about relativity. It even contained a very simple special relativity model of a (non-physical) universe that made it easy to see why there is no centre to the real universe. I think it was called the Milne universe.

18. 18. Chris Said：

I’ve started skimming my relativity book (second edition, 2006 version) and found the following. The background microwave radiation residue from the big bang is so isotropic that it’s been possible to measure a dipole variation (courtesy of Doppler shifting) and in consequence the speed of the Earth is 380 km/sec with respect to the background. The background is about as good as it gets for defining local absolute motion.

19. 19. JB Said：

Chris,

I have one question regarding velocity. You mentioned that the velocity of the earth is 0. Yet Johannes Kepler’s second law of planetary motion states that each planet sweeps out an equal area in equal times as the planet travels in its elliptical orbit (Kepler’s first law). This means that the planets slow down and speed up (conservation of momentum) as they make a complete yearly cycle. Wouldn’t this mean that the planets’ velocities are not equal to zero and is constantly changing. What part of this puzzle am I missing or misunderstanding?

Also, in your post #15 you mention that buses do not have a north or south. However, we can move further south from the front of the bus and its driver.

20. 20. John Said：

@Chris OMG dude climb back up the proverbial tree and re-read the question.It is asking “at that moment in time how many direction are you traveling?”It doesn’t state anywhere about time in the future or how many miles you have to travel,nor does it state mathematics about the Earth’s rotation,speed,axis etc.
It’s a simple question to answer without the need to dissect it into different theories.

I believe my answer is simple enough and there’s no need to try to convince me otherwise with your theories Chris because in my honest opinion,I think your head is too far up your intellectual ass where there is less oxygen thus cutting off logical thinking to make any sense of what i’m saying is right or wrong.
Everyon is entitled to their opinion but that doesn’t mean we have to agree with you.

Any further responses to my answer will be considered spam.
Let’s move on shall we?

21. 21. Karl Sharman Said：

John, just to be really clear about your post # 8 – your answer is that you’d be travelling in 2 directions at the same time… North and South – polar opposites?
Relative to what? That’s my question, as it is not clear in the original question.

It can’t be relative to a single point- that is the Hellraiser scenario where your soul/body is ripped apart.

It must therefore be more than one point that the direction(s) are relative to, and that brings in a whole load of variables.

I just thought I’d stir things up, because I’m like that
Now I’m going to sing the Spam song to myself from Monty Python…. before going down in flames…..

22. 22. Chris Said：

Hi JB. I can’t see where I said that, but the speed of the Earth is 0 with respect to the Earth. Keplers’s laws seem to be using the sun as the 0 reference velocity.

I’m happy to let the bus have North and South ends for the purpose of this discussion, but I think it would be clearer to say it had a front and a back end. I have no problem with you moving relatively South with respect to the bus even if you are moving North altogether.

As far as I can determine, you have the same understanding as I do about these matters. i.e. we both know that you can only be travelling in one direction at a time with respect to any given reference frame, and we both know that different observers may give a different description of that velocity. In some frames the bus passenger is stationary, and someone in an airplane might say the traveller is moving at several hundred miles per hour and depending on their direction of flight could nominate any point of the compass for the direction.

Hi John. Oh dear, I’m sorry that the problem and my whimsical attempt to illustrate the fault with your unreasoned assertion is is too hard for you to understand. In case you haven’t completely shut down your mind yet, try the following: if you are facing towards the South and walking on a bus that is travelling North, then if your walking speed is less than the bus’s ground speed then YOU are travelling North (even though you are walking relatively Southwards with respect to the bus). If your walking speed is greater than the bus’s ground speed then YOU are travelling South. If you still believe that you can travel North and South at the same time, then you are claiming that you can go towards the North pole and the South pole at the same time – I say that’s ludicrous. There are two ways that can be made true – you need to be on a spaceship heading towards the Earth along its axis of rotation.

23. 23. Karl Sharman Said：

Chris – your post 22, I don’t mean to be pedantic, but if the bus is a London “bendy” bus, and the front is going North, after a left, or right hand turn, and you are in the back section of the bus, halfway (for arguments sake) through the turn, then I am at a loss to configure my direction of travel – I think it may be 3 directions – North, South and Left, or Right.

Please factor this into your Kepler’s second law of planetary motion before you start to bring in spacecraft travelling towards Earth along the axis of rotation – and btw – is that magnetic north or true north, or where Santa lives?

See – I’m confused now! GRRR!

I think I can keep this up for a few more posts yet!!

24. 24. Chris Said：

Hi Karl. My cop-out response is that we are only considering an instant of time, so you have a velocity but you don’t change position.

I was hoping to avoid the problem of what heading North even means. The Earth is roughly spherical and so you won’t actually be heading in the direction of the pole (when you’re in London say), but to a point above it. All these considerations do is complicate the situation without getting to the heart of the problem.

25. 25. Karl Sharman Said：

I know Chris…. I’m attempting to be faecetious – gratuitously so, as I felt John’s post was a little OTT!

26. 26. Chris Said：

Hi Karl. I knew your post was a deliberate wind-up and probably was a reaction to John’s post. During editing, I unintentionally chopped the winks off. I apologise for that, I shouldn’t have left you with any doubt about my high respect for you.

I agree, John’s post was OTT. It demonstrated that he’s the baboon that he was trying to make out that I was. But he made up for it with a home goal by calling me an intellectual. It’s strange that he thought of that as being a handicap.

27. 27. John the "Baboon" Said：

Ok Chris since i’m the baboon,how come you haven’t given an answer to the question at hand yet?
Since this question was posted, all you have done here is Trolled on everyones answer except your own and trailed off to left field talking about spaceships which don’t exist except maybe in Star Trek movies which is pure science fiction.
I’m gonna add another scenario to the question and see what your answer would be.Since you are traveling southbound on a northbound bus and you are walking to the rear staring at your two left feet,,suddenly some asshole jumps up from where he’s sitting and socks you in the nose(blood flies everywhere),your feet go flying up as you land on your ass.
How many directions did you just travel in that split second not counting your 2 right shoes?

28. 28. John the "Baboon" Said：

Lets keep is short and simple for everyone shall we?Longwinded explanations gets awful tiring.
Gravity is your best ally.

29. 29. Chris Said：

Hi John. The blood splattering counts as micromovement and so is outside the scope of the question.

No spaceships! Do you believe that that Neil Armstrong was faking it?

Imagine the bus is moving at a speed of 15 mph Northwards and you are walking towards the rear of the bus at 2 mph. Altogether you will be moving at a speed of 13 mph Northwards. Didn’t you know that?

At any moment in time you will have a velocity v. In a reference Cartesian co-ordinate system you will have velocity (vx,vy,vz). The magnitude of that velocity is your speed, s = √(vx² + vy² + vz²) and you will have a direction (vx,vy,vz)/s. You will note that the direction is a single-valued quantity.

If an object is move with a velocity v with respect to a reference frame that is moving at a velocity V with respect to a second reference frame, then the velocity of of the object with respect to the second reference frame is the vector sum V+v, and is a single valued vector quantity. So the object still only has one direction.

I won’t attempt to prove those facts. They have the status of being “Laws of Physics” and can only be verified by experiment.

I’ve assumed Newtonian mechanics in the above. But it is not particularly difficult to find laws of addition of velocities in the domain of Special Relativity. But in the end, unique directions result at all times.

30. 30. Chris Said：

… nearly forgot. I see no trolling by me on this page. Could you give me an example (not involving you)?

31. 31. Karl Sharman Said：

Just to add to this, for the sake of keeping it going in the rumble in the Norwegian Jungle with the Troll vs. The Baboon….

“In the split second” – is this an actual second or is time taken out of the equation? Has time been frozen for the purpose of this example?

This is a trap – do not answer this question…..

Sorry Babs, but my money is on the Trollop!!!

BTW – what is trolling anyway? If anyone has the http address fror wikipedia, I’ll look it up…

32. 32. JB Said：

You guys need to patch things up and end the Rumble since the world is scheduled to end sometime today (film at 11), ending the Rumble anyway.

33. 33. JG Said：

First of all, I’m sorry it took me so long to post.

Second, some of you people are seriously overthinking this.

Third, Post 15 is on the right track, but way too complex.

Fourth, the bus is a normal bus and is going straight down a highway. No turns.

Fifth, the only way the world is going to end today is if someone discovers a type of bomb a million times more powerful than all of the nuclear weapons in the world and accidentally sets it off.

34. 34. JG Said：

PS: I said in that second and ignore micromovements so that you ignore the bouncing of the bus.

35. 35. JG Said：

I’m also looking for a number of directions, not the exact directions and not the speed. There are multiple directions. You must explain your answer.

36. 36. Chris Said：

Hi JG. In my opinion there is only one direction. There are infinitely many descriptions of it, due to both choice of the method of description, and the infinitude of reference frames from which the direction can be described. But those things are words and viewpoints – a rose by any other name is still a rose.

In your post you said “at that moment in time”. For that nothing can changes its position (even a photon doesn’t move). If you meant over an extended period of time, such as one second, then that’s another ball game. Then I’d be more than happy to accept that there are multiple directions involved. But I’m now very confused – I’ve never heard of a micromovements before (in the context of physics).

So if the passenger is in the process of exploding (say), then various parts of the passenger can be travelling in different directions. I had already covered that idea in my post (#2), but less dramatically.

I have assumed that we are ignoring quantum mechanics and the Heisenberg uncertainty principle in particular, one of Zeno’s paradoxes, a direction in time or some other sort of direction, like an instruction.

Other than that sort of thing, I can’t imagine what you’re getting at.

37. 37. Chris Said：

Hi again JG. I’ve just checked your post 33 which says my post 15 is on the right track. I think that I’ve been very clear that there is only one direction, not several; so how can I be nearly right when you say there are several directions?

Well done though, 37 posts, that’s pretty good going

38. 38. josh Said：

one……

objects can only travel in one direction at a time.

If you were to detemin more than one point of orgin that would be different.

object can in current day only travel point a to b.

39. 39. Chris Said：

Thank you josh, you’ve given me a clue. I’ve been thinking of point like objects. As we are extended objects, most parts of us will be moving in a different direction. More relevantly, taking the North pole to be a point, our whole body cannot be moving there without (eventually) squashing it down to a point. If that’s the case, then the bus wasn’t moving Northwards though. If it were at the equator then most of it would be moving Northwards, but parts of the engine and the wheels wouldn’t be.

I also omitted, in my simple calculation, that the bus might be going over a bump, so we might be moving up or down etc., at the moment of interest and possibly no part of our body would be travelling Northwards.

40. 40. John Paul Said：

Hi Chris, don’t over think. John’s solution is straight forward and i believe that’s correct.

41. 41. JG Said：

I am looking for the number of different directions, not the overall direction. Driving north is one, walking south is a second. Tell me how many there are in total, and explain why. I am looking for a number and an explanation, not complex physics equations.

42. 42. fateema Said：

i haveee nooo i dea loool

43. 43. Chris Said：

Hi JG. You have simply given two descriptions of one direction (in the context of the problem).

I accept that the second description is typical of what someone might really say. But that doesn’t mean that the description is correct. “I was walking towards the rear of the [Northward moving] bus whilst facing towards the South”, would be better (but still unsatisfactory); I doubt that anyone would be even that precise in practice though (including me).

But your question asked for how many directions there are, not how many descriptions, or for examples of how sloppy people can be when they describe a situation. There is an unlimited number of possible descriptions, because there’s an unlimited number of frames of reference and no limit to human stupidity

44. 44. Karl Sharman Said：

I suppose that if we are looking for a number of directions over, say, 1 second whilst the bus is travelling North and you are walking to the back, then I am going with a minimum of (360^2)+1 directions, working on base unit of 1 degree over three planes of movement (N.E.S & W on horizontal and vertical axis) and time (only 1 direction at the moment…). I know that the degrees can be divided into minutes/seconds etc, but I shall ignore that for the purpose of this answer.
I shall ignore involuntary body movements such as blinking, heartbeats, lung movement, blood etc.

But I suppose at the end of it all, the question is probably looking for 3 – Northwards, Southwards and Time. I still think that without a point of reference the North/South movements at the same time can only result in one direction => 2 directions – Overall Direction + Time

So – between 1 and infinity then – give or take….

I think we covered something along these line with regards newtownian/einstein relativity… now I’m rambling….

45. 45. Karl Sharman Said：

Sorry, post 44 – thats over 2 planes of movement, not three – Still getting to grips with counting 1 to 10… I’m up to six at the moment!

46. 46. JG Said：

Im going to explain this again. The answer is a number of different directions and an explanation of why. Not an overall direction or the exact directions. That would be way too complex. North is one. South is a second. How many are there in total and why?

47. 47. Chris Said：

Hi JG. I give up. I don’t know the answer to your riddle Is it to do with the game of Monopoly or something like that?

48. 48. Karl Sharman Said：

JG – Does this mean time does not count as a direction? I kinda like that one

1. North(ish) – Bus’s direction – relative to it’s starting point.
2. South(ish) – Travellers’ direction – relative to his starting point on the bus
3. Forward in Time – a constant(?)
4. Down(ish) – Earth is spherical – relative to his/bus’s starting point, although this would take some time, or assume the road follows the exact sphere of the planet…
5. His Left(ish) – East – Rotation of Earth – Traveller & Bus, relative to starting position
6. His Right(ish) – West – Direction of rotation of galaxy – Traveller & Bus, relative to starting position

Six general directions to be non-exact and simplistic.

In my answer above, I have assumed the bus is on the earth, which rotates etc etc. I am adding more assumptions and information than the question offers

1 direction only – South – The northbound bus is stationary, you are the only thing moving on it. As we all know, bus drivers won’t drive their bus until we are all seated.

In this answer I have assumed the bus is stationary, although by OED standards a bus that is northbound is moving towards the north.

Not enough information. I still believe that I need to know what the point of origin/frame of reference and relative speeds are to give directions any more than “Bus is going North” and “Traveller is walking towards the back of the bus => south”, and of course my favourite, “Time”.

49. 49. Chris Said：

Hi Karl. I cant believe that I hadn’t mentioned a direction in time. But I’d simply counter that by saying that’s still only one direction in space-time. Same if you add the other 7 space dimensions that are thought to exist.

50. 50. Karl Sharman Said：

Chris, you mean Buckaroo Banzai was right about 7 dimensions?

The more I read the question, I think that the trick in the question is that you are the only moving object (except planet, universe etc)…….?

51. 51. Chris Said：

Hi Karl. Apparently Buckaroo was wrong. 10 space + 1 time has been favoured for the past 20 or so years. The LHC experiments may help sort that out – and destroy the world for a bonus (but I gather that’d take about 300 years if a stable black hole escapes).

I’ve stopped treating this as a physics question. OTOH no version of Monopoly seems to have a bus in it. Maybe a non-UK game is involved. But the question doesn’t seem to be consistent with the game idea either.

I just noticed that I had included the direction in time idea after all – was that the reason for your comment?

52. 52. Karl Sharman Said：

I think you have mentioned the time factor peviously, as well as using velocity – no time, no velocity.

As far as Mr Banzai goes, I just remember it as an early 80’s oddity with Peter Weller, Jeff Goldblum and a bunch of other stars, taken from a comic book I think…

This question has stumped me, as I cannot grasp what the question is asking for. As you have stated previously, you can only travel in one direction, relative to the Earth, but JG seems to be positing that there are at least 2 + n directions in play here – north and south + n other directions…

I am looking forward to the answer!

53. 53. Chris Said：

OMG. Is the answer supposed to be referring to the 3 (or 10) spatial dimensions? I hope not.

Whatever the answer is, I realised that I didn’t know the formal definition of direction or dimension. So, just for possible interest http://en.wikipedia.org/wiki/Dimension says: “…informally defined as the minimum number of coordinates needed to specify each point within it…”,…”…the constituent structure of all space…” and “[dimensions are] from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three”. This one surprised me: “the circle is 1-dimensional even though it exists in the 2-dimensional plane” (that’s because it’s radius is it’s only parameter).

To me a dimension isn’t a direction, it is a component of a direction. If I’m travelling NE, I’m not travelling N and I’m not travelling E, I’m only travelling NE.

54. 54. JG Said：

Post 48’s answer one is close. There are six Directions, but Forward in time is not one of them. Chris, this question has nothing to do with Monopoly or spatial dimensions.

55. 55. Chris Said：

Hi JG. I’d really given up after reading your post 41.

I don’t think I’ve mentioned rotation yet, but there is only one direction of rotation as well. So I can bump it up to two directions, one translational and one rotational. I suppose I could double that with the direction of linear and rotational acceleration, but neither of those seem to fit with the notion of direction of travel. There is an unlimited chain of such things: the next is known as “jerk” and is the time rate of change of acceleration.

In view of your post 54, I haven’t the slightest idea of what the answer could be. Unless I have a revelation, I have completely given up

56. 56. JG Said：

For anyone who wants to figure out the answer for themselves, Dont read this post.

I have given up. Most people are going in the wrong direction completely and I believe none will answer it correctly.

There are six directions:
1. Walking South
2. Driving North
3. Rotation of the Earth
4. Movement of the Earth Around the Sun
5. Rotation of Our Galaxy
6. Expansion of the Universe

Sorry for any who wanted to figure it out, but everyone is completely off track and most have given up.

57. 57. Chris Said：

Hi JG. I asked John McEnroe for his opinion. He agrees with me. He said, “you cannot be serious”.

58. 58. Chris Said：

Those are 5 contributions to the passenger’s one and only direction.

The expansion of the Universe contribution is completely unacceptable. In principle, how do you think we could measure our velocity due to the expansion of the Universe (where is the 0 reference)?

In simple terms, the other 5 items, are merely a set of nested reference frames. The centre of our galaxy is the ultimate 0 reference in the above list. Better would be to add in the speed that our galaxy is moving with respect to centre of mass of the local group of galaxies. And then chain in the the local group’s motion in our local supercluster. I believe that superclusters don’t form hyperclusters, but I don’t know if it’s even meaningful way to talk of the velocity/direction of our local supercluster.

59. 59. Chris Said：

Hi JG. Another point. If two people happened to be running parallel and abreast, but one was on a vehicle and the other was directly on the ground. Would you say that one is travelling in 2 (+n) directions, and the other was only travelling in 1 (+n) directions (even though they are both travelling in the same direction)?

60. 60. Karl Sharman Said：

I thought I was being OTT in post 48 – Please also note, I kept referring to a point of reference.

- If I am walking North from my home, I have one direction of travel.
If I then get on a north travelling bus, and, whilst the bus is moving directly north, walk to the back seats towards the south, I will still be travelling North, unless my speed exceeds that of the bus (possible!) – Again, only one direction.
Start to throw in rotation of the earth, earth orbit etc etc then I still think I need to know what the reference/starting point is, and after some serious maths, will come to a combined single speed and direction of travel.
I wonder how Einstein and Newton would have argued this one out? Relatively speaking…

61. 61. JB Said：

Hi JG. Please refer to the very first post and post # 12.

62. 62. Chris Said：

Hi JG. .. also refer to my post (#2) where I concur with JB. Also see SP’s, post #5.

Except for a couple of the posters, we have all shown or indicated that we understand that we were walking on a bus that’s driving along a road that’s on a rotating planet, that’s orbiting a star that’s orbiting in the Milky way etc. I further assume that we also understand that those contributions to the passenger’s motion simply add up to one velocity and so one direction – I’ve been very clear about that throughout this blog, especially in my post #6.

I dealt with your item 6 (post 56) in my posts 10 and 13.

I’m utterly stunned that you haven’t developed any doubt about the correctness of your answer, or that you thought that there was even the slightest possibility that I was ever going to offer up your answer (without a fiscal renumeration). Nearly everything I wrote was about why answers like yours are profoundly incorrect.

Never mind. Next puzzle please.

63. 63. Chris Said：

Hi JB. I had accidentally merged my post with yours (#61). I hope that I have restored it correctly.

Hi Karl. Both Einstein and Newton would have said one direction. They’d say if you were going from A to B, then that has completely defined your direction of motion. Things like planets, stars, galaxies are irrelevant clutter.

Things get complicated in obvious and non-obvious ways if A and B are far apart. The non-obvious ways require General Relativity to understand. But the germ of the non-obvious ways is to do with the relativity of simultaneity, and the whole of it is caused by the curvature of space-time. On the large scale, there are several definitions of distance (ruler distance, radar distance, geodesic distance, co-moving distance) and generally speaking, none of them agree with each other.

To hope to gain a good understanding of this (cosmological) stuff, you need to learn about General Relativity (and the pre-requisite Special Relativity), and to do that you need to learn about Riemannian geometry and that requires learning about tensors. The last alone could keep you busy for a few months to many years (except slavy, who’d soak it up in no time flat – except he’s not a fan of geometry)). I know, because I learnt about them from an excellent book: “Applications of the Absolute Differential Calculus” by A J McConnell. But the Rindler book I mentioned above somewhere, gives a useful quickie introduction.

It happens that the centre of gravitation of our local group of galaxies is somewhere between the Milky Way and the Andromeda galaxy (those galaxies are the two most massive in the group). Our local group (currently believed to consist of 36 galaxies) is part of the Virgo Supercluster.

Despite the typical structures, some galaxies and clusters are completely independent of others. Clusters and Superclusters are simply the most common situation.

Superclusters, Clusters and Galaxies are gravitationally bound objects. Beyond the distance scale of Superclusters, the expansion of (the fabric of) space dominates.

64. 64. Chris Said：

Because of Karl’s comment about time, I’ll add that time can be considered as a 4th dimension, but it’s imaginary in the sense of imaginary numbers. We are used to recognising than an object whose end points have co-ordinate differences Δx,Δy,Δz has a length, Δl = √(Δx² + Δy² + Δz²), where we assume that the co-ordinates are measure at the same time, so Δt = 0. NB by convention Δx² => (Δx)². When you do Special Relativity, you associate a pair of events with co-ordinate differences Δx,Δy,Δz,Δt, then the thing that everyone agrees on is the “interval”, Δs = √(Δx² + Δy² + Δz² – Δt²) = √(Δx²+ Δy² + Δz² + (Δ(it))²), where i = √(-1). You can do all of SR using that trick. For that reason, a mathematician (but probably not a physicist) would be likely to say that the direction was (Δx,Δy,Δz,iΔt)/Δs or simply (Δx,Δy,Δz,Δt)/Δs, where “i” is understood to be present. More typically the substitution x1= x, x2= y, x3= z, x4= it, is used. Many author’s use 0 rather than 4 for the time dimension.

65. 65. Chris Said：

I’ve found a reference to the SR stuff: http://en.wikipedia.org/wiki/Special_relativity#The_geometry_of_space-time and one for 3D space http://en.wikipedia.org/wiki/Three-dimensional_space which at least partially discusses direction.

66. 66. Karl Sharman Said：

Nice links Chris. It is also worth noting that this is post 66 – just shy of reaching the top 5 popular posts!!

67. 67. Tom Said：

Possibly 7 directions, depending on whether or not the person is still growing upwards.

68. 68. JG Said：

Thanks for the idea Tom.

69. 69. Karl Sharman Said：

A very light bit (read – not a bit) of research into the growing element of movement posted by Tom, and I have concluded that this would come under “micromovement” and not qualify as a genuine direction.

As I did not post the question, I am not the overall arbiter of the validity of this direction of travel, and I await JG’s judgment in this matter.

This has been posted purely to help this question reach the Popular Posts section…

Go on, you know you think it should…..

70. 70. Chris Said：

Hi Karl. If we allow (for the sake of argument) that the traveller is growing, then that will only be another contribution to his direction. That is still only one direction altogether.

71. 71. Karl Sharman Said：

I agree with you Chris – there can be only one. Direction of travel, that is. I was just pointing out that this was a “micromovement”.

For equipment to measure micromovements, follow the link – http://www.freepatentsonline.com/6935200.html

Or something by the artist(?) Sark -
MICROMOVEMENTS – Tiny Little Baby Steps By SARK
Micromovements are tiny, tiny little steps you can take towards completions of your life.
I’m a recovering procrastinator and perfectionist and I have a short attention span, so I invented Micromovements as a method of completing projects in time spans of 5 minutes or less. I always feel like I can handle almost anything for 5 minutes!

Sark sounds like a self-help guru. Someone shoot him and put him out of my misery

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