Friday, May 27, 2011

The Boundary Between

A continuous system is one where no matter how small a section you exam, there is an infinite amount of further depth. A discrete one is where there are indivisible atomic pieces, which can be broken down no farther.

Initially, as a by-product of how we naturally view the world, our perceptions were likely that the things around us were continuous. The Ancient Greeks were one of the earliest to propose that everything was composed of an underlying discrete set of atoms. That view seemed to prevail, more or less until the Industrial Revolution launched us on a deeper perspective implicitly showing us that the world was continuous once again. But the rise of our computer technology has been gradually reversing our perceptions back towards the discrete. We’ve been flip-flopping between these two alternate perspectives as our knowledge of the world around us changes, and grows.

The change in perspective is not what I find most interesting. It’s the behavior of the boundaries between these conflicting views when they are layered that is most fascinating. That is, moving from a continuous system to an underlying discrete one or vice versa.

A great number of interesting details about the human body can be learned from Bill Bryson’s “A Short History of Nearly Everything”, a book I highly recommend because it is both entertaining and also enlightening. By now we accept that humans are a large collection of millions (billions?) of co-operating cells. Bryson also points out that we are also composed of a nearly equal number of bacteria, and other symbiotic living organisms (which we need to function). He also addresses that from a matter perspective, we’re basically replacing ourselves continuously. New matter comes in, old matter goes out. New cells grow, old ones die. I think he speculates that we are completely re-composed of new matter approx. every seven years. If you’re interested, you can get the full details from his book.

With that in mind, from a perspective purely based on particles, we can view ourselves as a big collection -- a cloud -- of related matter. For a given human being -- we’ll pick a male and call him Bob -- as he interacts with the world on a daily basis, he is leaving behind some of this cloud. That is, Bob’s discarded skin cells add to the dust in the room, his bacteria and fingerprints get left on everything he touches, and his moisture evaporates into the area around him. If Bryson’s speculation about seven years is correct, then over that period half of the particles that have made up Bob have been dissipated to wherever Bob has been. From a cloud of particles perspective, ‘Bob’ is the densest part, but the whole cloud covers a much wider area based on his travels.

If we could build a machine to detect ‘Bob’ particles over a period of time, then some really interesting things occur. For instance, on any average week, Bob would go back and forth between his house and work. The cloud would include both locations, but also to a much sparser degree, the pathways in between. Setting the machine for a granularity of 7 days, would show that Bob was both at home and he was at work. Depending the mechanics of the detector, the bulk of Bob might appear in either location. From this viewpoint, we might conclude that Bob was in both states simultaneously, and that when actuated he would appear randomly in one or the other. We could compile a set of Bob particle-cloud states, that he might be simultaneously inhibiting: work, home, traveling, cottage, etc.

One can easily suspect that Bob would easily disagree with this world view. He is, after all, either at work or he is at home. He knows where he is. Although he is a discrete entity, he likely sees himself as continuous. The detector however takes a discrete measurement over a continuous time period, which at 7 days is not in line with Bob’s continuous view of his discrete underpinning. Bob does not see himself as a cloud, and certainly not as a cloud over a long period of time.

If we set the detector’s time frame to 1ms, then the resulting Bob cloud would be roughly what we see and think of as ‘Bob’. Shortening it some more would produce gradually more refined Bob versions, until we get down to some discrete time-block where our perception of Bob matches the detectors. In this case, the detector’s information would align with Bob’s understanding of himself and his world. There would be no randomness with regard to Bob’s state.

What this comes down to is that as we are flipping back and forth between continuous and discrete perspectives, if our discrete boundaries are not perfectly aligned (even though they are not adjacent), then an element of randomness appears to creep into the mechanics. Since our continuous/discrete perceptions of the world around us are not explicit (we use both of them without being aware of it), we are not always aware of the affects this bias in the way we model the world. Thus one might conclude that the randomness isn’t actually there, but that it is just an artifact of the boundary.