A physical movement cant be completed (Mathematically)?
Discussion
A bit like radiation never completely disappears because of half lives ......
If a ball is dropped, you go to lean on wall, throw a dart into a dart board ... whatever ..... The action starts at lets say 'point A' aiming to end at the 'destination point'
Half way between 'point A' and the 'destination point' is 'point B' A--------------------------------------B------------------------------Destination
Half way between 'point B' and the 'destination point' is 'point C' B ---------------C------------Destination
Half way between 'point C' and the 'destination point' is 'point D' C-----D-----Destination
And so on, and so on, and so on.
So one movement can be measured to have a half way point, and every subsequent movement from that half way point can be measured to another (now new) half way point.
If there's always an ever decreasing yet measurable new half distance after each old half distance how does the ball reach the ground, do we lean on a wall or a dart hit the board?
If a ball is dropped, you go to lean on wall, throw a dart into a dart board ... whatever ..... The action starts at lets say 'point A' aiming to end at the 'destination point'
Half way between 'point A' and the 'destination point' is 'point B' A--------------------------------------B------------------------------Destination
Half way between 'point B' and the 'destination point' is 'point C' B ---------------C------------Destination
Half way between 'point C' and the 'destination point' is 'point D' C-----D-----Destination
And so on, and so on, and so on.
So one movement can be measured to have a half way point, and every subsequent movement from that half way point can be measured to another (now new) half way point.
If there's always an ever decreasing yet measurable new half distance after each old half distance how does the ball reach the ground, do we lean on a wall or a dart hit the board?
All models are abstracts, that is to say it loses some of the detail in order to simplify behaviour. If you use the wrong model for the system, you will get the wrong answer. Just because you can use a model doesn't make it the right one.
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes
An infinite series of numbers doesn't necessarily add up to an infinite result.
EG Achilles (think it was him) chasing a tortoise which is going at a tenth of his speed. He starts off 30 feet back, by the time he's run 30 feet it's gone 3 feet, by the time he's covered 3 feet it's done another 0.3 feet and so on.
So Achilles total distance in feet is 30 + 3 + 0.3 + 0.03 + 0.003.........
Or 33.3333.... infinitely recurring.
Which is 33 feet and 4 inches.
Not quite so easy in metric of course.
EG Achilles (think it was him) chasing a tortoise which is going at a tenth of his speed. He starts off 30 feet back, by the time he's run 30 feet it's gone 3 feet, by the time he's covered 3 feet it's done another 0.3 feet and so on.
So Achilles total distance in feet is 30 + 3 + 0.3 + 0.03 + 0.003.........
Or 33.3333.... infinitely recurring.
Which is 33 feet and 4 inches.
Not quite so easy in metric of course.
Dr Jekyll said:
An infinite series of numbers doesn't necessarily add up to an infinite result.
EG Achilles (think it was him) chasing a tortoise which is going at a tenth of his speed. He starts off 30 feet back, by the time he's run 30 feet it's gone 3 feet, by the time he's covered 3 feet it's done another 0.3 feet and so on.
So Achilles total distance in feet is 30 + 3 + 0.3 + 0.03 + 0.003.........
Or 33.3333.... infinitely recurring.
Which is 33 feet and 4 inches.
Not quite so easy in metric of course.
Pretty sure it was him - the race against the tortoise was how he got his famous foot injury, which he never recovered from. EG Achilles (think it was him) chasing a tortoise which is going at a tenth of his speed. He starts off 30 feet back, by the time he's run 30 feet it's gone 3 feet, by the time he's covered 3 feet it's done another 0.3 feet and so on.
So Achilles total distance in feet is 30 + 3 + 0.3 + 0.03 + 0.003.........
Or 33.3333.... infinitely recurring.
Which is 33 feet and 4 inches.
Not quite so easy in metric of course.
Part of this ' thought problem' is to decide when two thing 'touch'.
When does the ball touch the floor after leaving your hand for example.
Two things touch when the attractive forces and the repulsive forces between molecules/atoms are in balance.
So the ball is said to 'hit' the floor when this measurement is in balance.
Its all about how you set up a 'problem'.
If you set it up in a manner that you must divide by half each time with no end limit, then you have created an infinite series.
So you're measurements will go on infinite times. (Thankfully there is calculus to fall back on with regards to that).
But if you set finite definitions to the limits then you'll be able to measure physics much more meaningfully.
When does the ball touch the floor after leaving your hand for example.
Two things touch when the attractive forces and the repulsive forces between molecules/atoms are in balance.
So the ball is said to 'hit' the floor when this measurement is in balance.
Its all about how you set up a 'problem'.
If you set it up in a manner that you must divide by half each time with no end limit, then you have created an infinite series.
So you're measurements will go on infinite times. (Thankfully there is calculus to fall back on with regards to that).
But if you set finite definitions to the limits then you'll be able to measure physics much more meaningfully.
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