Nature has tuned us to think heavily in Cause and Effect. A chain, one thing proceeding to the next. Sometimes human choice dictates the direction of that chain, but human choice contains its own cause and effect cycle with choice and consequence. Only a few smart thinkers in history have seen beyond this, and only for a moment. Consider this quote from George Santayana, circa 1905-1906 in The Life of Reason. (Emphasis mine.)
Progress, far from consisting in change, depends on retentiveness. When change is absolute there remains no being to improve and no direction is set for possible improvement: and when experience is not retained, as among savages, infancy is perpetual. Those who cannot remember the past are condemned to repeat it.
A chain does not necessarily need (much) memory. If causes and effects are local, which we have reason to believe they are, it is sufficient to retain merely the present state's information. The causal chain forward and backward should be determined by the complete information of the current state, so we can always walk the chain if we need to remember something. Of course this takes lots of time, and hinders us from other things, like evading a Tiger about to eat us instead of walking the chain of causality backwards to remember what a Tiger is or why it's bad. Nature clearly would favor having memories of previous states.
Is reality a tree? Perhaps. Yet notice the section of the quote I bolded. Repetition.. A tree cannot have a branch connecting to a previous leaf up the tree, otherwise a loop is formed and a graph is created. Yet we notice as humans a sort of repetition to our lives, and to our history, where we seem to go in cycles between states.
Our graph theory is still, relatively speaking, quite limited. The big problem today is in Big Data Analysis, now that we've solved the problem of Big Data Management (storage, transfer, etc.). It requires a lot of insights into network topologies, yet it has implications for things like database joins and even AI.
But back to my musings. Not only are there strict repetitions, there are also feedback loops. Look at the news sometime, and you'll see that the thought-mode of Cause and Effect still reigns supreme in the public eye. People argue about the Causes of observed Effects, rarely stopping to consider that the Effect itself may be the Cause. Or at least part of it. (The idea of Effects having more than one Cause also escapes some people.) These feedback loops may be positive or negative.
The most potent example of a negative feedback loop I can think of is the "black community" in relationship with poverty and poor education. One might say "They're poor, they don't have access to good education, we should help them." Another might say "They're lazy, and they're genetically stupid. We shouldn't help them."
Alternatively, welfare support for their existence can make them lazy; breeding of stupid people will produce stupid children since smartness variation is very genetic. We should help them exist but not at the cost of their agency or dignity if you will. There should be breeding restrictions. (Any parent raising one or more children on $9/hr is irresponsible.)
People regardless of race who grow up in poor communities tend to be poor themselves, and in turn live in poor communities which in turn produce more poor people.
These feedback cycles can be represented in graphs. Not so easily by cause-effect chains (you can do it with causal graphs..) or trees. There is graph structure all around us. Networks are graphs, think about how many networks you know about or are involved in; your internal thought process just then can be represented as a graph. Even the government has some graph structure, though it's heavily biased to be tree-like since strict hierarchy is easier and more intuitive for us humans to think about, especially when it comes to authority.
Posted on 2011-10-21 by Jach