Bird Flies Between Two Trains Crashing at 60m/s

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SUMMARY

The discussion centers around a thought experiment involving two trains approaching each other at 60 m/s and a hypothetical bird flying between them at 120 m/s. Participants explore the implications of Zeno's paradox, concluding that while the bird can theoretically make an infinite number of trips before the trains collide, practical considerations such as the bird's mass and acceleration limit this to a finite number of transits. The mathematical model suggests that the bird's trips can be represented by a convergent series, ultimately summing to a finite duration of time despite the infinite nature of the intervals involved.

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  • Understanding of Zeno's paradox
  • Familiarity with convergent series in mathematics
  • Basic principles of relative motion
  • Knowledge of kinematics and acceleration
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  • Study Zeno's paradox in depth to grasp its implications in mathematics and physics
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This discussion is beneficial for mathematicians, physics students, and anyone interested in the philosophical implications of infinity and motion in theoretical scenarios.

  • #31
neutrino' said:
so it isn't conclusive proof that infinity exists? I mean the trains crash but how come the particle (the bird with ~0 mass) make inifintely many stops? THE TRAINS CRASH, RIGHT??

Once we add in assumptions that the particle has no dimensions, nor mass - so that the train don't both contact the particle until the trains are also touching each other - and the particle ca also change from velocity in one direction to velocity in the other direction [ie have infinite acceleration] it is not surprising that the number of trips the particle makes in infinite - but then only the first half of the infinite trips took any real time - the rest of them were done in an infinitely small time interval, perhaps?
 
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  • #32
neutrino' said:
so it isn't conclusive proof that infinity exists?

What does one man by "exist"? Is it a useful tool in mathematics? Absolutely. We just used it in one.

Does it exist in some physical way? This experiment gets us no closer to an answer, since this is so clearly an unphysical thought experiment (zero mass, point-sized birds and such).
 

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