Different kinds of impossible

Many of us engage in magical thinking -- attributing causal relationships between actions and events that are simply (often accidentally) correlated.  Superstitions are magical thinking; as nice as it would be if you could influence the win/loss ratio of your favorite team by wearing a particular shirt, the universe just isn't put together that way.

Where it gets interesting is that there are different degrees of magical thinking. A clever piece of research from the online journal PLoS-One, carried out by psychologists John McCoy of the University of Pennsylvania and Tomer Ullman of Harvard, illustrates that even those of us who engage in magical thinking seem to be intuitively aware of how impossible different false causations are.

So we can, like the White Queen in Through the Looking Glass, believe in six impossible things before breakfast.  [Image is in the Public Domain]

The paper, entitled "Judgments of Effort for Magical Violations of Intuitive Physics," asks test subjects to perform a simple task.  First, imagine a world where magic is real, where conjuring a spell could make things happen that are impossible in our world.  Then, they were asked to judge how difficult those spells would be.  What the researchers found is that the bigger the violation of physics required for the spell to work, the greater the effort by the conjurer must be.  The authors write:

People spend much of their time in imaginary worlds, and have beliefs about the events that are likely in those worlds, and the laws that govern them.  Such beliefs are likely affected by people’s intuitive theories of the real world.  In three studies, people judged the effort required to cast spells that cause physical violations.  People ranked the actions of spells congruently with intuitive physics.  For example, people judge that it requires more effort to conjure up a frog than to levitate it one foot off the ground.  A second study manipulated the target and extent of the spells, and demonstrated with a continuous measure that people are sensitive to this manipulation even between participants.  A pre-registered third study replicated the results of Study 2. These results suggest that people’s intuitive theories partly account for how they think about imaginary worlds.

After all, to levitate a frog using ordinary physics has already been achieved.  Frogs, like humans, are mostly water, and water is diamagnetic -- when exposed to a strong magnetic field, the constituent atoms align, inducing a magnetic field of the opposite polarity and triggering a repulsive force.  So it doesn't take any particular violation of physics to levitate a frog, although imagining a situation where it could be done without a powerful electromagnet is more of a reach.

Conjuring a frog out of nothing, though?  This is a major violation of a great many laws of physics.  First, if you imagine that the frog is coming from the air molecules in the space that it displaces when it appears, you have to believe that somehow oxygen, nitrogen, and the trace gases in the air have been converted to the organic molecules that make up living tissue.  Just getting from lightweight gaseous elements to the iron in the frog's hemoglobin isn't possible in the lab -- iron, in fact, is formed in the cores of supergiant stars, and only dispersed into space during supernova explosions.  (Pretty cool that the molecules that make up you were once in the ultra-hot cores of giant stars, isn't it?  Carl Sagan was spot-on when he said "We are made of star stuff.")

So there are different sorts of impossible.  You'd think that once you've accepted that the regular laws of physics don't apply -- that you're in a world where magic really happens -- you'd decide that all bets are off and anything can happen.  But our intuitive understanding of the laws of physics doesn't go away.  We still are, on some level, aware of what's difficult, what's impossible, and what's ridiculously impossible.  The authors write:

[P]eople’s ranking of the spells in all our studies were not affected by exposure to fantasy and magic in the media.  We suggest that the media does not primarily affect what spells are seen as more difficult, but rather that people bring their intuitive physics to bear when they engage with fiction.  That is, in line with previous research on myths and transformation, systems of magic are perceived as coherent to the extent to which they match people’s intuitive theories.  People perceive levitating a frog as easy not because they know it’s one of the first charms that any young wizard learns at Hogwarts, rather young wizards learn that spell first because readers expect that spell should be easy.

 
In his 1893 essay The Fantastic Imagination, the novelist George Macdonald wrote, “The natural world has its laws, and no man must interfere with them …but they themselves may suggest laws of other kinds, and man may, if he pleases, invent a little world of his own.”  It seems people’s little worlds do not stray far from home.

What's especially interesting to me about this study is that being an author of speculative fiction, tweaking the laws of physics is kind of my stock in trade.  I've messed around with time travel (Lock & Key), alternate/parallel worlds (Sephirot), machines that act as psychic amplifiers (Gears), and ordinary people gaining knowledge of the future (In the Midst of Lions), to name a few.  It's fascinating to think about my own writing -- and figure out which of the crazy plot points I've invented were impossible, and which were really impossible.

At least it's reassuring that the evil superpowerful shapeshifters in Signal to Noise fall into the latter category.

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The realm of the impossible

An article appeared in the July/August issue of the Skeptical Inquirer which, on first glance, you might expect me to agree with entirely.

It's entitled "Why Parapsychological Claims Cannot Be True," and is written by Arthur S. Reber and James E. Alcock, professors of psychology at (respectively) Brooklyn College and York University.  What Reber and Alcock are attempting to show is that physical law proves that claims of extrasensory perception and the like are theoretically impossible.

Reber and Alcock cite four tenets of physics that they say render parapsychological claims untenable:

1. Causality -- all effects have definite causes that preceded them.
2. Time's arrow -- the flow of time is one-directional, although its speed may vary from reference frame to reference frame.
3. Thermodynamics -- energy cannot be created or destroyed, so parapsychological claims (such as the future influencing the present) require energy transfer that breaks the First Law.
4. The inverse-square law -- the strength of a signal diminishes as a function of the square of the distance, and no such attenuation of signal strength is reported in cases of (for example) telepathy.

Certainly, these are powerful objections to many claims of parapsychology, and anyone who says (s)he has such abilities needs to have some pretty persuasive evidence backing it up.  But what I object to is that Reber and Alcock equate a claim violating science as we currently understand it with a claim being impossible even in the broadest theoretical sense.  Based on this, they say, all parapsychological claims should be dismissed out of hand.

[Image licensed under the Creative Commons, John Stephen Dwyer, PsychicBoston, CC BY-SA 3.0]

There are a number of problems with this conflation.  The first is that physics itself suggests some awfully bizarre things -- witness Saturday's post about two spaceships being in a state of superposition where both of them are destroyed and not destroyed simultaneously, an outcome that appears to be entirely consistent with what we know about quantum theory and general relativity.  Simultaneity was shown to be inconsistent between reference frames decades ago; one of the more bizarre outcomes of Einstein's discoveries is that two events that appear simultaneous in one frame might appear sequential in another, raising questions about what exactly we mean by "causality."  (And that's not even considering such loony -- but theoretically possible -- phenomena as wormholes, connecting two different bits of spacetime.)

The second problem, though, is the assumption that our understanding now is going to turn out to be true ten years (or even ten days) from now, and will apply equally well to every new discovery.  Consider one of their examples -- the inverse-square law.  It is true that many physical phenomena drop in magnitude as a function of the inverse square of the distance.  (These include light intensity, radiation, gravitational force, electromagnetic force, and sound volume.)  But it was recently discovered that gravitational waves don't decrease in intensity with the square of the distance; they decrease inversely simply with the distance.  The power of a radar signal diminishes with the distance of the source raised to the fourth power.  Up to a distance of one femtometer, the strong nuclear force doesn't vary with distance at all, and after that it drops to nearly zero.

So saying that physics demonstrates that all information transmission follows an inverse-square law simply isn't true, and even if you ignore the handful of counterexamples known, it also implies some significant hubris -- that any subsequent discoveries we make will automatically conform to what we already know.

What is at the root of this is a confusion between what is improbable and what is impossible.  I would argue that there's very little in the latter category -- even such written-in-stone laws such as the speed of light being the ultimate universal speed limit have been subject to thus-far unresolved questions (consider, for example, the Alcubierre warp drive, a solution to Einstein's field equations that appears to allow apparent hyperlight speeds).  As you move along the continuum from improbable to impossible, the demand for rigorous and high-quality evidence quite rightly increases (Carl Sagan's "ECREE" principle -- "Extraordinary Claims Require Extraordinary Evidence").  This is why it might take a lot to move me into the "true believer" column with respect to parapsychological claims, but am quite content to remain in the "undecided" column indefinitely.

As befits a good skeptic.

But no matter where you are along the continuum, you can never rule out what the next round of discoveries might uncover.  As Einstein remarked (although it may well be apocryphal) -- "A thousand experiments could never prove me right, but one could prove me wrong."

There are a good many other objections to Reber's and Alcock's argument.  One which I'll mention briefly, but which for a fuller explication you should go to the source, was outlined by Ian Wardell in his blog Philosophical Thoughts.  The gist of his rebuttal is that parapsychological claims all hinge on issues of consciousness, and we still don't have any explanation of a mechanism by which consciousness occurs -- so how can we say with confidence what its limitations are?

Again, I'm not arguing for parapsychological claims, and regular readers of Skeptophilia know all too well that I'm pretty dubious about a lot of the specific evidence these claims rest on.  But my doubt about particular bits of psi doesn't imply anything categorical about the possibility of those sorts of phenomena in general, any more than my demonstration that a purported Bigfoot femur came from a bear would mean that Bigfoot doesn't exist anywhere in time and space.

Such examples of scientific hubris always remind me of the famous quote from Lord Kelvin, one of the pre-eminent scientists of the late 19th and early 20th century, who said in 1907, "There is nothing new to be discovered in physics now.  All that remains is more and more precise measurement."  Within twenty years of that statement, Robert Millikan showed that photons exist in discrete quanta of energy; Einstein published his paper on the general theory of relativity; Louis-Victor de Broglie showed that matter has wavelike properties; Heisenberg demonstrated the bizarrely counterintuitive uncertainty principle; and Schrödinger wrote his famous wave equation governing the role of probability in quantum phenomena.

And we're still trying to figure out the fallout from all of that stuff.

So as far as Reber and Alcock go; I'm not quite the instantaneous ally you might have expected.  My general feeling is that any time you start talking about something being theoretically impossible, world without end amen, you're skating out onto some seriously thin ice.

********************************

This week's Skeptophilia book recommendation is about a subject near and dear to my heart; the possibility of intelligent extraterrestrial life.  In The Three-Body Problem, Chinese science fiction writer Cixin Liu takes an interesting angle on this question; if intelligent life were discovered in the universe -- maybe if it even gave us a visit -- how would humans react?

Liu examines the impact of finding we're not alone in the cosmos from political, social, and religious perspectives, and doesn't engage in any pollyanna-ish assumptions that we'll all be hunky-dory and ascend to the next plane of existence.  What he does think might happen, though, makes for fascinating reading, and leaves you pondering our place in the universe for days after you turn over the last page.

[Note: if you purchase this book from the image/link below, part of the proceeds goes to support Skeptophilia!]

Different kinds of impossible

Many of us engage in magical thinking -- attributing causal relationships between actions and events that are simply (often accidentally) correlated.  Superstitions are magical thinking; as nice as it would be if you could influence the win/loss ratio of your favorite team by wearing a particular shirt, the universe just isn't put together that way.

Where it gets interesting is that there are different degrees of magical thinking.  A clever piece of research appeared in the online journal PLoS-One last week, carried out by psychologists John McCoy of the University of Pennsylvania and Tomer Ullman of Harvard, which illustrates that even those of us who engage in magical thinking seem to be intuitively aware of how impossible different false causations are.

So we can, like the White Queen in Through the Looking Glass, believe in six impossible things before breakfast.  [Image is in the Public Domain]

The paper, entitled "Judgments of Effort for Magical Violations of Intuitive Physics," asks test subjects to perform a simple task.  First, imagine a world where magic is real, where conjuring a spell could make things happen that are impossible in our world.  Then, they were asked to judge how difficult those spells would be.  What the researchers found is that the bigger the violation of physics required for the spell to work, the greater the effort by the conjurer must be.  The authors write:

People spend much of their time in imaginary worlds, and have beliefs about the events that are likely in those worlds, and the laws that govern them.  Such beliefs are likely affected by people’s intuitive theories of the real world.  In three studies, people judged the effort required to cast spells that cause physical violations.  People ranked the actions of spells congruently with intuitive physics.  For example, people judge that it requires more effort to conjure up a frog than to levitate it one foot off the ground.  A second study manipulated the target and extent of the spells, and demonstrated with a continuous measure that people are sensitive to this manipulation even between participants. A pre-registered third study replicated the results of Study 2.  These results suggest that people’s intuitive theories partly account for how they think about imaginary worlds.

After all, to levitate a frog using ordinary physics has already been achieved.  Frogs, like humans, are mostly water, and water is diamagnetic -- when exposed to a strong magnetic field, the constituent atoms align, inducing a magnetic field of the opposite polarity and triggering a repulsive force.  So it doesn't take any particular violation of physics to levitate a frog, although imagining a situation where it could be done without a powerful electromagnet is more of a reach.

Conjuring a frog out of nothing, though?  This is a major violation of a great many laws of physics.  First, if you imagine that the frog is coming from the air molecules in the space that it displaces when it appears, you have to believe that somehow oxygen, nitrogen, and the trace gases in the air have been converted to the organic molecules that make up living tissue.  Just getting from lightweight gaseous elements to the iron in the frog's hemoglobin isn't possible in the lab -- iron, in fact, is formed in the cores of supergiant stars, and only dispersed into space during supernova explosions.  (Pretty cool that the molecules that make up you were once in the ultra-hot cores of giant stars, isn't it?  Carl Sagan was spot-on when he said "We are made of star stuff.")

So there are different sorts of impossible.  You'd think that once you've accepted that the regular laws of physics don't apply -- that you're in a world where magic really happens -- you'd decide that all bets are off and anything can happen.  But our intuitive understanding of the laws of physics doesn't go away.  We still are, on some level, aware of what's difficult, what's impossible, and what's ridiculously impossible.  The authors write:

[P]eople’s ranking of the spells in all our studies were not affected by exposure to fantasy and magic in the media.  We suggest that the media does not primarily affect what spells are seen as more difficult, but rather that people bring their intuitive physics to bear when they engage with fiction.  That is, in line with previous research on myths and transformation, systems of magic are perceived as coherent to the extent to which they match people’s intuitive theories.  People perceive levitating a frog as easy not because they know it’s one of the first charms that any young wizard learns at Hogwarts, rather young wizards learn that spell first because readers expect that spell should be easy. 

In his 1893 essay The Fantastic Imagination, the novelist George Macdonald wrote, “The natural world has its laws, and no man must interfere with them …but they themselves may suggest laws of other kinds, and man may, if he pleases, invent a little world of his own”. It seems people’s little worlds do not stray far from home.

What's especially interesting to me about this study is that being an author of speculative fiction, tweaking the laws of physics is kind of my stock in trade.  I've messed around with time travel (Lock & Key), alternate/parallel worlds (Sephirot), telepathic, energy-stealing aliens (Lines of Sight), and mythological creatures becoming real (The Fifth Day), to name a few.  It's fascinating to think about my own writing -- and figure out which of the crazy plot points I've invented were impossible, and which were really impossible.

At least it's reassuring that the evil superpowerful shapeshifters in Signal to Noise fall into the latter category.

***********************************

In 1919, British mathematician Godfrey Hardy visited a young Indian man, Srinivasa Ramanujan, in his hospital room, and happened to remark offhand that he'd ridden in cab #1729.

"That's an interesting number," Ramanujan commented.

Hardy said, "Okay, and why is 1729 interesting?"

Ramanujan said, "Because it is the smallest number that is expressible by the sum of two integers cubed, two different ways."

After a moment of dumbfounded silence, Hardy said, "How do you know that?"

Ramanujan's response was that he just looked at the number, and it was obvious.

He was right, of course; 1729 is the sum of one cubed and twelve cubed, and also the sum of nine cubed and ten cubed.  (There are other such numbers that have been found since then, and because of this incident they were christened "taxicab numbers.")  What is most bizarre about this is that Ramanujan himself had no idea how he'd figured it out.  He wasn't simply a guy with a large repertoire of mathematical tricks; anyone can learn how to do quick mental math.  Ramanujan was something quite different.  He understood math intuitively, and on a deep level that completely defies explanation from what we know about how human brains work.

That's just one of nearly four thousand amazing discoveries he made in the field of mathematics, many of which opened hitherto-unexplored realms of knowledge.  If you want to read about one of the most amazing mathematical prodigies who's ever lived, The Man Who Knew Infinity by Thomas Kanigel is a must-read.  You'll come away with an appreciation for true genius -- and an awed awareness of how much we have yet to discover.

[Note: If you purchase this book using the image/link below, part of the proceeds will go to support Skeptophilia!]