But let’s take a closer look at the assumptions we’re making. Astute readers may have noticed that in one of my examples, I assumed that the entire state of the Web was a constant. How ridiculous! In mathematical parlance, assumptions are known as “priors,” and in a certain widespread school of statistical thought they are considered the most important aspect of any process involving information. What we really want to know is if, given a set of existing priors, adding one piece of information (A) would allow us to update our estimate of the likelihood of another piece of information (B). Of course, this depends on the priors—for instance, if our priors include absolute knowledge of B, then an update will not be possible.
If, for most reasonable sets of priors, information about A would allow us to update our estimate of B, then it would seem there is some sort of causal connection between the two. But the form of the causal connection is unspecified—a principle often stated as “correlation does not imply causation.” The reason for this is that the essence of causation as a concept rests on our tendency to have information about earlier events before we have information about later events. (The full implications of this concept for human consciousness, the second law of thermodynamics, and the nature of time are interesting, but sadly outside the scope of this essay.)
If information about all events always came in the order in which the events occurred, then correlation would indeed imply causation. But in the real world, not only are we limited to observing events in the past but also we may discover information about those events out of order. Thus, the correlations we observe could be reverse causes (information about A allows us to update our estimate of B, although B happened first and thus was the cause of A) or even more complex situations (e.g., information about A allows us to update our estimate of B but is also giving us information about C, which happened before either A or B and caused both).
Information flow is symmetric: If information about A were to allow us to update our estimate of B, then information about B would allow us to update our estimate of A. But since we cannot change the past or know the future, these constraints are useful to us only when contextualized temporally and arranged in order of occurrence. Information flow is always from the past to the future, but in our minds some of the arrows may be reversed. Resolving this ambiguity is essentially the problem that science was designed to solve. If you can master the technique of visualizing all information flow and keeping track of your priors, then the full power of the scientific method—and more—is yours to wield from your personal cognitive toolkit.
Thinking in Time Versus Thinking Outside of Time
Lee Smolin
Physicist, Perimeter Institute; author, The Trouble with Physics
One very old and pervasive habit of thought is to imagine that the true answer to whatever question we are wondering about lies out there in some eternal domain of “timeless truths.” The aim of research is then to “discover” the answer or solution in that already existing timeless domain. For example, physicists often speak as if the final theory of everything already exists in a vast timeless Platonic space of mathematical objects. This is thinking outside of time.
Scientists are thinking in time when we conceive of our task as the invention of genuinely novel ideas to describe newly discovered phenomena and novel mathematical structures to express them. If we think outside of time, we believe these ideas somehow “existed” before we invented them. If we think in time, we see no reason to presume that.
The contrast between thinking in time and thinking outside of time can be seen in many domains of human thought and action. We are thinking outside of time when, faced with a technological or social problem to solve, we assume the possible approaches are already determined by a set of absolute preexisting categories. We are thinking in time when we understand that progress in technology, society, and science happens by the invention of genuinely novel ideas, strategies, and novel forms of social organization.
The idea that truth is timeless and resides outside the universe was the essence of Plato’s philosophy, exemplified in the parable of the slave boy, which was meant to argue that discovery is merely remembering. This is reflected in the philosophy of mathematics called Platonism, which is the belief that there are two ways of existing: Regular physical things exist in the universe and are subject to time and change, whereas mathematical objects exist in a timeless realm. The division of the world into a time-drenched earthly realm of life, death, change, and decay, surrounded by a heavenly sphere of perfect eternal truth, framed both ancient science and Christian religion.
If we imagine that the task of physics is the discovery of a timeless mathematical object that is isomorphic to the history of the world, then we imagine that the truth to the universe lies outside the universe. This is such a familiar habit of thought that we fail to see its absurdity: If the universe is all that exists, then how can something exist outside of it for it to be isomorphic to?
On the other hand, if we take the reality of time as evident, then there can be no mathematical object that is perfectly isomorphic to the world, because one property of the real world that is not shared by any mathematical object is that it is always some moment. Indeed, as Charles Sanders Peirce first observed, the hypothesis that the laws of physics evolved through the history of the world is necessary if we are to have a rational understanding of why one particular set of laws holds, rather than another.
Thinking outside of time often implies the existence of an imagined realm, outside the universe, where the truth lies. This is a religious idea, because it means that explanations and justifications ultimately refer to something outside the world we experience ourselves to be a part of. If we insist that there is nothing outside the universe, not even abstract ideas or mathematical objects, we are forced to find the causes of phenomena entirely within our universe. So thinking in time is also thinking within the one universe of phenomena our observations show us to inhabit.
Among contemporary cosmologists and physicists, proponents of eternal inflation and timeless quantum cosmology are thinking outside of time. Proponents of evolutionary and cyclic cosmological scenarios are thinking in time. If you think in time, you worry about time ending at space-time singularities. If you think outside of time, this is an ignorable problem, because you believe reality is the whole history of the world at once.
Darwinian evolutionary biology is the prototype for thinking in time, because at its heart is the realization that natural processes developing in time can lead to the creation of genuinely novel structures. Even novel laws can emerge when the structures to which they apply come to exist. Evolutionary dynamics has no need of abstract and vast spaces like all the possible viable animals, DNA sequences, sets of proteins, or biological laws. Exaptations are too unpredictable and too dependent on the whole suite of living creatures to be analyzed and coded into properties of DNA sequences. Better, as the theoretical biologist Stuart Kauffman proposes, to think of evolutionary dynamics as the exploration, in time, by the biosphere, of the adjacent possible.
The same goes for the evolution of technologies, economies, and societies. The poverty of the conception that economic markets tend to unique equilibria, independent of their histories, shows the danger of thinking outside of time. Meanwhile the path dependence that economist Brian Arthur and others show is necessary to understand real markets illustrates the kind of insights that are gotten by thinking in time.
Thinking in time is not relativism; it is a form of relationalism. Truth can be both time-bound and objective, when it is about objects that only exist once they are invented, by evolution or human thought.
When we think in time, we recognize the human ability to invent genuinely novel constructions and solutions to problems. When we think about the organizations and societies we live and work in outside of time, we unquestioningly accept their strictures and seek to manipulate the levers of bureaucracy as if they had an abso
lute reason to be there. When we think about organizations in time, we recognize that every feature of them is a result of their history and everything about them is negotiable and subject to improvement by the invention of novel ways of doing things.
Negative Capability Is a Profound Therapy
Richard Foreman
Playwright and director; founder, Ontological-Hysteric Theater
Mistakes, errors, false starts—accept them all. The basis of creativity.
My reference point (as a playwright, not a scientist) was Keats’s notion of negative capability (from his letters). Being able to exist with lucidity and calm amid uncertainty, mystery, and doubt, without “irritable [and always premature] reaching after fact and reason.”
This toolkit notion of negative capability is a profound therapy for all manner of ills—intellectual, psychological, spiritual, and political. I reflect it (amplify it) with Emerson’s notion that “Art [any intellectual activity?] is [best thought of as but] the path of the creator to his work.”
Bumpy, twisting roads. (New York City is about to repave my cobblestoned street with smooth asphalt. Evil bureaucrats and tunnel-visioned “scientists”—fast cars and more tacky upscale stores in SoHo.)
Wow! I’ll bet my contribution is shorter than anyone else’s. Is this my inadequacy or an important toolkit item heretofore overlooked?
Depth
Tor Nørretranders
Science writer; consultant; lecturer; author, The Generous Man: How Helping Others Is the Sexiest Thing You Can Do
Depth is what you do not see immediately at the surface of things. Depth is what is below that surface: water below the surface of a lake, the rich life of soil, the spectacular line of reasoning behind a simple statement.
Depth is a straightforward aspect of the physical world. Gravity stacks stuff, and not everything can be at the top. Below there is more, and you can dig for it.
Depth acquired a particular meaning with the rise of complexity science a quarter of a century ago: What is characteristic of something complex? Orderly things, such as crystals, are not complex; they are simple. Messy things, such as a pile of litter, are difficult to describe; they hold a lot of information. Information is a measure of how difficult something is to describe. Disorder has a high information content and order has a low one. All the interesting stuff in life is in between: living creatures, thoughts, and conversations. Not a lot of information, but not a little, either. So information content does not lead us to what is interesting or complex. The marker is, rather, the information that is not there but was somehow involved in creating the object of interest. The history of the object is more relevant than the object itself, if we want to pinpoint what is interesting to us.
It is not the informational surface of the thing but its informational depth that attracts our curiosity. It took a lot to bring it here, before our eyes. It is not what is there but what used to be there that matters. Depth is about that.
The concept of depth in complexity science has been expressed in different ways: You can talk about the amount of physical information involved in bringing about something (the thermodynamic depth) or the amount of computation it took to arrive at a result (the logical depth). Both express the notion that the process behind is more important than the eventual product.
This idea can also be applied to human communication.
When you say “I do” at a wedding, it (one hopes) represents a huge amount of conversation, coexistence, and fun you’ve had with that other person. And a lot of reflection upon it. There is not a lot of information in the “I do” (one bit, actually), but the statement has depth.
Most conversational statements have some kind of depth. There is more than meets the ear, something that happened between the ears of the person talking before the statement was made. When you understand the statement, the meaning of what is being said, you “dig it,” you get the depth, what is below and behind. What is not said but meant—the exformation content, information processed and thrown away before the actual production of explicit information.
2 + 2 = 4. This is a simple computation. The result, 4, holds less information than the problem, 2 + 2 (essentially because the problem could also have been 3 + 1 and yet the result would still be 4). Computation is wonderful as a method for throwing away information, getting rid of it. You do computations to ignore all the details, to get an overview, an abstraction, a result.
What you want is a way to distinguish between a very deep “I do” and a very shallow one: Did the guy actually think about what he said? Was the result “4” actually the result of a meaningful calculation? Is there, in fact, water below that surface? Does it have depth?
Most human interaction is about that question: Is this a bluff or for real? Is there sincere depth in the affection? Does the result stem from intense analysis or is it just an estimate? Is there anything between the lines?
Signaling is all about this question: fake or depth? In biology, the past few decades have seen the rise of studies on how animals prove to one another that there is depth behind a signal. The handicap principle of sexual selection is about a way to prove that your signal has depth: If a peacock has long, spectacular feathers, it proves that it can survive its predators despite its fancy plumage, which represents a disadvantage, a handicap. Hence, the peahen can know that the individual displaying the huge tail is a strong one or else it could not have survived with that extreme tail.
Among humans, you have what economists call costly signals, ways to show that you have something of value. The phenomenon of conspicuous consumption was observed by sociologist Thorstein Veblen in 1899: If you want to prove you have a lot of money, you have to waste it—that is, use it in a way that is absurd and idiotic, because only the rich can do so. But do it conspicuously, so that other people will know. Waste is a costly signal of the depth of a pile of money. Handicaps, costly signals, intense eye contact, and rhetorical gestures are all about proving that what seems so simple really has a lot of depth.
That is also the point with abstractions: We want them to be shorthand for a lot of information that was digested in the process leading to the use of the abstraction but not present when we use it. Such abstractions have depth. We love them. Other abstractions have no depth. They are shallow, just used to impress the other guy. They do not help us. We hate them.
Intellectual life is very much about the ability to distinguish between the shallow and the deep abstractions. You need to know if there is any depth before you make that headlong dive.
Temperament Dimensions
Helen Fisher
Research professor, Department of Anthropology, Rutgers University; author, Why Him? Why Her?: How to Find and Keep Lasting Love
“I am large, I contain multitudes,” wrote Walt Whitman. I have never met two people who were alike. I am an identical twin, and even we are not alike. Every individual has a distinct personality, a different cluster of thoughts and feelings that color all their actions. But there are patterns to personality: People express different styles of thinking and behaving—what psychologists call “temperament dimensions.” I offer this concept of temperament dimensions as a useful new member of our cognitive toolkit.
Personality is composed of two fundamentally different types of traits, those of “character” and those of “temperament.” Your character traits stem from your experiences. Your childhood games, your family’s interests and values, how people in your community express love and hate, what relatives and friends regard as courteous or perilous, how those around you worship, what they sing, when they laugh, how they make a living and relax: Innumerable cultural forces build your unique set of character traits. The balance of your personality is your temperament, all the biologically based tendencies that contribute to your consistent patterns of feeling, thinking, and behaving. As the Spanish philosopher José Ortega y Gasset put it, “I am I, plus my circumstances.�
� Temperament is the “I am I,” the foundation of who you are.
Some 40 percent to 60 percent of the observed variance in personality is due to traits of temperament. They are heritable, relatively stable across the life course, and linked to specific gene pathways and/or hormone or neurotransmitter systems. Moreover, our temperament traits congregate in constellations, each aggregation associated with one of four broad, interrelated yet distinct brain systems: those associated with dopamine, serotonin, testosterone, and estrogen/oxytocin. Each constellation of temperament traits constitutes a distinct temperament dimension.
For example, specific alleles in the dopamine system have been linked with exploratory behavior, thrill, experience- and adventure-seeking, susceptibility to boredom, and lack of inhibition. Enthusiasm has been coupled with variations in the dopamine system, as have lack of introspection, increased energy and motivation, physical and intellectual exploration, cognitive flexibility, curiosity, idea generation, and verbal and nonlinguistic creativity.
The suite of traits associated with the serotonin system includes sociability, lower levels of anxiety, higher scores on scales of extroversion, and lower scores on a scale of “No Close Friends,” as well as positive mood, religiosity, conformity, orderliness, conscientiousness, concrete thinking, self-control, sustained attention, low novelty-seeking, and figural and numeric creativity.
Heightened attention to detail, intensified focus, and narrow interests are some of the traits linked with prenatal testosterone expression. But testosterone activity is also associated with emotional containment, emotional flooding (particularly rage), social dominance and aggressiveness, less social sensitivity, and heightened spatial and mathematical acuity.
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