The Scale of the universe - Page 1
Forum section: electronics / general

author: AlxDroidDev
author_rank: Frequent Contributor
timestamp: January 05, 2016, 01:06:39 pm
content: Came across this link from NASA, which I think some of you might like: the scale of the universe, relative to 1 meter.http://apod.nasa.gov/apod/ap120312.htmlAfter the page lods, just press "Start".

author: dannyf
author_rank: Super Contributor
timestamp: January 05, 2016, 02:07:25 pm
content: It may not be that big if you think it from this perspective: assume that you have a knife. You cut the universe in half, and half one of the halves, and so on and so forth.In how many cuts will you have cut the universe to a single atom? Assuming that you make one cut per second, how long to you think it will take to do that?The answer may surprise most people.

author: bookaboo
author_rank: Frequent Contributor
timestamp: January 05, 2016, 02:23:49 pm
content: Nice find, that's 15 mins productivity gone.Had to laugh at "Russell's Teapot"

author: Tomorokoshi
author_rank: Super Contributor
timestamp: January 05, 2016, 05:47:59 pm
content: Quote from: dannyf on January 05, 2016, 02:07:25 pmI'm guessing around 107 cuts, or about 2 minutes.

author: os40la
author_rank: Regular Contributor
timestamp: January 05, 2016, 06:24:17 pm
content: 42?

author: Galenbo
author_rank: Super Contributor
timestamp: January 05, 2016, 06:57:26 pm
content: Quote from: dannyf on January 05, 2016, 02:07:25 pmBecause you converted it to exp/log, as the animation does.People are not compatible with exp/log, except when trained to do so.Visitors of the animation should be aware that when scrolling at a constant scrollbar speed, the animation speed is changing exponentially.

author: dannyf
author_rank: Super Contributor
timestamp: January 05, 2016, 11:07:00 pm
content: "Or about 2 minutes"Fairly close. The (observable) universe, subject to a few caveats, has about 1e77 to 1e81 atoms - fairly insensitive to heavier elements.That translates to about 255 cuts to 270 cuts. Or just shy of 5 minutes at a pace of 1 cut per second. That time estimate is remarkably robust to the number of atoms, thanks to its exponential nature.

author: Brumby
author_rank: Unknown
timestamp: January 06, 2016, 03:00:33 am
content: Quote from: dannyf on January 05, 2016, 02:07:25 pmI took that as being a dimensional challenge - cutting something the SIZE of the universe to something the SIZE of anatom-notfrom the largest scale in that animation to the smallest.The answer to THAT questions is closer to 2 minutes.

author: bookaboo
author_rank: Frequent Contributor
timestamp: January 06, 2016, 09:56:56 am
content: I have a hazy memory of being told that if you could fold a piece of paper 47 times it would be the thick enough to reach to the sun.

author: dannyf
author_rank: Super Contributor
timestamp: January 06, 2016, 10:35:02 am
content: The distance from earth to the sun, or 1 au, is 150 billion meters. Paper is about 0.1 mm thick. So the distance to the sun is about 1.5e14 times the thickness of a paper. Or about 47.09 folds,.

author: miguelvp
author_rank: Super Contributor
timestamp: January 06, 2016, 10:58:46 am
content: I think minecraft is misrepresented in there since it doesn't really have dimensions.

author: dannyf
author_rank: Super Contributor
timestamp: January 06, 2016, 11:56:45 am
content: QuoteAgreed. I got to 122 cuts / seconds: 1e27 m for the size of the universe, end to end; 1e-10 m for the size of an atom -> 122 cuts.

author: FrankBuss
author_rank: Unknown
timestamp: January 06, 2016, 12:24:01 pm
content: Quote from: dannyf on January 05, 2016, 11:07:00 pmBut not all atoms are in one long string. If we assume a cube and equal distribution, its diameter in number of atoms is the cube root of the number of atoms, so only from 4.6e25 to 1e27 atoms, which translates to 1.5 minutes. For a sphere it is the same, because it is only a small factor which doesn't matter because of the exponential process.

author: branadic
author_rank: Super Contributor
timestamp: January 06, 2016, 01:11:38 pm
content: Quote from: dannyf on January 06, 2016, 10:35:02 amAre you sure?0.1mm * 2^47,09 = 14.979.678.615.878,8mm or 14.979.678km so you are off by one decadeThe correct answer is somewhat near 50,41 folds resulting in 149.596.723km which is pretty close to the 149.600.000km.

author: AlxDroidDev
author_rank: Frequent Contributor
timestamp: January 06, 2016, 01:19:07 pm
content: Fun - and useless - fact of the day:You can fit all 9 planets in the space between Earth and Moon, and still have a few thousand km of empty space.However, if you take Jupiter's equatorial circumference, you can go from Earth to Moon and even get about 1/4 of the way back to Earth.

author: Brumby
author_rank: Unknown
timestamp: January 06, 2016, 02:39:06 pm
content: Quote from: dannyf on January 06, 2016, 11:56:45 amYep. That's the answer I got.

author: dannyf
author_rank: Super Contributor
timestamp: January 06, 2016, 04:23:47 pm
content: QuoteI think you are right on that - I must have made a mistake somewhere along the way.QuoteMy candidate in the fun/useless fact of day category,1) assume that you tie a rope along the earth's equator. how much longer is the rope if it has to be raised 1 meter everywhere along the equator?2) answer the same question if you were on Jupiter.

author: AlxDroidDev
author_rank: Frequent Contributor
timestamp: January 06, 2016, 06:01:16 pm
content: Quote from: dannyf on January 06, 2016, 04:23:47 pm1,2) 2*PI meters, or:

author: dannyf
author_rank: Super Contributor
timestamp: January 06, 2016, 09:06:35 pm
content: AlxDroidDev: spot on. Interesting that it only takes additional 6 meters to lift the circumference around such a big circle.Now, a harder one: the amount of additional rope needed is always 6 meters, independent of the radius of the globe, even for a globe with an infinitely large radius.However, an infinitely large global is essentially a flat surface. To lift the rope above a flat surface requires no additional rope.How to reconcile the two?

author: Galenbo
author_rank: Super Contributor
timestamp: January 08, 2016, 07:45:00 am
content: Quote from: dannyf on January 06, 2016, 09:06:35 pmYes it does. For the converging+sampling you made, you have to assume the rope is attached on the surface, at the "ends"

author: AlxDroidDev
author_rank: Frequent Contributor
timestamp: January 08, 2016, 11:01:06 am
content: Quote from: dannyf on January 06, 2016, 09:06:35 pmEasy: as the diameter tends to infinity, so will the length of the rope. Thus we'll get a length of infinity + 2.PI, which is still infinity.

author: Brumby
author_rank: Unknown
timestamp: January 08, 2016, 11:02:33 am
content: Quote from: dannyf on January 06, 2016, 09:06:35 pmVery wrong, I'm afraid - and you already gave the right answer:Quote from: dannyf on January 06, 2016, 09:06:35 pmIt's basic linear algebra 101.

author: Brumby
author_rank: Unknown
timestamp: January 08, 2016, 11:06:00 am
content: Quote from: AlxDroidDev on January 08, 2016, 11:01:06 amPhilosophically, you can argue that they are the same, but mathematically, infinity + 2.PI will always be greater than infinity.Again, fundamental algebra will show this - as the limiting condition of infinity is irrelevant.

author: Armxnian
author_rank: Regular Contributor
timestamp: January 08, 2016, 11:25:06 am
content: Quote from: Brumby on January 08, 2016, 11:06:00 amReally? Philosophically? Are you saying that math doesn't have a strong enough objective base that you need to bring philosophical BS to it?Quote from: Brumby on January 08, 2016, 11:06:00 amNo it won't. Infinity = Infinity + n where n is an integer.Infinity is not a single number, it is a concept, which means it can be ANY number. Same reason why infinity = infinity + infinity. Also the reason why infinity - infinity does not = 0.

author: Brumby
author_rank: Unknown
timestamp: January 08, 2016, 11:29:13 am
content: Just use junior high school algebra.

author: Brumby
author_rank: Unknown
timestamp: January 08, 2016, 11:31:04 am
content: ... algebra that describes this:Quote from: dannyf on January 06, 2016, 09:06:35 pm

author: mtdoc
author_rank: Super Contributor
timestamp: January 08, 2016, 11:43:09 am
content: Quote from: Brumby on January 08, 2016, 11:29:13 amOr junior high geometry. Is that what this forum has come to?

author: dannyf
author_rank: Super Contributor
timestamp: January 08, 2016, 12:19:03 pm
content: QuoteThe point is that two approaches, one with a flat surface, and one with a circle approaching a flat surface, provide two different answers for the same measurement.

author: Brumby
author_rank: Unknown
timestamp: January 08, 2016, 01:00:13 pm
content: The point is -One IS a flat surface (well, technically, a straight line) - which absolutely excludes any closed shape such as a circle. Mathematically it is defined in a way that is completely distinct from that of a circle and shares nothing in common - no derivatives, integrals or any other formulae.The other being a circle willnever be - andcannever be- aflat surfacestraight line, BY DEFINITION. It will certainly be asymptotic, but it can never achieve straightness. The formulae to describe it is completely distinct. Certainly you can apply the limiting condition to sufficiently small arc segment, but you cannot apply this logic to the full circle. No matter what the limiting condition is, thecompleteentity is still a circle.You are, thereforenotmaking the same measurement.

author: zapta
author_rank: Super Contributor
timestamp: January 08, 2016, 03:06:46 pm
content: Quote from: dannyf on January 06, 2016, 09:06:35 pmThat's an incorrect statement. Just like saying that a as a radius of a circle goes to infinity, the shape of the circle approaches a straight line. It doesn't.

author: ruffy91
author_rank: Regular Contributor
timestamp: January 08, 2016, 04:50:20 pm
content: A quarter sector of a circle will always have a 90 degree curve, even when the radius approaches infinity.

author: zapta
author_rank: Super Contributor
timestamp: January 08, 2016, 05:07:12 pm
content: It's amazing that math can deal with this kind of magnitudes so easily and represent them in such a compact form. Good job!

author: bookaboo
author_rank: Frequent Contributor
timestamp: January 09, 2016, 10:53:03 am
content: Quote from: ruffy91 on January 08, 2016, 04:50:20 pmTrue no matter how large the circle is, but how do we "approach" infinity

author: Brumby
author_rank: Unknown
timestamp: January 09, 2016, 11:14:21 am
content: How 'easy' it is to 'approach infinity' depends on the function under consideration.In the case of an inverse function like y = 1 / x then when x 'approaches infinity', y 'approaches zero'. To determine the function value at the limiting condition is simple and easily comprehended.In the case of a circle, it's not really straightforward other than saying it's bigger than anything you can measure. It's kinda hard to wrangle infinite stuff outside of maths.

author: dannyf
author_rank: Super Contributor
timestamp: January 09, 2016, 12:02:44 pm
content: QuoteTwo cars, 1 mile apart, are driving towards each other, at speed 1 and speed 2 respectively. A fly flies, at speed 3 (speed 3 > speed 2 and speed 1) from the first car towards the second car. When it hits the 2nd car, it turns around and flies back towards the first car and so on and so forth. The fly is assumed to be infinitesimal dimension wise.Q1: how long (time wise) does the fly fly before it is smashed by the two cars?Q2: how many turns does the fly make before its demise?Q3: how did the fly do that in Q2?

author: Brumby
author_rank: Unknown
timestamp: January 09, 2016, 01:51:18 pm
content: ... and that's supposed to mean what, exactly?

author: miguelvp
author_rank: Super Contributor
timestamp: January 09, 2016, 08:00:17 pm
content: Assuming you mean, speed 1 as in 1 mph and the same with 2 and 3.Q1: 20 minutesQ2: infinite number of turnsQ3: 3/5 of a mile on the 1st trip to reach the 2nd car, 1st car only traveled 1/3 of that distance.Then use what is left and do the same the other way until infinity.But instead of that you can just ignore the fly and check when the cars are going to collide because the fly does not matter.

author: calexanian
author_rank: Super Contributor
timestamp: January 09, 2016, 08:00:26 pm
content: There you go for you young kids who have never seen this.

author: zapta
author_rank: Super Contributor
timestamp: January 09, 2016, 09:56:38 pm
content: Quote from: bookaboo on January 09, 2016, 10:53:03 amThe mathematical model of approaching infinity is well defined. Realty is something else.

author: dannyf
author_rank: Super Contributor
timestamp: January 09, 2016, 09:58:52 pm
content: QuoteHow did the fly make infinite number of turns within a finite period of time?

author: zapta
author_rank: Super Contributor
timestamp: January 09, 2016, 10:02:32 pm
content: Quote from: dannyf on January 09, 2016, 09:58:52 pmIt's a series of flys at increasing speeds

author: Armxnian
author_rank: Regular Contributor
timestamp: January 09, 2016, 10:18:42 pm
content: Quote from: zapta on January 09, 2016, 10:02:32 pmNa, it's a magical fly that has infinite velocity.

author: miguelvp
author_rank: Super Contributor
timestamp: January 09, 2016, 10:30:47 pm
content: Quote from: Armxnian on January 09, 2016, 10:18:42 pmNo, the fly is always at the same speed, but the problem mentioned the fly is infinitesimal in size, so it never endsupbouncing.You can compute the rate of the remaining distance and that rate will be constant ad infinitumEdit: note I said speed not velocity because that changes per trip with an instant acceleration when bouncing, also the rate to compute is the round trip or the combined rate of each direction.

author: Armxnian
author_rank: Regular Contributor
timestamp: January 09, 2016, 11:06:35 pm
content: Quote from: miguelvp on January 09, 2016, 10:30:47 pmNot sure what you mean. What does the size of the fly have to do with the number of trips it makes? And you only have 20 minutes, so it will run out.My example is better. With infinite velocity the fly can cover the distance in zero time. Plus infinite velocity implies infinite acceleration, because without infinite acceleration you would never reach infinite velocity. So the fly could fly towards one car, stop instantly, turn around instantly, and fly towards the other car instantly, and repeat, an infinite amount of times as you complete everything in 0 time.

author: miguelvp
author_rank: Super Contributor
timestamp: January 09, 2016, 11:31:10 pm
content: So the fly is going at a speed of 3 and the car coming towards goes at a speed of 2.The fly will reach the car at 3*t miles where t is the point in time for the 1st trip.the car2 will reach the fly at 2*t miles.The distance of both added will be one mile.So we have.dFly+dCar2=1 miledFly = 3*t milesdCar2 = 2*t milesso 2*t+3*t = 1 or 5*t = 1 so t is 1/5 of an hour.The fly would have traveled 3/5 miles.Car1 travels at 1 mph, so when the fly changes direction Car1 has traveled 1/5 of a mile so the fly needs to now travel 3/5-1/5 or 2/5 of a mile to reach car 1.So dFly+dCar1=2/5 milesso 1*t+3*t = 2/5 or 4*t = 2/5 so it's t = 1/10 of an hourin 1/10th of an hour the fly would have traveled 3/10 miles before heading back to car2 once more.The rate from fly to car2 is the same as in the 1st part just the distance has gotten shorter.Going back the rate from fly to car1 is the same as in the 2nd part, again the distance has gotten shorter.This will keep on happening with the same combined rate, but since the fly is infinitesimal, there is always a distance to travel and that distance will approach 0 but never reach it. Also the time will get shorter per trip and will approach 0 but it will never reach that value either.

author: miguelvp
author_rank: Super Contributor
timestamp: January 09, 2016, 11:44:38 pm
content: To probably make it more clear, the rate of the fly to car2 is 1/5th of the remaining distance and the rate from the fly to car1 is 1/4th of the remaining distance. Those rates remain constant as the distance and the time per trip approaches 0 but never reaching 0.

author: dannyf
author_rank: Super Contributor
timestamp: January 09, 2016, 11:51:56 pm
content: QuoteMuch simpler than that. The time it takes for the two cars to reach each other - they will for sure crash into each other - is 1 mile / (car 1's speed + car 2's speed), an definitive number.Over that period of time, the fly is flying at speed 3 so the total distance the fly has traveled before it is crashed by the bumpers is the time it takes the two cars to crash (calculated above) * the fly's speed.QuoteThat distance sure will reach zero. If it didn't, we wouldn't have head on collisions.The interesting thing here is that an infinite number of things (making turns in this case) is being done in a finite period of time -> different for the brain to handle, at least intuitively.It is, conceptually, the same as the hotel with infinite rooms, even when full, the hotel with infinite rooms can always take on new guests. aka the "infinite" hotel is bigger than infinite.

author: Armxnian
author_rank: Regular Contributor
timestamp: January 09, 2016, 11:52:41 pm
content: Quote from: miguelvp on January 09, 2016, 11:31:10 pmOh okay, so you're saying that since the fly is infinitesimally small, it can fit in between the atoms of the front bumpers of each car and will never be smashed, so it can fly around all it wants.

author: Brumby
author_rank: Unknown
timestamp: January 09, 2016, 11:58:19 pm
content: The question does not contain the necessary information to produce a solution:Quote from: dannyf on January 09, 2016, 12:02:44 pmThe phrase 'it turns around' defines a specific action, but no parameter is supplied to describe the time taken for this action to be performed.You can certainly assert that this took no time at all, where the above efforts make sense - but if you really want to make it more interesting in a practical setting, give that parameter a finite value.

author: Brumby
author_rank: Unknown
timestamp: January 09, 2016, 11:59:49 pm
content: Quote from: Armxnian on January 09, 2016, 11:52:41 pmNice observation.

author: miguelvp
author_rank: Super Contributor
timestamp: January 10, 2016, 12:08:58 am
content: Quote from: dannyf on January 09, 2016, 11:51:56 pmAnd that's why I ignored the fly on my answer as I statedQuoteThe rest was on response on how the fly does that, so then the fly can't be ignored

author: Rick Law
author_rank: Super Contributor
timestamp: January 10, 2016, 12:42:15 am
content: Quote from: dannyf on January 09, 2016, 12:02:44 pmYou missed one additional assumption: "You should assume the fly is zero mass."Absent that assumption, you must factor in acceleration != infinity, and without knowing the acceleration the fly is capable of, you cannot evaluate the actual time it takes the time to fly between cars.Party Pooper has spoken

author: Rick Law
author_rank: Super Contributor
timestamp: January 10, 2016, 12:58:23 am
content: Quote from: Brumby on January 09, 2016, 11:59:49 pmSpace between atoms is held by electromagnetic forces. When you drop a ping-pong ball, the atoms of the ball doesn't hit the atoms of the ground. It bounces off "empty space." The EM force of repulsion from the atoms of the ground is what "bounced" the ball away.So, the fly will die. Crushed by the electromagnetic repulsive force.Unless of course if the fly is smaller than one plank's length. By definition, it is zero dimension, so it is smaller than one plank's length. In which case, we don't know if the fly even exists. Lets just assume it is really really really small... So, quantum effects dominate - it could simply disappear and re-materialize behind the car.

author: Brumby
author_rank: Unknown
timestamp: January 10, 2016, 01:00:43 am
content: Quote from: Rick Law on January 10, 2016, 12:42:15 amTechnically, the acceleration is basically irrelevant to the time the fly flies. As long as the fly is airborne, it will be 'in flight'. If we then add the assumption that the time it takes to 'turn around' is zero, then the fly can be considered as 'flying' for the entire time the two vehicles are approaching. Thus, by definition, the flight time of the fly is the same as the travel time of the vehicles.

author: Brumby
author_rank: Unknown
timestamp: January 10, 2016, 01:05:56 am
content: Quote from: Rick Law on January 10, 2016, 12:58:23 amHmmm....OK ..... quantum mechanics ........The questions now become moot. Newtonian mechanics doesn't work plus we can't be sure where the fly is and know what it's doing.

author: miguelvp
author_rank: Super Contributor
timestamp: January 10, 2016, 01:11:08 am
content: Changing the velocity vector instantly when bouncing of any of the cars implies infinite acceleration as Rick mentioned, but if the fly is infinitesimal so it will be the mass of the fly.As for the electromagnetic fields since the fly is an observant the field sure will collapse but then there will be no bouncing it will just go through or collide with a collapsed electron fieldBut kidding of course, the fly at 3 mph wouldn't have the energy needed to collapse the field but since it's smaller than the atom it wouldn't interact at the same level, it probably would get absorbed and emitted out of the atom as a photon.I guess it will become a firefly

author: Rick Law
author_rank: Super Contributor
timestamp: January 10, 2016, 01:16:36 am
content: Quote from: Brumby on January 10, 2016, 01:00:43 amNo you cannot (assume acceleration is irrelevant because it is airborne). Even if the fly makes a turn in a circular path like an air-plane, you have angular acceleration. So, unless the fly is zero mass thus acceleration is infinity, acceleration must be taken into account.

author: Rick Law
author_rank: Super Contributor
timestamp: January 10, 2016, 01:36:13 am
content: Bottom line is, there is a reason to my madness here. I want to point out:Down at that scale (near zero dimension), calculus doesn't work. When you cut something in half, fine, you can do it again, and again.But in Physics, you cannot really have dy/dx where dx-> zero.When dx approaches plank's length, the world is gone. We don't know what is going on there. Time is undefined (or rather, we don't know how to handle).Oh, by the way, just because the fly is assumed to have zero dimension, it doesn't mean it has zero mass - black hole. Black hole, a singularity. A singularity with: infinitely small circumference, infinite radius, finite mass, infinite density.

author: miguelvp
author_rank: Super Contributor
timestamp: January 10, 2016, 04:56:33 am
content: More than calculus the problem is pretty much a geometry ordeal.Physics have no bearing in the case but you are right, at the quantum level geometry doesn't apply.

author: Rick Law
author_rank: Super Contributor
timestamp: January 10, 2016, 07:53:20 am
content: Yeah, I was just being... well myself... trying to be a party popper and throw a monkey wrench in there. I am not as much a gentleman as I like to be.A different monkey wrench more appropriate to topic "the scale of the universe"...There is no reason to assume that the visible universe is the entire universeeither. The replies thus far did not touch on this and assumed observable universe being the entire universe. We estimate the universe is about 13 billion years old. Our observable universe is 13 billion light years, plus expansion. (Since light that was emitted 13 billion years ago started heading our way, the space along the path it took expanded, so they are more than 13 billion light year away now.)Could the entire universe be much much bigger than the observable universe? Of course it could be, but we simply don't know.So, straightly speaking, the scale of the universe is unknown. We only know the scale of the observable universe.Even assume if indeed the observable universe is the entire universe today, it wont be some day. The rate of expansion is increasing, that is a known fact as every observation confirmed that. So, in time, the very very far away stuff visible today would expand out of light's ability to get to us. Because the remaining space that the light still has to travel to get to us expands faster and faster. Worst yet, as it expands, there is more space to expand! The compounded expansion will eventually expand the remaining distance faster than the speed of light could cover in the same duration. So it tries to get to us, but we are getting away faster than the light is coming to us.We have a dark future. In the scale of trillion trillion years give-or-take another trillion multiplier, assuming we human is around and orbiting a sun somewhere, lights from "near by" stars can't get to us. When the sun we are orbiting burns out... Darkness. Eternal darkness.On that bright note, I am going to bed.

author: Brumby
author_rank: Unknown
timestamp: January 10, 2016, 09:48:07 am
content: Quote from: Rick Law on January 10, 2016, 01:16:36 amWhether acceleration is relevant or not depends on the questions you want answered.If you want to know how long the fly was in the air, you are after a time. To determine that time you look at all the constraints and then choose a subset that is valid and adequate for determining the answer. In this case, the total time of flight of the fly is exactly the same as the time taken for the vehicles to collide. Thus, by determining that time, you have determined the time that the fly is flying. The dynamics of the fly's flight is not required for this calculation.

author: Rick Law
author_rank: Super Contributor
timestamp: January 10, 2016, 06:30:16 pm
content: Quote from: Brumby on January 10, 2016, 09:48:07 amAgreed. If the question is flight-time, acceleration is not relevant. In fact, if the question concerns only the flight-time, the presence of the fly is not relevant as well. Nothing will depend on it except the gravitational pull of the fly which would be too insignificant to consider.

author: dannyf
author_rank: Super Contributor
timestamp: January 10, 2016, 06:33:44 pm
content: QuoteThat shows the risk of knowing too much: it distracts you from knowing what matters here.

author: Rick Law
author_rank: Super Contributor
timestamp: January 10, 2016, 11:08:48 pm
content: Quote from: dannyf on January 10, 2016, 06:33:44 pmYup, I agree with you... I did that to stimulate learning when I was a TA, but it is a distraction in this environment - hopefully, it is an interesting one.From my point of view, that part of the discussion here is actually more applicable to the thread "What did your degree teach you?" Such analysis and the determination of its applicability (does the fly's mass need to be considered, at what point does the solution break down) are things that one learn in college. Why does it matter? How does ignoring it impact the accuracy of the solution?... ... ... ...

author: CatalinaWOW
author_rank: Super Contributor
timestamp: January 13, 2016, 04:58:48 am
content: Here is a math problem which will stump many engineers and mathematicians, but is easily solved by many tradesmen and technicians. The trained professionals will prove that it is insoluble. It requires practical experience to solve. I am sure many of you have encountered this yourselves.There is a long road, with a single narrow bridge 125 km from one end of the road and 263 km from the other end of the road. There is a large truck eastbound on the road traveling at 80 km/hour. A trekker is also walking east on the road at 6 km/hr. A pair of bicyclists are westbound on the road traveling at 35 km/hr, and coming up behind them is a small sports car traveling at 155 km/hr. Where do the four meet?

author: miguelvp
author_rank: Super Contributor
timestamp: January 13, 2016, 05:02:24 am
content: The sports car gave it away.At the BarOf course I didn't do any math for it so I can't prove it

author: Galenbo
author_rank: Super Contributor
timestamp: January 13, 2016, 03:30:37 pm
content: Quote from: CatalinaWOW on January 13, 2016, 04:58:48 amWhat means eastbound and westbound?What is the original position of all travelers, and what conditions are included in "do meet"Is this a one-dimensional problem? does the road go from east to west?

author: AlxDroidDev
author_rank: Frequent Contributor
timestamp: January 13, 2016, 04:03:20 pm
content: Quote from: CatalinaWOW on January 13, 2016, 04:58:48 amI could solve this one if it were north & south directions! Making it east-west completely messes up my logic!Giving it a shot: I guess everyone will meet at the west end of the bridge, because it was blocked by the truck - it was too wide for the narrow bridge.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: January 13, 2016, 05:45:12 pm
content: There were two points to my post. First, the joke, which reflects our practical experience. They will all meet at the bridge, the most difficult place for them to pass. It is another application of Murphy's law. Second, there is much passion here and elsewhere about things we don't understand, and may never be able to understand. Extending our models to their limits and being passionate about the truth of our models is pointless. While these models give useful results within their domain, they do not necessarily reflect absolute truth.

author: mtdoc
author_rank: Super Contributor
timestamp: January 13, 2016, 07:16:37 pm
content: Quote from: CatalinaWOW on January 13, 2016, 05:45:12 pmYes. This. Absolutely. It also applies to endless debate inthis thread.

author: Galenbo
author_rank: Super Contributor
timestamp: January 14, 2016, 01:17:42 pm
content: Quote from: CatalinaWOW on January 13, 2016, 05:45:12 pmThere's nothing difficult about the bridge to pass, because you declared constant velocity of all vehicles.And if it would be, you declare to have stated wrong values or deceptive information.

author: AlxDroidDev
author_rank: Frequent Contributor
timestamp: January 14, 2016, 02:17:19 pm
content: Quote from: Galenbo on January 14, 2016, 01:17:42 pmHe (or she, IDK) stated that the truck is large and the bridge is narrow. This suggests that the bridge isn't wide enough for the truck. He also stated that the sports car is small, which suggest it's able to pass the bridge.By my calculations, the truck will reach the bridge in 1:33' and the sport car in 1:41'. When the car gets there, the bridge is already blocked by the truck. The information given was not deceptive, but some of it was irrelevant (like the speed of the biker and trekker) and some of it was subjective (like the sizes of the car, truck and bridge).If the car driver speeds up gets at the bridge before the truck, he'll be able to pass and go on with his life, and a lot of road rage will be avoided.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: January 14, 2016, 07:42:25 pm
content: Perhaps a more explanation will help the more literal among us. Since no initial conditions other than velocity are specified for any of the parties the problem cannot be solved mathematically.The truck and the trekker (hiker/walker/pedestrian whatever word works for you) are travelling the same direction. The only time they have any interaction is if the truck is initially behind the trekker, in which case his higher speed means he will need to pass the trekker at some point (assuming the trekker is not very near the end of the road and the truck is not initially close behind him). This is not an issue unless the roadway is narrow and there is oncoming traffic.The same general analysis applies to the car and the bicycle riders. Under a wide variety of initial conditions the various parties will all pass each other. What is the most difficult possible solution? When the trekker and the bicyclists meet in the middle of the bridge at the exact moment they are being overtaken by the truck and the car respectively. This condition requires both the car and the truck to change their speed (either slower or faster) to avoid a collision and allow a pass. Usually causing significant nervousness on the part of all involved. The Murphy criterion selects this condition.This is also either a demonstration of something about human psychology or something deep about the universe that we don't understand. As a relatively frequent hiker and rider of bicycles I have observed this solution a great number of times. Either something about the way my brain works selectively remembers these cases, while discarding all of the other cases observed, or Murphy's law is more than a humorous observation.

author: Grayfox
author_rank: Regular Contributor
timestamp: January 15, 2016, 08:22:58 am
content: Hope they make an updated one.Saw an error.

author: Galenbo
author_rank: Super Contributor
timestamp: January 15, 2016, 01:01:00 pm
content: Quote from: CatalinaWOW on January 14, 2016, 07:42:25 pmIndeed. I think we were 15 when we got such examples to solve. "Not enough/conflicting info" was sometimes the only correct answer.