The combination of double-sided laser heating in the diamond anvil cell and detailed chemical analysis of the recovered samples is a promising approach to explore the chemistry of the Earth’s deep interior from the lower mantle to the core. Routine recovery of laser-heated samples coupled with chemical and textural characterization at the submicron scale is the key to expand knowledge of chemical interactions and melting at extreme conditions, particularly in complex systems. Recent technical developments have allowed us to investigate element partitioning and melting relations at pressures approaching the Earth’s inner-core boundary. In this chapter, we review the techniques used for recovering tiny laser-heated samples and analyzing their chemical compositions and quenched textures, while highlighting key experiments that address silicate–metal element partitioning during mantle–core differentiation, silicate melting relations with applications to early magma ocean crystallization and deep mantle melting, and melting relations in iron-alloy systems relevant to the core. The results have drastically expanded our understanding of element redistribution at deep chemical boundaries and the chemical evolution of the deep mantle and the inner core. Finally, we emphasize the need for standardized protocols to obtain consistent, reproducible results and streamlined procedures to promote good practice and increase productivity. A broad collaboration with a systematic approach would further advance the field of high-pressure geochemistry.

The combination of double-sided laser heating in the diamond anvil cell and detailed chemical analysis of the recovered samples is a promising approach to explore the chemistry of the Earth’s deep interior from the lower mantle to the core. Routine recovery of laser-heated samples coupled with chemical and textural characterization at the submicron scale is the key to expand knowledge of chemical interactions and melting at extreme conditions, particularly in complex systems. Recent technical developments have allowed us to investigate element partitioning and melting relations at pressures approaching the Earth’s inner-core boundary. In this chapter, we review the techniques used for recovering tiny laser-heated samples and analyzing their chemical compositions and quenched textures, while highlighting key experiments that address silicate–metal element partitioning during mantle–core differentiation, silicate melting relations with applications to early magma ocean crystallization and deep mantle melting, and melting relations in iron-alloy systems relevant to the core. The results have drastically expanded our understanding of element redistribution at deep chemical boundaries and the chemical evolution of the deep mantle and the inner core. Finally, we emphasize the need for standardized protocols to obtain consistent, reproducible results and streamlined procedures to promote good practice and increase productivity. A broad collaboration with a systematic approach would further advance the field of high-pressure geochemistry.

Congress is the centerpiece institution of Madison’s Republic. Article I of the Constitution starts with Congress, enumerating an impressive list of specific powers given to government because they are vested in the national legislature. And, if we have a republic, it is because the Congress somehow represents the national interest. It does this, as the above quote from Federalist 10 suggests, by bringing into government the range of interests in society. This is necessarily a messy business. The “necessary and ordinary operations of government” involve the range of factions in society? No wonder there is so much conflict, noise, frustration, posturing, and gridlock in Washington. Congressional politics, in other words, is untidy by design.

For James Madison, self-interest is the problem. It is the problem because it is an immutable part of human nature and because its consequences in politics are potentially devastating. People act for their own gain without thinking of the interests of others, or of the larger public good. Although everyone benefits in the long run from a stable social order, people may pursue their short-run interests in ways that harm or even destroy that order. This consequence of self-interest – social instability and chaos – is relatively easily managed. The problem is complicated because the governments created to protect against instability and disorder are themselves subject to self-interest. This problem is the possibility of tyranny. The people with power naturally use it to pursue their own interests, without concern for the interests of others or for the larger public good. Those with power often have a compelling interest in avoiding instability and chaos, but stability is not enough. Great care must be taken to avoid tyranny – by a majority over the minority, or by the government over the governed.

This book critically examines the following claim: Self-interest is the problem; it is also the only possible solution. The problem with what? The solution to what? This is a book about American government and politics, and both the problem and the solution are concerned with how best to conduct our politics. The title to this introduction states a paradox: The thing that causes the predicament – self-interest – also gets us out of it. To put it more precisely (and optimistically): All that is required in a well-ordered political system for the public good to be achieved is for everyone – politicians, citizens, leaders of special interest groups – to pursue their own selfish interests. The political system does not require anyone to set aside his or her interests in the name of the public good for that good to be achieved. We describe in detail the source of this claim in Chapter 2 and devote the rest of the book to some critical questions about whether the claim that self-interest is sufficient to resolve the problems it creates in politics fits with the reality of American politics today.

Setting aside Donald Trump’s typical braggadocio, when he claimed he alone could fix the mess that was America after eight years under Democratic President Barack Obama, he was following a long-standing political tradition in at least two ways: Presidential candidates from the party not currently in power emphasize what is wrong in American national life, not what is going well, and presidential candidates of both parties promise more than they can deliver. Whether it was Jimmy Carter promising independence from foreign oil, Ronald Reagan promising to balance the budget, cut taxes, and increase spending on the military, or Barack Obama promising healthcare reform that would require little inconvenience or change from those satisfied with their insurance coverage, presidential candidates assume the mantle of responsibility for the nation’s well-being well beyond their constitutional capacity to deliver.

Before beginning in earnest our exposition of Madison’s Republic in the next chapter, we spell out some key concepts and questions that help to give context to the next chapter and the rest of the book. We discuss concepts such as the meaning of democracy, the principal–agent problem, and collective action because these concepts relate directly to an understanding of how theories relate to the world of politics. We also introduce basic ideas about how political scientists approach the study of politics especially by using models that simplify some important aspect of the political world under study.

Citizen participation in politics is a good place to begin our analysis of the Republic. Madison expected self-interested participation by citizens to be the foundation of the system. Political participation can be defined as any attempt to influence what the political system does. Madison’s theory expects everyone in the Republic to be self-interested, and citizens who become involved in politics to compel political leaders to respond to their interests.

On the first Monday in October and continuing into late June or early July of the following year, the US Supreme Court sits in session. Unlike the executive and legislative branches of government, the day-to-day business of the Court is largely removed from public view. The nine justices who serve on the bench give interviews only sparingly, and television cameras are not allowed in the courtroom when hearings or deliberations are taking place. When appearing at formal public events, such as the annual State of the Union address given to Congress or the swearing in of a president, a justice is easy to spot because of his or her unusual attire – a black silk robe worn over a business suit.