Heisenberg and The Conscious Object

From "Seven Attempts at Liquifying the Self" by N. Schultz in his Experiment in Private Self-Consciousness Heisenberg's Uncertainty Principle is rightly seen as the first 20th Century result that puts an absolute limit on what can be measured, and, by implication, known about the world.  The principle states that complementary variables such as the position and momentum  of a particle  cannot be simultaneously discerned to any arbitrary degree of precision.  The principle is often illustrated with a standard thought experiment:  in trying to observe smaller and smaller objects, the wavelength of the light used to "illuminate" the object must use a smaller and smaller wavelength, i.e. photons with larger and larger energy.  This large energy then gives the particle to be sighted some momentum change that makes it impossible to determine the particle's momentum.  This explanation, referred to as the Gamma-Ray Microscope thought-experiment,  is widely used at many educational levels. See the Discovery Education site for Grades 9-12, for example.   A more interesting use of the  illumination example can be found at the Fly in the Honey blog ,  posted by Mary (that's all the info I can determine about the author other than I believe that she is a teacher), where she claims to be very poor in math and science, yet is incredibly moved by the standard conclusion of the Uncertainty Principle: "the very act of observation changes the object being observed." 

The Gamma-Ray Microscope thought-experiment, a mythological story that began with Heisenberg himself, has been de-valued as a good example of the principle. It turns out that the world is much weirder than that pictured in the thought-experiment. (I will explain this in a future post.) Regardless, it does not diminish from the fundamental idea that observation affects the observed in fundamental ways that cannot be eliminated with more precise and careful instrumentation and methodology.

On one hand this is a very deep concept;  on the other it appears to be tautological, especially when both the experimenter and experimental subject are conscious agents.

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Copenhagen, Quantum Mechanics, and a Shot of Glen Livet

The tag line for this blog, indeed the overarching theme of the Chaos and Fractals course is the fuzzy three-legged monster of Modeling, Understanding, and Prediction. Fuzzy because the boundaries are never clear; they are themselves fractal-like. Suffice it to say that the non-linear dynamic modeling of most systems is used for both the understanding the models provide about why something happens the way that it does as well as the prediction of future states.

Which brings me to quantum mechanics - a field where models routinely predict experimental results with extraordinary accuracy, yet there is still debate on what it all means. Taking this to an extreme, if there is disagreement among physicists on the meaning of quantum mechanics (specifically, the meaning of the quantum mechanical wave function and the nature of observation) then there is a lack of understanding. Whether one considers this "good prediction, no understanding" scenario unsatisfying or not comes down to one's proclivity for philosophizing.

Actually, for me I developed a "proclivity for philosophizing" because of Quantum Mechanics.

I remember as a physics student being totally mystified at and angry with quantum mechanics. Sure I could do the mathematics, but I really had no clue as to what a stationary state was, or what it meant for a wavefunction to collapse. Even after getting very good grades in both semesters of quantum, I really couldn't articulate the connection between the mathematics and reality in a reasonable way, or at least not in the tangible way that I could describe the (apparent) reality of Newtonian physics.

Click to enlarge the Quantum CatGrad school and a post-doc in solid state physics finally did bring some aha! quantum moments; I could finally talk-the-talk of quantum mechanics interpretation as well as theory. Like most students, I was taught the Copenhagen Interpretation of Quantum Mechanics as promulgated by Bohr and Heisenberg in the 1920's. I adopted it whole heartedly, and soon Schrödinger Cats and Wave-Particle Duality were common topics of late-night sessions, often fueled by single-malt ...

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Stanislaw Lem: The Passing of a Deep Spirit

Stanislaw Lem, the great Polish "science fiction" writer died on March 27, 2006, at the age of 85. Two of Lem's works have played a role in the Chaos and Fractals course, and I describe the connection below. First, though, must be a tribute to this extraordinary writer.

Even though I know many who read, or have read a great deal of science fiction, I know very few who have read any of Lem's works. This is very odd, given that Lems' works have been translated into over 40 languages, with an estimated 27 million sold. (Some do read and prosper: Will Wright, the creator of the wildly popular SimCity simultaion game credits Lem's The Cyberiad as inspiration. )

With sci-fi readers (in the U.S., at least) not paying attention, what hope is there for more readership of this essential 20th-century author who is usually listed as I wrote above - a science -fiction writer, only without the quotes.

It has always been unfortunate that Lem's works are described as science fiction. This is itself a fiction. Lem - a brilliant scientist, writer, and thinker - told wonderful tales with an unnerving mixture of darkness, humor, philosophy, and theology that just happened to be placed deep in space, or inside a computer. While the location and time period of his stories are essential to their plots, Lem's stories are often more relevant to our current time and place because of his ability to paint rich characters in situations that are paradoxically both imaginable and impossibly strange.

Lem's life as a scientist and writer growing up in Poland, through Nazi occupation and Soviet rule, is much of the reason for his chosen genre, as described in the Times of London obituary -

He began to write fiction, his first works being in the tradition of socialist realism acceptable to the authorities. But he graduated to literary "fantasies", which he succeeded in hoodwinking the humourless and dogma-bound authorities into believing were innocuous, though they were in fact highly subversive and satirical.

I first read Lem in 1983, when my best friend, Eric Törnqvist, gave me a copy of Solaris as a birthday gift and demanded that I read it. To this day it remains not just the greatest "science fiction" that I have ever read, but one of the best books I have ever read. It is a book in which there is no action of the type usually associated with a sci-fi stories. Instead, Solaris chronicles centuries of observation of a liquid planet and its seemingly non-descript moons, a planet that may be sentient, and may be malicious. With this simple idea , an idea that seems to present little opportunity for

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Uncertainty, Impossibility, and Reality: Heisenberg, Gödel, Einstein

Click for the Heisenberg CafeThe underlying structure of the Chaos and Fractals course is the understanding-prediction continuum. Starting with the Chaos Game and proceeding through all of the readings and Classroom Chaos exercises, the elusiveness of true understanding of non-linear dynamical systems and the need to "settle" for mere prediction is common and unsettling.

One can only wonder, then, about the possibility of true understanding of anything more complex than linear processes. Maybe this inability to understand is a symptom of a world that is fundamentally unknowable.

Now I should know better than to leave the understanding-prediction axis and question the fundamental nature of reality. Jumping into the philosopher's sandbox is often a prescription that leads one to lose sight of the day-to-day business of actually doing science or mathematics. So let me turn to those who really could live in that sandbox, mix it up with the philosophers, and jump out again to do their science and mathematics.

The defining work of 20th Century science and mathematics may just be the development of theories that posit fundamental limits to what we can do, what we can measure, and what we can know. Einstein's relativity rests on the postulate that the speed of light is constant in all reference frames; a result that leads to limits on the velocity of particles with mass, and destroys the notion of absolute time and simultaneity. Heisenberg's Uncertainty Principle puts an inviolable restriction on what we can measure and therefore know about a physical system. Gödel's Incompleteness Theorem denies us the possibility of knowing or proving all mathematical truths.

Do these limits tell us something about the world, or just about our ability to understand the world? Einstein, Heisenberg, and Gödel were very clear on this question: they believed that they were discovering the true nature of the world.

This point is espoused by philosopher Palle Yourgrau in his book "A World Without Time: The Forgotten Legacy of Gödel and Einstein":

Einstein, Gödel, Heisenberg: three men whose fundamental scientific results opened up new horizons, paradoxically, by setting limits to thought or reality. Together they embodied the zeitgeist, the spirit of the age. Mysteriously, each had reached an ontological conclusion about reality through the employment of an epistemic principle concerning knowledge. The dance or dialectic of knowledge and reality -- of limit and limitlessness -- would become a dominant theme of the 20th century.

Ok. Back out of the sandbox and back to work. If the world is unknowable, I don't want to know it. In fact I don't want to think about it - it's time to get back to modeling and prediction. And if I don't really understand what's going on in my dynamical system, or why my predictions work, who is going to know it?

(Heisenberg cartoon by Mark Stivers)

Pondering Life...A Reaction to Non Serviam

Originally Posted by Meridyth Mascio

In the personal struggle to determine whether my mind has been created to think mathematically, I have started to look at my general feelings of disdain for computers. In actuality, I realize their usefulness, but I struggle with my one-on-one daily encounters with them. It has always bothered me that if a program stopped running or an error occurred, then I could not obtain a direct response to my questioning what had caused the error. I think that I now see that I find it unnatural to communicate with this entity as it does not possess consciousness (a term described frequently in Non Serviam).

A computer does not perceive the contradictions that qualify humanity. Logic is not the only component of a person; beings are diverse. As mathematics underlies the structure of the world, the "chaotic" element are the perspectives of human beings. We see things as we perceive them, and so the world is defined intrinsically to each individual as such. However, are these decisions and perspectives "programmed" into us? If so, can is it possible for us to ever replicate this program?

So many other questions remain in my mind from this reading: Why have we been "created"? What is the general purpose of humanity? What is my individual purpose? Are humans guided by some unknowing force? How do religious beliefs factor into our existence?

I had never before considered the idea of an "intermediate" God, where the one who has directly created us has been created by yet another "higher" power. Is this chain infinite? Can a process then ever be broken down to one?...

These questions plague my mind. I feel as though humans are trapped in the midst of incomprehensible infinities, never able to grasp the full extent of everything in the universe and yet not ever quite able to break down one situation, one entity completely (some sort of fractal nature).

What I do realize is that the scope of the world is beyond me; more specifically, I think that the reality of one's individuality is beyond any limited human perspective.

God

Originally Posted by Matt Venanzi

It never ceases to amaze me, even before "Chaos & Fractals," how random, yet logical, strange, yet sensible, intricate, yet explicable the world is. Could God just be watching us discover every little intricacy he has made about the world, like a proud parent, or an accomplished inventor, marveling at their "creation"? What, then, is still left to be discovered? And I mean that, not in that we have discovered it all, but in that we have barely touched the tip of the iceberg!

Is it laughable, then, that we think we are so far "advanced"?

But how could God, Him Herself, have done all of this?
It just seems like too much! Then again, is it all relative?
Do we have the capacity to fathom all that there is?
Is that "capacity" expanding ~ with each generation"? "Evolutionarily"?
Do some have more "capacity" than others?

This all seems so esoteric, yet comprehensible-----
I guess its just another one of those woes of God...
I'll keep trying...

On Non Serviam and Personoids

Originally Posted by Sean Houlihan

The concept of "personoids" from Non Servium is really interesting. What does this mean about God, life, etc? Could we be living in a fractal-like, self-similar world? Could our decisions be governed by mathematics?

In essence I hope nope. The reality portrayed in this work is a little scary. I would hope certain aspects of the fractal nature of personoids is not present in reality.

Intro to FractaLog

Trying to pin down Chaos and Fractals is a lot like pushing a very full drawer closed only to have a different drawer pop open. The concepts are groundbreaking and mysterious. Just when you think you understand them and, by applying them, a bit more of the workings of the world, you are reminded that your level of understanding may be much more tenuous. Instead, you find yourself predicting only, without any understanding deeper than a surface level. Or perhaps you are postdicting, and you only have a quasi-understanding after the fact.

It's my hope that this FractaLog serves as a place of comments, questions, and provocative speculations based on our readings in our Chaos and Fractals course. May the dialogue lead to a deeper appreciation of how we model, predict, and understand our corner of the universe.

And just maybe we can keep some of those drawers closed a little longer. But don't be surprised if we find many more drawers nested within drawers within drawers ...