I hated this "paradox" from the first time I encountered it sometime in grade school. I didn't have the mathematical language for it at the time, but I distinctly remember arguing that as the number of intervals increases, the time to move one subdivision decreases, so there is no paradox at all. Basically, it doesn't take much creativity to have a qualitative feeling for the concept of a convergent infinite series (which is what this is), but the teacher insisted it was a paradox, I couldn't prove them wrong, and it frustrated the crap out of me.
One of the definitions of paradox is a thing you know for sure is wrong, but can't disprove it. Zeno knew Acchiles would reach the turtle in his paradox somehow, but without calculus (or algebra, for that matter) he couldn't explain it
Yes but the point was that it couldn't be proved using the construction that he defined. You can prove it easily with a different construction, such as defining the hand moves 1 meter per second and the object is 1 meter away, therefore takes 1 second to reach. But they couldn't yet deal with this alternate definition that still followed all the existing mathematical rules they had at the time. A finite distance could be divided in half, creating two smaller finite distances, but they had no concept of infinity or convergence, so they had no tools to deal with a recursive division.
Yeah same. An infinite converging series isn't an impressive paradox, all he did was argue you could split an ever smaller fraction of space in half. After learning about it i spent a frustrating amount of time trying to fogure out "how is this a paradox?"
Time for the Feynman defense stain that even though it seems like objects touch, there's no connection between the atoms of both objects (which is knife of why Zeno's paradox is ultimately true)
12 Comments
thebestaquaman@lemmy.world · 28 pts · 110d
I hated this "paradox" from the first time I encountered it sometime in grade school. I didn't have the mathematical language for it at the time, but I distinctly remember arguing that as the number of intervals increases, the time to move one subdivision decreases, so there is no paradox at all. Basically, it doesn't take much creativity to have a qualitative feeling for the concept of a convergent infinite series (which is what this is), but the teacher insisted it was a paradox, I couldn't prove them wrong, and it frustrated the crap out of me.
ShinkanTrain@lemmy.ml · 12 pts · 110d
One of the definitions of paradox is a thing you know for sure is wrong, but can't disprove it. Zeno knew Acchiles would reach the turtle in his paradox somehow, but without calculus (or algebra, for that matter) he couldn't explain it
SARGE@startrek.website · 2 pts · 110d
hobovision@mander.xyz · 7 pts · 110d
Yes but the point was that it couldn't be proved using the construction that he defined. You can prove it easily with a different construction, such as defining the hand moves 1 meter per second and the object is 1 meter away, therefore takes 1 second to reach. But they couldn't yet deal with this alternate definition that still followed all the existing mathematical rules they had at the time. A finite distance could be divided in half, creating two smaller finite distances, but they had no concept of infinity or convergence, so they had no tools to deal with a recursive division.
drcobaltjedi@programming.dev · 10 pts · 110d
Yeah same. An infinite converging series isn't an impressive paradox, all he did was argue you could split an ever smaller fraction of space in half. After learning about it i spent a frustrating amount of time trying to fogure out "how is this a paradox?"
Akasazh@lemmy.world · 13 pts · 110d
Time for the Feynman defense stain that even though it seems like objects touch, there's no connection between the atoms of both objects (which is knife of why Zeno's paradox is ultimately true)
RustyNova@lemmy.world · 8 pts · 110d
This looks like a Saturday morning breakfast cereals comic. I love it
Hadriscus@jlai.lu · 5 pts · 109d
wow ok. That's the second poor taste comic I see posted by you in a minute. Do you specialize in reactionary humor ?
turdas@suppo.fi · -6 pts · 110d
Oh look, it's the unfunny nu-boomer comic by renowned Israeli cartoonist Idan Schneider.
luthis@lemmy.nz · 2 pts · 110d
Israeli? OK i don't like it anymore.
ripcord@lemmy.world · 1 pts · 110d
How the fuck is this nu-boomer
turdas@suppo.fi · 5 pts · 110d
Casual sexual harassment humour. But I think if you look at his other comics you'll have your answer:
FelixCress@lemmy.world · 1 pts · 110d
Hadriscus@jlai.lu · 2 pts · 109d
This is how you react to critique ?