It will also discuss Aristotle's theory of four causes, specifically the material, formal, efficient, and final causes of being. Metaphysics Although I'm not really into antiques or memorabilia, two of my favorite possessions are our family's old farm table and my grandma's chocolate chip cookie recipe actually written by her, not a copy! Material Let's start with the material cause.
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Formal Next is the formal cause. Efficient Aristotle's next cause is known as the efficient cause. Final Our last cause is aptly named the final cause. Try it risk-free No obligation, cancel anytime. Want to learn more? Review Keeping all this in mind, let's pretend I just used my grandma's cookie recipe to make some cookies for us. Here we go. I'll ask the question and give you a few seconds to answer. First, what are the material causes of the cookie?
Remember, the material cause of the table is wood. Now, what is the formal cause? Here's another hint, the formal cause of the table is its original blueprint or design plan. Almost finished…What is the efficient cause of the cookies?
As a tip, think carpenter. Last, what is the final cause of our cookies? Lesson Summary Metaphysics is the branch of philosophy that deals with concepts like being, substance, cause and identity. Learning Outcomes Completion of this lesson means you now can: Define metaphysics Describe Aristotle's four causes of being.
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It was an interesting idea. Maybe all that has to exist in the universe is the network, and then the matter in the universe just corresponds to particular features of this network. Even though every cell follows the same simple rules, there are definite structures that exist in the system—and that behave quite like particles, with a whole particle physics of interactions.
Back in the s, there was space and there was time. Both were described by coordinates, and in some mathematical formalisms, both appeared in related ways. It makes a lot of sense in the formalism of Special Relativity, in which, for example, traveling at a different velocity is like rotating in 4-dimensional spacetime. So how does that work in the context of a network model of space? And then one just has to say that the history of the universe corresponds to some particular spacetime network or family of networks.
Which network it is must be determined by some kind of constraint: our universe is the one which has such-and-such a property, or in effect satisfies such-and-such an equation. And, for example, in thinking about programs, space and time work very differently. In a cellular automaton, for example, the cells are laid out in space, but the behavior of the system occurs in a sequence of steps in time. How does this network evolve?
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But now things get a bit complicated. Because there might be lots of places in the network where the rule could apply. So what determines in which order each piece is handled? In effect, each possible ordering is like a different thread of time. And one could imagine a theory in which all threads are followed—and the universe in effect has many histories. Needless to say, any realistic observer has to exist within our universe. So if the universe is a network, the observer must be just some part of that network. Now think about all those little network updatings that are happening.
If you trace this all the way through —as I did in my book, A New Kind of Science —you realize that the only thing observers can ever actually observe in the history of the universe is the causal network of what event causes what other event. Causal invariance is an interesting property, with analogs in a variety of computational and mathematical systems—for example in the fact that transformations in algebra can be applied in any order and still give the same final result.
So what about spacetime and Special Relativity?
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In other words, even though at the lowest level space and time are completely different kinds of things, on a larger scale they get mixed together in exactly the way prescribed by Special Relativity. But because of causal invariance, the overall behavior associated with these different detailed sequences is the same—so that the system follows the principles of Special Relativity.
At the beginning it might have looked hopeless: how could a network that treats space and time differently end up with Special Relativity? But it works out. OK, so one can derive Special Relativity from simple models based on networks. The whole story is somewhat complicated. First, we have to think about how a network actually represents space.
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Now remember, the network is just a collection of nodes and connections. Just start from a node, then look at all nodes that are up to r connections away. If the network behaves like flat d -dimensional space, then the number of nodes will always be close to r d. One has to look at shortest paths—or geodesics—in the network. One has to see how to do everything not just in space, but in networks evolving in time.
And one has to understand how the large-scale limits of networks work. But the good news is that an incredible range of systems, even with extremely simple rules, work a bit like the digits of pi , and generate what seems for all practical purposes random.
I think this is pretty exciting. Which means that these simple networks reproduce the features of gravity that we know in current physics. There are all sorts of technical things to say, not suitable for this general blog. Quite a few of them I already said long ago in A New Kind of Science —and particularly the notes at the back.
A few things are perhaps worth mentioning here. All these things have to emerge. When it comes to deriving the Einstein Equations, one creates Ricci tensors by looking at geodesics in the network, and looking at the growth rates of balls that start from each point on the geodesic. The Einstein Equations one gets are the vacuum Einstein Equations.
One puts remarkably little in, yet one gets out that remarkable beacon of 20th-century physics: General Relativity. Another very important part is quantum mechanics.
But then their behavior must follow the rules we know from quantum mechanics—or more particularly, quantum field theory. A key feature of quantum mechanics is that it can be formulated in terms of multiple paths of behavior, each associated with a certain quantum amplitude. But what about in a network? Because everything is just defined by connections.