On Predictability

Some time ago on this blog, I posted an essay called “The Free Will Manifesto.”  It was one of my longer reads — fifteen minutes! — but even so, I left some avenues unexplored.  Thirteen more minutes of avenues, as it turns out.

In my effort to show that free will is an illusion, I argued for an alternate view, that human decision-making is an algorithmic process — less linear and more complex than ordinary computation but with no extraphysical mumbo-jumbo.  What I did not address in my argument is why our decisions appear to involve something like free will — why it is hard for us to think of ourselves as, essentially, computers.

Photo of Branching Tree with Lane Change Sign by CHCollinsI think a key to this question is our notion of predictability People tend to associate predictable things with mechanical processes and unpredictable things with living agents or complex, natural processes.  This leads to the logical fallacy called denying the antecedent, a line of thinking that goes something like this:

Mechanical operations are fairly predictable.  So if a thing is unpredictable, it is probably not mechanical.  Since our actions are unpredictable, they surely do not arise from mechanical computations.

But we are not entitled to make this leap, that unpredictability implies free will.  If we take a closer look at predictability, we will find many rich sources of unpredictability that have nothing to do with will.

Random, Arbitrary, Willful, Determined.

Teenagers!  No, no, no.  Those words may apply to them, but that is not what this section is about.  It is about different types of processes — events that transform one state into another — and the relative predictability of their outcomes.  Here, I consider a variety of processes, from Arithmetic to Zeus, and rank them in terms of predictability:

A chart of relative predictability

My predictability chart has an arbitrary scale, with more predictable processes at upper left and less predictable at lower right.  As you take a moment to digest this, I would point out that unpredictabilty is not the same as uncertainty.  This UK website said it well:  “Uncertainty refers to a state of having limited knowledge.  Uncertainty can result from lack of information or from disagreement over what is known or even knowable.”  Strictly speaking, uncertainty is one possible cause of unpredictability, our inability to know, control or explain the future.

I would like to discuss my predictability rankings, starting with arithmetic.  The outcome of any arithmetic probem or series of them is totally predictable, if one knows the rules.  One plus two will be three today, tomorrow, whenever and wherever.  Any unpredictability in arithmetic arises from failure to follow the rules, due to inexperience, lack of knowledge, or mechanical breakdown.

Tang and Koolaid Test TubesYou may be surprised to see chemical reactions in the next slot on my predictability scale.  Chemistry is not as predictable as arithmetic, but thanks to centuries of empirical and fundamental research, chemists know what to expect when hydrogen meets oxygen, silver nitrate meets potassium chloride, or benzylmagnesium chloride meets acetaldehyde methylimine (one of many ways to make meth).  Unpredictability of chemical reactions increases when the chemicals are complex in structure or greater in number, both of which create avenues for competing reactions.  Unpredictability also arises from lack of control over the environment — reactions take place on a much smaller scale (molecular) than the bulk conditions (temperature, mixing, etc.) that we are easily able to control.  Finally, in chemistry as in all of science, we cannot predict what we do not understand.  As my friend and chemistry department head Eric says: “Chemical research isn’t (yet) a follow-the-cookbook, everything-is-known, can-be-taught-as-a-trade discipline.  So much is unknown and yet to be explored.”[1]

Now compare chemistry to another physical process, radioactive decay.  The decay of an unstable element (plutonium, say) is a quantum-level process — it is totally unpredictable on an event-by-event basis but is very predictable in terms of how many nuclei decay over a given time.  Physicists (including a reluctant Einstein) were forced to accept, by virtue of experiment, that radioactive decay and other quantum events are fundamentally random processes that follow probabilistic rules.  God does indeed play dice (as Einstein put it) but radioactive decay and other quantum-level events have no resemblance to dice thrown in our macro world, as I will discuss in a few moments.

One may argue that my predictabilty score for radioactivity is trivial and misguided, as the only thing predictable about it is the average decay rate.  Predictability of this sort may be no more meaningful than “predicting” the average value of many rolls of a six-sided die.[2]  In my defense, the decay rates of radioactive isotopes are well-known and predictable in the sense that my lump of uranium-235 will decay in the same proportion as your lump and Vladimir Putin’s lump.  I can safely predict that each of us, even Mr. Putin, will have half-a-lump in our respective pockets 703.8 million years from now.

Such repeatable and statistical behavior is the reason I ranked the radioactive decay of a given substance as a rather predictable process overall.  Kvetch if you wish.

• • • • •

Photo of Clemente throwingThrow a ball!  Where will it land?  If we are in your backyard, probably within a foot or so of your target.  But if we are in a ballpark in Baltimore, and you are right-fielder Roberto Clemente, and you have a 300-foot throw to home?  It will probably land within a foot or so of your target (watch the clip).

Adult humans throw things with surprising accuracy (young ones not so much).  It is an acquired skill.  After many misses, we eventually learn hand-eye coordination, and we start celebrating wastebasket goals and vicious dodge-ball hits.  The results of our throws are fairly predictable, but only after we have practiced, and only if the object being thrown is massive enough to overcome air resistance and wind currents.  If you ever tried to throw a balloon, you know what I mean.  A high “signal-to-noise” ratio seems to be a general requirement for predictability, for throws and other physical processes.

Predicitability Animation by CHCollinsAnd now, dice.  For most of us, dice were our introduction to the notion of chance.  Since a die roll is impossible to predict, we often say it is random, but that is not quite true.  Dice and other macro objects follow well-known laws of mechanics: if one knows enough about the system, one should be able to — in principle — predict the result of a die toss.  This is a fundamentally different situation than the random nature of radioactive decay.

As others have noted, when we talk about randomness, we should distinguish between random processes and effectively random results.  Radioactivity, being a quantum event, is an inherently random process (as is a recently-discovered method of generating random numbers by shooting a laser through a diamond).  Tossing a die, on the other hand, is just a series of ordinary physical events that somehow produces an effectively random result.  How can that be?  Where does the random come from?

• • • • •

I can predict a die toss and so can you!  It’s very simple.  Place a standard 16mm die on a hard level surface.  Lift the die 6mm (¼-inch) from the surface, hold it level and let go.  My prediction: nine times (or more) out of ten, the top face of the die will be the same as when you released it.  Try it yourself!  Amaze your friends!

Result of releasing a die from 6mm above a surfaceNow, try the same except: mark the 1-3-5 corner of the die with a pencil; hold the die 6mm above the surface; turn the die so that the marked corner points upward; and then release it.  My prediction: you will not even bother to try this experiment, since you can already guess the outcome.

The chart above shows the result of what you rightly figured to be a waste of time.  It took less than 50 trials to demonstrate that dropping a die onto its corner (and the same corner each time, no less) from a small distance, was enough to produce an effectively random set of results.  This simple experiment shows that all that dice-rattling and hand-flinging by rec-room gamblers is mostly for show.

What I wanted to illustrate is how the unpredictabilty of a die throw arises from small variations in initial conditions (mass and shape of the die, direction and speed of the toss) which are then amplified or dampened by external factors, such as stray dribbles of nacho cheese.  Whereas throwing a ball harder often produces a more predictable outcome, tossing dice harder has the opposite result: the extra energy increases the number of bounces (think of them as branching points) and thus “locks in” the many uncertainties, sensitivities and instabilities of the system.[3]

In the end, when you roll a die, you have a one-in-six chance of rolling any given number, unless you do something to dampen the effects that lock in the unpredictability. This is commonly known as cheating.  Good luck with that.

Weather.  Or not.

I put weather forecasts next on my predictability chart, but only reluctantly, because the topic is such a cliché.  In some places (Hawaii comes to mind), the day-to-day weather is very predictable — and wonderful, I have heard — but on the continent, local weather is mostly unpredictable beyond a three-day window.  Christopher Danforth of Bates College in Maine wrote, as an honors thesis for his bachelor’s degree, an accessible treatise on this topic, titled “Why the Weather is Unpredictable: An Experimental and Theoretical Study of the Lorenz Equations.”  Mr. Danforth (now Dr. Danforth) is today an endowed chair in mathematics and science at the University of Vermont and — in spite of having chosen to live where the temperature dips below freezing 144 days a year — looks to be an intelligent and interesting person.  He and his colleagueChris Danforth, Mathematician and Physicist Peter Dodds have developed a project called the Hedonometer, “an instrument that measures the happiness of large populations in real time.”  This endeavor is much more interesting than anything I have to say about the unpredictability of weather (one word: chaos), so I’m just going to go on to the next category, and you can read more of Danforth’s work (as will I) when we finish this essay.[4]

Which brings us to animal behavior and human behavior.  It is not my impatience with the growing length of this post that I chose to discuss the two together — this was always my intent, because our behaviors are so similar with respect to predictability.  Yes, animals (especially insects) exhibit programmatic behavior, which lets us predict (and counteract) many of their future actions, but humans also have characteristic behaviors that are not much more unpredictable than those of animals.

Consider: we are as wary of unpredictable people as we are of large or venomous animals.  We evolved the ability to observe the behavior of living agents and then pattern-match their behaviors as typical or unusual.  We monitor the actions of spiders and snakes and view the unpredictability of other agents as signs of danger.  We tolerate a moderate amount of unpredictability from artists and cats, because their actions surprise us and delight us (well, except for cats) in a benign way.  But in the main, we value predictability in our friends, family, lovers and merchants — we refer to this value as trust.

I maintain that we evolved routine behaviors (and the brain pathways to support them) that are socially and economically successful.  These routines are what make humans and other animals predictable as a group, even as an individual agent’s behaviors are unique, due to the unique experiences that shape each of our decisions.  When faced with similar situations, people rarely do totally surprising things.  In fact, a mobility study by Northeastern University of Boston concluded that “human behavior is 93 percent predictable” and that “spontaneous individuals are largely absent from the population.”  Our brains may be complex and our minds unique, but our decision-making networks are very similar to each other and, importantly, they are robust.  Most human brains do a great job of filtering out unnecessary information (noise) and amplifying the most important signals so that we can settle on a course of action.  Otherwise, our forebears would have been bear-food.

• • • • •

If human behavior (allowing for our flexibility of response to complex situations) is really that predictable, how does this square with the idea of free will?  After all, if we are fully free agents, should we not be capable of any act at any time?  In other words, arbitrary!

I don’t believe for a minute that humans are arbitrary, but I will return to this point later (or as soon as I damn well feel like it).  One scenario that is practically unpredictable, but not arbitrary, is unbounded choice.  I struggled a little to come up with a vivid example of unbounded choice, and this is the best I could do:

The prolific science-fiction writer Isaac Asimov (may God bless his atheist soul) is now in Heaven, and God has asked him to pick a star from the universe, any star at all — just by drawing its name out of God’s hat.  (God has already named all the stars, and He has a big hat.)  So, can you predict what star Asimov will pick?

Rowena Morrill is the creator of this derivative work, based on an original work of which she is the creator. (Click to enlarge)Asimov on Throne, by Rowena Morrill

Of course not.  There are some 1025 stars in our universe, give or take many powers of ten.  Our ability to predict which star Asimov would pick is essentially nil.  This is unpredictability by virtue of unbounded possibility.  Guessing a number from one to ten is a fundamentally different game than guessing a number from negative to positive infinity.[5]

Speaking of God, which I rarely do, we finally arrive at what I call Acts of God.  Here I use the term literally, meaning something only a god can do: perform a willful and totally arbitrary act, observing no law or logic, and bounded by no constraints or limits on possibilities.

Are acts of god possible?  Some people think so.  Our very existence may be an example of an arbitrary event — one that could have happened, or not, depending on whether the name of our particular universe was drawn out of some quantum hat.  Evidently it was, because here we are.  When it comes to acts of god, anything can happen.

Will It?  Or Not?

Some people think free will is the human equivalent of an act of god — a willful, arbitrary (and hence unpredictable) result of our decision-making prowess, constrained to some extent by physical and mental limitations, but otherwise free!  It has to be free, because it is unpredictable, right?  Well, no.  As the chart below sums up, there are many sources of unpredictability other than arbitrary choices:

Why Things are Unpredictable (Click to Zoom)Our difficulty in explaining our own unpredictability (the so-called “mystery” of human behavior) is nicely stated in the introduction to Alwyn Scott’s essay, Physicalism, Chaos and Reductionism:

As presently understood, nonlinear dynamical systems – of which the brain is clearly one – exhibit the twin phenomena of chaos and emergence.  The first of these impedes reductionist formulations … and the second leads to hierarchical structures in biological organisms and cognitive systems, which are difficult to analyze reductively.

It defies logic for us to attribute our “predictable” behaviors to the influences of culture, genes or upbringing, while also maintaining that our “unpredictable” behaviors arise from something called free will, as if we were free to turn our will on and off like a light switch.  Occam’s Razor demands the simplest explanation for our apparent unpredictability (to the small extent that it is!) and to me that is the phenomena Scott cites above.[6]

The chaotic interaction among impossibly large numbers of particles at the system level, along with the macro effects (such as gamma rays) of quantum-level processes, is what makes the future both practically and fundamentally unpredictable.  Its unpredictability gives the impression that the future is also undetermined, offering those with free will the tiny crack in the door they need to burst into the scene and take control!  But as I asserted in my earlier post, if two scenarios could be constructed with identical initial conditions, down to the atom — including the atoms in the brains of all agents on the scene — then the outcomes of the scenarios would be the same, i.e., no free will would pop up.  The fact that this experiment is impossible to conduct puts a bit of a damper on my assertion.

As my fellow traveller Christopher Hitchens said, “That which can be asserted without evidence, can be dismissed without evidence.”  The question thus becomes, which is the assertion lacking evidence, that free will exists or that it does not?  I would love to cite any evidence, but as the essay Uncomputability and Free Will (Nayakar and Srikanth, 2012) states in its introduction:

The basic problem posed by free will …  appears to be not the physical one of whether it is compatible with the laws of physics, but the logical one of how to consistently define it, since it incorporates the contrary notions of freedom, which suggests indeterminism, as well as control, which bespeaks determinism.  We argue that it must be a fundamentally new causal primitive, in addition to determinism and indeterminism. … An implication for neuroscience is that [free will] will in general be experimentally undemonstrable.  Apparently, it can only be subjectively experienced.

After all that, an inconclusive conclusion.  Just as you might have predicted.

Metalogue

This post turned out to be quite different than I originally intended.  I had hoped I could put the related notions of predictability, randomness, arbitrariness and determinism on some kind of two-dimensional continuum, then draw up a chart that showed familiar processes and behaviors plotted on this x-y plane, discuss my reasoning a bit, and then my work would be done — an appendix to the original post.  But I never managed to come up with the predictability vs determinism vs randomness graph that I had imagined.  Either my imagination failed or the dimensions of the problem stymied me.

So the post became less graphical and more wordy, and I inserted illustrations to stave off terminal glaze-over.  The illustrations were fun to do but took time.  This all helps explain why three weeks passed from my last post to this one.

In the end, I hope you were entertained and saw things in a different way.  With regard to the links in my posts, I included them not just to be polite to those I cite, but to stimulate your curiosity as mine was as I wrote this post.  Check them out.  And thanks for staying with me.

_______________________

[1] Eric also told me something about chemistry I didn’t know before:  “You surely know about nano-stuff, yes?  Turns out that when particles of … pure elements or compounds … shrink below about 100 nm in size (i.e., depart from the regime of “bulk” materials), their physical, chemical and spectroscopic properties change dramatically. Even things that we were taught as “givens”, such as melting point (!), absorption and emission behavior with light, reactivity or not toward various substrates, etc., are no longer fixed on that size scale.”  I would not have predicted that.  The smallest particles I ever dealt with at Kodak were about 120 nanometers (nm) in diameter.
By the way, if any of you can come up with a good punchline for “What do you get when you mix Tang and Kool-Aid?” please post it as a comment.
[2] The answer 3.5 can be calculated from the description of the die without ever having to toss it.
[3] The late Michel Baranger, professor at MIT and student of Richard Feynman, published a paper (in April 2000) titled “Chaos, Complexity, and Entropy: A physics talk for non-physicists.”  If you remember anything about calculus, you may enjoy it.
[4] It would be fun to have people like Chris Danforth and Carlo Rovelli as friends.  But I am not smart enough to be their friend, and I am too old to be their friend, and we have not had any shared experiences save for what I have read of what they have written.  Maybe I could invite them here to dinner — my wife’s cooking would be a far better draw than my armchair admiration.
[5] For some fun further reading about the so-called “random” numbers that people pick, try this article from the blog Data Colada.  After reading it, you might think about changing your PIN numbers.
[6] I do recommend Alwyn Scott’s essay, as well as the book Dice World by Brian Clegg.  The link leads to a podcast interview with Clegg about his book.
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3 Responses to On Predictability

  1. Anonymous says:

    Geez, buddy – this might be my fave and most thought-provoking entry of yours ever. Clearly a lot of research went into this one . . . so many great thoughts and work on display here.

    Your pal,

    Eric

  2. I like the idea of thinking about “predictability” as a continuum, but I wonder about putting “acts of God” on the far end of the spectrum because of the “paradox of the stone.” In other words, assume God created the laws of the physical universe, like gravitation, upper limit to the speed of light, etc. Don’t these same laws then apply to God? For example, can God travel faster than the speed of light?

  3. Postscript: I add the essays by Michel Baranger, Alywn Scott, et al. to my reading list, so consider my previous comment not as the ‘last word’ on this problem but rather as an opening salvo, like 1 — e4 in chess.

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