Are Zeno's paradoxes solved by modern science?

[wandelaar]

Are Zeno's paradoxes indeed already solved by modern science? My thesis is that they are indeed solved although the solution requires one to delve into some mathematical and logical subtleties that escaped the ancient philosophers. I hope this bold position will create enough controversy for an entertaining topic. We (including myself!) might even learn something by participating.

[Lost in Translation]

Zeno's paradoxes seem to conflict with observation, thus either observation is flawed or the paradoxes are flawed.

[Rocky Lionmouth]

Since i am a mere man of minor ambitions and no fame nor intelligence to speak of i’ve always thought Zeno to be a funny guy in a very important position: ”oh, thats a very nifty idea this motion you speak of, but what if...”

His formulations femind me of the initial problem in most koans.

 

I’m inclined to say Diogenes already fixed the problem, but then again i am biased in favour of his take on most things except, among orher minute details, his purported claims to the uselessness of recreational sex as an argument in favour of masturbation. (The two might lead to similar results but cannot, imho, be compared with any satisfactory conclusions, ahremm.)

 

His reply to Zenos paradoxes was to stand up and walk away, now wether or not this was just his usual short temper or a demonstration of his reply we cannot know.

But his practical approaches to philosophy and human interaction also remind me of ”the twist” in many koans, like the one where a monk places a sandal on his head and leaves.

 

I think Zenos paradoxes ultimately serve a very good purpose as cautionary examples of how easily Really Clever Stuff can topple itself because of the absurd extremities excessive deductive reasoning can present. Beware overconfident reasoning, all of a sudden you’ll get caught trying to verbally prove motion exists because you dug your own hole regardless of wether Zeno or one of his heirs handed you a shovel:

Science is dependent on the investigation and critique of science to function usefully, proving and disproving are not as important as what we can use and understand.

 

Sherlock Holmes has been casted quite often to illustrate how delicate the matter of inferring conclusions can be when important but easily overlooked details are in the mix. 

 

Case in point: ”featherless biped” needed the addition of ”with big, flat toenails” because some joker brought Plato a plucked chicken to illustrate a minor flaw in the theory of what a human is.

 

 

* I reserve the right to be verbally inconsistent on this matter in favour of my appreciation of the topic and the paradoxes themselves. It’s also 3 in the morning and i’m still nursing my overcofident libationing yesterday. Happy New silly-Western-rational-linear-logic-antiwisdom Year!

 

Edited January 2, 2019 by Rocky Lionmouth

[rideforever]

You can see the state of much mankind from Zeno's paradox.   Humans treat themselves and life as a kind of game that they play with, and what they enjoy is a game that lasts a thousand years and a thousand headaches.

They do not value reality, which is why they do not enter it.
When they die they are still caught in the idiotic and meaningless masturbation of their mind, having successfully avoided existing.   Somewhere inside is a monkey terrified of waking up and doing everything to prevent it.  Nothing can be said to such people to come to a solution, because they seek their own confusion and will die pleased that they did not solve anything.   It is a deceit.

Such people are against life and should be avoided.

"Whoever is not with me is against me; whoever does not gather with me truly is scattering."

[wandelaar]

9 hours ago, Lost in Translation said:

Zeno's paradoxes seem to conflict with observation, thus either observation is flawed or the paradoxes are flawed.

 

Probably the latter.

 

See:

 

https://books.google.nl/books?id=0AzP9WLLJLcC&pg=PR6#v=onepage&q&f=false

 

[wandelaar]

9 hours ago, Rocky Lionmouth said:

I think Zenos paradoxes ultimately serve a very good purpose as cautionary examples of how easily Really Clever Stuff can topple itself because of the absurd extremities excessive deductive reasoning can present. Beware overconfident reasoning, all of a sudden you’ll get caught trying to verbally prove motion exists because you dug your own hole regardless of wether Zeno or one of his heirs handed you a shovel:

Science is dependent on the investigation and critique of science to function usefully, proving and disproving are not as important as what we can use and understand.

 

Yes - in my opinion mere rationalism independent of observation and/or common sense is just as silly as confidently trusting in "what resonates with you" without caring about known facts.

[wandelaar]

I will simply ignore the irrelevant mechanically self-repeating rantings of rideforever, ViYY, etc. They are not here to discuss anything, but only to preach to the supposedly unknowing masses about their own supposedly superior understandings. I have no need for nor interest in that kind of stuff.

[Taoist Texts]

11 hours ago, Lost in Translation said:

observation is flawed or the paradoxes are flawed.

how about the comprehension of the both is flawed

[OldDog]

Back to the paradoxes. Let's beg a couple of questions before we actually begin picking at a particular Zeno paradox.

 

Why do you suppose Zeno created these paradoxes to begin with?

 

I have not studied western philosophy much. In my limited experience, it suffers from over-analysis ... seemingly endless cycles of reasoning and deduction, which incrementally seem to make sense but in the end leave you wondering where you are.

 

Are western philosophical paradoxes analogous to koans? Do they serve a similar purpose? If so, what.

 

Koans are usually simple dirct statements that appear as absurd or nonsensical ... they defy reason and so solution must be sought elsewhere.

 

Paradoxes often required extensive set up to establish a path of constraining reasoning that appears to lead to an absurdity. 

 

Both koan and paradox seem to require breaking out of an either implicit or explicit pattern of thought to arrive at a satisfactory position.

 

 

[Wu Ming Jen]

The ancient achieved one's realized and asked the same questions as modern science does today. Back in the day there was no difference between science and the great arts. Science will only confirm what the ancients are describing.

 

Our vision is so small that we may forget that all the rules of matter and everything in the universe, vibrations, the spiral, the tree, all forms are physically within our body. the tree of the nervous system the spiral of dna the vibration of life force running through everything connected by an unseen web of dark energy connecting everything. The ancient achieved ones looked inside for answers and discovered the entire universe is in our hand.

 

 

Modern humans think a lot and have created many problems and try to think how to make everything better. Making better the same problems we have created. Thinking does not make the world a better place.

 

Knowing that everything in the universe is connected knowing that our eye seeing is also the eye of creation seeing.  Seeing ourselves in others and all things makes the world a better place.

 

which way are we looking? outside for knowledge or inside for awareness of what already is.

[rideforever]

Why did Zeno consider his paradoxes ?   
If you ask this seriously and don't want to play games, what is the actual answer to this scene?

The answer actually is that Zeno was busy playing with his mind because he couldn't feel who he was, he could not feel the "subject" of the mind.   It is like someone who looks in a lake but cannot comprehend his face, so he stirs the water with his hand.   But still no recognition.   He just doesn't get it.   He is not conscious.   

 

For somebody like that and perhaps most of mankind is like that what does he really need ?   He needs close contact with someone that understands 1 to 1, and he needs joy and pain, light and dark .... or he needs to live more lives and he will surely get enough shocks and pain to eventually create understanding.   Then one day Zeno will see himself in the lake, he will no longer be a monkey, but approaching a man.

 

Diogenese was correct and brilliant like lightning, a flash of ... truth, shattering the darkness of the daytime of man.   
Shattering.
But .... is it understood by Zeno ?
Anyway sorry for the interruption, I shall foff now.

 

 

[Taoist Texts]

1 hour ago, OldDog said:

Why do you suppose Zeno created these paradoxes to begin with?

Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490–430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. It is usually assumed, based on Plato's Parmenides (128a–d), that Zeno took on the project of creating these paradoxes because other philosophers had created paradoxes against Parmenides' view. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one."^[1] Plato has Socrates claim that Zeno and Parmenides were essentially arguing exactly the same point.^[2]

[wandelaar]

1 hour ago, Taoist Texts said:

how about the comprehension of the both is flawed

 

That is another quite exotic possibility, but you need to provide some reasons for us to join you on that road or it will end in pure speculation. And from there to bizarre conspiracy or pseudoscientific theories is but a small step...

[Taoist Texts]

3 minutes ago, wandelaar said:

but you need to provide some reasons for us

err, u all just admitted that you dont even know why paradoxes were created or what they even mean. Is not that a reason to suspect that y'all do not comprehend them?

[wandelaar]

1 hour ago, OldDog said:

Both koan and paradox seem to require breaking out of an either implicit or explicit pattern of thought to arrive at a satisfactory position.

 

That is correct. But the paradoxes in western philosophy are posed in the context of rational thought and the solution is also (usually) sought by means of rationale thought. But koans are expressly not supposed to be solved by means of rational thought. They have a quite different purpose. 

[Jeff]

15 hours ago, wandelaar said:

Are Zeno's paradoxes indeed already solved by modern science? My thesis is that they are indeed solved although the solution requires one to delve into some mathematical and logical subtleties that escaped the ancient philosophers. I hope this bold position will create enough controversy for an entertaining topic. We (including myself!) might even learn something by participating.

 

The paradoxes are simply faulty logic traps. Take Achilles and the tortoise for example...

 

Rather than two independent beings racing, it assumes one being is a subset of (and therefore trapped by) the second. Rather than the silly 1/2 of the other logic, the answer should be based upon the relative goal (or time) of the race.

 

Speed of Achilles = X

Speed of Tortoise = 1/2 X

Head start is 100 meters for tortoise

 

So as long as Achilles is actually moving, he will pass the tortoise when Time * ( X - 1/2X) = 100. If the race is shorter than that time, then the Tortoise wins, if longer then Achilles wins.

 

 

[wandelaar]

13 minutes ago, Taoist Texts said:

err, u all just admitted that you dont even know why paradoxes were created or what they even mean. Is not that a reason to suspect that y'all do not comprehend them?

 

I'm not aware of having admitted that I don't even know why the paradoxes were created or what they even mean.

 

Edited January 2, 2019 by wandelaar

[Taoist Texts]

Just now, wandelaar said:

 

I'm not aware of having admitted that I don't even know why paradoxes were created or what they even mean.

if you know all that then you just started the discussion in order to show off your knowledge. Which is ok, please proceed

[Taoist Texts]

6 minutes ago, Jeff said:

The paradoxes are simply faulty logic traps.

ahh, the 'silly ancient people' theory

[Jeff]

5 minutes ago, Taoist Texts said:

ahh, the 'silly ancient people' theory

 

Taking 1/2 of 1/2 forever is simply a limit function in math, with the limit being zero.  But in this case, they are not the same thing, and hence the logic fails.  

[wandelaar]

@ Taoist Texts

 

There you go again! The usual fallacies (the straw man, false generalisation, PC tabooing). Don't expect me to waste my time on that.

[rideforever]

Concrete Technical Solution

 

Right, 5 minutes thought and I have the answer.`

 

Real Life A

The tortoise running against Achilles in an open race, Achilles always wins.

 

Model A

Consider tortoise moves 100m and stops, then Achilles follows.   Then tortoise moves half that distance again 50m, then Achilles follows.  And so on.   In this way Achilles never overtakes the tortoise, hence the paradox.

 

Consideration

Okay, well let's take Model A into a real life situation and see what happens.   We can call it Real Life B.

 

Real Life B

Tortoise runs against Achilles, but in the following manner, tortoise goes first runs 100m, then stops, Achilles catches up then stops, then tortoise runs half the distance again (50m) then stops, then Achilles etc...
In this case, in real life, Achilles would never pass the tortoise.

 

Hence it is evident that Model A is not modelling Real Life A, it is modelling Real Life B.   And it models it correctly.

 

Real Life A and Model A have little to do with each other, and Zeno has made an error in the setting of the paradox.   One might as well ask to model the weighing of oranges through a model involving throwing oranges out of a window !   And then saying that the oranges weight nothing .... it's a paradox.   No, it's not a paradox.

 

Why can't Model A be used to model Real Life A ?   Because they are different.    

 

In this "paradox" it includes both a Real Life case and a "Model".   Why does it include a "Model", it should not, that should already be a red flag.

 

Model A is an accurate model for Real Life B, but not for Real Life A.

 

Edited January 2, 2019 by rideforever

[Taoist Texts]

12 minutes ago, Jeff said:

 

Taking 1/2 of 1/2 forever is simply a limit function in math, with the limit being zero.  But in this case, they are not the same thing, and hence the logic fails.  

thats not the point. The point is that you claim that zenon was stupider than you for not understanding limits and zeroes that you understand.

[wandelaar]

24 minutes ago, Jeff said:

The paradoxes are simply faulty logic traps. Take Achilles and the tortoise for example...

 

Rather than two independent beings racing, it assumes one being is a subset of (and therefore trapped by) the second. Rather than the silly 1/2 of the other logic, the answer should be based upon the relative goal (or time) of the race.

 

Speed of Achilles = X

Speed of Tortoise = 1/2 X

Head start is 100 meters for tortoise

 

So as long as Achilles is actually moving, he will pass the tortoise when Time * ( X - 1/2X) = 100. If the race is shorter than that time, then the Tortoise wins, if longer then Achilles wins.

 

A paradox cannot be solved by placing another correct reasoning besides it, you have to actually pinpoint the error(s) in the paradoxical reasoning.

[Jeff]

28 minutes ago, wandelaar said:

 

A paradox cannot be solved by placing another correct reasoning besides it, you have to actually pinpoint the error(s) in the paradoxical reasoning.

 

Faulty logic is faulty logic...  

 

But if you are going to assume the logic stream, and want to break it, simply have Achilles run farther than the 100 meters before checking. Have him run 200 meters and then check where the tortoise is relative to him.  If he goes 2x the distance, he will pass. Or, since it is a relative time based logic trap, simply have Achilles constantly watching the tortoise, so that you get infinite looks at the infinite 1/2, which then also breaks the paradox and he passes the Tortoise, as Infinity * 1/2 is still = Infinity.

 

The math here is calculus. Newton and Leibniz solved it in the 1700s, bypassing the old greek method of exhaustion that your paradox states. Can read about the death of Zeno paradox here...

 

https://en.wikipedia.org/wiki/History_of_calculus

 

Edited January 2, 2019 by Jeff