Since it looks to be hundreds of videos about Zeno's Paradox, I'll share my joke again. There's an old joke back in Engineering School about the difference between Engineers and Mathematicians. The high school dance starts off in the gym with all the girls on one wall and all the boys on the opposite wall. The Mathematicians reason that, in order to get to the other side to ask a girl to dance, they have to first cross half the distance across the gym. Then cross half the distance of what remains. Then half again, half again, on to infinity. Since it is impossible to ever cross the gym a full 100% to reach the girls, they give up and go home. The Engineers reason that, yes, it is impossible to cross the gym a full 100% -- but we can get close enough!!
@@uncaboat2399 Consider a triangle whose sides have a length of 1 unit. What is the length of the hypotenuse? An engineer might say 1.414. Is that a guess or an approximation? Can the length of the hypotenuse ever be perfectly measured and if not, are we in a position to say that it has a length? Or can we only speak of the imperfect measurements, as is done by an engineer?
@@keystoneperspectives _Consider a triangle whose sides have a length of 1 unit. What is the length of the hypotenuse?_ A triangle with sides the length of 1 unit is an equilateral triangle which does not have a hypotenuse.
This is a problem of semantics only. It's easy to be lured in to thinking problems like this are matters for mathematicians or philosophers. They are not! Zeno was a rich guy who was most probably trying to justify his idle, wasteful existence by posing questions like this to make himself seem wise.
Amazing video, thanks
Indeed this now makes sense to me. Thank you Keystone
just found ur channel and gotta say, your vids have the same quality of other big mathematicians (dunno english spelling) so keep up the good work !
Loved your video, keep up the good work!
Felt like an Nolan movie but this is wat our teachers ain't teaching us.
Great passion and content, keep on boy!
Thank you ☺️
Since it looks to be hundreds of videos about Zeno's Paradox, I'll share my joke again.
There's an old joke back in Engineering School about the difference between Engineers and Mathematicians.
The high school dance starts off in the gym with all the girls on one wall and all the boys on the opposite wall. The Mathematicians reason that, in order to get to the other side to ask a girl to dance, they have to first cross half the distance across the gym. Then cross half the distance of what remains. Then half again, half again, on to infinity. Since it is impossible to ever cross the gym a full 100% to reach the girls, they give up and go home.
The Engineers reason that, yes, it is impossible to cross the gym a full 100% -- but we can get close enough!!
I'm an engineer. I see the value in approximations. But shouldn't we know what we're approximating?
@@keystoneperspectives If you don't know what you're approximating, it's not an approximation -- it's a guess.
@@uncaboat2399 Consider a triangle whose sides have a length of 1 unit. What is the length of the hypotenuse? An engineer might say 1.414. Is that a guess or an approximation? Can the length of the hypotenuse ever be perfectly measured and if not, are we in a position to say that it has a length? Or can we only speak of the imperfect measurements, as is done by an engineer?
@@keystoneperspectives _Consider a triangle whose sides have a length of 1 unit. What is the length of the hypotenuse?_
A triangle with sides the length of 1 unit is an equilateral triangle which does not have a hypotenuse.
I should have been more clear. Consider a square whose sides have length 1. What is the length of the diagonal?
This is a problem of semantics only. It's easy to be lured in to thinking problems like this are matters for mathematicians or philosophers. They are not! Zeno was a rich guy who was most probably trying to justify his idle, wasteful existence by posing questions like this to make himself seem wise.
As long as infinity lies at the heart of mathematics this will remain a relevant and important paradox.