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HOWARD GARDNER
Psychologist, Harvard University; Author, Truth, Beauty, And Goodness Reframed: Educating For The Virtues In The 21St Century

"How Would You Disprove Your Viewpoint?!"

Thanks to Karl Popper, we have a simple and powerful tool: the phrase "How Would You Disprove Your Viewpoint?!"

In a democratic and demotic society like ours, the biggest challenge to scientific thinking is the tendency to embrace views on the basis of faith or of ideology. A majority of Americans doubt evolution because it goes against their religious teachings; and at least a sizeable minority are skeptical about global warming — or more precisely, the human contributions to global change — because efforts to counter climate change would tamper with the 'free market'.

Popper popularized the notion that a claim is scientific only to the extent that it can be disproved — and that science works through perpetual efforts to disprove claims.

If American citizens, or, for that matter, citizens anywhere were motivated to decribe the conditions under which they would relinquish their beliefs, they would begin to think scientifically. And if they admitted that empirical evidence would not change their minds, then at least they'd have indicated that their views have a religious or an ideological, rather than a scientific basis.


BRUCE HOOD
Director of the Bristol Cognitive Development Centre in the Experimental Psychology Department at the University of Bristol; Author, Supersense

Haecceity

Understanding the concept of haecceity would improve everybody's cognitive toolkit because it succinctly captures most people's intuitions about authenticity that are increasingly threatened by the development of new technologies. Cloning, genetic modification and even digital reproduction are some examples of new innovations that alarm many members of the public because they appear to violate a belief in the integrity of objects

Haecceity is originally a metaphysical concept that is both totally obscure and yet very familiar to all of us. It is the psychological attribution of an unobservable property to an object that makes it unique among identical copies. All objects may be categorized into groups on the basis of some shared property but an object within a category is unique by virtual of its haecceity. It is haecceity that makes your wedding ring authentic and your spouse irreplaceable, even though such things could be copied exactly in a futuristic science fiction world where matter duplication had been solved.

Haecceity also explains why you can gradually replace every atom in an object so that it not longer contains any of the original material and yet psychologically, we consider it to be the same object. That transformation can be total but so long as it has been gradual, we consider it to be the same thing. It is haecceity that enables us to accept restoration of valuable works of art and antiquities as a continuous process of rejuvenation. Even when we discover that we replace most of the cellular structures of our bodies every couple of decades, haecceity enables us to consider the continuity of our own unique self.

Haecceity is an intellectually challenging concept attributable to the medieval Scottish philosopher, John Duns Scotus, who ironically is also the origin of the term for the intellectually challenged, "dunces." Duns Scotus coined haecceity to address the confusion in Greek metaphysics between the invisible property that defines the individual, as opposed to "quiddity" which is the unique property that defines the group.

Today, both haecceity and quiddity have been subsumed under the more recognizable term, "essentialism." Richard Dawkins has recently called essentialism, "the dead hand of Plato," because, as he points out, a intuitive belief in distinct identities is a major impediment to accepting the reality that all diverse life forms have a common biological ancestry. However drawing the distinction within essentialism is important. For example, it is probably intuitive quiddity that makes some people unhappy about genetic modification because they see this as a violation of integrity of the species as a group. On the other hand it is intuitive haecceity that forms our barrier to cloning, where the authenticity of the individual is compromised.

By reintroducing haecceity as a scientific concept, albeit one that captures a psychological construct, we can avoid the confusion over using the less constrained term of essentialism that is applied to hidden properties that define both the group and the individual identity. It also provides a term for that gut feeling that many of us have when the identity and integrity of objects we value are threatened and we can't find the word for describing our concerns.


JOHN ALLEN PAULOS
Professor of Mathematics, Temple University, Philadelphia; Author, Irreligion: A Mathematician Explains Why the Arguments ofr God Just Don't Add Up

A Probability Distribution

The notion of a probability distribution would, I think, be a most useful addition to the intellectual toolkits of most people.

Most quantities of interest, most projections, most numerical assessments are not point estimates. Rather they are rough distributions — not always normal, sometimes bi-modal, sometimes exponential, sometimes something else.

Related ideas of mean, median, and variance are also important, of course, but the simple notion of a distribution implicitly suggests these and weans people from the illusion that certainty and precise numerical answers are always attainable.


W. DANIEL HILLIS
Physicist, Computer Scientist; Chairman, Applied Minds, Inc.; Author, The Pattern on the Stone

Possibility Spaces: Thinking Beyond Cause and Effect

One of the most widely-useful (but not widely-understood) scientific concepts is that of a possibility space. This is a way of thinking precisely about complex situations. Possibility spaces can be difficult to get your head around, but once you learn how to use them, they are a very powerful way to reason, because they allow you to sidestep thinking about causes and effects.

As an example of how a possibility space can help answer questions, I will use "the Monty Hall problem," which many people find confusing using our normal tools of thought. Here is the setup: A game-show host presents a guest with a choice of items hidden behind three curtains. Behind one is a valuable prize; behind the other two are disappointing duds. After the guest has made an initial choice, the host reveals what is behind one of the un-chosen curtains, showing that it would have been a dud. The guest is then offered the opportunity to change their mind. Should they change or stick with their original decision?

Plausible-sounding arguments can be made for different answers. For instance, one might argue that it does not matter whether the guest switches or not, since nothing has changed the probability that the original choice is correct. Such arguments can be very convincing, even when they are wrong. The possibility space approach, on the other hand, allows us skip reasoning about complex ideas like probabilities and what causes change. Instead, we use a kind of systematic bookkeeping that leads us directly to the answer. The trick is just to be careful to keep track of all of the possibilities.

One of the best ways to generate all the possibilities is to find a set of independent pieces of information that tell you everything you could possibly need to know about what could happen. For example, in the case of the Monty Hall problem, it would be sufficient to know what choice the guests is going to make, whether the host will reveal the leftmost or rightmost dud, and where the prize is located. Knowing these three pieces of information would allow you to predict exactly what is going to happen. It is also important that these three pieces of information are completely independent, in the sense that knowing one of them tells you nothing about any of the others. The possibility space is constructed by creating every possible combination of these three unknowns.

In this case, the possibility space is three-dimensional, because there are three unknowns. Since there are three possible initial choices for the guest, two dud options for the host, and three possible locations for the prize, there are initially 3x2x3=18 possibilities in the space. (One might reasonably ask why we don't just call this a possibility table. In this simple case, we could. But, scientists generally work with possibility spaces that contain an infinity of possibilities in a multidimensional continuum, more like a kind of physical space space.) This particular possibility space starts out as three-dimensional, but once the guest makes their initial choice, twelve of the possibilities become impossible and it collapses to two dimensions.

Let's assume that the guest already knows what initial choice they are going to make. In that case they could model the situation as a two-dimensional possibility space, one representing the location of the prize, the other representing whether the host will reveal the rightmost or leftmost dud. In this case, the first dimension indicates which curtain hides the prize (1, 2 or 3), and the second represents the arbitrary choice of the host (left dud or right dud), so there are six points in the space, representing the six possibilities of reality. Another way to say this is that the guest can deduce that they may be living in one of six equally-possible worlds. By listing them all, they will see that in four of these six, it is to their advantage to switch from their initial choice.

 

Host reveals left dud

Host reveals right dud

Prize is behind 1

2 revealed, better to stick

3 revealed, better to stick

Prize is behind 2

3 revealed, better to switch

3 revealed, better to switch

Prize is Behind 3

2 revealed, better to switch

2 revealed, better to switch

Example of a two-dimensional possibility space, when guest's initial Choice is 1

After the host makes his revelation, half of these possibilities become impossible, and the space collapses to three possibilities. It will still be true that in two out of three of these possible worlds it is to the guest's advantage to switch. (In fact, this was even true of the original three-dimensional possibility space, before the guest made their initial choice.)

This is a particularly simple example of a possibility space where it is practical to list all the possibilities in a table, but the concept is far more general. In fact one way of looking at quantum mechanics is that reality actually consists of a possibility space, with Schrödinger's equation assigning a probability to each possibility. This allows quantum mechanics to explain phenomena that are impossible to account for in terms of causes and effects. Even in normal life, possibility spaces give us a reliable way the solve problems when our normal methods of reasoning seem to give contradictory or paradoxical answers. As Sherlock Holmes would say,  "Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth."


HAIM HARARI
Physicist, former President, Weizmann Institute of Science; Author, A View from the Eye of the Storm

The Edge of the Circle

My concept is important, useful, scientific and very appropriate for Edge, but it does not exist. It is: The Edge of the Circle.

We know that a circle has no edge, and we also know that, when you travel on a circle far enough to the right or to the left, you reach the same place. Today's world is gradually moving towards extremism in almost every area: Politics, law, religion, economics, education, ethics, you name it. This is probably due to the brevity of messages, the huge amounts of information flooding us, the time pressure to respond before you think and the electronic means (Twitter, text messages) which impose superficiality. Only extremist messages can be fully conveyed in one sentence.

In this world, it often appears that there are two corners of extremism: Atheism and religious fanaticism; Far right and far left in politics; Suffocating bureaucratic detailed regulatory rules or a complete laissez faire; No ethical restrictions in Biology research and absolute restrictions imposed by religion; one can continue with dozens of examples.

But, in reality, the extremists in the two edges always end up in the same place. Hitler and Stalin both murdered millions, and signed a friendship pact. Far left secular atheist demonstrators in the western world, including gays and feminists, support Islamic religious fanatics who treat women and gays as low animals. It has always been known that no income tax and 100% income tax yield the same result: no tax collected at all, as shown by the famous Laffer curve. This is the ultimate meeting point of the extremist supporters of tax increase and tax reduction.

Societies, preaching for absolute equality among their citizens, always end up with the largest economic gaps. Fanatic extremist proponents of developing only renewable energy sources, with no nuclear power, delay or prevent acceptable interim solutions to global energy issues, just as much as the oil producers. Misuse of animals in biology research is as damaging as the objections of fanatic animal right groups. One can go on and on with illustrations, which are more visible now than they were a decade or two ago. We live on the verge of an age of extremism.

So, the edge of the circle is the place where all of these extremists meet, live and preach. The military doctor who refuses to obey orders "because Obama was born in Africa" and the army doctor, who murdered 12 people in Texas, are both at the edge of the circle.

If you are a sensible moderate thinking person, open any newspaper and see how many times you will read news items or editorials, which will lead you to say: "Wow, these people are really at the edge of the circle" ...


CHRISTIAN KEYSERS
Neuroscientist; Scientific Director, Neuroimaging Center, University Medical Center Groningen

The Mirror Fallacy

With the discovery of mirror neurons and similar systems in humans, neuroscience has shown us that when we see the actions, sensations and emotions of others, we activate brain regions as if we were doing similar actions, were touched in similar ways or made similar facial expressions. In short, our brain mirrors the states of the people we observe. Intuitively, we have the impression that while we mirror, we feel what is going on in the person we observe. We empathize with him or her.

When the person we see has the exact same body and brain as we do, mirroring would tell us what the other feels. Whenever the other person is different in some relevant way, however, mirroring will mislead us. Imagine a masochist receiving a whiplash. Your mirror system might make you feel his pain — because you would feel pain in his stead. What he actually feels though is pleasure. You committed the mirror fallacy of incorrectly feeling that he would have felt what you would have felt — not what he actually felt.

The world is full of such fallacies: we feel dolphins are happy just because their face resembles ours while we smile or we attribute pain to robots in sci-fi movies. We feel an audience is Japan failed to like a presentation we gave because their poise would be our boredom. Labeling them, and realizing that the way we interpret the social world is through projection might help us reappraise these situations and beware.


NICHOLAS HUMPHREY
Psychologist, London School of Economics; Author, Soul Dust

The "Multiverse"

The scientific concept of the "multiverse" has already entered popular imagination. But the full implications of the idea that every possible universe has been and will be actualised have yet to sink in. One of these, which could do more to change our view of things than anything is that we are all destined to be immortal.

This welcome news (if indeed it is welcome) follows on two quite different grounds. First, death normally occurs to human bodies in due time either as the result of some kind of macro-accident — for example a car crash, or a homicide; or a micro-one — a heart attack, a stroke; or, if those don't get us, a nano-one — accidental errors in cell division, cancer, old age. Yet, in the multiverse, where every alternative is realised, the wonderful truth is that there has to be at least one particular universe in which by sheer luck each of us as individuals have escaped any and all of these blows.

Second, we live in a world where scientists are, in any case, actively searching for ways of combatting all such accidents: seat belts to protect us in the crash, aspirin to prevent stroke, red wine oxidants to counter heart attacks, antibiotics against disease. And in one or more of the possible universes to come these measures will surely have succeeded in making continuing life rather than death the natural thing.

Taking these possibilities — nay certainties — together, we can reasonably conclude that there will surely be at least one universe in which I — and you — will still find ourselves living in a thousand years, or a million years time.

Then, when we get there, should we, the ultimate survivors, the one in a trillion chancers, mourn our alter-egos who never made it? No, probably no more than we do now. We are already, as individuals, statistically so improbable as to be a seeming miracle. Having made it so far, shouldn't we look forward to more of the same?


GEORGE LAKOFF
Cognitive Scientist and Linguist; Richard and Rhoda Goldman Distinguished Professor of Cognitive Science and Linguistics, UC Berkeley; Author, The Political Mind

Conceptual Metaphor

Conceptual Metaphor is at the center of a complex theory of how the brain gives rise to thought and language, and how cognition is embodied. All concepts are physical brain circuits deriving their meaning via neural cascades that terminate in linkage to the body. That is how embodied cognition arises.

Primary metaphors are brain mappings linking disparate brain regions, each tied to the body in a different way. For example, More Is Up (as in "prices rose") links a region coordinating quantity to another coordinating verticality. The neural mappings are directional, linking frame structures in each region. The directionality is determined by First-Spike-Dependent Plasticity. Primary metaphors are learned automatically and unconsciously by the hundreds prior to metaphoric language, just by living in the world and having disparate brain regions activated together when two experiences repeatedly co-occur.

Complex conceptual metaphors arise via neural bindings, both across metaphors and from a given metaphor to a conceptual frame circuit. Metaphorical reasoning arises when source domain inference structures are used for target domain reasoning via neural mappings. Linguistic metaphors occur when words for source domain concepts are used for target domain concepts via neural metaphoric mappings.

Because conceptual metaphors unconsciously structure the brain's conceptual system, much of normal everyday thought is metaphoric, with different conceptual metaphors used to think with on different occasions or by different people.

A central consequence is the huge range of concepts that use metaphor cannot be defined relative to the outside world, but are instead embodied via interactions of the body and brain with the world.

There are consequences in virtually every area of life. Marriage, for example, is understood in many ways, as a journey, a partnership, a means for grown, a refuge, a bond, a joining together, and so on. What counts as a difficulty in the marriage is defined by the metaphor used. Since it is rare for spouses to have the same metaphors for their marriage, and since the metaphors are fixed in the brain but unconscious, it is not surprising that so many marriages encounter difficulties.

In politics, conservatives and progressives have ideologies defined by different metaphors. Various concepts of morality around the world are constituted by different metaphors. These results show the inadequacy of experimental approaches to morality in social psychology (e.g, Haidt's moral foundations theory) which ignore both how conceptual metaphor constitutes moral concepts and why those metaphors arise naturally in cultures around the world.

Even mathematical concepts are understood via metaphor, depending on the branch of mathematics. Emotions are conceptualized via metaphors that are tied to the physiology of emotion. In set theory, numbers are sets of a certain structure.

On the number line, numbers are points on a line. "Real" numbers are defined via the metaphor that infinity is a thing; an infinite decimal like pi goes on forever, yet it is a single entity — an infinite thing.

Though conceptual metaphors have been researched extensively in the fields of cognitive linguistics and neural computation for decades, experimental psychologists have been experimentally confirming their existence by showing that, as circuitry physically in the brain they can influence behavior in the laboratory. The metaphors guide the experimenters, showing them what to look for. Confirming the conceptual metaphor that The Future Is Ahead; The Past is Behind, experimenters found that subjects thinking about the future lean slightly forward, while those thinking about the past lean slightly backwards. Subjects asked to do immoral acts in experiments tended to wash or wipe their hands afterwards, confirming the conceptual metaphor Morality Is Purity. Subjects moving marbles upward tended to tell happy stories, while those moving marbles downward tended to tell sad stories, confirming Happy Is Up; Sad is Down. Similar results are coming in by the dozens. The new experimental results on embodied cognition are mostly in the realm of conceptual metaphor.

Perhaps most remarkable, there appear to be brain structures that we are born with that provide pathways ready for metaphor circuitry. Edward Hubbard has observed that critical brain regions coordinating space and time measurement are adjacent in the brain, making it easy for the universal metaphors for understanding space in terms of time to develop (as in "Christmas is coming" or "We're coming up on Christmas.") Mirror neuron pathways linking brain regions coordinating vision and hand actions provide a natural pathway for the conceptual metaphor that Seeing Is Touching (as in "Their eyes met").

Conceptual metaphors are natural and inevitable. They begin to arise in childhood just by living in the everyday world. For example, a common conceptual metaphor is Events with Causal Effects Are Actions by a Person. That is why the wind blows, why storms can be vicious, and why there is religion, in which the person causing those effects is called a god, or God if there is only one. The most common metaphors for God in the Western traditions is that God is a father, or a person with father-like properties — a creator, lawgiver, judge, punisher, nurturer, shepherd, and so on — and that God is The Infinite: the all-knowing, all-powerful, all-good, and first cause. These metaphors are not going to go away. The question is whether they will continue to be taken literally.

Those who believe, and promote the idea, that reason is not metaphorical —that mathematics is literal and structures the world independently of human minds —are ignoring conceptual metaphor and encouraging false literalness, which can be harmful.

The science is clear. Metaphorical thought is normal. That should be widely recognized.

Every time you think of paying moral debts, or getting bogged down on a project, or losing time, or being at a crossroads in a relationship, you are unconsciously activating a conceptual metaphor circuit in your brain, reasoning using it, and quite possibly making decisions and living your life on the basis of your metaphors. And that's just normal. There's no way around it!

Metaphorical reason serves us well in everyday life. But it can do harm if you are unaware of it.


MILFORD H. WOLPOFF
Professor of Anthropology and Adjunct Associate Research Scientist, Museum of Anthropology at the University of Michigan; Author, Race and Human Evolution

GIGO

A shorthand abstraction I find to be particularly useful in my own cognitive toolkit comes from the world of computer science, and applies broadly in my experience to science and scientists. GIGO means "garbage in, garbage out." Its application in the computer world is straightforward and easy to understand, but I have found much broader applications throughout my career in paleoanthropology.

In computer work, garbage results can arise from bad data or from poorly conceived algorithms applied to analysis — I don't expect that the results from both of these combined are a different order of garbage because bad is bad enough. The science I am used to practicing has far too many examples of mistaken, occasionally fraudulent data and inappropriate, even illogical analysis, and it is all too often impossible to separate conclusions from assumptions.

I don't mean to denigrate paleoanthropology, which I expect is quite like other sciences in these respects, and wherein most work is superbly executed and cannot be described this way. The value of GIGO is to sharpen the skeptical sense and the critical facility because the truth behind GIGO is simple: science is a human activity.


GEORGE DYSON
Science Historian; Author, Darwin Among the Machines

Analog Computing

Imagine you need to find the midpoint of a stick. You can measure its length, using a ruler (or making a ruler, using any available increment) and digitally compute the midpoint. Or, you can use a piece of string as an analog computer, matching the length of the stick to the string, and then finding the middle of the string by doubling it back upon itself. This will correspond, without any loss of accuracy due to rounding off to the nearest increment, to the midpoint of the stick. If you are willing to assume that mass scales linearly with length, you can use the stick itself as an analog computer, finding its midpoint by balancing it against the Earth's gravitational field.

There is no precise distinction between analog and digital computing, but, in general, digital computing deals with integers, binary sequences, and time that is idealized into discrete increments, while analog computing deals with real numbers and continuous variables, including time as it appears to exist in the real world. The past sixty years have brought such advances in digital computing that it may seem anachronistic to view analog computing as an important scientific concept, but, more than ever, it is.

Analog computing, once believed to be as extinct as the differential analyzer, has returned. Not for performing arithmetic — a task at which even a pocket calculator outperforms an analog computer — but for problems at which analog computing can do a better job not only of computing the answer, but of asking the questions and communicating the results. Who is friends with whom? For a small high school, you could construct a database to keep track of this, and update it every night to keep track of changes to the lists. If you want to answer this question, updated in real time, for 500 million people, your only hope is to build an analog computer. Sure, you may use digital components, but at a certain point the analog computing being performed by the system far exceeds the complexity of the digital code with which it is built. That's the genius that powers Facebook and its ilk. Your model of the social graph becomes the social graph, and updates itself.

In the age of all things digital, "Web 2.0" is our code word for the analog increasingly supervening upon the digital — reversing how digital logic was embedded in analog components, sixty years ago. The fastest-growing computers of 2010 — search engines and social networks — are analog computers in a big, new, and important way. Instead of meaningful information being encoded as unambiguous (and fault-intolerant) digital sequences referenced by precise numerical addressing, meaningful information is increasingly being encoded (and operated upon) as continuous (and noise-tolerant) variables such as frequencies (of connection or occurrence) and the topology of what connects where, with location being increasingly defined by fault-tolerant template rather than by unforgiving numerical address.

Complex networks — of molecules, people, or ideas — constitute their own simplest behavioral descriptions. This behavior can be more easily and accurately approximated by continuous, analog networks than it can be defined by digital, algorithmic codes. These analog networks may be composed of digital processors, but it is in the analog domain that the interesting computation is being performed.

Analog is back, and here to stay.


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