Wolfram and the Origins of Randomness
Monday, November 21, 2005 
Stephen Wolfram's short article The Origins of Randomness in Physical Systems is like a black hole, or at the very least a neutron star. Incredibly short for the ideas elaborated - only 4 pages - the manuscript is incredibly dense. Each line is a distillation of entire courses of study.
How is this possible? The endnotes: there are 28, and many of them are full paragraphs of further information, and contain their own set of references.
How did you react when reading this paper? Did you recognize any of the ideas/statements as any that we have covered this semester? Or perhaps ideas you are familiar with from past study?
And what is your personal belief of randomness in physical systems? Does randomness arise from the interaction between your system and the outside world, or does randomness arise from deterministic processes within the system? If you answer that randomness comes from outside the system, how do you explain randomness if the system is the universe?
And, if the system is the universe, does this mean that all random processes are deterministic?
Are there no random processes?
(Image drawn using the EdgeOfChaosCA Java applet.)
Reader Comments (6)
My personal belief is that chaos is deterministic and in a sense orderly. Randomness arises from deterministic processes within the system, the system being the universe. As a result of the butterfly effect (sensitivity to initial conditions), there is randomness in physical systems even though the systems are deterministic (deterministic meaning that they have no random parameters). Examples of deterministic systems are population growth, economies, and solar system.
All random processes are in a sense deterministic in that they all have some sort of pattern to them. Take for instance fractals including Kotch curve and Mandelbrot set. One can keep zooming into them and still see the same pattern.
There are random processes. A process can still be random yet have some sort of pattern/order to it.
In this respect, I am reminded of D'Arcy Thompson's contrasting of the final and physical causes of evolution. The final cause is the "goal" that nature has, so to speak - this is hidden from us, more so than the physical cause of evolution (mutation in DNA). If we knew why nature favored one mutation over another, or favored mutation over the lack thereof, we would not for one second call it random.
To answer where the randomness comes from, then, I would say that the randomness we see in the universe comes from our minds. If the universe is deterministic but our thoughts are random (non-deterministic), that would seem to conflate the two... or perhaps our thoughts seem random simply because we don't know their source - we can't wrap our heads around them....
(I apologize if this reads like a rambling - the lucidity doesn't turn on till three in the morning.)
Also, the idea of randomness coming from within the system or from outside the system reminded me of the world-view discussions presented earlier in class this year.
For example, a bear's fur in the arctic is white. Is this because the outside world forced the bear to evolve to a white furred species? Remember, DNA structure for all bear's is quite similar, so how did this mutation of sorts come about. It had to be forced upon the bear. This would be a top-down view.
One could also view the change as originating on a molecular/cellular level first. This change would then be viewed as a bottom-up aspect.
My question is, how can we be sure only one of these views (randomness from within or randomness from beyond) is the right one. Could it not vary from case to case. If not, I would not know which to say.
I would probably side with the randomness from outside the system view. Yes, there are limits, however, I am falling back on the I believe in God theory. In essence everything is deterministic to a point. There are different ways of getting to a point, however, there are different routes to the destination.
This comment leads me to believe that randomness arises from within the system. Also, if the universe is he system, what external forces could be acting on it? Unless the belief of a higher power meddling with the universe, I do not know of any other possilble solution.
I feel that all random processes are deterministic because, as tom points out in his example, that there is usually a "final goal" or point to actions in the universe. There are many times when people think that something random occurs when it can later be explained.
Since taking this class, my definition of random has changed to represent more of something that has no immediate pattern or understood meaning. So I would say that random processes are just processes that have yet to be understood.
The concept of "effective randomness" better defines this aspect of limitation.
In the article, Wolfram utilizes the example of cryptography. Having studied cryptography and its historical origins for my Honors Project, I have seen how humans attempt to camouflage languauge in order to create an illusion of randomness. As years progressed and different ciphers were being "cracked," systems became more complicated, i.e. a greater number of factors were introduced.
Currently, internet security is based upon human inability to find an algorithm for the factorization of numbers which are products of two large prime numbers. This process exemplifies that working backward creates a new level of difficulty. However, the solution, although hard to find, does exist as the " effective randomness" which spun the creation of this chaos has been calculated mathematically.
For every cryptographer, there is a cryptanaylst attempting to "solve" the system and find meaning in a seemingly chaotic, incoherent "universe." Simply because one cannot find a solution, i.e. a meaningful ordering, does not imply that one does not exist. Thus, I feel that it is naive to conclude that the universe is not deterministic.
In my opinion the creation of randomness comes from the border of the system and that which is outside. Randomness is created along the edge of order and complete chaos. This does not work with the idea of the universe as being the system through which randomness works, but it should also be pointed out that there are smaller systems within the universe where randomness can be found. I also believe that we consider things to be random because we have not yet been able to understand them. This class has shown me that there is structure behind many things that were thought to be purely random, which leads me to believe that other randomness has a structure that we just have not been able to unconver thus far.