, Heaven in a Chip

Any challenge to the normal probability bell curve can have far-reaching consequences because a great deal of modern science and engineering rests on this special bell curve. Most of the standard hypothesis tests in statistics rely on the normal bell curve either directly or indirectly. These tests permeate the social and medical sciences and underlie the poll results in the media. Related tests and assumptions underlie the decision algorithms in radar and cell phones that decide whether the incoming energy blip is a 0 or a 1. Management gurus exhort manufacturers to follow the "six sigma" creed of reducing the variance in products to only two or three defective products per million in accord with "sigmas" or standard deviations from the mean of a normal bell curve. Models for trading stock and bond derivatives assume an underlying normal bell-curve structure. Even quantum and signal-processing uncertainty principles or inequalities involve the normal bell curve as the equality condition for minimum uncertainty. Deviating even slightly from the normal bell curve can sometimes produce qualitatively different results.

The proposed dangerous idea stems from two facts about the normal bell curve.

First: The normal bell curve is not the only bell curve. There are at least as many different bell curves as there are real numbers. This simple mathematical fact poses at once a grammatical challenge to the title of Charles Murray's IQ book The Bell Curve. Murray should have used the indefinite article "A" instead of the definite article "The." This is but one of many examples that suggest that most scientists simply equate the entire infinite set of probability bell curves with the normal bell curve of textbooks. Nature need not share the same practice. Human and non-human behavior can be far more diverse than the classical normal bell curve allows.

Second: The normal bell curve is a skinny bell curve. It puts most of its probability mass in the main lobe or bell while the tails quickly taper off exponentially. So "tail events" appear rare simply as an artifact of this bell curve's mathematical structure. This limitation may be fine for approximate descriptions of "normal" behavior near the center of the distribution. But it largely rules out or marginalizes the wide range of phenomena that take place in the tails.

Again most bell curves have thick tails. Rare events are not so rare if the bell curve has thicker tails than the normal bell curve has. Telephone interrupts are more frequent. Lightning flashes are more frequent and more energetic. Stock market fluctuations or crashes are more frequent. How much more frequent they are depends on how thick the tail is — and that is always an empirical question of fact. Neither logic nor assume-the-normal-curve habit can answer the question. Instead scientists need to carry their evidentiary burden a step further and apply one of the many available statistical tests to determine and distinguish the bell-curve thickness.

One response to this call for tail-thickness sensitivity is that logic alone can decide the matter because of the so-called central limit theorem of classical probability theory. This important "central" result states that some suitably normalized sums of random terms will converge to a standard normal random variable and thus have a normal bell curve in the limit. So Gauss and a lot of other long-dead mathematicians got it right after all and thus we can continue to assume normal bell curves with impunity.

That argument fails in general for two reasons.

The first reason it fails is that the classical central limit theorem result rests on a critical assumption that need not hold and that often does not hold in practice. The theorem assumes that the random dispersion about the mean is so comparatively slight that a particular measure of this dispersion — the variance or the standard deviation — is finite or does not blow up to infinity in a mathematical sense. Most bell curves have infinite or undefined variance even though they have a finite dispersion about their center point. The error is not in the bell curves but in the two-hundred-year-old assumption that variance equals dispersion. It does not in general. Variance is a convenient but artificial and non-robust measure of dispersion. It tends to overweight "outliers" in the tail regions because the variance squares the underlying errors between the values and the mean. Such squared errors simplify the math but produce the infinite effects. These effects do not appear in the classical central limit theorem because the theorem assumes them away.

The second reason the argument fails is that the central limit theorem itself is just a special case of a more general result called the generalized central limit theorem. The generalized central limit theorem yields convergence to thick-tailed bell curves in the general case. Indeed it yields convergence to the thin-tailed normal bell curve only in the special case of finite variances. These general cases define the infinite set of the so-called stable probability distributions and their symmetric versions are bell curves. There are still other types of thick-tailed bell curves (such as the Laplace bell curves used in image processing and elsewhere) but the stable bell curves are the best known and have several nice mathematical properties. The figure below shows the normal or Gaussian bell curve superimposed over three thicker-tailed stable bell curves. The catch in working with stable bell curves is that their mathematics can be nearly intractable. So far we have closed-form solutions for only two stable bell curves (the normal or Gaussian and the very-thick-tailed Cauchy curve) and so we have to use transform and computer techniques to generate the rest. Still the exponential growth in computing power has long since made stable or thick-tailed analysis practical for many problems of science and engineering.

This last point shows how competing bell curves offer a new context for judging whether a given set of data reasonably obey a normal bell curve. One of the most popular eye-ball tests for normality is the PP or probability plot of the data. The data should almost perfectly fit a straight line if the data come from a normal probability distribution. But this seldom happens in practice. Instead real data snake all around the ideal straight line in a PP diagram. So it is easy for the user to shrug and a call any data deviation from the ideal line good enough in the absence of a direct bell-curve competitor. A fairer test is to compare the normal PP plot with the best-fitting thick-tailed or stable PP plot. The data may well line up better in a thick-tailed PP diagram than it does in the usual normal PP diagram. This test evidence would reject the normal bell-curve hypothesis in favor of the thicker-tailed alternative. Ignoring these thick-tailed alternatives favors accepting the less-accurate normal bell curve and thus leads to underestimating the occurrence of tail events.

Stable or thick-tailed probability curves continue to turn up as more scientists and engineers search for them. They tend to accurately model impulsive phenomena such as noise in telephone lines or in the atmosphere or in fluctuating economic assets. Skewed versions appear to best fit the data for the Ethernet traffic in bit packets. Here again the search is ultimately an empirical one for the best-fitting tail thickness. Similar searches will only increase as the math and software of thick-tailed bell curves work their way into textbooks on elementary probability and statistics. Much of it is already freely available on the Internet.

Thicker-tail bell curves also imply that there is not just a single form of pure white noise. Here too there are at least as many forms of white noise (or any colored noise) as there are real numbers. Whiteness just means that the noise spikes or hisses and pops are independent in time or that they do not correlate with one another. The noise spikes themselves can come from any probability distribution and in particular they can come from any stable or thick-tailed bell curve. The figure below shows the normal or Gaussian bell curve and three kindred thicker-tailed bell curves and samples of their corresponding white noise. The normal curve has the upper-bound alpha parameter of 2 while the thicker-tailed curves have lower values — tail thickness increases as the alpha parameter falls. The white noise from the thicker-tailed bell curves becomes much more impulsive as their bell narrows and their tails thicken because then more extreme events or noise spikes occur with greater frequency.

Competing bell curves: The figure on the left shows four superimposed symmetric alpha-stable bell curves with different tail thicknesses while the plots on the right show samples of their corresponding forms of white noise. The parameter describes the thickness of a stable bell curve and ranges from 0 to 2. Tails grow thicker as grows smaller. The white noise grows more impulsive as the tails grow thicker. The Gaussian or normal bell curve has the thinnest tail of the four stable curves while the Cauchy bell curve has the thickest tails and thus the most impulsive noise. Note the different magnitude scales on the vertical axes. All the bell curves have finite dispersion while only the Gaussian or normal bell curve has a finite variance or finite standard deviation.

My colleagues and I have recently shown that most mathematical models of spiking neurons in the retina can not only benefit from small amounts of added noise by increasing their Shannon bit count but they still continue to benefit from added thick-tailed or "infinite-variance" noise. The same result holds experimentally for a carbon nanotube transistor that detects signals in the presence of added electrical noise.

Thick-tailed bell curves further call into question what counts as a statistical "outlier" or bad data: Is a tail datum error or pattern? The line between extreme and non-extreme data is not just fuzzy but depends crucially on the underlying tail thickness.

The usual rule of thumb is that the data is suspect if it lies outside three or even two standard deviations from the mean. Such rules of thumb reflect both the tacit assumption that dispersion equals variance and the classical central-limit effect that large data sets are not just approximately bell curves but approximately thin-tailed normal bell curves. An empirical test of the tails may well justify the latter thin-tailed assumption in many cases. But the mere assertion of the normal bell curve does not. So "rare" events may not be so rare after all.

MATT RIDLEY
Science Writer; Founding chairman of the International Centre for Life; Author, The Agile Gene: How Nature Turns on Nature

Government is the problem not the solution

In all times and in all places there has been too much government. We now know what prosperity is: it is the gradual extension of the division of labour through the free exchange of goods and ideas, and the consequent introduction of efficiencies by the invention of new technologies. This is the process that has given us health, wealth and wisdom on a scale unimagined by our ancestors. It not only raises material standards of living, it also fuels social integration, fairness and charity. It has never failed yet. No society has grown poorer or more unequal through trade, exchange and invention. Think of pre-Ming as opposed to Ming China, seventeenth century Holland as opposed to imperial Spain, eighteenth century England as opposed to Louis XIV's France, twentieth century America as opposed to Stalin's Russia, or post-war Japan, Hong Kong and Korea as opposed to Ghana, Cuba and Argentina. Think of the Phoenicians as opposed to the Egyptians, Athens as opposed to Sparta, the Hanseatic League as opposed to the Roman Empire. In every case, weak or decentralised government, but strong free trade led to surges in prosperity for all, whereas strong, central government led to parasitic, tax-fed officialdom, a stifling of innovation, relative economic decline and usually war.

Take Rome. It prospered because it was a free trade zone. But it repeatedly invested the proceeds of that prosperity in too much government and so wasted it in luxury, war, gladiators and public monuments. The Roman empire's list of innovations is derisory, even compared with that of the 'dark ages' that followed.

In every age and at every time there have been people who say we need more regulation, more government. Sometimes, they say we need it to protect exchange from corruption, to set the standards and police the rules, in which case they have a point, though often they exaggerate it. Self-policing standards and rules were developed by free-trading merchants in medieval Europe long before they were taken over and codified as laws (and often corrupted) by monarchs and governments.

Sometimes, they say we need it to protect the weak, the victims of technological change or trade flows. But throughout history such intervention, though well meant, has usually proved misguided — because its progenitors refuse to believe in (or find out about) David Ricardo's Law of Comparative Advantage: even if China is better at making everything than France, there will still be a million things it pays China to buy from France rather than make itself. Why? Because rather than invent, say, luxury goods or insurance services itself, China will find it pays to make more T shirts and use the proceeds to import luxury goods and insurance.

Government is a very dangerous toy. It is used to fight wars, impose ideologies and enrich rulers. True, nowadays, our leaders do not enrich themselves (at least not on the scale of the Sun King), but they enrich their clients: they preside over vast and insatiable parasitic bureaucracies that grow by Parkinson's Law and live off true wealth creators such as traders and inventors.

Sure, it is possible to have too little government. Only, that has not been the world's problem for millennia. After the century of Mao, Hitler and Stalin, can anybody really say that the risk of too little government is greater than the risk of too much? The dangerous idea we all need to learn is that the more we limit the growth of government, the better off we will all be.

DAVID PIZARRO
Psychologist, Cornell University

Hodgepodge Morality

What some individuals consider a sacrosanct ability to perceive moral truths may instead be a hodgepodge of simpler psychological mechanisms, some of which have evolved for other purposes.

It is increasingly apparent that our moral sense comprises a fairly loose collection of intuitions, rules of thumb, and emotional responses that may have emerged to serve a variety of functions, some of which originally had nothing at all to do with ethics. These mechanisms, when tossed in with our general ability to reason, seem to be how humans come to answer the question of good and evil, right and wrong. Intuitions about action, intentionality, and control, for instance, figure heavily into our perception of what constitutes an immoral act. The emotional reactions of empathy and disgust likewise figure into our judgments of who deserves moral protection and who doesn't. But the ability to perceive intentions probably didn't evolve as a way to determine who deserves moral blame. And the emotion of disgust most likely evolved to keep us safe from rotten meat and feces, not to provide information about who deserves moral protection.

Discarding the belief that our moral sense provides a royal road to moral truth is an uncomfortable notion. Most people, after all, are moral realists. They believe acts are objectively right or wrong, like math problems. The dangerous idea is that our intuitions may be poor guides to moral truth, and can easily lead us astray in our everyday moral decisions.

RANDOPLH M. NESSE
Psychiatrist, University of Michigan; Coauthor (with George Williams), Why We Get Sick: The New Science of Darwinian Medicine

Unspeakable Ideas

The idea of promoting dangerous ideas seems dangerous to me. I spend considerable effort to prevent my ideas from becoming dangerous, except, that is, to entrenched false beliefs and to myself. For instance, my idea that bad feelings are useful for our genes upends much conventional wisdom about depression and anxiety. I find, however, that I must firmly restrain journalists who are eager to share the sensational but incorrect conclusion that depression should not be treated. Similarly, many people draw dangerous inferences from my work on Darwinian medicine. For example, just because fever is useful does not mean that it should not be treated. I now emphasize that evolutionary theory does not tell you what to do in the clinic, it just tells you what studies need to be done.

I also feel obligated to prevent my ideas from becoming dangerous on a larger scale. For instance, many people who hear about Darwinian medicine assume incorrectly that it implies support for eugenics. I encourage them to read history as well as my writings. The record shows how quickly natural selection was perverted into Social Darwinism, an ideology that seemed to justify letting poor people starve. Related ideas keep emerging. We scientists have a responsibility to challenge dangerous social policies incorrectly derived from evolutionary theory. Racial superiority is yet another dangerous idea that hurts real people. More examples come to mind all too easily and some quickly get complicated. For instance, the idea that men are inherently different from women has been used to justify discrimination, but the idea that men and women have identical abilities and preferences may also cause great harm.

While I don't want to promote ideas dangerous to others, I am fascinated by ideas that are dangerous to anyone who expresses them. These are "unspeakable ideas." By unspeakable ideas I don't mean those whose expression is forbidden in a certain group. Instead, I propose that there is class of ideas whose expression is inherently dangerous everywhere and always because of the nature of human social groups. Such unspeakable ideas are anti-memes. Memes, both true and false, spread fast because they are interesting and give social credit to those who spread them. Unspeakable ideas, even true important ones, don't spread at all, because expressing them is dangerous to those who speak them.

So why, you may ask, is a sensible scientist even bringing the idea up? Isn't the idea of unspeakable ideas a dangerous idea? I expect I will find out. My hope is that a thoughtful exploration of unspeakable ideas should not hurt people in general, perhaps won't hurt me much, and might unearth some long-neglected truths.

Generalizations cannot substitute for examples, even if providing examples is risky. So, please gather your own data. Here is an experiment. The next time you are having a drink with an enthusiastic fan for your hometown team, say "Well, I think our team just isn't very good and didn't deserve to win." Or, moving to more risky territory, when your business group is trying to deal with a savvy competitor, say, "It seems to me that their product is superior because they are smarter than we are." Finally, and I cannot recommend this but it offers dramatic data, you could respond to your spouse's difficulties at work by saying, "If they are complaining about you not doing enough, it is probably because you just aren't doing your fair share." Most people do not need to conduct such social experiments to know what happens when such unspeakable ideas are spoken.

Many broader truths are equally unspeakable. Consider, for instance, all the articles written about leadership. Most are infused with admiration and respect for a leader's greatness. Much rarer are articles about the tendency for leadership positions to be attained by power-hungry men who use their influence to further advance their self-interest. Then there are all the writings about sex and marriage. Most of them suggest that there is some solution that allows full satisfaction for both partners while maintaining secure relationships. Questioning such notions is dangerous, unless you are a comic, in which case skepticism can be very, very funny.

As a final example, consider the unspeakable idea of unbridled self-interest. Someone who says, "I will only do what benefits me," has committed social suicide. Tendencies to say such things have been selected against, while those who advocate goodness, honesty and service to others get wide recognition. This creates an illusion of a moral society that then, thanks to the combined forces of natural and social selection, becomes a reality that makes social life vastly more agreeable.

There are many more examples, but I must stop here. To say more would either get me in trouble or falsify my argument. Will I ever publish my "Unspeakable Essays?"  It would be risky, wouldn't it?

GREGORY BENFORD
Physicist, UC Irvine; Author, Deep Time

Think outside the Kyoto box

Few economists expect the Kyoto Accords to attain their goals. With compliance coming only slowly and with three big holdouts — the US, China and India — it seems unlikely to make much difference in overall carbon dioxide increases. Yet all the political pressure is on lessening our fossil fuel burning, in the face of fast-rising demand.

This pits the industrial powers against the legitimate economic aspirations of the developing world — a recipe for conflict.

Those who embrace the reality of global climate change mostly insist that there is only one way out of the greenhouse effect — burn less fossil fuel, or else. Never mind the economic consequences. But the planet itself modulates its atmosphere through several tricks, and we have little considered using most of them. The overall global problem is simple: we capture more heat from the sun than we radiate away. Mostly this is a good thing, else the mean planetary temperature would hover around freezing. But recent human alterations of the atmosphere have resulted in too much of a good thing.

Two methods are getting little attention: sequestering carbon from the air and reflecting sunlight.

Hide the Carbon

There are several schemes to capture carbon dioxide from the air: promote tree growth; trap carbon dioxide from power plants in exhausted gas domes; or let carbon-rich organic waste fall into the deep oceans. Increasing forestation is a good, though rather limited, step. Capturing carbon dioxide from power plants costs about 30% of the plant output, so it's an economic nonstarter.

That leaves the third way. Imagine you are standing in a ripe Kansas cornfield, staring up into a blue summer sky. A transparent acre-area square around you extends upwards in an air-filled tunnel, soaring all the way to space. That long tunnel holds carbon in the form of invisible gas, carbon dioxide — widely implicated in global climate change. But how much?

Very little, compared with how much we worry about it. The corn standing as high as an elephant's eye all around you holds four hundred times as much carbon as there is in man-made carbon dioxide — our villain — in the entire column reaching to the top of the atmosphere. (We have added a few hundred parts per million to our air by burning.) Inevitably, we must understand and control the atmosphere, as part of a grand imperative of directing the entire global ecology. Yearly, we manage through agriculture far more carbon than is causing our greenhouse dilemma.

Take advantage of that. The leftover corn cobs and stalks from our fields can be gathered up, floated down the Mississippi, and dropped into the ocean, sequestering it. Below about a kilometer depth, beneath a layer called the thermocline, nothing gets mixed back into the air for a thousand years or more. It's not a forever solution, but it would buy us and our descendents time to find such answers. And it is inexpensive; cost matters.

The US has large crop residues. It has also ignored the Kyoto Accord, saying it would cost too much. It would, if we relied purely on traditional methods, policing energy use and carbon dioxide emissions. Clinton-era estimates of such costs were around $100 billion a year — a politically unacceptable sum, which led Congress to reject the very notion by a unanimous vote.

But if the US simply used its farm waste to "hide" carbon dioxide from our air, complying with Kyoto's standard would cost about $10 billion a year, with no change whatsoever in energy use.
The whole planet could do the same. Sequestering crop leftovers could offset about a third of the carbon we put into our air.

The carbon dioxide we add to our air will end up in the oceans, anyway, from natural absorption, but not nearly quickly enough to help us.

Reflect Away Sunlight

Hiding carbon from air is only one example of ways the planet has maintained its perhaps precarious equilibrium throughout billions of years. Another is our world's ability to edit sunlight, by changing cloud cover.

As the oceans warm, water evaporates, forming clouds. These reflect sunlight, reducing the heat below — but just how much depends on cloud thickness, water droplet size, particulate density — a forest of detail.

If our climate starts to vary too much, we could consider deliberately adjusting cloud cover in selected areas, to offset unwanted heating. It is not actually hard to make clouds; volcanoes and fossil fuel burning do it all the time by adding microscopic particles to the air. Cloud cover is a natural mechanism we can augment, and another area where possibility of major change in environmental thinking beckons.

A 1997 US Department of Energy study for Los Angeles showed that planting trees and making blacktop and rooftops lighter colored could significantly cool the city in summer. With minimal costs that get repaid within five years we can reduce summer midday temperatures by several degrees. This would cut air conditioning costs for the residents, simultaneously lowering energy consumption, and lessening the urban heat island effect. Incoming rain clouds would not rise as much above the heat blossom of the city, and so would rain on it less. Instead, clouds would continue inland to drop rain on the rest of Southern California, promoting plant growth. These methods are now under way in Los Angeles, a first experiment.

We can combine this with a cloud-forming strategy. Producing clouds over the tropical oceans is the most effective way to cool the planet on a global scale, since the dark oceans absorb the bulk of the sun's heat. This we should explore now, in case sudden climate changes force us to act quickly.
Yet some environmentalists find all such steps suspect. They smack of engineering, rather than self-discipline. True enough — and that's what makes such thinking dangerous, for some.

Yet if Kyoto fails to gather momentum, as seems probable to many, what else can we do? Turn ourselves into ineffectual Mommy-cop states, with endless finger-pointing politics, trying to equally regulate both the rich in their SUVs and Chinese peasants who burn coal for warmth? Our present conventional wisdom might be termed The Puritan Solution — Abstain, sinners! — and is making slow, small progress. The Kyoto Accord calls for the industrial nations to reduce their carbon dioxide emissions to 7% below the 1990 level, and globally we are farther from this goal every year.

These steps are early measures to help us assume our eventual 21st Century role, as true stewards of the Earth, working alongside Nature. Recently Billy Graham declared that since the Bible made us stewards of the Earth, we have a holy duty to avert climate change. True stewards use the Garden's own methods.

MARCO IAC0BONI
Neuroscientist; Director, Transcranial Magnetic Stimulation Lab, UCLA

Media Violence Induces Imitative Violence: The Problem With Super Mirrors

Media violence induces imitative violence. If true, this idea is dangerous for at least two main reasons. First, because its implications are highly relevant to the issue of freedom of speech. Second, because it suggests that our rational autonomy is much more limited than we like to think. This idea is especially dangerous now, because we have discovered a plausible neural mechanism that can explain why observing violence induces imitative violence. Moreover, the properties of this neural mechanism — the human mirror neuron system — suggest that imitative violence may not always be a consciously mediated process. The argument for protecting even harmful speech (intended in a broad sense, including movies and videogames) has typically been that the effects of speech are always under the mental intermediation of the listener/viewer. If there is a plausible neurobiological mechanism that suggests that such intermediate step can be by-passed, this argument is no longer valid.

For more than 50 years behavioral data have suggested that media violence induces violent behavior in the observers. Meta-data show that the effect size of media violence is much larger than the effect size of calcium intake on bone mass, or of asbestos exposure to cancer. Still, the behavioral data have been criticized. How is that possible? Two main types of data have been invoked. Controlled laboratory experiments and correlational studies assessing types of media consumed and violent behavior. The lab data have been criticized on the account of not having enough ecological validity, whereas the correlational data have been criticized on the account that they have no explanatory power. Here, as a neuroscientist who is studying the human mirror neuron system and its relations to imitation, I want to focus on a recent neuroscience discovery that may explain why the strong imitative tendencies that humans have may lead them to imitative violence when exposed to media violence.

Mirror neurons are cells located in the premotor cortex, the part of the brain relevant to the planning, selection and execution of actions. In the ventral sector of the premotor cortex there are cells that fire in relation to specific goal-related motor acts, such as grasping, holding, tearing, and bringing to the mouth. Surprisingly, a subset of these cells — what we call mirror neurons — also fire when we observe somebody else performing the same action. The behavior of these cells seems to suggest that the observer is looking at her/his own actions reflected by a mirror, while watching somebody else's actions. My group has also shown in several studies that human mirror neuron areas are critical to imitation. There is also evidence that the activation of this neural system is fairly automatic, thus suggesting that it may by-pass conscious mediation. Moreover, mirror neurons also code the intention associated with observed actions, even though there is not a one-to-one mapping between actions and intentions (I can grasp a cup because I want to drink or because I want to put it in the dishwasher). This suggests that this system can indeed code sequences of action (i.e., what happens after I grasp the cup), even though only one action in the sequence has been observed.

Some years ago, when we still were a very small group of neuroscientists studying mirror neurons and we were just starting investigating the role of mirror neurons in intention understanding, we discussed the possibility of super mirror neurons. After all, if you have such a powerful neural system in your brain, you also want to have some control or modulatory neural mechanisms. We have now preliminary evidence suggesting that some prefrontal areas have super mirrors. I think super mirrors come in at least two flavors. One is inhibition of overt mirroring, and the other one — the one that might explain why we imitate violent behavior, which require a fairly complex sequence of motor acts — is mirroring of sequences of motor actions. Super mirror mechanisms may provide a fairly detailed explanation of imitative violence after being exposed to media violence.

BARRY C. SMITH
Philosopher, Birbeck, University of London; Coeditor, Knowing Our Own Minds

What We Know May Not Change Us

Human beings, like everything else, are part of the natural world. The natural world is all there is. But to say that everything that exists is just part of the one world of nature is not the same as saying that there is just one theory of nature that will describes and explain everything that there is. Reality may be composed of just one kind of stuff and properties of that stuff but we need many different kinds of theories at different levels of description to account for everything there is.

Theories at these different levels may not be reduced one to another. What matters is that they be compatible with one another. The astronomy Newton gave us was a triumph over supernaturalism because it united the mechanics of the sub-lunary world with an account of the heavenly bodies. In a similar way, biology allowed us to advance from a time when we saw life in terms of an elan vital. Today, the biggest challenge is to explain our powers of thinking and imagination, our abilities to represent and report our thoughts: the very means by which we engage in scientific theorising. The final triumph of the natural sciences over supernaturalism will be an account of nature of conscious experience. The cognitive and brain sciences have done much to make that project clearer but we are still a long way from a fully satisfying theory.

But even if we succeed in producing a theory of human thought and reason, of perception, of conscious mental life, compatible with other theories of the natural and biological world, will we relinquish our cherished commonsense conceptions of ourselves as human beings, as selves who know ourselves best, who deliberate and decide freely on what to do and how to live? There is much evidence that we won't. As humans we conceive ourselves as centres of experience, self-knowing and free willing agents. We see ourselves and others as acting on our beliefs, desires, hopes and fears, and has having responsibility for much that we do and all that we say. And even as results in neuroscience begin to show how much more automated, routinised and pre-conscious much of our behaviour is, we are remain unable to let go of the self-beliefs that govern our day to day rationalisings and dealings with others.

We are perhaps incapable of treating others as mere machines, even if that turns out to be what we are. The self-conceptions we have are firmly in place and sustained in spite of our best findings, and it may be a fact about human beings that it will always be so. We are curious and interested in neuroscientists findings and we wonder at them and about their applications to ourselves, but as the great naturalistic philosopher David Hume knew, nature is too strong in us, and it will not let us give up our cherished and familiar ways of thinking for long. Hume knew that however curious an idea and vision of ourselves we entertained in our study, or in the lab, when we returned to the world to dine, make merry with our friends our most natural beliefs and habits returned and banished our stranger thoughts and doubts. It is likely, as this end of the year, that whatever we have learned and whatever we know about the error of our thinkings and about the fictions we maintain, they will still remain the most dominant guiding force in our everyday lives. We may not be comforted by this, but as creatures with minds who know they have minds — perhaps the only minded creatures in nature in this position — we are at least able to understand our own predicament.

Economy as a Complex Evolving System

Let's try one in cosmology. The universe contains at least 3 and perhaps 4 very different kinds of matter, whose origins probably are physically completely different. There is the Cosmic Background Radiation (CBR) which is photons from the later parts of the Big Bang but is actually the residue of all the kinds of radiation that were in the Bang, like flavored hadrons and mesons which have annihilated and become photons. You can count them and they tell you pretty well how many quanta of radiation there were in the beginning; and observation tells us that they were pretty uniformly distributed, in fact very, and still are.

Next is radiant matter — protons, mostly, and electrons. There are only a billionth as many of them as quanta of CBR, but as radiation in the Big Bang there were pretty much the same number, so all but one out of a billion combined with an antiparticle and annihilated. Nonetheless they are much heavier than the quanta of CBR, so they have, all told, much more mass, and have some cosmological effect on slowing down the Hubble expansion. There was an imbalance — but what caused that? That imbalance was generated by some totally independent process, possibly during the very turbulent inflationary era.

In fact out to a tenth of the Hubble radius, which is as far as we can see, the protons are very non-uniformly distributed, in a fractal hierarchical clustering with things called "Great Walls" and giant near-voids. The conventional idea is that this is all caused by gravitational instability acting on tiny primeval fluctuations, and it barely could be, but in order to justify that you have to have another kind of matter.

So you need — and actually see, but indirectly — Dark Matter, which is 30 times as massive, overall, as protons but you can't see anything but its gravitational effects. No one has much clue as to what it is but it seems to have to be assumed it is hadronic, otherwise why would it be anything as close as a factor 30 to the protons? But really, there is no reason at all to suppose its origin was related to the other two, you know only that if it's massive quanta of any kind it is nowhere near as many as the CBR, and so most of them annihilated in the early stages. Again, we have no excuse for assuming that the imbalance in the Dark Matter was uniformly distributed primevally, even if the protons were, because we don't know what it is.

Finally, of course there is Dark Energy, that is if there is. On that we can't even guess if it is quanta at all, but again we note that if it is it probably doesn't add up in numbers to the CBR. The very strange coincidence is that when we add this in there isn't any total gravitation at all, and the universe as a whole is flat, as it would be, incidentally, if all of the heavy parts were distributed everywhere according to some random, fractal distribution like that of the matter we can see — because on the largest scale, a fractal's density extrapolates to zero. That suggestion, implying that Dark Energy might not exist, is considered very dangerously radical.

The posterior probability of any particular God is pretty small

Here's another, which compared to many other peoples' propositions isn't so radical. Isn't God very improbable? You can't in any logical system I can understand disprove the existence of God, or prove it for that matter. But I think that in the probability calculus I use He is very improbable.

There are a number of ways of making a formal probability theory which incorporate Ockham's razor, the principle that one must not multiply hypotheses unnecessarily. Two are called Bayesian probability theory, and Minimum Entropy. If you have been taking data on something, and the data are reasonably close to a straight line, these methods give us a definable procedure by which you can estimate the probability that the straight line is correct, not the polynomial which has as many parameters as there are points, or some intermediate complex curve. Ockham's razor is expressed mathematically as the fact that there is a factor in the probability derived for a given hypothesis that decreases exponentially in the number N of parameters that describe your hypothesis — it is the inverse of the volume of parameter space. People who are trying to prove the existence of ESP abominate Bayesianism and this factor because it strongly favors the "Null hypothesis" and beats them every time.

Well, now, imagine how big the parameter space is for God. He could have a long gray beard or not, be benevolent or malicious in a lot of different ways and over a wide range of values, he can have a variety of views on abortion, contraception, like or abominate human images, like or abominate music, and the range of dietary prejudices He has been credited with is as long as your arm. There is the heaven-hell dimension, the one vs three question, and I haven't even mentioned polytheism. I think there are certainly as many parameters as sects, or more. If there is even a sliver of prior probability for the null hypothesis, the posterior probability of any particular God is pretty small.

Archaeologist, University of Bradford; Author, The Buried Soul
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The human brain is a cultural artefact.

Phylogenetically, humans represent an evolutionary puzzle. Walking on two legs free the hands to do new things, like chip stones to make modified tools — the first artefacts, dating to 2.7 million years ago — but it also narrows the pelvis and dramatically limits the size of possible fetal cranium. Thus the brain expansion that began after 2 million years ago should not have happened.

But imagine that, alongside chipped stone tools, one genus of hominin appropriates the looped entrails of a dead animal, or learns to tie a simple knot, and invents a sling (chimpanzees are known to carry water in leaves and gorillas to measure water depth with sticks, so the practical and abstract thinking required here can be safely assumed for our human ancestors by this point).

In its sling, the hominin child can now hip ride with little impairment to its parent's hands-free movement. This has the unexpected and certainly unplanned consequence that it is no longer important for it to be able to hang on as chimps do. Although, due to the bio-mechanical constraints of a bipedal pelvis, the hominin child cannot be born with a big head (thus large initial brain capacity) it can now be born underdeveloped. That is to say, the sling frees fetuses to be born in an ever more ontogenically retarded state. This trend, which humans do indeed display, is called neoteny. The retention of earlier features for longer means that the total developmental sequence is extended in time far beyond the nine months of natural gestation. Hominin children, born underdeveloped, could grow their crania outside the womb in the pseudo-marsupial pouch of an infant-carrying sling.

From this point onwards it is not hard to see how a distinctively human culture emerges through the extra-uterine formation of higher cognitive capacities — the phylogenetic and ontogenic icing on the cake of primate brain function. The child, carried by the parent into social situations, watches vocalization. Parental selection for smart features such as an ability to babble early may well, as others have suggested, have driven the brain size increases until 250,000 years ago — a point when the final bio-mechanical limits of big-headed mammals with narrow pelvises were reached by two species: Neanderthals and us.

This is the phylogeny side of the case. In terms of ontogeny the obvious applies — it recapitulates phylogeny. The underdeveloped brains of hominin infants were culture-prone, and in this sense, I do not dissent from Dan Sperber's dangerous idea that ‘culture is natural'. But human culture, unlike the basic culture of learned routines and tool-using observed in various mammals, is a system of signs — essentially the association of words with things and the ascription and recognition of value in relation to this.

As Ernest Gellner once pointed out, taken cross-culturally, as a species, humans exhibit by far the greatest range of behavioural variation of any animal. However, within any on-going community of people, with language, ideology and a culturally-inherited and developed technology, conformity has usually been a paramount value, with death often the price for dissent. My belief is that, due to the malleability of the neotenic brain, cultural systems are physically built into the developing tissue of the mind.

Instead of seeing the brain as the genetic hardware into which the cultural software is loaded, and then arguing about the relative determining influences of each in areas such as, say, sexual orientation or mathematical ability (the old nature-nurture debate), we can conclude that culture (as Richard Dawkins long ago noted in respect of contraception) acts to subvert genes, but is also enabled by them. Ontogenic retardation allowed both environment and the developing milieu of cultural routines to act on brain hardware construction alongside the working through of the genetic blueprint. Just because the modern human brain is coded for by genes does not mean that the critical self-consciousness for which it (within its own community of brains) is famous is non-cultural any more than a barbed-and-tanged arrowhead is non-cultural just because it is made of flint.

The human brain has a capacity to go not just beyond nature, but beyond culture too, by dissenting from old norms and establishing others. The emergence of the high arts and science is part of this process of the human brain, with its instrumental extra-somatic adaptations and memory stores (books, laboratories, computers), and is underpinned by the most critical thing that has been brought into being in the encultured human brain: free will.

However, not all humans, or all human communities, seem capable of equal levels of free-will. In extreme cases they appear to display none at all. Reasons include genetic incapacity, but it is also possible for a lack of mental freedom to be culturally engendered, and sometimes even encouraged. Archaeologically, the evidence is there from the first farming societies in Europe: the Neolithic massacre at Talheim, where an entire community was genocidally wiped out except for the youngest children, has been taken as evidence (supported by anthropological analogies) of the re-enculturation of still flexible minds within the community of the victors, to serve and live out their orphaned lives as slaves. In the future, one might surmise that the dark side of the development of virtual reality machines (described by Clifford Pickover) will be the infinitely more subtle cultural programming of impressionable individuals as sophisticated conformists.

The interplay of genes and culture has produced in us potential for a formidable range of abilities and intelligences. It is critical that in the future we both fulfil and extend this potential in the realm of judgment, choice and understanding in both sciences and arts. But the idea of the brain as a cultural artefact is dangerous. Those with an interest in social engineering — tyrants and authoritarian regimes — will almost certainly attempt to develop it to their advantage. Free-will is threatening to the powerful who, by understanding its formation, will act to undermine it in sophisticated ways. The usefulness of cultural artefacts that have the degree of complexity of human brains makes our own species the most obvious candidate for the enhanced super-robot of the future, not just smart factory operatives and docile consumers, but cunning weapons-delivery systems (suicide bombers) and conformity-enforcers. At worst, the very special qualities of human life that have been enabled by our remarkable natural history, the confluence of genes and culture, could end up as a realm of freedom for an elite few.