Complexity and the Edge of Chaos Revisited

I’ve just finished re-reading Mitchel Wladrup’s Complexity: The Emerging Science at the Edge of Order and Chaos to followup on the Chaos discussion. About halfway through I realized that the book is now 20 years old. Perhaps because it was written so close to the founding of the Santa Fe Institute and was based primarily on interviews with key figures in that exciting flowering of ideas it still provides a vivid read.

I was struck by how little impact these big ideas seem to have had on the usual way of seeing the world. Perhaps chaos, complexity and emergence have entered the language, but dreams of improved prediction tools or appreciation of principles like unintended consequences don’t seem to have been achieved. There was a feeling when the book was written that we were on the verge of new forms of artificial intelligence and new approaches to economics that would help us understand the interconnectedness of the global economy. We have Google and mobile devices like the iPad. Sadly, it seems like more of the same only faster and in more places.

I had hoped that tools of decision theory, modeling and simulation would change difficult research and development projects like drug development. In my current job I get a pretty fair overview of the industry on a daily basis and can report that little has changed.

Insights from behavioral economics and advances in cognitive science that have had less impact one we way we see the world. There’s a constant stream of media reports about the science, but little evidence that these fundamental insights are informing our discussions about human behavior and ethics.

My original impulse when I started writing On Deciding . . . Better in late 1999 was to be at least one voice discussing what I thought were important implications of decision theory and Bayesian approaches to probability theory. Over the years, I’ve explored the sources of uncertainty in the world and most recently the emerging insights of Cognitive Neuroscience. I admit that mostly I write for myself, to get ideas out into better organized form and critically review them for myself.

My view of the value of writing and publishing on the net hasn’t changed in the last decade. I have a free, universally accessible publishing platform for my ideas. I’ve been fortunate over the years to actually have kindred spirits interested enough to read and comment on my efforts. I’ve been further encouraged over the last few months finding how Twitter as a microblogging environment provides a new venue to widen that circle of interaction like a virtual interdisciplinary conference.

The world of ideas is still vibrant. Its bigger and noisier than it was in 1992 or at the founding of the Santa Fe Institute in 1984. Certainly its bigger than the world of physics was at the time of either Einstein or Newton. However, I’m brave enough to suggest that like our world, those worlds also were ruled by a power law dictating the impact of ideas.

Making Decisions Under Conditions of Chaos

In 1961, Edward Lorenz discovered chaos in the clockwork universe.

Lorenz was running a computer simulation of the atmosphere to help forecast the weather. He wanted to rerun just part of one sequence, so instead of starting at the beginning, he started the run in the middle. In order to start in the middle, he used the output of the program at its midpoint as a new starting point, expecting to get the same result in half the time.

Unexpectedly, even though he was using a computer, following strict deterministic rules, the second run started with the same values as before but produced a completely different result. It was as if uncertainty and variability had some how crept into the orderly, deterministic world of his computer program.

As it turned out, the numbers used from the middle of the run were not quite the same as the ones used when the program was at that same point the first time because of rounding or truncation errors. The resulting theory, Chaos Theory, described how for certain kinds of computer programs, small changes in initial conditions could result in large changes later on. These systems change over time where each condition leads to the next. This dependence on initial conditions has been immortalized as “the butterfly effect” where a small change in initial conditions- the wind from a butterfly’s wings in China, can have a large effect later on- rain in New York.

This sensitivity to the exact values of parameters in the present makes it very hard to know future values in the future. As its been formalized mathematically, chaos theory applies to “dynamical system” which simply is a system that changes over time according to some rule. The system starts in some initial state at the beginning. For our purposes, think of it as now, time zero. Rules are applied and the system changes to its new state- wind is blowing, temperature is changing, etc based on rules applied to the initial state of the atmosphere. The rules are applied to the new state to produce the next state, etc.

Chaos may not have been the best word to describe this principle though. To me it suggests complete unpredictability. Most real or mathematically interesting dynamical systems don’t blow up like that into complete unpredictability. Using the weather, for example, even if the butterfly or small differences in ocean surface temperature makes it impossible to know whether the temperature in TImes Square in New York will be 34 degrees or 37 degrees on February 7th, either one is a likely value to be found in the system at that time in that place. Measuring a temperature of 95 degrees F in New York in February is impossible or nearly so.

Dynamical systems like the weather often show recurrent behavior, returning to similar but non-identical states over and over as the rules are applied. Following the values over time describes a path that wanders over values, returning after some time to the same neighborhood. Not exactly the same place because it started in a slightly different place than the last time around, but in the same neighborhood. Just unpredictably in the same neighborhood.

This returns us to the distinction between knowing the future and predicting it. The future state of chaotic system can be known because small changes in initial conditions result in large changes in result. But those large changes recur in a predictable range of values. A chaotic system can be predicted even though its future state can’t be known. When it comes to the TImes Square temperature, climate data tells us what range the chaotic values move within from season’s cycle to season’s cycle. In drug development, the chaotic system of taking a pill every day and a measuring drug levels in the blood allows prediction as the range of likely values, but because initial conditions change and cause large, unpredictable effects one can’t know in advance whether today’s measure will be high or low. Its almost never the average, it varies around the average.

It’s important to see how important prediction is for making decisions when the future is unknown. Because the uncertain future is orderly we actually know a lot about it; we don’t know it in all of its particulars. We must make decisions knowing what range of possibilities the future can assume. Chaos Theory suggests that this kind of uncertainty is in the very nature of the world because of the behavior of dynamical systems, any rules dictate how a system changes over time.

The Difference Between Predicting and Knowing

There’s a difference between predicting and knowing the future.

Predicting decreases uncertainty but does not eliminate it. We’ll call that level of certainty “knowing the future”. Predicting involves beliefs about the future state of the world and should be probabilistic, dealing in likelihoods of events, often describing a range of possible outomes.

I can make an excellent, accurate prediction about the card that will drawn from a deck. It will be one of the 52 cards in the deck.

Trivial? Not really. I’ve used my knowledge of the nature of card decks to constrain the possible range of outcomes to only those that are possible outcomes.

With more information about the particular deck I’d might be able to narrow the odds of various cards being drawn. For example armed with the exact order of cards in the deck and a historical dataset describing how often each card in each deck position is chosen, I could actually know which card is the single most likely to be drawn. Perhaps if we studied how people tend to draw cards we’d find that the center 25% got 60% of the draws, increasing the probability of those cards being selected over the top and bottom of the deck. Probably I’d be able to provide a list of the cards from most likely to be chosen through least likely.

Just because I know which card is most likely, it doesn’t mean that if the mostly likely card is not drawn in any particular trial that my prediction is wrong or inaccurate. The prediction only allowed me to strengthen my belief in some cards being drawn over other cards.

In selling any prediction service, If I only get one chance to test my ability to predict there’s no way to prove why I happened to be right or wrong. If my knowledge of the order of the deck and human behavior in selecting cards improved my ability to predict the card selected from 1 in 52 to 1 in 20, I’d be more than twice as good at picking the card to be drawn in advance, butits still overwhelming probable that my guess on any particular trial will be wrong.

It makes for a lousy magic trick but a very good way to make better decisions.

Image: The Glamour TIle



The Glamour Tile, originally uploaded by jjvornov.

I’ve probably photographed my front walk more than any other subject in the last few years. There’s a nice combination of textures in the brick and garden elements particularly when there’s been rain or snow.

Today the world here is buried under a few inches of snow with more on the way tonight. If I want to do some more practice with coach Vince (Versace), I’ll need to use some archive images.

Making Decisions Under Conditions of Ignorance

In this deterministic world, one of the most important sources of uncertainty is ignorance. In the Schrödinger’s cat thought experiment, we don’t know whether the cat is alive or dead. The source of that uncertainty at the macroscopic level is ignorance. The chamber is sealed and we can’t look inside of it.

From a macroscopic perspective, it’s no different from guessing what’s inside a sealed envelope or any other situation where some state of affairs exists but lack certain knowledge.

From a probability perspective, since we understand the physics of the cat in chamber system well enough, the probability of the cat being alive or dead is known. One could put that probability into a decision tree with a high level of confidence. If the probability of a decay event is 0.5, then the cat is not half dead and half alive, it has a 50 −50 chance of being alive. The event is determined, we just don’t know the answer until we open the box.

I want to completely blur past, present and future when it comes to ignorance since for decision making becaus it makes no difference. If the cat was unlucky enough to die in the first 5 minutes of being in the chamber, then the event occurred in the past we remain uncertain in the present. If we’re making a decision at the 30 minute mark the cat has a higher probability of being alive at present than if we make it at an hour just before opening the chamber, but since we won’t open the chamber until later, it doesn’t matter to us making the decision at 30 minutes. The event may or may not have occurred; ignorance obscures equally from the start to the finish. This is true of the future as well. If we substitute a coin flip to occur in an hour with the same 0.5 probability of success, the fact that the event occurs in the future makes no difference.

Let me also point out that knowledge without communication doesn’t dispel ignorance and thus has no influence on decision making. If we assume that the cat knows that it’s still alive inside the chamber, it makes no difference to us outside of the chamber. The outcome when the box is opened remains uncertain to us. Similarly, if I have a tape or transcript of an event in the past as long as I can’t time travel to influence those events my knowledge has no effect on decisions in the past. I know the text of Lincoln’s Gettysburg Address but that doesn’t affect the choices he had in writing it in 1863.

In the same context, consider the effect of an omniscient God who controls events in the world. Whether its a God that created a clockwork universe that plays out over time or a God that intervenes in events in the time stream, it makes no difference. Whether its a God who knows the full history of creation from the inception of the world to its end or a God that steers events with some ongoing intent also makes no difference. The knowledge and power of this God has no influence on our decisions unless knowledge is granted us about the world in the past present or future. Without knowledge, the veil of ignorance is itself enough to create conditions of uncertainty. As the world is presented to us, our ignorance requires us to make probabilistic decisions based on belief.

Knowledge has positive value in decision making. The more we approach the god-like state of knowing past, present and future, the better we can make decisions. Either probabilistic states can be made to collapse into certainty, like opening up the chamber and determining the state of the cat, or probability estimates can be refined, like checking on the cat halfway through its time in the chamber. Information that is irrelevant to the decision doesn’t help refine the probability estimate. Telling me its snowing outside can’t help refine the probability of whether the cat’s alive when the chamber is opened.

Making decisions under conditions of uncertainty is no different from making decisions under conditions of ignorance. Choosing ignorance over available knowledge is a completely different case

Perfect Practice



Winter Grass, originally uploaded by jjvornov.

I’ve been writing more than photographing in the last few months. I’ve set up the MacBook Air as a fast and light photo processing station.

I’ve moved Aperture and Photoshop CS3 over to the new machine. Nikon Capture NX2 didn’t make it because of serial number issues, but I’m fine with that for now. Based on Thom Hogan’s recent recommendations I feel pretty comforatable with RAW conversion in Aperture with a Vincent Versace influenced OZ 2.0 post processing in Photoshop.

The speed of the workflow is perfectly fine as Derrick Story described soon after the release of the new Airs. I was a bit hesitant about ordering this base 2GB model, but would have had to pay too much of a premium for the 4 GB. And it was suggested to me that with the SSD serving as scratch disk and memory paging there wasn’t going to be a huge hit compared to a conventional HD system.

I like the Tamron zoom with Nikon D7000 combination for image capture and I’d prefer to practice with my favored tools- a DSLR and fast lens, rather than try to get by with a compact. Switching to the Sigma DP1 hasn’t worked because of the fixed wide lens. Its a great travel camera, but not flexible enough to grab a shot like this one from a car window in very dead overcast light.

The Deterministic Universe

There’s really nothing very mysterious about uncertainty. We’re soaking in it every moment of our lives. We generally don’t know what’s happened in the past, we don’t fully know the current state of affairs in the world and we have even less of an idea of how events will unfold. While some have looked to the uncertainty that’s part of the current quantum physical models of the universe, there’s really no need to invoke such esoteric mechanisms. Its part of the nature of being human that we experience the world as uncertain. Yet it appears that in a material world working according to Newtonian physics, there is no real uncertainty. The current state of the universe determines the next state of the universe.

The prospect of a “clockwork universe” is frightening. In the most extreme conception, we live in a universe which began its existence with a set of initial conditions that then is playing out the predetermined events implied in those initial conditions. Whether those initial conditions were intelligently set by a creator or “just happened” doesn’t matter for us,we are each actors playing out our parts in a predetermined script. Theoretically, a sufficiently powerful being could have access to all of the initial conditions and the ability to calculate all of the interactions. Prediction would be easy enough by simply running the calculations needed to predict any future event.

I’m going to unilaterally cut off debate on this interesting topic (author’s privilege!) by assuming that this is exactly the kind of world we live in. I’ll ignore quantum effects because at physical level the world appears to be mostly deterministic. Actually, I believe that the uncertainty at the atomic level makes the clockwork universe conception untenable. It appears that events at some physical level like radioactive decay are truly probabilistic. As long as these random events have effects at a macroscopic level (producing a click in a geiger counter for example) then if the world were started over again with exactly the same initial conditions, it would turn out differently because these random events would be different the second time around.
We can use the famous thought experiment of Schrödinger’s cat to illustrate this.

Schrödinger wrote:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

Schrödinger has successfully introduced the odd mathematics of quantum uncertainty into the realm of our experience. There are interesting questions about whether the cat is conscious and thus an observer of its own state and whether there is a difference between the unknown and indeterminacy that are beyond the scope of the current discussion. We want to focus on the fact that the quantum event of decay, an event that can’t be predicted only observed to have occurred, can dictate the fate of the cat.

If there was no random decay, the cat walks out of the chamber and continues to influence the world, shedding fur and ending the lives of mice and birds. If the cat is dead when the chamber is opened, there is a different set of events because of the random quantum event of radioactive decay.

But as I think Schrödinger is arguing, to say that reality itself is blurred seems ridiculous. The macroscopic world operates under deterministic Newtonian physics where theoretically every event is mechanistically caused by the immediately preceding state of the system. My next thought is determined by the current state of my brain, not some mystical non-physical spirit that is free of the physics of our deterministic world. There is no quantum level entanglement like our blurred cat where the next thought both exists and does not exist.

We’ve come to the first philosophical barrier in Deciding Better, the nature of free will in a deterministic universe.

MacBook Air Review

WinterWalk

This evening I put a copy of Photoshop on the new MacBook Air. I then downloaded the plug-ins that Vincent Versace includes with Welcome to Oz 2.0.

OK, this isn’t much of an image, but it was a jpeg captured with a compact camera that I had at hand. I can confirm that my typical workflow is fine on the Air. Never more than 10 layers or so. Some NIK filters. Not significantly different in feel from the MacBook Pro. I’ll need to work on a workflow, but I’m encouraged that I’ll be able to do my usual post-processing activities without much trouble on the machine.

With a few days of use in general, I can make some comments. Of course, look elsewhere for the specs. Lets skip what everyone knows: It’s fast, it’s small, it’s light, it’s supercool.

I bought it as my Mac content creation device. As I wrote about in my discussion of the decision to buy it, the iPad just doesn’t work for me as for writing because of a combination of lack of keyboard and tools (Tinderbox, Scrivener, MarsEdit).

1. Get the 13″ screen. Its got the resolution of a 15″ MacBook Pro, so it’s not at all cramped.

2. Compared the old MBP, what have I gained? Portability. Battery life. Cooler running temp. The current glass trackpad with multitouch gestures and inertial scrolling.

3. WIth the small screen and high resolution, the pinch to zoom function on the trackpad becomes important. I’ve become used to it on the iPhone and iPad. The old MBP didn’t support it, but I never really needed it. But with my 53 year old eyes, the ability to zoom and pan a web page or pdf is great if some print or illustration is too small. You also tend to want to keep this very small device closer to you than a bigger laptop. More like an iPad than a conventional laptop. It would be nice if it was universally supported in programs. I can’t zoom in on a Tinderbox map with it for example.

4.A media management strategy is needed because of the small hard drive. 128 is enough for my purposes outside of media storage. The combination of Home Sharing and Airplay makes this pretty easy now. At home, you need a mac with the full media library always on and running iTunes. You can then stream music though an Airport Express (I have 2) or AppleTV (none yet). That’s now the older MBP. I find this conducive to writing because I can put on music through the stereo using the tool I’m writing with. Its less context switching for me. I may end up with no music on the MacBook Air itself since out of the house, I generally have the iPhone for headphone listening.

5. The lack of a fast external port is an inconvenience. No FW800, no Gigabit ethernet. Just USB2. But the drive is small and I don’t expect to be moving large files around.

Thinking Without Knowing

We have less free will than we think. Our thoughts are severely constrained by both brain mechanisms and the metaphors that the brain has been filled with from environmental input. Physics, culture, experience.

We have more free will than we think because this remarkable consciousness we’re all endowed with can act back on the brain and change it. We can also hack the brain in new and interesting ways to create.

John Cleese on Creativity:

John Cleese on how to put your mind to work via John Paul Caponigro

Cleese points out two important non-conscious phenomenon. First there’s the “sleep on it” effect where upon taking something up again the next morning the solution often appears obvious. The answer presents itself without thinking; it’s just there. Of course most thought is “just there”, but the previous effort makes it seem remarkable that you can fail to think of something one day but succeed the next. The brain is an odd muscle indeed. Imagine if you failed to hold something one day but could grasp it the next morning.

And his point that you need to put in the work of thinking the night before shouldn’t be lost. He calls it “priming the pump”, but I think of it as one long thinking process. Its useful to interrupt the conscious work to free the brain to produce a solution. This is brain work without knowing.

His second point about recreation from memory is related. We now know that remembering is a creative act, not a playback of a brain tape of events. Its easy to remember something into a different form than the original. Creatively, the new version may be better.

Cleese tells a story about losing and recreating a script. The second version, the one from memory, was funnier and crisper. I use this trick all the time in creating presentations or writing. I step away from the words or slide and get myself to say in words what it is I’m trying to convey. I’ve realized also that if I can’t say it easily, my problem is that I don’t know what to say, not that I don’t know how to say it.

It’s always fun to turn to someone during a prep meeting who’s struggling to create a slide. They’re lost in a verbal maze trying to find the right words as if it were some magical incantation that will unlock the meaning. I’ll say, “Tell me what you’re trying to convey here.” Once they’ve told me, I say, “Well, write that down” and we get a clear and crisp rendering of the thought in words.