{"id":10290,"date":"2015-11-17T21:19:59","date_gmt":"2015-11-18T02:19:59","guid":{"rendered":"http:\/\/chcollins.com\/100Billion\/?p=10290"},"modified":"2022-08-01T07:43:02","modified_gmt":"2022-08-01T11:43:02","slug":"predictability","status":"publish","type":"post","link":"https:\/\/chcollins.com\/100Billion\/2015\/11\/predictability\/","title":{"rendered":"On Predictability"},"content":{"rendered":"

Some time ago on this blog, I posted an essay called “The Free Will Manifesto<\/a>.”\u00a0 It was one of my longer reads \u2014 fifteen minutes!\u00a0\u2014 but even so, I left some avenues unexplored.\u00a0 Thirteen more minutes of avenues, as it turns out.<\/p>\n

In my effort to show that free will<\/em> 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.\u00a0 What I did not address in my argument is why our decisions appear<\/em> to involve something like free will — why it is hard for us to think of ourselves as, essentially, computers.<\/p>\n

\"Photo<\/a>I think a key to this question is our notion of predictability<\/a>.\u00a0<\/em> People tend to associate predictable things with mechanical processes and unpredictable things with living agents or complex, natural processes.\u00a0 This leads to the logical fallacy called denying the antecedent<\/a><\/em>, a line of thinking that goes something like this:<\/p>\n

Mechanical operations are fairly predictable.\u00a0 So if a thing is unpredictable, it is probably not mechanical.\u00a0 Since our actions are unpredictable, they surely do not arise from mechanical computations.<\/em><\/p>\n

But we are not entitled to make this leap, that unpredictability implies free will.\u00a0 If we take a closer look at predictability<\/em>, we will find many rich sources of unpredictability that have nothing to do with will.<\/p>\n

Random, Arbitrary, Willful, Determined.<\/span><\/strong><\/h3>\n

Teenagers<\/em>!\u00a0 No, no, no.\u00a0 Those words may apply to them, but that is not what this section is about.\u00a0 It is about different types of processes —<\/em> events that transform one state into another — and the relative predictability of their outcomes.\u00a0 Here, I consider a variety of processes, from Arithmetic to Zeus, and rank them<\/a> in terms of predictability:<\/p>\n

\"A<\/a><\/p>\n

My predictability chart has an arbitrary scale, with more predictable processes at upper left and less predictable at lower right.\u00a0 As you take a moment to digest this, I would point out that unpredictabilty<\/em> is not the same as uncertainty<\/em>.\u00a0 This UK website<\/a> said it well:\u00a0 “Uncertainty refers to a state of having limited knowledge.\u00a0 Uncertainty can result from lack of information or from disagreement over what is known or even knowable.”\u00a0 Strictly speaking, uncertainty is one possible cause<\/em> of unpredictability, our inability to know, control or explain the future.<\/p>\n

I would like to discuss my predictability rankings, starting with arithmetic<\/em>.\u00a0 The outcome of any arithmetic probem or series of them is totally predictable, if one knows the rules.\u00a0 One plus two will be three today, tomorrow, whenever and wherever.\u00a0 Any unpredictability in arithmetic arises from failure to follow the rules, due to inexperience, lack of knowledge, or mechanical breakdown.<\/p>\n

\"Tang<\/a>You may be surprised to see chemical reactions<\/em> in the next slot on my predictability scale.\u00a0 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<\/a> to make meth).\u00a0 Unpredictability of chemical reactions increases when the chemicals are complex in structure or greater in number, both of which create avenues for competing reactions.\u00a0 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.\u00a0 Finally, in chemistry as in all of science, we cannot predict what we do not understand.\u00a0 As my friend and chemistry department head Eric says: “Chemical research isn\u2019t (yet) a follow-the-cookbook, everything-is-known, can-be-taught-as-a-trade discipline.\u00a0 So much is unknown and yet to be explored.”[1]<\/span><\/p>\n

Now compare chemistry to another physical process, radioactive decay.<\/em>\u00a0 The decay of an unstable element (plutonium, say) is a quantum-level process — it is totally un<\/em>predictable on an event-by-event basis but is very predictable in terms of how many nuclei decay over a given time.\u00a0 Physicists (including a reluctant Einstein<\/a>) were forced to accept, by virtue of experiment, that radioactive decay and other quantum events are fundamentally random<\/em> processes that follow probabilistic rules.\u00a0 God does indeed play dice<\/a> (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.<\/p>\n

One may argue that my predictabilty score for radioactivity is trivial and misguided, as the only thing predictable about it is the average<\/em> decay rate.\u00a0 Predictability of this sort may be no more meaningful than “predicting” the average value of many rolls of a six-sided die.[2]<\/span>\u00a0 In\u00a0my defense, the decay rates of radioactive isotopes are well-known and predictable<\/em> in the sense that my lump of uranium-235 will decay in the same proportion as your lump and Vladimir Putin’s lump.\u00a0 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.<\/p>\n

Such repeatable and statistical behavior is the reason I ranked the radioactive decay of a given substance as a rather predictable process overall.\u00a0 Kvetch if you wish.<\/p>\n

\u2022 \u2022\u00a0\u2022\u00a0\u2022\u00a0\u2022<\/p>\n

\"Photo<\/a>Throw a ball!\u00a0 Where will it land?\u00a0 If we are in your backyard, probably within a foot or so of your target.\u00a0 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?\u00a0 It will probably land within a foot or so of your target<\/a> (watch the clip).<\/p>\n

Adult humans throw things with surprising accuracy (young ones not so much).\u00a0 It is an acquired skill.\u00a0 After many misses, we eventually learn hand-eye coordination, and we start celebrating wastebasket goals and vicious dodge-ball hits<\/a>.\u00a0 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.\u00a0 If you ever tried to throw a balloon, you know what I mean.\u00a0 A high “signal-to-noise” ratio seems to be a general requirement for predictability, for throws and other physical processes.<\/p>\n

\"Predicitability<\/a>And now, dice.\u00a0 For most of us, dice were our introduction to the notion of chance<\/em>.\u00a0 Since a die roll is impossible to predict, we often say it is random,<\/em> but that is not quite true.\u00a0 Dice and other macro objects follow well-known laws of mechanics: if one knows enough about the system, one should\u00a0be able to — in principle<\/em> — predict the result of a die toss.\u00a0 This is a fundamentally different situation than the random nature of radioactive decay.<\/p>\n

As others<\/a> have noted, when we talk about randomness, we should distinguish between random processes<\/em> and effectively random results.<\/em>\u00a0 Radioactivity, being a quantum event, is an inherently random process (as is a recently-discovered method<\/a> of generating random numbers by shooting a laser through a diamond).\u00a0 Tossing a die, on the other hand, is just a series of ordinary physical events that somehow produces an effectively random result.\u00a0 How can that be?\u00a0 Where does the random come from?<\/p>\n

\u2022 \u2022\u00a0\u2022\u00a0\u2022\u00a0\u2022<\/p>\n

I can predict a die toss and so can you!\u00a0 It’s very simple.\u00a0 Place a standard 16mm die on a hard level surface.\u00a0 Lift the die 6mm (\u00bc-inch) from the surface, hold it level and let go.\u00a0 My prediction: nine times (or more) out of ten, the top face of the die will be the same as when you released it.\u00a0 Try it yourself!\u00a0 Amaze your friends!<\/p>\n

\"Result<\/a>Now, 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.\u00a0 My prediction: you will not even bother to try this experiment, since you can already guess the outcome.<\/p>\n

The chart above<\/a> shows the result of what you rightly figured to be a waste of time.\u00a0 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<\/em> random set of results.\u00a0 This simple experiment shows that all that dice-rattling and hand-flinging by rec-room gamblers is mostly for show.<\/p>\n

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.\u00a0 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]<\/span><\/p>\n

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<\/em> the effects that lock in the unpredictability. This is commonly known as cheating<\/em>.\u00a0 Good luck with that.<\/p>\n

Weather.\u00a0 Or not.
\n<\/span><\/strong><\/h3>\n

I put weather forecasts<\/em> next on my predictability chart, but only reluctantly, because the topic is such a clich\u00e9.\u00a0 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<\/a>.\u00a0 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<\/a>: An Experimental and Theoretical Study of the Lorenz Equations.”\u00a0 Mr. Danforth (now Dr. Danforth) is today an endowed chair in mathematics and science<\/a> at the University of Vermont and — in spite of having chosen to live where the temperature dips below freezing 144 days a year<\/a> — looks to be an intelligent and interesting person<\/a>.\u00a0 He and his colleague\"Chris<\/a> Peter Dodds have developed a project called the Hedonometer<\/a>, “an instrument that measures the happiness of large populations in real time.”\u00a0 This endeavor is much more interesting than anything I have to say about the unpredictability of weather (one word: chaos<\/em>), 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]<\/span><\/p>\n

Which brings us to animal behavior<\/em> and human behavior<\/em>.\u00a0 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.\u00a0 Yes, animals (especially insects) exhibit programmatic<\/em> behavior, which lets us predict (and counteract) many of their future actions, but humans also have characteristic <\/em>behaviors that are not much more unpredictable than those of animals.<\/p>\n

Consider: we are as wary of unpredictable people as we are of large or venomous animals.\u00a0 We evolved the ability to observe the behavior of living agents and then pattern-match their behaviors as typical<\/em> or unusual<\/em>.\u00a0 <\/em> We monitor the actions of spiders and snakes and view the unpredictability of other agents as signs of danger.\u00a0 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.\u00a0 But in the main, we value predictability<\/em> in our friends, family, lovers and merchants — we refer to this value as trust<\/em>.<\/p>\n

I maintain that we evolved routine behaviors (and the brain pathways to support them) that are socially and economically successful.\u00a0 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.\u00a0 When faced with similar situations, people rarely do totally surprising things.\u00a0 In fact, a mobility study by Northeastern University<\/a> of Boston concluded that “human behavior is 93 percent predictable” and that “spontaneous individuals are largely absent from the population.”\u00a0 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<\/em>.\u00a0 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.\u00a0 Otherwise, our forebears would have been bear-food.<\/p>\n

\u2022 \u2022\u00a0\u2022\u00a0\u2022\u00a0\u2022<\/p>\n

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<\/em>?\u00a0 After all, if we are fully free agents, should we not be capable of any act at any time?\u00a0 In other words, arbitrary!<\/em><\/p>\n

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).\u00a0 One scenario that is practically unpredictable, but not arbitrary, is unbounded choice.<\/em>\u00a0 I struggled a little to come up with a vivid example of unbounded choice, and this is the best I could do:<\/p>\n

The prolific science-fiction writer Isaac Asimov (may God bless his atheist soul<\/a>) 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.\u00a0 (God has already named all the stars, and He has a big hat.)\u00a0 So, can you predict what star Asimov will pick?<\/span><\/em><\/p>\n\n\n\n
\"RowenaAsimov on Throne, by Rowena Morrill<\/span><\/a><\/td>\n\n

Of course not.\u00a0 There are some 1025<\/sup> stars in our universe, give or take many powers of ten.\u00a0 Our ability to predict which star Asimov would pick is essentially nil.\u00a0 This is unpredictability by virtue of unbounded possibility.\u00a0 Guessing a number from one to ten is a fundamentally different game than guessing a number from negative to positive infinity.[5]<\/span><\/p>\n

Speaking of God, which I rarely do, we finally arrive at what I call Acts of God.\u00a0 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.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Are acts of god possible?\u00a0 Some people think so.\u00a0 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.\u00a0 Evidently it was, because here we are.\u00a0 When it comes to acts of god, anything can happen.<\/p>\n

Will It?\u00a0 Or Not?<\/span><\/strong><\/h3>\n

Some people think free will<\/em> 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!<\/em>\u00a0 It has to be free, because it is unpredictable, right?\u00a0 Well, no.\u00a0 As the chart below<\/a> sums up, there are many sources of unpredictability other than arbitrary choices:<\/p>\n

\"Why<\/a>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<\/a>, Physicalism, Chaos and Reductionism<\/em>:<\/p>\n

As presently understood, nonlinear dynamical systems \u2013 of which the brain is clearly one \u2013 exhibit the twin phenomena of chaos and emergence.\u00a0 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.<\/em><\/span><\/p>\n

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<\/em>, as if we were free<\/em> to turn our will <\/em>on and off like a light switch.\u00a0 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]<\/span><\/p>\n

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.\u00a0 Its unpredictability gives the impression that the future is also undetermined<\/em>, offering those with free will<\/em> the tiny crack in the door they need to burst into the scene and take control!\u00a0 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<\/em> would pop up.\u00a0 The fact that this experiment is impossible to conduct puts a bit of a damper on my assertion.<\/p>\n

As my fellow traveller Christopher Hitchens said, “That which can be asserted without evidence, can be dismissed without evidence.”\u00a0 The question thus becomes, which is the assertion lacking evidence, that free will exists or that it does not?\u00a0 <\/span>I would love to cite any evidence, but as the essay Uncomputability and Free Will<\/a><\/em> (Nayakar and Srikanth, 2012) states in its introduction:<\/p>\n

The basic problem posed by free will …\u00a0 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.\u00a0 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.\u00a0 Apparently, it can only be subjectively experienced.<\/em><\/span><\/p>\n

After all that, an inconclusive conclusion.\u00a0 Just as you might have predicted.<\/p>\n

Metalogue
\n<\/span><\/strong><\/h3>\n

This post turned out to be quite different than I originally intended.\u00a0 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.\u00a0 But I never managed to come up with the predictability vs determinism vs randomness graph that I had imagined.\u00a0 Either my imagination failed or the dimensions of the problem stymied me.<\/p>\n

So the post became less graphical and more wordy, and I inserted illustrations to stave off terminal glaze-over.\u00a0 The illustrations were fun to do but took time.\u00a0 This all helps explain why three weeks passed from my last post to this one.<\/p>\n

In the end, I hope you were entertained and saw things in a different way.\u00a0 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.\u00a0 Check them out.\u00a0 And thanks for staying with me.<\/p>\n

_______________________<\/p>\n

[1] Eric also told me something about chemistry I didn’t know before:\u00a0 “You surely know about nano-stuff, yes?\u00a0 Turns out that when particles of … pure elements or compounds … shrink below about 100 nm in size (i.e., depart from the regime of \u201cbulk” materials), their physical, chemical and spectroscopic properties change dramatically. Even things that we were taught as \u201cgivens\u201d, 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.”\u00a0 I would not have predicted that.\u00a0 The smallest particles I ever dealt with at Kodak were about 120 nanometers (nm) in diameter.<\/h5>\n
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.<\/h5>\n
[2] The answer 3.5 can be calculated from the description of the die without ever having to toss it.<\/h5>\n
[3] The late Michel Baranger, professor at MIT and student of Richard Feynman, published a paper<\/a> (in April 2000) titled “Chaos, Complexity, and Entropy: A physics talk for non-physicists.”\u00a0 If you remember anything about calculus, you may enjoy it.<\/h5>\n
[4] It would be fun to have people like Chris Danforth and Carlo Rovelli<\/a> as friends.\u00a0 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.\u00a0 Maybe I could invite them here to dinner — my wife’s cooking would be a far better draw than my armchair admiration.<\/h5>\n
[5] For some fun further reading about the so-called “random” numbers that people pick, try this article<\/a> from the blog Data Colada.\u00a0 After reading it, you might think about changing your PIN numbers.<\/h5>\n
[6] I do recommend Alwyn Scott’s essay<\/a>, as well as the book Dice World<\/em><\/a> by Brian Clegg.\u00a0 The link leads to a podcast interview with Clegg about his book.<\/h5>\n","protected":false},"excerpt":{"rendered":"

Some time ago on this blog, I posted an essay called “The Free Will Manifesto.”\u00a0 It was one of my longer reads \u2014 fifteen minutes!\u00a0\u2014 but even so, I left some avenues unexplored.\u00a0 Thirteen more minutes of avenues, as it … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[39],"tags":[],"class_list":["post-10290","post","type-post","status-publish","format-standard","hentry","category-interests"],"_links":{"self":[{"href":"https:\/\/chcollins.com\/100Billion\/wp-json\/wp\/v2\/posts\/10290","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/chcollins.com\/100Billion\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/chcollins.com\/100Billion\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/chcollins.com\/100Billion\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/chcollins.com\/100Billion\/wp-json\/wp\/v2\/comments?post=10290"}],"version-history":[{"count":263,"href":"https:\/\/chcollins.com\/100Billion\/wp-json\/wp\/v2\/posts\/10290\/revisions"}],"predecessor-version":[{"id":28288,"href":"https:\/\/chcollins.com\/100Billion\/wp-json\/wp\/v2\/posts\/10290\/revisions\/28288"}],"wp:attachment":[{"href":"https:\/\/chcollins.com\/100Billion\/wp-json\/wp\/v2\/media?parent=10290"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/chcollins.com\/100Billion\/wp-json\/wp\/v2\/categories?post=10290"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/chcollins.com\/100Billion\/wp-json\/wp\/v2\/tags?post=10290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}