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There we learn that Zeno was nearly 40 years old when Socrates was a young man, say Sadly this book has not survived, and what we know of his arguments is second-hand, principally through Aristotle and his commentators here we draw particularly on Simplicius, who, though writing a thousand years after Zeno, apparently possessed at least some of his book. Aristotle speaks of a further four arguments against motion and by extension change generally , all of which he gives and attempts to refute.

In addition Aristotle attributes two other paradoxes to Zeno. Before we look at the paradoxes themselves it will be useful to sketch some of their historical and logical significance.

First, Zeno sought to defend Parmenides by attacking his critics. Parmenides rejected pluralism and the reality of any kind of change: for him all was one indivisible, unchanging reality, and any appearances to the contrary were illusions, to be dispelled by reason and revelation.

Not surprisingly, this philosophy found many critics, who ridiculed the suggestion; after all it flies in the face of some of our most basic beliefs about the world.

Interestingly, general relativity—particularly quantum general relativity—arguably provides a novel—if novelty is possible—argument for the Parmenidean denial of change: Belot and Earman, You think that there are many things? Then you must conclude that everything is both infinitely small and infinitely big!

You think that motion is infinitely divisible? Then it follows that nothing moves! As we read the arguments it is crucial to keep this method in mind. They are always directed towards a more-or-less specific target: the views of some person or school. Then, if the argument is logically valid, and the conclusion genuinely unacceptable, the assertions must be false after all.

If we find that Zeno makes hidden assumptions beyond what the position under attack commits one to, then the absurd conclusion can be avoided by denying one of the hidden assumptions, while maintaining the position. Indeed commentators at least since Aristotle have responded to Zeno in this way.

As we shall discuss briefly below, some say that the target was a technical doctrine of the Pythagoreans, but most today see Zeno as opposing common-sense notions of plurality and motion. We shall approach the paradoxes in this spirit, and refer the reader to the literature concerning the interpretive debate.

This is not necessarily to say that modern mathematics is required to answer any of the problems that Zeno explicitly wanted to raise; arguably Aristotle and other ancients had replies that would—or should—have satisfied Zeno. However, as mathematics developed, and more thought was given to the paradoxes, new difficulties arose from them; these difficulties require modern mathematics for their resolution.

Thus we shall push several of the paradoxes from their common sense formulations to their resolution in modern mathematics. Between any two of them, he claims, is a third; and in between these three elements another two; and another four between these five; and so on without end. So our original assumption of a plurality leads to a contradiction, and hence is false: there are not many things after all. Let us consider the two subarguments, in reverse order. Suppose that we had imagined a collection of ten apples lined up; then there is indeed another apple between the sixth and eighth, but there is none between the seventh and eighth!

On the assumption that Zeno is not simply confused, what does he have in mind? And one might think that for these three to be distinct, there must be two more objects separating them, and so on this view presupposes that their being made of different substances is not sufficient to render them distinct.

So perhaps Zeno is arguing against plurality given a certain conception of physical distinctness. But second, one might also hold that any body has parts that can be densely ordered. Indeed, if between any two point-parts there lies a finite distance, and if point-parts can be arbitrarily close, then they are dense; a third lies at the half-way point of any two. In particular, familiar geometric points are like this, and hence are dense. So perhaps Zeno is offering an argument regarding the divisibility of bodies.

Can this contradiction be escaped? The assumption that any definite number is finite seems intuitive, but we now know, thanks to the work of Cantor in the Nineteenth century, how to understand infinite numbers in a way that makes them just as definite as finite numbers. With such a definition in hand it is then possible to order the infinite numbers just as the finite numbers are ordered: for example, there are different, definite infinite numbers of fractions and geometric points in a line, even though both are dense.

See Further Reading below for references to introductions to these mathematical ideas, and their history. Though of course that only shows that infinite collections are mathematically consistent, not that any physically exist.

But if it exists, each thing must have some size and thickness, and part of it must be apart from the rest. And the same reasoning holds concerning the part that is in front. For that too will have size and part of it will be in front. Now it is the same thing to say this once and to keep saying it forever. For no such part of it will be last, nor will there be one part not related to another.

Therefore, if there are many things, they must be both small and large; so small as not to have size, but so large as to be unlimited. According to his conclusion, there are three parts to this argument, but only two survive. The first—missing—argument purports to show that if many things exist then they must have no size at all. Second, from this Zeno argues that it follows that they do not exist at all; since the result of joining or removing a sizeless object to anything is no change at all, he concludes that the thing added or removed is literally nothing.

The argument to this point is a self-contained refutation of pluralism, but Zeno goes on to generate a further problem for someone who continues to urge the existence of a plurality.

And the parts exist, so they have extension, and so they also each have two spatially distinct parts; and so on without end. And hence, the final line of argument seems to conclude, the object, if it is extended at all, is infinite in extent.

But what could justify this final step? And neither does it follow from any other of the divisions that Zeno describes here; four, eight, sixteen, or whatever finite parts make a finite whole. Again, surely Zeno is aware of these facts, and so must have something else in mind, presumably the following: he assumes that if the infinite series of divisions he describes were repeated infinitely many times then a definite collection of parts would result.

Now, if—as a pluralist might well accept—such parts exist, it follows from the second part of his argument that they are extended, and, he apparently assumes, an infinite sum of finite parts is infinite.

Here we should note that there are two ways he may be envisioning the result of the infinite division. What is often pointed out in response is that Zeno gives us no reason to think that the sum is infinite rather than finite. He might have had the intuition that any infinite sum of finite quantities, since it grows endlessly with each new term must be infinite, but one might also take this kind of example as showing that some infinite sums are after all finite.

Thus, contrary to what he thought, Zeno has not proven that the absurd conclusion follows. However, what is not always appreciated is that the pluralist is not off the hook so easily, for it is not enough just to say that the sum might be finite, she must also show that it is finite—otherwise we remain uncertain about the tenability of her position.

As an illustration of the difficulty faced here consider the following: many commentators speak as if it is simply obvious that the infinite sum of the fractions is 1, that there is nothing to infinite summation. Surely this answer seems as intuitive as the sum of fractions.

Such a theory was not fully worked out until the Nineteenth century by Cauchy. In this case the pieces at any particular stage are all the same finite size, and so one could conclude that the result of carrying on the procedure infinitely would be pieces the same size, which if they exist—according to Zeno—is greater than zero; but an infinity of equal extended parts is indeed infinitely big.

But this line of thought can be resisted. First, suppose that the procedure just described completely divides the object into non-overlapping parts.

There is a problem with this supposition that we will see just below. This result poses no immediate difficulty since, as we mentioned above, infinities come in different sizes. However, we could consider just countably many of them, whose lengths according to Zeno—since he claims they are all equal and non-zero—will sum to an infinite length; the length of all of the pieces could not be less than this.

We shall postpone this question for the discussion of the next paradox, where it comes up explicitly. The second problem with interpreting the infinite division as a repeated division of all parts is that it does not divide an object into distinct parts, if objects are composed in the natural way.

Since the division is repeated without end there is no last piece we can give as an answer, and so we need to think about the question in a different way. Thus the only part of the line that is in all the elements of this chain is the half-way point, and so that is the part of the line picked out by the chain.

In fact, it follows from a postulate of number theory that there is exactly one point that all the members of any such a chain have in common. And so both chains pick out the same piece of the line: the half-way point. And so on for many other pairs of chains. Hence, if we think that objects are composed in the same way as the line, it follows that despite appearances, this version of the argument does not cut objects into parts whose total size we can properly discuss.

You might think that this problem could be fixed by taking the elements of the chains to be segments with no endpoint to the right. Then the first of the two chains we considered no longer has the half-way point in any of its segments, and so does not pick out that point.

What then will remain? A magnitude? No: that is impossible, since then there will be something not divided, whereas ex hypothesi the body was divisible through and through. But if it be admitted that neither a body nor a magnitude will remain … the body will either consist of points and its constituents will be without magnitude or it will be absolutely nothing.

If the latter, then it might both come-to-be out of nothing and exist as a composite of nothing; and thus presumably the whole body will be nothing but an appearance. But if it consists of points, it will not possess any magnitude. Aristotle On Generation and Corruption , a Once again what matters is that the body is genuinely composed of such parts, not that anyone has the time and tools to make the division; and remembering from the previous section that one does not obtain such parts by repeatedly dividing all parts in half.

So suppose the body is divided into its dimensionless parts. And, the argument concludes, even if they are points, since these are unextended the body itself will be unextended: surely any sum—even an infinite one—of zeroes is zero. Could that final assumption be questioned? There is no way to label all the points in the line with the infinity of numbers 1, 2, 3, … , and so there are more points in a line segment than summands in a Cauchy sum.

In short, the analysis employed for countably infinite division does not apply here. So suppose that you are just given the number of points in a line and that their lengths are all zero; how would you determine the length?

It turns out that that would not help, because Cauchy further showed that any segment, of any length whatsoever and indeed an entire infinite line have exactly the same number of points as our unit segment.

Thus we answer Zeno as follows: the argument assumed that the size of the body was a sum of the sizes of point parts, but that is not the case; according to modern mathematics, a geometric line segment is an uncountable infinity of points plus a distance function. Hence, if one stipulates that the length of a line is the sum of any complete collection of proper parts, then it follows that points are not properly speaking parts of a line unlike halves, quarters, and so on of a line.

Like the other paradoxes of motion we have it from Aristotle, who sought to refute it. Suppose a very fast runner—such as mythical Atalanta—needs to run for the bus. Clearly before she reaches the bus stop she must run half-way, as Aristotle says.

 
 

How much is apple motion 5 free

 
Motion is a powerful motion graphics tool that makes it easy to create 2D, 3D, and music creation at a special price — including Final Cut Pro, Motion. Motion 5 is Apple’s professional motion graphics software for creating titles, Motion 5. S$ Inline – 1. Delivers: 16/08/ – 18/08/ — Free.

 

How much is apple motion 5 free

 

The following data may be collected but it is not linked to your identity:. Privacy practices may vary, for example, based on the features you use or your age. Learn More. Mac App Store Preview. Description Designed for video editors, Motion is a powerful motion graphics tool that makes it easy to create cinematic 2D and 3D titles, fluid transitions, and realistic effects in real time. Oct 24, Version 5. Ratings and Reviews. When collaborating with other editors, sometimes there can be problems getting their title, effect, transition or generator plugins working on […].

This excerpt from Office Hours is a short discussion about Apple Motion 5. I asked Alex Lindsay what features he […]. This project consists of four different views of our animating circles and pulses.

Let’s look at this project a bit deeper. Go to the beginning of the project. Click the disclosure triangle for the Text Elements group, as shown in the following screenshot. Notice how the group is slightly less highlighted than the Camera Light Graphics and Background Elements groups. This indicates that at the current frame, this group doesn’t exist. We get further confirmation of this by looking in our mini-Timeline and seeing the Text Elements group start a lot later.

Notice how the group now becomes highlighted but the Subtitle layer does not, as shown in the following screenshot:. Drag your playhead forward until you see the word Subtitle onscreen or go to frame Notice it’s now highlighted. Hit the disclosure triangle for the Subtitle group. Notice that there is a Sequence Text behavior on the text. We will be going in depth with behaviors in Chapter 3 , Making It Move with Behaviors , but right now think of it as what’s causing the text to animate in.

Sometimes when we add filters, masks, and behaviors to clips, our workspace in the Layers tab can get cluttered. We can easily turn off the visibility of these filters, behaviors, and masks at the bottom of the Layers tab.

Press the gear icon shown in the following screenshot and notice how the Sequence Text disappears. Press it again so you can see it. When we work, it’s also advantageous to solo elements in the project.

It allows us to focus our work rather than worry about hundreds of items. To see the layers in the Text Elements group by themselves, select it and click the square within the rectangle icon. Notice how the graphic disappears and the text moves slightly to the side. Click it again to unsolo it. Notice there are four scenes in this group that correspond to the four circle and pulse animations that take place over time. Get a feel for when each scene starts and stops by looking in the Layers tab and in the mini-Timeline for when a group is highlighted.

Twirl open scenes four through one by clicking the disclosure triangle for each of them. This may cause some of the layers to go outside the view, and in order to see them you have to scroll. Instead, click the icon at the bottom-left of the Layers tab with the little head on it.

Drag the slider to your right to resize the layers. Changing the text format in Chapter 5 , Let’s Make Text. Changing the text style in Chapter 5 , Let’s Make Text. He has an uncanny ability to engage his students and create a level of relatedness that keeps them coming back for more. In , Nick founded Inconscience Productions and continues to work with domestic and international brands to shoot, produce, and cut masterpieces.

In , he was handed the opportunity of a lifetime to co-edit a feature documentary entitled My Father and the Man in Black; the untold story of a bad boy Johnny Cash, his talented but troubled manager, Saul Holiff, and a son searching for his father in the shadow of a legend.

When he is not busy impressing his students at Witz Education and travelling to or from post-production conferences, this half Ukrainian, half Trinidadian can be found playing tennis. This is his first book! Publication date: May Publisher Packt. Pages ISBN Chapter 1. Getting Around the Interface. Choosing a Motion project Importing files to the Canvas, Layers tab, and Timeline Importing Photoshop and Illustrator files Making selections with Expose Changing the layer order Groups versus layers Making changes in the Properties tab, HUD, and Canvas Moving and trimming layers in the Timeline and the mini-Timeline Launching and customizing a template Keyboard customization Looking under the hood — key preferences for your workflows Sequencing stills in the Timeline Managing the Layers tab.

Choosing a Motion project. How to do it The high resolution colored images of the book can also be found in the code bundle. There’s more…. Motion templates. Rigging and publishing. Note Project properties for Motion can be adjusted in the Project Properties menu. Project Properties. See also. Importing files to the Canvas, Layers tab, and Timeline. Getting ready. Tip Make sure your playhead is on the first frame of your project throughout the exercises. Locate the movie file on you system that matches your project’s settings.

Locate the movie file on your system that matches your project’s settings. Wait for the plus icon and release your mouse, as shown in the following screenshot:.

There’s more Know where your playhead is. Viewing and previewing files in the File Browser. The Importing Photoshop and Illustrator files recipe.

Importing Photoshop and Illustrator files. Making selections with Expose. Move your playhead to 5 seconds. Changing the layer order. Moving layers with shortcuts.

The Groups versus layers recipe. Groups versus layers. How it works. Locate a still image file on your system that is large enough for your project’s settings. Moving and trimming layers in the Timeline and the mini-Timeline. Launching and customizing a template. How it works Let solo be your friend. Tip Motion is a big program but with a little practice you’ll get better everyday! Don’t be intimidated. Keyboard customization. Looking under the hood — key preferences for your workflows.

The Keyboard customization recipe. The Sequencing stills in the Timeline recipe. Sequencing stills in the Timeline.

Managing the Layers tab. Read more Unlock this book with a 7 day free trial. Browse publications by this author. I purchased a copy of Apple Motion 5 Cookbook Motion 5 download for mac free dmg full version. Complete setup Motion 5. Apple Motion 5. Designed for skilled video editors, it helps users to form cinematic 2d and 3D titles, fluid transitions, and realistic effects in real-time. Apple Motion 5 is a complete application that offers impressive tools and features for creating cinematic 2D and 3D titles, fluid transitions, and realistic effects in real time.

Apple Motion 5 is a powerful motion graphics tool that makes it easy to create cinematic 2D and 3D titles, fluid transitions, and realistic effects in real-time. This update from Apple primarily designed to streamline and speed up the workflow of video editors, particularly those who work with proxies. It comes with a more efficient environment and tools for creating cinematic 2D and 3D titles, fluid transitions, and realistic effects in real-time.