Quotes About Complexity

The existence of many gods conveys true complexity of mortal life. Conversely, the assertion of but one god leads to a denial of complexity, and encourages the need to make the world simple. Not the fault of the god, but a crime committed by its believers.

On a cobbled beach, a man looks down and sees one rock, then another and another. A woman looks down and sees…rocks. But perhaps even this is simplistic. Man as singular and women as plural. More likely we are bits of both, some of one in the other. We just don't like admitting it.

We are contrary creatures, us humans, but that isn't something we need be afraid of, or even much troubled by. And if you make a list of those people who worship consistency, you'll find they're one and all tyrants or would-be tyrants. Ruling over thousands, or over a husband or a wife, or some cowering child.

quagmire of verbosity

Perhaps this. The existence of many gods conveys true complexity of mortal life. Conversely, the assertion of but one god leads to a denial of complexity, and encourages the need to make the world simple. Not the fault of the god, but a crime committed by its believers.

Always keep it simple. Complex ideas make people nervous. Complex ideas as people to think, and people don't want to think.

At what point in the history of Letheras, he wondered, did rampant greed become a virtue? The level of self-justification required was staggering in its tautological complexity, and it seemed language itself was its greatest armour against common sense.

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the entire notion of cause and effect, suddenly revealing its true level of complexity, simply overwhelmed.

From a purely mathematical perspective, a power law signifies nothing in particular—it's just one of many possible kinds of algebraic relationship. But when a physicist sees a power law, his eyes light up. For power laws hint that a system may be organizing itself. They arise at phase transitions, when a system is poised at the brink, teetering between order and chaos. They arise in fractals, when an arbitrarily small piece of a complex shape is a microcosm of the whole.

In a chaotic system, the required precision in the initial measurement grows exponentially, not linearly.

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To shed light on any continuous shape, object, motion, process, or phenomenon—no matter how wild and complicated it may appear—reimagine it as an infinite series of simpler parts, analyze those, and then add the results back together to make sense of the original whole.

determinism does not imply predictability.

In a nutshell, calculus wants to make hard problems simpler.

If real numbers are not real, why do mathematicians love them so much?

Our analysis revealed that whether the nodes in the network are neurons or computers, people or power plants, everyone is connected to everyone else by a short chain of intermediaries. In other words, the "small world" phenomenon is much more than a curiosity of human social life: It's a unifying feature of diverse networks found in nature and technology.

that raises a profound mystery: Scientists have long been baffled by the existence of spontaneous order in the universe. The laws of thermodynamics seem to dictate the opposite, that nature should inexorably degenerate toward a state of greater disorder, greater entropy. Yet all around us we see magnificent structures—galaxies, cells, ecosystems, human beings—that have somehow managed to assemble themselves.

In a nutshell, calculus wants to make hard problems simpler. It is utterly obsessed with simplicity.

Once that's done, it solves the original problem for all the tiny parts, which is usually a much easier task than solving the initial giant problem. The remaining challenge at that point is to put all the tiny answers back together again. That tends to be a much harder step, but at least it's not as difficult as the original problem was.

Cubism Meets Calculus

Calculus succeeds by breaking complicated problems down into simpler parts. That strategy, of course, is not unique to calculus. All good problem-solvers know that hard problems become easier when they're split into chunks. The truly radical and distinctive move of calculus is that it takes this divide-and-conquer strategy to its utmost extreme — all the way out to infinity.

we've come to realize that most systems of differential equations are unsolvable, in that same sense; it's impossible to find a formula for the answer. There is, however, one spectacular exception. Linear differential equations are solvable.

a big, messy linear problem can always be broken into smaller, more manageable parts. Then each part can be solved separately, and all the little answers can be recombined to solve the bigger problem. So it's literally true that in a linear problem, the whole is exactly equal to the sum of the parts.