In daily life, we often don't know the answer to a complex question. It usually involves morality, ethics, definitions, authority, politics, love, hate ... As I said, complex. Some people believe they have a big, magic calculator in the sky to help them out. Maybe they do. And maybe there are several, which explains why everyone seems to still disagree, even after consulting their calculator in the sky. Go figure.
In mathematics, there are also problems with no easily calculable solution. Instead of attempting a formal, proof-driven solution, we can use self-organizing systems. The emergent property of that system is the solution, if the system works correctly (and assuming there's a solution.) We use it on this website to organize articles and other items -- we don't know what the best place is for a node, so we let it work itself out over time. Artificial intelligence researchers often use such systems in the hope that some form of higher intelligence, some form of sentience, will be achieved semi-automatically by letting a computer 'evolve', with a little bit of outside help. They don't know how to make it happen, but they hope to have the seeds of a solution, that they simply have to help grow.
The stock market, and in fact all markets, are self-organizing systems. We don't know what the best solution is for assigning resources to projects for completing goals efficiently. We don't know how to manage our economy formally, to achieve specific results. Instead, we have a system where requirements are allowed to change constantly, where supply and demand affect each other, and the entire system seeks to adapt itself to changing conditions. Entrepreneurs will take the risk of untested markets, while others will compete for better prices. Marketing will shape demand, while demand will shape supply ... and supply pays for marketing. Communism (simplified) attempted the "N-year plan" idea, seeking to maximize output. Without competition or redundancy, less energy would be wasted, more resources committed to getting something serious, something useful done. The problem is knowing what we need and how to get it -- we don't. Thus the free-market system.
The same applies to other realms, like politics. Today's politics involve a constant back-and-forth fight between idealists on every side of an issue. At the center of the tug-of-war sits our justice system, following the tide of opinion. We don't know how to run an entire country formally -- we don't know the answer. Instead, we rely on millions of people who don't even know the names of the candidates to take us in one direction or another. As ideas are tested, we find flaws. And sometimes we fix them. Only a few rules are set in stone, but even stone can't generally stand up to a revolution.
And then there's the direction that our entire world is taking. We don't agree on who we are, and what our purpose is. We don't agree on what's right and wrong. We don't agree on a language, a culture, a religion, or even our basic desires. (No, really, some people do not wake up every morning wanting to be rich!) We disagree so strongly that we are willing to kill. We hope that somehow, fighting will eliminate opposition -- and by eliminating opposition, purify a single, coherent position. Strife, even through murder, is our social struggle to find a solution.
At different levels, we've somewhat agreed on ground rules for this strife. Polite conversation, office meetings, elections, money, the use of armies between nations. We're offended when anyone takes advantage of these systems, or circumvents them. Black-mail, abuse of power, fraud, theft, terrorism ... People can't stand it when you don't play by the rules. And then the rules change. The very rules of our strife are in play, changing, evolving as time goes forward.
I've learned one thing from building self-organizing systems like the graph of nodes on this website. Just when you think you've found the perfect solution, try stirring up the system a bit. Suddenly things move, pop, flow, and find you a new, different, and possibly better solution. Just as you reach the goal of having a good, final, emergent property, you find you're only part of the way there. So long as it's all moving, so long as there's energy, tension, will-power in the system, you're heading for a solution. We don't even have a way of proving that the solution is final! Had we such a method, we might have found the solution right away. As it is, we could have the best possible world before our very eyes, and not know it.
It's a beautiful world. Enjoy it!