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This isn t a book on GR, but we can give a very brief overview of the theory here (see Relativity Demysti ed for details). The central ideas of general relativity are the notion that geometry is dynamic and that the speed of light limits the speed of all interactions, including gravity. We start with the notion of the metric, which is a way of describing the distance between two points. In ordinary three-dimensional space the metric is ds 2 = dx 2 + dy 2 + dz 2 (1.1)

A common method for designing applications is to organize them around an eventdriven user interface. In this design pattern, the developer creates the interface and subsequently writes code that will execute the desired application actions in response to user gestures. This structure can be successful for small, single-user systems that will require little alteration to the functionality over time. However, it is not suitable for larger, distributed projects for the following reasons:

CHAPTER 2: Blast-Off!

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This metric follows from the pythagorean theorem by making the distances involved in nitesimal. Note that this metric is invariant under rotations. Something that is key to relativistic thinking is focusing on those quantities that are invariant. To move up to a relativistic context, we extend the notion of a measure of distance between two points to a notion of distance between two events that happen in space and time. That is, we measure the distance between two points in space-time. This is done with the metric ds 2 = c 2 dt 2 + dx 2 + dy 2 + dz 2 (1.2)

manipulated in several different ways. When business logic is implemented in the display code, display inconsistencies can result because the logic can be copied and modified in one object and not another. In addition, any change to the data display requires updates in several places.

This metric extends the idea of geometry to include time as well. But not only that, it also extends the notion of a distance measure between two points that is invariant under rotations to one that is also invariant under Lorentz transformations, that is, Lorentz boosts between one inertial frame and another. While adding time to the mix certainly extends the notion of geometry into an unfamiliar realm, we still have a xed geometry that does not take into account gravitational elds. To extend the metric in a way that will do this, we have to enter the domain of non-euclidean geometry. This is geometry which does not require

handling are entangled, application maintenance can be very difficult, especially over a long span of time.

n Changes to a single piece of code may have far-reaching side effects. n Development cannot occur on a modular basis, as everything is dependent

Figure 2 27. By using the indicated shortcut, we exit the Simulator and go back into Xcode, so that we may begin entering our new code.

A normal ordered product is denoted using two colons, that is : a a :. In the case of the Virasoro operator, we write Lm = 1 : m n n : 2 n

on everything else. This problem is amplified on large-scale development projects because it is difficult for a large team of developers to split tasks.

Lm will lower the eigenvalue of the number operator by m. Looking at the commutation relation Eq. (4.10), you can see that m n and n commute when m 0. This means that when m 0 we can simply move raising and lowering operators where we want in the expression for the Virasoro operator because no extra terms will be added from the commutator. Normal ordering L0 gives 1 2 L0 = 0 + n n 2 n =1 Now, to get this result, note that 1 1 1 1 n n = 2 0 0 + 2 n n + 2 n n 2 n= n =1 n =1

n Code is less reusable, because components are dependent on one another;

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