Forecasts, Futures and Fractals

It has been the rare snowy winter in Baltimore, and I have found myself increasingly obsessed with the amateur meteorological websites that predict the weather with both greater passion and precision than the pros. My favorite site is Footsforecast.org, which is really two sites in one given the comments section featuring the prognostications of Andy from southern York County, Pa., as thusly identified by his screen name. Other contributors to the comments section typically ignore Foot’s forecasts altogether, and address themselves directly to Andy, even going so far as to band together in commenting uproar should anyone post a snide remark highlighting the fact that Andy just blew another forecast. It’s like watching a cult of personality form around that greatest of all know-it-alls, Cliff Clavin from Cheers. I do, however, sympathize with Andy’s defenders in that it has always irked me to hear complaints about the inaccuracy of weather forecasts. Because unless they make a living by trading stocks, betting on sports, or telling fortunes, these whingers have no concept of the difficulties involved in predicting the future.

It was with proper respect for these difficulties, a respect redoubled by the precision with which Foot’s Forecast nailed the timing, intensity, and duration of the whopper that dropped 12 inches on Baltimore last week, that I got to thinking about what really goes into the human process of predicting future events. I kept circling back to the phrase I have learned from Becky Bailey’s book, Conscious Discipline: “The brain is a pattern-seeking device.” Could predicting the future, be it in the form of a weather forecast or an investment scheme sans insider trading, simply be the brain’s pattern-seeking function taken to its logical end? Put another way, is successfully predicting the future in actuality an accurate reading of the past, i.e. the art of recognizing (pre-existing) patterns? If so, increasingly accurate predictions should be understood as increasingly detailed reports on events that have already taken place.

In the Newtonian clockwork universe it was widely held that if you could somehow know all of the variables you would necessarily then know exactly what’s coming next, seeing as Newton’s universe “continues clicking along, as a perfect machine, with its gears governed by the laws of physics, making every aspect of the machine predictable.” (http://en.wikipedia.org/wiki/Clockwork_universe) This understanding was, of course, displaced by quantum mechanics and its uncertainty principle that “the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.” (http://en.wikipedia.org/wiki/Uncertainty_principle) Following this, if we understand predicting the future as the recognition of patterns, then the uncertainty principle may place an outer limit on the accuracy of our predictions. We can only get but so fine grained in our perception of these patterns. But this is hardly discouraging given that quantum effects occur on such a microscopic scale that they are quite literally undetectable; our Newtonian clockwork universe may be an illusion, but that just means prognosticators are in the business of predicting the future of an illusion (which, we should note, isn’t quite what Freud had in mind when he attempted to debunk religion in his own The Future of an Illusion).

So, in our illusory Newtonian universe, if we knew everything there was to know about the past, we would obtain foreknowledge of everything there is to know about the future. This wouldn’t include any information about either where all the particles happened to be or how fast they were going, but should conceivably still include e.g. the revelation of the next 50 Super Bowl winners. I.e. we would still have access to all of the really important information.

The natural objection to all of this is that there is more to the future than the repetition of pre-existing patterns. This takes us all the way back to the debate that raged between the thinking of two great pre-Socratic philosophers, Parmenides and Heraclitus, a debate that can be boiled down to the tension between two truisms: 1) “change is the only constant in life,” which is a direct quote from Heraclitus, who also gave us the more poetic “You could not step twice into the same river; for other waters are ever flowing on to you,” and 2) “the more things change, the more they stay the same,” which Parmenides didn’t exactly say, but which nicely sums up his attitude towards genuine change, i.e. that it was impossible and that all apparent change and motion was mere illusion.

It is as easy as opening your eyes to side with Heraclitus, which is why Zeno and his paradoxes are so important in the debate. Zeno, Parmenides’ leading disciple, crafted several ingenious paradoxes to support his teacher’s claims about the impossibility of change or motion. My mother shared one of these paradoxes with me when I was a boy, and it remains as perplexing to me now as it did then. Here is the paradox, as described on Wikipedia:

“Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth, before one-eighth, one-sixteenth; and so on….This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility. This sequence also presents a second problem in that it contains no first distance to run, for any possible (finite) first distance could be divided in half, and hence would not be first after all. Hence the trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, so all motion must be an illusion.” (http://en.wikipedia.org/wiki/Zeno's_paradoxes)

In other words, everything our senses tell us about the world says that Heraclitus must be right and Parmenides wrong, requiring Zeno to demonstrate that what our senses tell us about the world can’t possibly be right and must therefore be an illusion. One can refute the paradox like Diogenes the Cynic, who “said nothing upon hearing Zeno’s arguments, but stood up and walked, in order to demonstrate the falsity of Zeno’s conclusions.” (ibid) But, per the paradox, this would simply be using an illusion to disprove the selfsame illusion. (Could Guns N' Roses’ Use Your Illusion, with an album cover featuring a portion of Raphael’s painting “The School of Athens,” have been an esoteric endorsement of just such a maneuver, and Axl Rose an unwitting mouthpiece for Cynic philosophy?) Like most proofs deployed in philosophy, one either finds Zeno’s paradox intuitively convincing or one doesn’t, leaving strenuous efforts to undermine the logic of the proof mostly beside the point. For example, I, like many, find Anselm’s ontological proof of God’s existence iron clad. To paraphrase Anselm, God is a being than which nothing greater can be imagined, and since a God which exists is necessarily greater than a God which does not exist, the fact that we can imagine a God than which nothing greater can be imagined means that the God we are imagining must necessarily exist. Deep thinkers have tried to poke holes in Anselm’s proof in the millennium since Anselm first formulated it, but none of them have had a definitive success. The proof still stands, and all we can really decide is whether we find it a persuasive reason to believe in God. (I, for one, do not; my reasons for belief lie in other, arational directions.) Just so, I would suggest that Zeno’s paradoxes are as stout as Anselm’s proof, and will never fall despite being under continual intellectual siege. One simply must decide for one’s self if the paradoxes make a convincing case that the world of motion and change we perceive is an illusion. On balance, even taking into consideration the endless wading through one river after another, I am convinced.

This makes it my job to justify the chutzpah of refuting all of the impressions ever given to me by my five senses. But relying strictly on Zeno’s paradoxes in refuting the given facts of the phenomenal world is to lean a tad too heavily on what can come to feel like intellectual parlor tricks. Something tangible is required to bolster Zeno’s defense of his teacher, something from the illusion which, opposite Diogenes, marks it as just that. Which brings us back to our pattern-seeking brains and their quarry. Because if “the brain is a pattern-seeking device,” then it must have evolved in adaptation to an environment churning with repeating patterns. And patterns, I would argue, are nothing but changelessness in motion over time.

All of which got me to thinking about fractals: “A fractal is a mathematical set that typically displays self-similar patterns, which means it is ‘the same from near as from far.’” (http://en.wikipedia.org/wiki/Fractal) Which is a fancy way of saying that if you look at fractals microscopically close you will see the same patterns repeating that you see when you pull back for a “God’s eye view.” Unless one is a PhD mathematician, the only really interesting thing about fractals would seem to be the groovy psychedelic patterns they make. But one key line about fractals caught my eye, and hints at the potential of fractals as a foundational element in a changeless Parmenidean universe: “Fractals are not limited to geometric patterns, but can also describe processes over time.” (ibid) Could the phenomenal universe be something of an infinitely intricate fractal pattern in process over time, making it the job of our pattern-seeking brains to “read” the fractals, and making the geniuses amongst us those with the greatest gift in “reading” certain of the infinitely intricate fractal strands? E.g., Shakespeare, Marx, and Freud could “read” the patterns of human behavior better than anyone else while Einstein and Darwin could best “read” the patterns of the physical world. And there is no reason not to think that Jesus, Moses, Mohammed, and the Buddha were the very best at “reading” the most important patterns of all.

If reality is indeed an infinitely intricate fractal pattern in process over time, a few people are going to come out smelling like roses. To name a few: Nietzsche, whose beat up old jalopy, the theory of eternal return, would be in for a fresh coat of paint and some shiny new rims; Daniel Pinchbeck, doyen of all things 2012 and a strong proponent of a switch from a linear to a cyclical (i.e. pattern-based) calendar; and my late father, Jess, who always stressed the importance of trusting his intuition, which intuition could now be understood as the unconscious recognition of patterns discerned by way of globs of information too large for the conscious mind to handle, much less manipulate. Because if, again, the brain is a pattern-seeking device, and if the conscious mind is but the tip of the unconscious’ iceberg, then it stands to reason that it is the unconscious doing the great bulk of the “reading” of fractals.

Earlier this month The New York Times published an article by Edward Frenkel exploring the fact that “Mathematical knowledge is unlike any other knowledge. Its truths are objective, necessary, and timeless.” (http://www.nytimes.com/2014/02/16/opinion/sunday/is-the-universe-a-simulation.html?_r=0) As scientists explore this mystery, Frenkel explains that “one fanciful possibility is that we live in a computer simulation based on the laws of mathematics- not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used.” (ibid) Frenkel further reports that there are even “certain kinds of asymmetries” which, if present in the universe “would indicate that we might- just might- ourselves be in someone else’s computer simulation.” (ibid) Frenkel closes with the obvious pop culture connection to The Matrix. As someone who knows what-all about math and computers, I would nevertheless (intuitively?) suggest that the computer-simulated “matrix” we (might) inhabit may well be a fractal, or something like it. If nothing else, this would go a long way towards explaining why our brains work the way they do.

It would also prove Parmenides right, and, by extension, Plato, at least as regards the nature of our “matrix” and the eternal, changeless mathematical “forms” that underwrite it. As Frenkel reports, “the possibility of the Platonic nature of mathematical ideas remains- and may hold the key to understanding our own reality.” (ibid) But as one who esteems the truth of reality as either, inevitably, one of Wittgenstein’s lions or the face of God, depending on my mood, (“If a lion could speak, we could not understand him,” or, more dramatically, “You cannot see My face, for no man can see Me and live!”), I’ll settle for knowing if, and how much, it will snow this Wednesday.