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Re: Is movement impossible?
[Re: PHeMoX]
#154130
09/21/07 21:44
09/21/07 21:44
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Joined: Oct 2006
Posts: 1,245
AlbertoT
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Joined: Oct 2006
Posts: 1,245
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Quote:
If you keep dividing a cake by two forever, you'll only get smaller and smaller crumbles, but never the full cake.
....
the 'formula' you would use to move is one of slowing down for infinity dividing your distance by two.
Again you are treating the "infinitesim" and the "infinite " separatly
Try to "blend" them
If you halve and halve , the number of steps get bigger and bigger but the time interval to cover each step get shorter and shorter
Why do you suppose that total time become infinite ?
In practice yes because you must waste time to measure the intervals ,as well as other operations but
Is it logic ?
In my opinion it is not
The total time which is given by the sum of all the time intervals is finite
Anyway, this is the basic of that branch of the modern math called analysis
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Re: Is movement impossible?
[Re: PHeMoX]
#154132
09/22/07 00:19
09/22/07 00:19
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Joined: Oct 2006
Posts: 1,245
AlbertoT
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Quote:
The paradox doesn't say anything about time, except that speed will logically slow down.
The original paradox speaks of time
Zeno claimed that an arrow will never reach its target because it will take an infinite time to reach the target for the raeson already discussed
This is false also from a logical point of view even though it seems to make sense
The reason being that the sum of infinite terms can be a finite value
It may be not intuitive but it is like that
Why should speed logically slow down ?
Speed is given by : distance / time
Distance gets smaller and smaller but also time does the same , so their ratio can remain constant along the path
In modern math "Infinity" must be understood as a "actual " number
it is not a "potential" number
Infinity in math must not be understood as something that is growing and growing
This is the common idea of infinity
I made the example of the diagonal of the square
It is measured by the irrational number
d = sqrt(2) = 1.4121....
this number never ends
if you trunk it even 1.000.000.000 positions after the decimal point you get a segment that is shorter than the diagonal of the square
Would you claim that the diagonal of a square does not exist, then?
No the diagonal exists same as the infinite number which is its measure
it is not a potentiality it is a reality
These arguments are valid in the domain of the logic and math
In this domain and in this domain only the Zeno's paradox make sense and consequently can be solved
In the domain of physics it simply does not make any sense
How would you define for example the event :
the arrow hits the target
The arrow has a dimension, which part of the arrow should hit the target to trig the event ?
The tip of the arrow , maybe ?
Well , the arrow is made of atoms
Ok , let's say the more external atom of the tip of arrow hits the target
The atom is made of protons and neutrons
Ok the most external proton or neutron of the most external atom of the tip of the arrow hits the target
The proton has a dimension
Ok, the baricenter of the most external atom of the most external proton hit the target
OK that's clear now, but a baricenter is not physical entity , the baricenter is a mathematical entity
You are again back in the domain of logic and math
and you have already got the solution
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Re: Is movement impossible?
[Re: AlbertoT]
#154133
09/23/07 17:40
09/23/07 17:40
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Joined: Mar 2003
Posts: 5,377
USofA
fastlane69
Senior Expert
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Senior Expert
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Isn't the bottom line to this WHOLE thread what I said a few post back: Philosophically the paradox exsists because of the semantics on "movement" and "the infinite". Physically there is no paradox; there is obviously movement and people don't move the way zeno described. Mathematically there is no paradox; an infinite series can still be summed to one. Am I wrong on any of the above three steps for if not, this thread seems to have reached a "zeno-esque" paradox of it's own: if a thread is allowed to be posted on forever, how can a thread ever reach a concludion? 
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Re: Is movement impossible?
[Re: AlbertoT]
#154134
09/23/07 19:22
09/23/07 19:22
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Joined: Jan 2004
Posts: 3,023
The Netherlands
Helghast
Expert
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Expert
Joined: Jan 2004
Posts: 3,023
The Netherlands
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Quote:
Quote:
The paradox doesn't say anything about time, except that speed will logically slow down.
The original paradox speaks of time
Zeno claimed that an arrow will never reach its target because it will take an infinite time to reach the target for the raeson already discussed
tell that to the hundreds of thousand knights (if not millions) that died because of arrows... yeah, sorry, you didnt die, the arrow never reached it's target.
I agree with fastlane here, if you look at it from a mathematical point of view, it can allways be summed up to 1.
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Re: Is movement impossible?
[Re: fastlane69]
#154136
09/23/07 23:50
09/23/07 23:50
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Joined: Sep 2002
Posts: 8,177
Netherlands
PHeMoX
Senior Expert
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Senior Expert
Joined: Sep 2002
Posts: 8,177
Netherlands
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Quote:
Physically there is no paradox; there is obviously movement and people don't move the way zeno described.
True, couldn't agree more, but isn't this "paradox" about the theoretical situation in which people would move like that? Off course it's no physical paradox, but a theoretical one if you do move like Zeno said,
Quote:
Am I wrong on any of the above three steps for if not, this thread seems to have reached a "zeno-esque" paradox of it's own: if a thread is allowed to be posted on forever, how can a thread ever reach a concludion?
Yes, indeed, but I think it's a matter of miscommunication in a way, although I still do not agree on some points. (For example adding up the infinite time you divide your next step 'reaching' a total of 100%, physically that's impossible, logically it doesn't make much sense to jump from infinite to finite especially when you divide by two never reaching it, but tending towards it..)
Cheers
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Re: Is movement impossible?
[Re: PHeMoX]
#154137
09/24/07 02:33
09/24/07 02:33
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Joined: Mar 2003
Posts: 5,377
USofA
fastlane69
Senior Expert
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Senior Expert
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Posts: 5,377
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Quote:
For example adding up the infinite time you divide your next step 'reaching' a total of 100%, physically that's impossible, logically it doesn't make much sense to jump from infinite to finite especially when you divide by two never reaching it, but tending towards it..)
Exactly... it's not physical nor philosophical... so what your confusion lies in the mathematical description of a finite sum to an infinite series. It's math. It doesn't have to make sense, it just has to be mathematically correct.
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