A Universal Principle in Routers

Several years ago, after I got my first router, I posted this on my Geocities page. Geocities is closing in October 2009, so I pulled it off and posted it here.

mosthubsI’m still struck by the profound notion of a universal principle, which I have to say was discovered by application of another universal principle, which again, relates to a not-so-universal principle. With me so far? I think this would be best illustrated through the use of an anecdote – so humor me for a moment and try to pay attention.

One day I was starring at my computer-network’s hardware, specifically the cable-modem and router. Then I was struck by the thought of what I remembered about the router: it can be ‘daisy-chained’ together with more routers – within a limit – to produce a massive network. I think logically in stream-of-consciousness thinking so what was my next logical thought. Of course, how many routers in a limit – or what is the limit. Well that was easy, 255. It said it in the manual. But, this wouldn’t be a story if it ended there. I wondered ‘how’ to get to 255 and what is the significance of one path over another. Is one path more efficient than another? Check out my chicken scratch below for two possible daisy-chains.

leasthubsMy conclusion was that the chain with more routers should be less efficient, but what proof could I offer to justify this conclusion? Another mystery had arisen. A mystery which lead to this paper. My proof comes from the first universal principle: action = reaction (to paraphrase). Then I started thinking about this principle, and why I thought it was the answer. What I concluded (about my method of conclusion on the universal principle) is the not-so-universal principle: it seems reasonable because I cannot think of another explanation nor a contradiction. All I came up with were euphemisms or the same universal principle. A eureka moment. I realized that I had stumbled upon a universal principle. So am I wrong or do these phrases echo the same thought: equal and opposite reaction, yin and yang, give and take, do unto others as you would have them do unto you!

So, I can justify my conclusion by saying that more routers means more signals passing through the same ending wires (per second) means more collisions means less efficient; more take equals less give.

Web Site Navigation Schema Proof

As a proof of concept I came up with a outline which led to a picture of a navigation schema. The idea is to link children through tags to their parents and to other families. I think it is better to start with grandchildren and work your way backward in lineage. Also, where families link, think of the intersection as one bond of two children. In the schema below, GrandChild-1 and GrandChild-2 are the same but separate.

Reference http://en.wikipedia.org/wiki/Matryoshka_doll.

Outline

  • Parent-1
    • Child-1
      • GrandChild-1
  • Parent-2
    • Child-2
      • GrandChild-2

Picture

In practice I wasn’t able to work out the nature of siblings and the relationship between families. Also, I think the picture is wrong: if GrandChild-1 and GrandChild-2 are the same then the small circle and the small square should be connected.

This post is unfinished….