# Part II- Discarding Complexity Without Losing Information

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You’ve divided your hard problems into manageable pieces. You’ve found transferable, reusable ideas. When these tools are not enough and problems are still too complex, you need to discard complexity—the theme of our next three tools. They help us discard complexity without losing information. If a system contains a symmetry (Chapter 3)—or what is closely related, it is subject to a conservation law—using the symmetry greatly simplifies the analysis. Alternatively, we often do not care about a part of an analysis, because it is the same for all the objects in the analysis. To ignore those parts, we use proportional reasoning (Chapter 4). Finally, we can ensure that our equations do not add apples to oranges. This simple idea—dimensional analysis (Chapter 5)—greatly shrinks the space of possible solutions and helps us master complexity.