I read an interesting essay this morning about recursive algorithms and how the algorithms are structured ( The age of spiritual machines by Ray Kurzweil). I wish I would have read this before reading Katherine Hayles How We Became Post Human. She describes reflexive thought and reflexivity in a manner that was wholeheartedly confusing. First she compares mathematical models as well as a Freudian approach to reflexivity, all of this condensed into one chapter. At first I was taken a back by the complexity of her work. I drew flow charts of her sentences and paragraphs to better understand the logic that she was creating. The vocabulary and background to begin her book was extraordinary, nonetheless it was a fascinating book to read. But reading again 5 years after its first publication The Age of Spiritual Machines, gave me a deeper understanding of Hayles work in Posthuman. First Kurzwiel writes in a simple and easy to access manner. Laying out the complex theory that evolved from Plato to our current theory of computer science, taking a look at the far reaching implications of technology throughout history. Sounds like a daunting task to even read, it is easy to approach and actually fun to read. Kurzweil attempts to simplify the most complex ideas of theoretical computer science into simplified models that we can all understand. Here is a simple model that he creates for the recursive algorithm. This is the context of designing a program for chess.
For my next step, take my best next step. If IÂm done, IÂm done.
This is defined as a task to finish a process however chess is a game played one move at a time. The next step applies the same recursive formula but rephrases to pick Âgood movesÂ
PICK MY BEST MOVE: pick my best move, assuming my opponent will do the same. If IÂve won, IÂm done.
At this point he Kurzweil defines the nature of Recursion A recursive rule is one that is defined in terms of itself. A recursive rule is circular, but to be useful he says that we do not want to go around in circles forever (in the organic/molecular world this behaviour is called Neurotic). We need an escape hatch. To illustrate this he uses the example of a simple factorial function. To compute n, we multiply by factor of (n-1) We have defined this in terms of itself. We need to specify that factorial of 1=1. thatÂs our escape hatch.
Using another example he computes a factorial of 2, according to the same definition,
Factorial of 2=2 times ( factorial of 1)
We know know directly what ( factorial of 1) there's theres our escape from infinite recursion. Plugging in (factorial of 1)=1 , we can now write
Factorial of 2=2 times 1=2.
This is a factor that ends the process otherwise the machine would have no way of knowing when it had completed its task of playing a chess game.
Please follow this link to see how an algorithm like the one described above might look like in a visual model. CHESS MATCH
the computer plots every possible move for you and the computer everytime that you make a move.. try it out.
In regards to the recursive algorithms I have to say that I think human behaviour gets stuck in theses recursive though patterns. But unlike machine theory and information theory design which is modeled after electronic models, our thoughts are not generally modeled in such a way that is constructive.. Humans sometimes forget to create an escape hatch for thought, as a result discursive thought patterns can arise also known as neurosis. lets take for example someone who falls in love with someone else, after falling the person has fallen in love the other person at some point in decides that being in love and having the affections of the other persons are no longer desirable. The person who has not fallen out of love with the other person has not perpared themselves for this event. They as a response after the event of a conversation explaining the end of the emotion love for the other; begin a cycle of trying to solve a puzzle to somehow recreate the physical and emotional conditions of the previous emotional experience. often times this behaviour can turn from Neuropsychoticchcotic ( that is adiscussionccusion). The persons life falls into a state of disarray because the emotional loop that the person created to navigate through the world has been disrupted while still within that thought. It is as if a machine is playing it's self in a game of chess that constantly ends in a call, no wins ever. This is the nature of human neurotic thought. I think sometImes ( i am laughing at the sometimes part) get into theses loops, I will get upset and cannot get out of the loop about selse'se elses behaviour while driving, or something someone has said. This is because I have crereflexivelexsive loop for how I think reality should exists,when something contary to this occurs it is meet with my mind trying to solve it and understand it within the realm of reflexivelexsive loop. My subjective nature has given ablatedbiltity to create unique perspective but at the cost of being trapped within the mind in the midst of an objective world. Reality is in a sense then perhaps a combination of both the subjective and the objective unraveling to my fragile pitiful one moment at a time, soon in perhaps 20 years I will amassed enought experience to know that the words that I am writing now are only the beginning of a recursive algorithm of my creation to a deeper understanding of how I might perhaps fold my towels in a manner that optimizes shelf spaceffectivelyctivlpresentpersenI time i do not fold towels and my wife does not fold them either)