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I once saw a particularly interesting physical manifestation of this paradox (performed I believe by Chris Bishop), where a weight was suspended from two partia

by Leszek 11y ago

I once saw a particularly interesting physical manifestation of this paradox (performed I believe by Chris Bishop), where a weight was suspended from two partially elastic ropes, both attached to the ceiling. These two suspending ropes were connected in the middle by another rope. The weight was analogous to the destination, and the ropes were the roads, with the total duration of the route being analogous to the distance of the weight from the ceiling. When we removed the central road (by cutting the connecting rope), the weight paradoxically went up instead of down. I wish I had a video of this demonstration, it really hammered in the point (for me) that this is a real phenomenon and not just mathematical trickery or electrical weirdness.

Leszek 11y ago
This is close enough, it's not quite as clear as the demonstration I saw but it shows the same effect: https://www.youtube.com/watch?v=xiOEYNGV5P8 https://www.youtube.com/watch?v=xiOEYNGV5P8
- eru 11y ago
  I found https://www.youtube.com/watch?v=nMrYlspifuo https://www.youtube.com/watch?v=nMrYlspifuo linked from your video. It has much more explanation.
ricksplat 11y ago
That's really interesting. I presumed that Braess' paradox was as a result of the overhead of competition but this demonstration doesn't seem to model that. I presume in the demonstration you're describing the central rope was not partially elasticated as the other two? (as demonstrated in the two videos) Does Braess' paradox apply if the central rope is elasticated? Does it apply for a parallel route also or just for a route that joins to existing series routes? I think if it's just a joining link then the effect could be modelled in signal theory as the result of partial feedback. Still no idea how the experiment works though :-)
- jamessb 11y ago
  I think the original mechanical analogy is due to Cohen and Horowitz: http://www.nature.com/nature/journal/v352/n6337/abs/352699a0.html http://www.nature.com/nature/journal/v352/n6337/abs/352699a0... In this setup, cutting the link essentially converts the two springs from being in series to parallel: http://ibin.co/2JEsCKEYRisb http://ibin.co/2JEsCKEYRisb If the central string was elastic, this would cause the weight to initially hang lower, but have no effect on the position reached after it is cut (assuming that it does not stretch so much that the other strings stop being slack). The effect would thus appear larger.

by Leszek 11y ago

Leszek 11y ago

This is close enough, it's not quite as clear as the demonstration I saw but it shows the same effect: https://www.youtube.com/watch?v=xiOEYNGV5P8 https://www.youtube.com/watch?v=xiOEYNGV5P8

eru 11y ago
I found https://www.youtube.com/watch?v=nMrYlspifuo https://www.youtube.com/watch?v=nMrYlspifuo linked from your video. It has much more explanation.

ricksplat 11y ago

That's really interesting. I presumed that Braess' paradox was as a result of the overhead of competition but this demonstration doesn't seem to model that. I presume in the demonstration you're describing the central rope was not partially elasticated as the other two? (as demonstrated in the two videos) Does Braess' paradox apply if the central rope is elasticated? Does it apply for a parallel route also or just for a route that joins to existing series routes? I think if it's just a joining link then the effect could be modelled in signal theory as the result of partial feedback. Still no idea how the experiment works though :-)

jamessb 11y ago
I think the original mechanical analogy is due to Cohen and Horowitz: http://www.nature.com/nature/journal/v352/n6337/abs/352699a0.html http://www.nature.com/nature/journal/v352/n6337/abs/352699a0... In this setup, cutting the link essentially converts the two springs from being in series to parallel: http://ibin.co/2JEsCKEYRisb http://ibin.co/2JEsCKEYRisb If the central string was elastic, this would cause the weight to initially hang lower, but have no effect on the position reached after it is cut (assuming that it does not stretch so much that the other strings stop being slack). The effect would thus appear larger.