|
|
25 Apr 2008 @ 11:32, by anandavala. Systems Thinking
Before joining the conversation, please read and accept this Invitation to a Conversation.
Here's a posting to let you know what
I'm up to lately. Like I said in the post on What
exactly is SMN and how does it connect with other technologies?
I've been focussing on concrete implementations lately, rather than
on discussions. One project was an artistic collaboration with
Glistening Deepwater, called Mystic
Visions. I've explored quite deeply into semantic and web 2.0
technologies. I've implemented the core algorithm for SMN in Java and
the system simulation engine now has full functionality and the
models can be imported or exported as XML files (this is still in
further development but will be available for download soon).
But the current project on my mind is
the idea of a System Oriented Modelling Paradigm. To give you
some idea of what I mean, below are some excerpts from recent design
documents – they are just a brainstorm at present. If these ideas
make sense to you and you want to get involved then contact
me – it will soon be released as an open source project.
The
project involves an analysis of general computational processes and
general systems, which re-orients system modelling practices upon a
coherent metaphysical foundation rather than on a
commonsense naïve realist foundation. Traditional modelling
practices are seen in a new light and minor optimisations are
proposed that can considerably extend the potential and overall
functionality of designed systems. A detailed example is given in the
context of software engineering.
More >
|
|
|
|
23 Apr 2008 @ 09:25, by johnjoseph. Systems Thinking
Pascal’s Triangle, Self-Similarity and Phi
In maths the simple operation of adding two consecutive elements in a sequence and then iterating, which process is well-known to us in the Fibonacci sequence, leads to many of the more remarkable properties we come across in nature and mathematics. The Fibonacci sequence, as I pointed out in my last article, is based on self-similarity and exhibits the mystical number and proportion called the “Sacred Ratio”, approximately 1.618… which is an irrational number.
Now something very similar occurs in that very famous table of numbers, known to the ancient Chinese, but known to us as Pascal’s Triangle. This is a symmetrical table, with ones at the apex and at each edge, with the intervening numbers created by adding together the two numbers directly above and to either side. Pascal’s triangle has a multitude, maybe indeed an infinite number of remarkable properties. Every interesting thing in mathematics more or less, can be found in different ways in this pyramid. Fibonacci itself, can be found in sequence if you add the short diagonals. This of course yields Phi, the Golden Proportion. However, this is a bit misleading, because Phi is conspicuously absent from the other patterns you will find in this triangle. This is because if you divide any two of the numbers in the table they will be a rational fraction, not irrational. Adding different numbers together, as in the Fibonacci example, is the only way to get a sequence which gives Phi. The whole structure is based on the iterative technique mentioned above, and I suspect that this technique is a cornerstone of self-similarity, though I can’t demonstrate it as convincingly here as I did in my previous article on Fibonacci.
I believe, since Nature produces Phi all over the place, and Fibonacci sequences in the number of petals of flowers and the spirals of shells, that at an early stage in the evolution of life, in plant RNA and animal DNA, the simple iterative technique I refer to, was encoded and passed down to following generations. Thus we find Phi everywhere in Nature. Why it leads to very remarkable properties in mathematics is another issue and one I will address in a later article. More >
|
|
|
|
23 Apr 2008 @ 05:48, by deepwater. Spirituality
|
|
