Zeno's Paradoxes (is motion possible?)

Give him a chance m8, he was born around 490 BC and was probably drunk when he wrote this.

As poor as his writings were, they make a lot more sense than the world being created in 7 days.... etc. :wink:

I didn't even know Zeno spoke English.


Jeez...in A2K, you learn something new every day.

Mr Apisa just gave a classic demo of reaching for simple and selfish satisfactions.

spendius.

He didn't speak English, he spoke gibberish

Not so.

But just in case anyone in A2K is interested in "a classic demo of reaching for simple and selfish satisfactions"....

...Spendius' pompous posting pictured above is a wonderful example.



And you are all welcome to it.

The infinite numbers in between 0 and 1 would eventually add up to 1, so it is reachable since .1+.2... etc add up to 1.

Spendius: would you care to comment on the status of philosophy in pre-pagan times? The inference to be drawn from your post is that the sophistry of pagan times changed radically with the coming of Christianity (i.e. post-pagan times). But didn't some of the Church fathers spend a somewhat inordinate amount of time discussing such weighty problems as how many angels could dance on the head of a pin? Now there's a problem Zeno would have been proud to consider, had he but had the advantages of being a Christian.

Happy Andy:-

My views on philosophy in "pre-pagan" times,if such existed,would get me thrown off the forum.
The oldest known work of art is,I think,the figurine known as the Venus of Wallendorf.I don't know where it can be seen;Eastern Europe I would guess.A photo of it is in Neuman's (?spelling) The Great Mother.A long.concentrated look at that will give you an idea if you have an open and receptive mind which I assume to be the case.The cave paintings of Southern France are also useful in this regard.There is another Venus figurine but I have forgotten the name our world has labelled it with.It is of later date than the Wallendorf.
But I would consider all those to be in pagan times and not the pre-pagan.The best guesses for the pre-pagan might be derived from a close study of your own body and the interaction of it with the "other".You would have to think about aspects which are essentially independent of outward forms either social,spiritual or political.
Zeno was a pagan.470 BC.
Generally,I don't see any relevance in philosophy in a stage of the culture where electricity and other portable energy forms govern every aspect of life.In such an epoch politics is the governing principle if we ignore the vagaries of nature and philosophy is nothing if it is not a governing process.Nature,of course,is the final arbiter but for practical purposes it can be ignored so long as it remains in a stable (for us)state.
Obviously radical changes took place when the pagan cultures of classical times gave way to a Christian orientation which is all that took place at first.But the full blown Faustian culture,in which we live,has many pagan residues.A fair example is a street in our city centres when the pubs close.
But one shouldn't forget other cultures which were trundling along in the "unknown" world.One interesting feature of Pacific cultures which we discovered when our technologies enabled us to penetrate them was that they hadn't seen the connection between fornication and reproduction.
This might be linked to the fact that their population densities remained stable for long periods of time.That has not been the case with our more scientific ideas.
I hope that helps a little.It is meant as a signpost.

spendius.

Or another way to view it...
If the finite distances are infinitely small, as implied by the division of the original distance into an infinite number of finites, they will each take an infinitely small time to traverse, regardless of relative speed, which actually means that you traverse the entire distance instantaneously.

I think I was being abtuse there, just for the hell of it....

Yo spendius! Whenever I see a post of your making it has christian slurr all over it like coffe spilled over a newspaper. Is this intentional?

By the way, motion is not impossible. It is the oposite of motion that is impossible. Existence is change. What is evolution but movement?

Ok, so we've established that Zeno's paradoxes were the works of an infantile mind.... Maybe this is because Zeno was a mere teenager when he wrote these paradoxes?
Little or no written evidence of Zeno's work exists today, what we do know of his writings, is what other philosophers of his time (and later) wanted us to know... the easiest way to discredit someone's work, is to publicise any bad work they may have done.
Zeno had some excellent ideas for his time and with the mathematical tools and beliefs of the time, could hardly have come to any other conclusions (see "respect of beliefs" thread)

So, if a logical thinker (Albert Einstein) and a mathmatical genius (Mileva Maric) were to take Zeno's paradoxes and apply modern knowledge (see "respect of beliefs" thread) Could theories such as the theories of general and special relativity ( Space time continuum) be extracted from Zeno's works?

Twincams,

There is nothing here.

Zeno's "apparant" paradox is no paradox at all. It simply shows the need for concepts in math that have been understood for a good 500 years.

The main mathematical concept addressed by Zeno's paradox is the limit. Mathmeticians This topic is learned in any pre-calculus class that a typical high school student takes.

Zeno's paradox does point toward calculus. And, yes, calculus is an integral (pun intended) part of most modern scientific theories including general and special relativity.

But there is no real paradox here, and there is nothing new that hasn't been understood for centuries.

I think we have a small misunderstanding here, when I mentioned Zeno's "Works", I was referring to his collective works, not just his schoolboy rantings.

Ok, let's take a look at his "schoolboy rantings" and compare them to modern day thinking....
Zeno's integers have been replaced by the contemporary notion of real numbers. The new one-dimensional continuum, the standard model of the real numbers under their natural (less-than) order, it is the modern day equivelant of Zeno's infinitely divisible line. The new line is now the basis for the scientist's notion of distance in space and duration through time. The line is no longer a sum of points, but a set-theoretic union of a non-denumerably infinite number of unit sets of points. Only in this way can we make sense of higher dimensional objects such as the one-dimensional line and the two-dimensional plane being composed of zero-dimensional points, for, as Zeno knew, a simple sum of even an infinity of zeros would never total more than zero. The points in a line are so densely packed that no point is next to any other point. Between any two there is a third, all the way 'down.' The infinity of points in the line is much larger than any infinity Zeno could have imagined. The non-denumerable infinity of real numbers (and thus of points in space and of events in time) is much larger than the merely denumerable infinity of integers. Also, the sum of an infinite series of numbers can now have a finite sum, unlike in Zeno's day.

So, was Zeno actually wrong, or was he right.... in his time? .... should we respect his beliefs or merely dismiss his works as 'Rantings', simply because we now have the knowledge to work with "infinity"??

I'm just killing some time here and attempting to draw some thinkers out of the woodwork. We all know Zeno IS wrong, but WAS he wrong?

Not to keep straying off the subject (hey! I didn't start it!) but for the benefit of Spendius -- as far as I know the Venus of Willendorf statuette still resides somewhere in Austria, where archeologists first unearthed it.

Actually, I think it's in the Naturhistorisches Museum in Vienna

Twincams,

Everything you are describing (assuming I understand correctly) is modern math. The infintessimal points are a basis of calculus. You axiom on infinity is also standard math.

I don't get what the question is. If Zeno really said these things (and I kind of doubt it because some of the ideas you have expressed are Rennaisance or higher) than he was in agreement with 21st century mathematics.

Twin: Zeno was, is and ever will be wrong.

Just catching up to the thread - but I have yet to see any of you prove Zeno wrong.

I hear a lot of bluster - and a lot of statements that he is wrong - but no proof.

Frank attempted to give us a practical application as proof - but remember that Zeno's basis for his arguments was Parminidean Monism.

Whether he would take Mr. Apisa's bet is irrelevent because it would prove nothing. Motion is apperant and our senses are deceiving us. It is odd that the Bibleguru is so against this statement.

It could be argued that Sin is inbetween perfect sight and the sight of humans - that is why we have the ignorance and concupienscence of humans.

I have yet to be impressed by the bluster - now prove the syllogism wrong.

1) If anything moves from one place to another, then it performs infinitely many tasks.

(2) Nothing can perform infinitely many tasks.

Therefore,

(3) Nothing moves.

The appeal seems to be to attack the first premise - but any two points of any distance has an infinite amount of points inbetween.

If you choose to say that Math is not applicable to life - that seems odd too - because 1+1=2 every time I add my Cheerio's together (or whatever I choose to add).

'Limit' has been mentioned - but it was just mentioned as an answer to the paradox without explanation. Give up the goods... and drop the huffing and puffing.

TF

To make things short however - I will use the answer I give in class:

"the solution to all of the mentioned paradoxes then,9 is that there isn't an instant in time underlying the body's motion (if there were, it couldn't be in motion), and as its position is constantly changing no matter how small the time interval, and as such, is at no time determined, it simply doesn't have a determined position.

The paradoxes of Achilles and the Tortoise and the Dichotomy are also resolved through this realisation: when the apparently moving body's associated position and time values are fractionally dissected in the paradoxes, an infinite regression can then be mathematically induced, and resultantly, the idea of motion and physical continuity shown to yield contradiction, as such values are not representative of times at which a body is in that specific precise position, but rather, at which it is
passing through them.

The body's relative position is constantly hanging in respect to time, so it is never in that position at any time.

Indeed, and again, it is the very fact that there isn't a static instant in time underlying the motion of a body, and that is doesn't have a determined position at any time while in motion, that allows it to be in motion in the first instance. Moreover, the associated temporal (t) and spatial (d) values (and thus, velocity and the derivation of the rest of physics) are just an imposed static (and in a sense, arbitrary) backdrop, of which in the case of motion, a body passes by or through while in motion, but has no inherent and intrinsic relation. For example, a time value of either 1 s or 0.001 s (which indicate the time intervals of 1 and 1.99999's, and 0.001 and 0.00199999. s, respectively), is never indicative of a time at which a body's position might be determined while in motion, but rather, if measured accurately, is a representation of the interval in time during which the body passes through a certain distance interval, say either 1 m or 0.001 m (which indicate the distance intervals of 1 and 1.99999'.m, and 0.001 and 0.0019999'. m, respectively).

THis is taken from:

http://philsci-archive.pitt.edu/archive/00001197/02/Zeno_s_Paradoxes_-_A_Timely_Solution.pdf

TTF

p.s. This has jack to do with math - it speaks clearly and distinctly about our conception of movement and our thoughts of space. It just took a thinker quite some time to say that when something is moving - it is not in any space for any given time - it is moving though it.