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bradleyland 15y ago
My problem with this representation is that it assumes the pursuer is unable to "lead" its target. The pursuit curve, as modeled in mathematical representations constrains the pursuer to traveling only on a path that points directly at the pursued. Lions are highly adapted hunters that frequently take down prey that are much faster than them. It would seem that they would have to develop strategies for optimizing the distance-to-intercept in order to be successful as a species. Thus, I believe the man is eaten rather quickly, even if the two are equal in speed.
- gcp 15y ago
  My problem with this representation is that it assumes the pursuer is unable to "lead" its target. How can the pursuer lead the target when the target moves randomly? At best, he can adjust his lead with an infinitesimal delay, but its not clear this allows him to catch the target in finite time.
  - bradleyland 15y ago
    And yet Lions catch faster prey all the time. Just because something occurs randomly doesn't mean it always results in a net loss for the pursuer. All the time spent in pursuit on an optimized (leading) path results in closed distance. Within the constraints of the cage the pursued can only choose to zig or to zag, so if the lion uses a leading path, and is correct in anticipating directional changes only half the time, he's still going to have lunch sooner rather than later. There are visual "tells" that allow the lion to anticipate directional shifts on the part of their prey, so I'd argue that his percentages will be significantly better. I guess I'm struggling with understanding the value of the exercise. If we're talking inanimate bodies, I get it. This kind of physics is valuable. However, choosing arbitrary constraints in order to make interesting maths out of natural scenarios is low hanging fruit. I just don't see it as all that interesting.

bradleyland 15y ago

My problem with this representation is that it assumes the pursuer is unable to "lead" its target. The pursuit curve, as modeled in mathematical representations constrains the pursuer to traveling only on a path that points directly at the pursued. Lions are highly adapted hunters that frequently take down prey that are much faster than them. It would seem that they would have to develop strategies for optimizing the distance-to-intercept in order to be successful as a species. Thus, I believe the man is eaten rather quickly, even if the two are equal in speed.

gcp 15y ago
My problem with this representation is that it assumes the pursuer is unable to "lead" its target. How can the pursuer lead the target when the target moves randomly? At best, he can adjust his lead with an infinitesimal delay, but its not clear this allows him to catch the target in finite time.
- bradleyland 15y ago
  And yet Lions catch faster prey all the time. Just because something occurs randomly doesn't mean it always results in a net loss for the pursuer. All the time spent in pursuit on an optimized (leading) path results in closed distance. Within the constraints of the cage the pursued can only choose to zig or to zag, so if the lion uses a leading path, and is correct in anticipating directional changes only half the time, he's still going to have lunch sooner rather than later. There are visual "tells" that allow the lion to anticipate directional shifts on the part of their prey, so I'd argue that his percentages will be significantly better. I guess I'm struggling with understanding the value of the exercise. If we're talking inanimate bodies, I get it. This kind of physics is valuable. However, choosing arbitrary constraints in order to make interesting maths out of natural scenarios is low hanging fruit. I just don't see it as all that interesting.