Ideas – Iterations of Zero

The Irony of Entropy

If you’ve studied or read much physics, or science in general—or, more recently, information theory—you’ve probably come across the subject of entropy. Entropy is one of the most prominent and respected, if not revered, concepts in all of science. It’s often roughly characterized as a measure of the “disorder” in a system, but this doesn’t refer to disorder in the sense of “chaos”, where outcomes are so dependent upon initial states, at such high degrees of feedback and internal interaction, that there’s no way to know based on any reasonable amount of information what those specific outcomes will be. Entropy is, in a sense, just the opposite of that. A state of maximal entropy is a state where the outcome is always—or near enough that it doesn’t matter—going to be pretty much the same as it is now. A cliché way of demonstrating this is to compare a well-shuffled deck of cards to one with the cards “in order”. Each possible shuffled configuration is unique, but for practical purposes nearly all of them are indistinguishable, and there are vastly greater numbers of ways for a deck to be “out of order” than “in order”.

Let’s quickly do that math. The number of orders into which a deck of fifty-two cards can be randomly shuffled is 52 x 51 x 50 x……x 3 x 2 x 1, notated traditionally as 52! It’s a big number. How big?

80658175170943878571660636856403766975289505440883277824000000000000.

To quote Stephen Fry on Q.I., “If every star in our galaxy had a trillion planets, and each planet had a trillion people living on it, and each person had a trillion packs of cards, which they somehow managed to shuffle simultaneously at 1000 times per second, and had done this since the Big Bang, they would only just, in 2012, be starting to get repeat shuffles.” Now, how many ways are there to have a deck of cards arranged with the cards in increasing order (Ace to King) within each suit, even without worrying about the ordering between the suits? If my math is correct, there are only 4! ways to do that, which is 4 x 3 x 2 x 1, or 24. To call that a tiny fraction of the above number is a supreme understatement. This comparison should give you an idea of just how potent the tendencies are with which we’re dealing.

You could describe entropy as a state of “useless” energy. Entropy is, famously, the subject of the Second Law of Thermodynamics, and that law states that, in any closed system, entropy always tends to stay the same or increase, usually the latter. (The First Law is the one that says that in a closed system total energy is constant.)

When energy is “partitioned”—say you have one part of a room that’s hot and another part of a room that’s cold—there’s generally some way to harness that energy’s tendency to want to equilibrate, and to get work done that’s useful for creatures like us. Entropy is the measure of how much that energy has achieved a state of equilibrium, in which there’s no useful difference between one part of the room and the other.

This draws attention to the irony of entropy. The tendency of systems to become more entropic drives the various chemical and physical processes on which life depends. Energy tends to flow down gradients until there’s no energy gradient left, and its this very tendency that creates the processes that life uses to make local order. But that local order can only be accomplished by allowing, and even encouraging, the entropy of the overall world to increase, often leading to a more rapid general increase than would have happened otherwise. Think of burning gasoline to make a car go. You achieve useful movement that can accomplish many desired tasks, but in the process, you burn fuel into smaller, simpler, less organized, higher entropy states than they would have arrived at, if left alone, for a far longer time. The very processes that sustain life—that are life—can only occur by harnessing and accelerating the increase of net entropy in the world around them.

Although it seems like the principle most well-embodied in Yeats’s Second Coming, wherein he states, “Things fall apart, the centre cannot hold; / mere anarchy is loosed upon the world,” entropy is held in highest regard—or at least unsurpassed respect—by physicists. Sir Arthur Eddington famously pointed out that, if your ideas seem to contradict most understood laws of physics, or seem to go against experimental evidence, it’s not necessarily disreputable to maintain them, but if your ideas contradict the Second Law of Thermodynamics, you’re simply out of luck. And Einstein said of the laws of thermodynamics, and of entropy in particular, “It is the only physical theory of universal content, which I am convinced, that within the framework of applicability of its basic concepts will never be overthrown.”

The reason the Second Law of Thermodynamics is so indisputable is because, at root, it owes its character to basic mathematics, to probability and statistics. As I demonstrated in the playing card example, there are vastly more ways for things to be “disordered”—more arrangements of reality that are indistinguishable one from another—than there are configurations that contain gradients or differences that can give rise to patterns and “useful” information. WAAAAAAY more.

The Second Law isn’t at its heart so much a law of physics as it is a mathematical theorem, and mathematical theorems don’t change. You don’t need to retest them, because logic demands that, once proven, they remain correct. We know that, in a flat plane, the squares of the lengths of the two shorter sides of a right triangle add up to the square of the length of the longest side (You can prove this for yourself relatively easily; it’s worth your time, if you’re so inclined.) We know that the square root of two is an irrational number (one that cannot be expressed as a ratio of any two whole numbers, no matter how large). We know that there are an infinite number of prime numbers, and that the infinity of the “real” numbers is a much larger infinity than that which describes the integers. These facts have been proven mathematically, and we need no longer doubt them, for the very logic that makes doubt meaningful sustains them. It’s been a few thousand years since most of these facts were first demonstrated, and no one has needed to update those theorems (though they might put them in other forms). Once a theorem is done, it’s done. You’re free to try to disprove any of the facts above, but I would literally bet my life that you will fail.

The Second Law of Thermodynamics has a similar character, because it’s just a statement of the number of ways “things” can be ordered in indistinguishable ways compared to the number of ways they can be ordered in ways that either carry useful information or can be harnessed to be otherwise useful in supporting—or in being—lifeforms such as we. Entropy isn’t the antithesis of life, for without its tendency to increase, life could neither exist nor sustain itself. But its nature demands that, in the long run, all relative order will come to an end, in the so-called “heat death” of the universe.

Of course, entropy is probabilistic in character, so given a universe-sized collection of random elementary particles, if you wait long enough, they will come together in some way that would be a recognizable universe to us. Likewise, if you shuffle a deck of cards often enough, you will occasionally shuffle them into a state of ordered suits, and if you play your same numbers in the Powerball lottery often enough, for long enough, you will eventually win.

Want my advice? Don’t hold your breath.

Playing with space-time blocks

According to General Relativity, our experience of space and time is a bit like seeing shadows in a higher-order, four-dimensional space-time. This is probably not news to many of you; the basics of Relativity have become almost common knowledge, which is no doubt a good thing. But many people may not realize that the tenets of General Relativity and Special Relativity, with their abolition of simultaneity or any privileged point of view in space-time also imply that the entire past, and the entire future, of every point in space and every moment in time, already or still exist, permanently. I’m not going to get too much into the how’s of this—I refer you to, and heartily recommend, Brian Greene’s The Fabric of the Cosmos, which has an excellent explication of this notion.

The upshot of this principle is that, in a very real sense, our past is never gone, but is still there, just where it was when we lived it. Similarly, the future is also already in existence (applying time-specific terms to such things is a little iffy, but we use the words we have I suppose, even though we must accept them as metaphors). In this sense, a human life is not an isolated, ever-changing pattern in some greater, flowing stream so much as a pre-existing rope of pattern in a higher-dimensional block of space-time, like a vein of gold running through a fissure in a rock formation. Its beginning is as permanent as its end.

We know that General Relativity cannot be absolutely and completely correct—its mathematics breaks down at singularities such as those in the center of black holes, for instance. But within its bailiwick, it seems to be spectacularly accurate, so it’s not unreasonable to conclude that it’s accurate in the above description of a human life—indeed, of all events in the universe.

But what does this mean for us? How does it impact the fact that we experience our lives as though the sands of the future are flowing through the narrow aperture of the present to fall into the receiving chamber of the past? How does General Relativity interact with consciousness? We seem to experience the present moment only as an epiphenomenon of the way fundamental principles translate themselves into chemistry and biology as measured along some fourth-dimensional axis. We can’t decide to reel ourselves backward and reexperience the past, or fast-forward into the future, even though it seems that our existence has much in common with the permanently-encoded data on a digital video file. We cannot choose to rewind or lives any more than can the characters within a movie we are watching.

Similarly, according to this implication of General Relativity, we could not, even in principle, have lived our past differently. Were we to rewind and then replay events, they would work out exactly as they had before, just as a movie follows the same course no matter how many times you watch it. The characters in a movie might learn later in the film that they had made some tragic error, yet when you rewind the show, they revert to their previous selves, ignorant of what they are always ignorant of at that point in time, subject to the same story arc, unable to change anything that they did before. Likewise, it’s conceivable that, when our lives end—when we reach the point where our pattern decomposes, diffuses, and fades—we may go back to the start and reexperience life again from the beginning. (This depends heavily on what the nature of consciousness is). Indeed, we may be constantly reexperiencing it, infinitely many times.

Though this seems to be a kind of immortality, it’s not a particularly rewarding one, as we wouldn’t gain anything no matter how many times we replayed our lives. For those of us with regrets it would be a mixed blessing, at best. For those who have endured lives of terrible suffering, it seems almost too much to bear. But, of course, reality isn’t optional. It is what it is, and there is no complaint department.

Ah, but here’s the rub. We know, as I said, that General Relativity cannot be quite right; crucially, it does not allow for the implications of the Uncertainty Principle, that apparently inescapable fact at the bedrock of Quantum Mechanics. Quantum Mechanics is, if anything, even more strongly supported by experiment and observation than is General Relativity; I’m aware of no serious physicists who don’t think that General Relativity will have to be Quantized before it can ever be complete.

But of course, as the name implies, the Uncertainty Principle says that things are—at the fundamental level—uncertain. How this comes about is the subject of much debate, with the two main views being the “interaction is everything, the wave-function just collapses and probabilities turn into actualities and there’s no point in asking how” that is the Copenhagen Interpretation, and the Many Worlds Interpretation, originated by Hugh Everett, in which, at every instance where more than one possible outcome of a quantum interaction exists, the universe splits into appropriately weighted numbers of alternate versions, in each of which some version of the possible outcomes occurs. It’s hard to say which of these is right, of if both are wrong—though David Deutsch does a convincing job of describing how, among other things, quantum interference and superposition implies the many-worlds hypothesis (see his books The Fabric of Reality and The Beginning of Infinity).

But what does the Everettian picture imply for our higher-dimensional block space-time that is at once all of space and time, already and permanently existing? Are there separate, divergent blocks for every possible quantum divergence? Or does the space-time block just have a much higher dimensionality that merely four, instantiating not just one but every possible form of space-time at once?

If this is the case, why do we conscious beings each seem to experience only one path through space-time? Countless quantum events are happening within and around us, with every passing Planck Time (about 10^-43 seconds). The vast majority of these events wouldn’t make any noticeable difference to our experiences of our lives, but a small minority of them would.

This is the new thought that occurred to me today. It’s thoroughly and entirely speculative, and I make no claims about its veracity, but it’s interesting. What if, whenever we die, we start over again, as if running the DVD of our lives from the beginning yet again, but with this important difference: Each time it’s rerun, we follow a different course among the functionally limitless possible paths that split off at each quantum event? Even though most of these alterations would surely lead to lives indistinguishable one from another, everything that is possible in such a multiverse is, somewhere (so to speak) instantiated. Reversion to the mean being what it is, this notion would be hopeful for those who have suffered terribly in a given life, but rather worrisome for those who’ve had lives of exceptional happiness. At the very least, it implies that there would be no sense in which a person is trapped in the inevitable outcome of a given life. You can’t decide to behave differently next time around, but you can at least hope that you might (while reminding yourself that you may do even worse).

Of course, all this is beyond even science fiction—well, the earlier parts aren’t, just the notions of a person’s consciousness reexperiencing life, either the same or different, over again. But it was and is an interesting thought to have on a lazy, early Sunday afternoon in the spring of the year, and I thought I would share it with you.

We shouldn’t assume that we know other people’s motives and character based on limited data (and it’s almost always limited)

I have a long and very important letter to write today (I haven’t been this nervous about writing something since college), so I’m going to keep this relatively short, but I did want to write something, at least. It’s on a subject that troubles me quite a bit, that apparent tendency—at least on social media—for people to act as if they were telepathic or clairvoyant regarding other people’s motives and thoughts.

It happens so easily, and probably without much thought (probably without much ill-intent). We see a post or declaration, or a political or social statement, and we infer from it all sorts of things about the source’s character, intentions, and morality. It’s remarkable that we imagine we’re so good at such interpretations, since most of us very rarely have any idea what our own motivations and deeper thoughts are. It’s apparently true that often we can recognize by facial expression and body language how our friends and colleagues are feeling more clearly than they recognize it themselves, but this is broad and crude. Recognizing that someone is sad or angry before they realize it themselves doesn’t give us any reason to think we know why someone is sad or angry.

Yet if a person posts a meme supportive of the Second Amendment—or conversely, one supportive of stricter gun control—those who see this meme often seem to draw far-reaching conclusions, straw-manning the person and their supposed motivations. The sharer must be a right-wing, racist, homophobic, misogynistic, anti-government bigot, say; or alternatively, they must be a “regressive leftist,” communist, SJW, crusading vegan, who wants to emasculate all men.

How many people in the world would meet those descriptions accurately? There are probably a few—there are a lot of people in the world, after all, and the Gaussian is broad. But surely, most people don’t honestly fit into any such broad stereotypes.

Of course, maybe I’m making my own error by guessing that people perform such acts of unwarranted attribution based on limited statements and data. Maybe I’m straw-manning the people online. Certainly, there are many to whom I’m being unjust—or would be if I were thinking of them. But mostly, I’m thinking of the people who respond to trolling and counter-trolling, and the ones who take part in internet-based debates that rapidly, or immediately, degenerate into name-calling matches of which most six-year-olds would be ashamed.

I wonder how people can feel comfortable engaging in such interactions on a regular basis. Perhaps the anonymity, or pseudo-anonymity, of the online world helps people let slip their baser natures more easily. We are free from the subtle cues of body language and expression that, as I stated above, give us a sense of how our interlocutor feels. Also, the nearly-automatic echo-chamber effect of social media tends to reinforce our sense of identity as a member of a particular group, and that leads us to be more inclined to react to perceived outsiders as enemies—this is probably both defensive and a matter of “virtue-signaling,” or what would probably be better understood as tribe-signaling. We are declaring to those in our tribe that we are members in good standing, and thus should remain welcome.

A similar phenomenon might be behind why a lot of people, many of whom don’t honestly subscribe to the tenets of their stated religion, continue to go church (or mosque, or synagogue, or whatever) on a regular basis. They demonstrate not their actual beliefs, but that they are committed members of the tribe.

This is, I suppose, often relatively harmless. But it is anathema to honest discourse. And it’s only through honest discourse (as far as I can see) that we can come to an ever-improving model of the world, to come nearer to truth and understanding. We can see how tribalism and partisanship, a reflexive judgmentalism and name-calling, has poisoned much of our political system, creating deadlocks even in a government currently dominated by a single political party. Nothing gets done—or at least very little does—when those involved are just trying to demonstrate their “virtue” by assailing those on the other side. At least, it seems like that’s what they’re doing. Maybe I’m misjudging.

I don’t know what the fix for this tribalism is; it seems to be something innate in the human character. But it’s surely not the only thing, or we would never have created modern civilization. Perhaps a place to start, a small step, would be for us to try to curtail our instinct to lead or to respond with accusation and insult. If we think we know someone else’s motives, we should stop and think again before believing ourselves. If we want to bring a point of criticism to their attention, instead of reflexively spewing, “It’s gross! It’s racist!” we might start by saying, “I don’t know what your intentions are here, but when you say something like that, it comes across—to me at least—as racist. Is that what you wanted?”

I don’t know if that will work better or not, but I’d love to see the experiment tried on a large scale. In the meantime, remember, just because you infer something doesn’t mean that it was actually implied.

Tweets and memes on complex themes

Okay, well, I’m feeling under-the-weather today, so I’m not sure how good this post will be, but I wanted to maintain my recently-instituted policy of writing at least one post per week, on Sundays, so I’m going to charge forward.

I had a hard time deciding what to write about today, given the above problem; I have a list of many one-to-two-line ideas for blog posts in my cell phone (I jot the ideas down there when they occur to me, and come back to them later when deciding what to write), and I chose to stick with something simple, but which I consider important.

The topic is a pet peeve of mine about Facebook-style memes relating to political and social issues, and it involves the poor quality of reasoning one often sees in such posts. Obviously, a meme—or a tweet—is not going to be the ideal medium through which to convey detailed and careful reasoning on any deep subject, which is why I write blogs, relying on language rather than eye-catching pictures designed to trigger an emotional response (see last week’s post to read what I think of relying on emotions to decide important matters). But memes are often disappointingly lacking even for what they are.

The meme that caught my attention today consists entirely of words, with no underlying picture, but still demonstrates the problem I see in so much of modern discourse. It’s a meme I’ve seen before; it starts by detailing the consequences that might be met by a person illegally entering North Korea, Afghanistan, or Iran. Then it introduces a strawman-style, exaggerated statement about the many benefits available to illegal immigrants in the U.S., and concludes with something along the lines of, “No wonder we’re a country in so much debt,” which is almost—though not quite—a complete non-sequitur.

This meme blatantly shoots itself in the foot by comparing the United States’ immigration policy—in clearly intended unfavorable light—with that of three of the most benighted and oppressive regimes in the world today. Is this really expected to convince anyone, or to sway a reader’s thinking? I suspect that even most conservatives, toward whom this meme is likely directed, wouldn’t consider North Korea, Afghanistan, or Iran to be role models on the national or international stage. Why on Earth would anyone bring them up for such a comparison? I almost suspect that this meme was made by a troll from the Left, intended as a caricature of Right-wing arguments, but it was shared, with all apparent earnestness, by someone who is clearly conservative.

It would have been much better—more effective in getting an argument across, and possibly even thought-provoking—if the poster had compared our immigration policy to that of, say, Canada or Japan. These nations are modern and high-functioning and enact at least some policies which we might consider better solutions to specific problems than those we apply in the U.S. I’m not making the argument that their situations are the same as ours, nor do I mean to start a discussion about the benefits and detriments of their policies relative to those of the United States. I’m just saying that citing those examples would probably have been a more effective means of eliciting actual thought on the matter, even from those who might lean to the Left.

I’ve quoted a conservative post above because it’s the one I last encountered, but I find similar dubious posts—often even more egregious in their seeming manipulativeness and illogic—shared from Left-leaning sites such as “Occupy Democrats” and “The Other 98%”.

Memes—and tweets, even with their now-doubled character-length—seem to be the ultimate distillation of the lamentable phenomenon of “sound-bite as news”. I’m not broadly against Facebook, Twitter, et al. I use both social media platforms. But they are rarely venues in which to gain or to share deep arguments about complicated problems (at least, they’re rarely used that way, though they do occasionally produce high quality discussion). They could, however, easily be venues in which honest thought is at least provoked in someone who reads a tweet, or a meme, perhaps leading such a person to investigate some matter more thoroughly than they had in the past. They can also link to articles and other sources that further explore interesting issues. Unfortunately, as far as I can see, they are usually used for coarse, ham-handed virtue signaling and name-calling. I’m not sure how often a given person changes his or her mind in response to being insulted; in my experience, it almost never happens in real time, at the very least. This is likely especially true when the quality of the call-out is so logically faulty and ill-conceived as memes like the one I reference above.

Reality is messy. Most issues are complex. That’s the nature of the universe in which we find ourselves. This shouldn’t surprise us; we ourselves are ridiculously complicated Rube Goldberg machines cobbled together over the course of eons from the spare parts left lying around by prior biology. That anything works at all is probably more a testament to the brutally sharp and ruthless character of natural selection (at all levels) than it is to any clever or efficient design of the systems we have put in place. Given this, it’s going to be a rare case indeed in which a single picture with overlying words (and not very many of these) is going to capture, or meaningfully contribute to, any debate about substantive issues. Any such simple solution or argument is a low-hanging fruit that likely would have been plucked long ago, if it were available.

Such tweets and memes, in many cases, seem simply to serve as virtue signals, calling out to others of like mind with the sharer. If that’s all you want to do—to display your tattoos on the prison rec-yard so you can be welcomed into the gang most likely to protect you—then I suppose that’s fine. But if you want to try to understand, and to spread understanding of, complex scientific, social, or political issues, with an eye toward fostering improvement in society and civilization, then you’re going to have to do more work. At bare minimum, you should try to make your memes as honest and as rational as you can and to maintain that policy in choosing the memes you share.

Otherwise, you might as well just stick to sharing jokes and picture of kittens. The latter, at least, usually tend to improve the moods of those who see them…and that may just make them ever-so-slightly more considerate and less reactionary in their own posting.

It’s a place to start.

Stop respecting emotions so much

I’ve said it before in other venues, but it bears repeating: as a society, we need to stop giving so much respect and deference to emotions. I’ve gotten push-back on this idea before, but it’s really not that radical, nor that negative, a proposal.

I’m not recommending that we abandon emotions altogether (if that were even possible), or try to suppress them, a la the Vulcans in Star Trek. Emotions are a real, and significant, part of the experience of life. Everyone has them, and they are interesting and important. I don’t want to deny the validity and reality of any person’s emotional experiences, nor to dismiss the real pain and joy that emotional reactions can entail. The human experience is an emotional one, and emotional states can be useful in many ways. Joy over a success can lead one to try to repeat it in the future. Outrage over injustice can drive a person to act against it. Fear, as Gavin deBecker has eloquently pointed out, can protect us from real danger, which still exists in the world despite all our advances. Continue reading “Stop respecting emotions so much”

Flat-Earthers and “hate speech” are good for us

I don’t know how often most of you notice the occasional noises of Flat-Earthers online, and particularly on social media, but I notice. Encountering such absurdities can at times lead a reasonably educated person to feel that the world is going mad, that society is collapsing, and that—despite the cornucopia of information available to us—humans are breathtakingly stupid.

However, I’ve recently been reading John Stuart Mill’s “On Liberty,” and it gave me a new insight: The fact the we encounter such vociferous and seemingly ridiculous expressions of contra-factual ideas is a sign of the health and strength of our discourse, rather than its deterioration. Continue reading “Flat-Earthers and “hate speech” are good for us”

Treat new laws like experiments

Some years ago, when I first read Carl Sagans’s The Demon-Haunted World, I encountered a notion that stuck in my mind and has grown more prominent as the years have passed. This is the idea that laws, as made in a democracy, are a form of experiment, but that they are carried out without any of the sensible objective measures and controls that make scientific experiments so useful. I think this is clearly true, and I think we should all try to petition our legislators to approach laws in this scientific fashion.

Many—perhaps most—new laws are proposed to prevent, or correct, or create some specific situation…presumably altering something that isn’t quite the way we want it to be. Unfortunately, the way laws are proposed and assessed is through public debate—at best. As civil and criminal courtrooms demonstrate, when an important matter is addressed mainly through debate, the outcome isn’t necessarily that the best or truest idea is chosen, but that those who are most skilled at rhetoric and manipulation rule the day. This is not a much more reliable way to make good decisions than by holding a jousting match. It’s not good in court, and it’s worse in the halls of legislature, where the quality of discourse is often even lower than one often finds among courtroom lawyers (“If the glove does not fit, you must acquit,” is at least mildly clever, as opposed to the appalling spectacle of an elected legislator in the Federal Government bringing a snowball into the Capitol Building as evidence against climate change).

Wouldn’t it be wonderful if, with every proposed new bill, the proposer had to articulate what problem was to be addressed by the legislation, and what result was being sought. Then, in the subsequent discussions, legislators could better focus their inquiries, bringing existing information to bear, including the outcomes of prior, similar legislation. Also—and here is a key point—each bill could contain specific language detailing by what means its relative success of failure would be measured, how that data would be collected, at what frequency it would be evaluated, and at what point—if ever—the measure would have been found to fail. We know that most measures, if measured, would fail, based on the experience of science, in which the vast majority hypotheses end up disproven, even when proposed by the best and brightest minds in the world. How much more likely is it that ideas proposed by the likes of our legislators are going to be shown to be ineffective?

Of course, the real world—the laboratory where each new law would be tested—is a messy place, with innumerable confounding variables, correlations which have nothing to do with causation, unreliable data, and so on. So, we wouldn’t necessarily want to hold legislative outcome checks to quite the same standards of rigor as those to which we hold particle physics. But simply requiring each new bill to contain a statement of hoped-for outcomes, of measures by which it would be considered to have succeeded or failed, and a required time of review, could produce better laws, influenced from the beginning by more information and logic than rhetoric. Even if no definitive answer was available at the time of a planned review, that review might still inspire new ideas about how better to measure outcomes, and perhaps even ways to tweak a law to make its outcome more clearly beneficial. Most importantly, it would be much easier to recognize and discard the failures.

Of course, to initiate such a policy of lawmaking would require something even more sweeping than a Constitutional amendment. It would require that we elect representatives capable of bringing a scientific mindset to matters of fact. This, in turn, would require a voting population with the ability to judge among and select such individuals, rather than the charlatans and hucksters they tend to elect. This in turn would require both a change in the educational style of the country and a cultural shift in which we give greater precedence to logic and reason, rather than our usual approaches to life, which are only more sophisticated than those of chimpanzees in that they are more complicated, but which are not necessarily any more rational.*

It’s a tall order, I know. But the possible improvements in our laws, in the way public policy is carried out, and in the general health and well-being of the nation would be potentially vast.

They would also be much more measurable.

*See last week’s post on teaching probability and statistics, for instance.