Paradox

[notb665]

Hoping you can help.

What is the name of the paradox that states if you are X and you are travelling towards Y going half-way every time, that you never actually reach Y?

 

[Moz]

The Twin's Paradox !!?

 

[ellal]

The 'arrow paradox'

An Arrow
in Flight One can imagine an arrow in flight, toward a target. For the arrow to
reach the target, the arrow must first travel half of the overall distance from
the starting point to the target. Next, the arrow must travel half of the
remaining distance. For example, if the starting distance was 10m, the arrow
first travels 5m, then 2.5m. If one extends this concept further, one can
imagine the resulting distances getting smaller and smaller. Will the arrow ever
reach the target?

The answer is, of course, yes the arrow will
reach the target. Our common sense tells us so. But, mathematically, this fact
can be proven because the sum of an infinite series can be a finite number. The
question contains a premise, which implies that the infinite series will result
in an infinite number. Thus, 1/2 + 1/4 + 1/8 + ... = 1 and the arrow hits the
target

 

[notb665]

Thank you.

 

[bennettp23]

Arrow... for gods sake

Zeno's paradox.

 

[notb665]

Ah. It seems that Zeno noticed several paradoxes. One was the Arrow Paradox, another was the Dichotomy Paradox. The one I originally referred to is properly called the Dichotomy Paradox.

I love/hate paradoxes! I think they are amusing but they make me overthink!

 

[kendor]

The 'arrow paradox'

An Arrow
in Flight One can imagine an arrow in flight, toward a target. For the arrow to
reach the target, the arrow must first travel half of the overall distance from
the starting point to the target. Next, the arrow must travel half of the
remaining distance. For example, if the starting distance was 10m, the arrow
first travels 5m, then 2.5m. If one extends this concept further, one can
imagine the resulting distances getting smaller and smaller. Will the arrow ever
reach the target?

The answer is, of course, yes the arrow will
reach the target. Our common sense tells us so. But, mathematically, this fact
can be proven because the sum of an infinite series can be a finite number. The
question contains a premise, which implies that the infinite series will result
in an infinite number. Thus, 1/2 + 1/4 + 1/8 + ... = 1 and the arrow hits the
target

But surely an arrow travels further as it slows down? producing an arc, same as a bullet does.

 

[Nige F]

Arrow... for gods sake

Zeno's paradox.

Eno`s paradox states that on a moving train having drunk liver salts..when using the WC. does the effluent overtake the train because eno`s goes thru you like a dose of salts....can the effect be nullified by settlers bringing express relief.where is this train of thought going

 

[pickles]

The 'arrow paradox'

An Arrow
in Flight One can imagine an arrow in flight, toward a target. For the arrow to
reach the target, the arrow must first travel half of the overall distance from
the starting point to the target. Next, the arrow must travel half of the
remaining distance. For example, if the starting distance was 10m, the arrow
first travels 5m, then 2.5m. If one extends this concept further, one can
imagine the resulting distances getting smaller and smaller. Will the arrow ever
reach the target?

The answer is, of course, yes the arrow will
reach the target. Our common sense tells us so. But, mathematically, this fact
can be proven because the sum of an infinite series can be a finite number. The
question contains a premise, which implies that the infinite series will result
in an infinite number. Thus, 1/2 + 1/4 + 1/8 + ... = 1 and the arrow hits the
target

which just goes to show why mathematics appears to be impenetrable b******s to most of the population and that you don't need maths if you have common sense

 

[notb665]

But surely an arrow travels further as it slows down? producing an arc, same as a bullet does.

For the purposes of this argument, it is probably assumed that it travels in a straight line with no air resistance. Probably.

 

[notb665]

which just goes to show why mathematics appears to be impenetrable b******s to most of the population and that you don't need maths if you have common sense

Yep, tell that to engineers and scientists.

 

[Thermo]

heres a thought. As stated before commo sense tells us that the arrow hits the target. We all know it does because it does! Yet mathematically according to this theory it never does. Does this not worry you that all science etc is based on maths. eg black holes, time travel etc etc and its taken as gospel as being correct. Maybe its not!

 

[notb665]

heres a thought. As stated before commo sense tells us that the arrow hits the target. We all know it does because it does! Yet mathematically according to this theory it never does. Does this not worry you that all science etc is based on maths. eg black holes, time travel etc etc and its taken as gospel as being correct. Maybe its not!

No it doesn't worry me, because 'infinity' is just one branch of maths. Stuff to do with forces/pressures etc, actual physical stuff, is useful. Why have 7N blocks? Why not 6N? You do the 'math'.

 

[kendor]

Eno`s paradox states that on a moving train having drunk liver salts..when using the WC. does the effluent overtake the train because eno`s goes thru you like a dose of salts....can the effect be nullified by settlers bringing express relief.where is this train of thought going

Very clever!