Tuesday, December 27, 2011

Definition of Linearity

A system is said to be linear if it meets the following two criteria:

1. If input x to the system results in output X, then an input of 2x will produce output of 2X. In other words, the magnitude of the system output is proportional to the magnitude of the system input.

2. If input x produces output X, and input y produces output Y, then an input of x + y will produce an output of X + Y. In other words, the system handles two simultaneous inputs independently, and they do not interact within the system. Implicit in these criteria is the fact that a linear system will not produce any frequencies in the output that are not present in the input.

Note that there is nothing in these criteria that says the system output is the same as the system input, or even that it resembles the system input. For instance, the input could be an electric current, and the output could be a temperature. In the case of mechanical structures such as machines, we will consider the input to be a vibratory force and the output to be the measured vibration itself.

No clue who this man is or where I took it.

If you look at the 11 images here you will arrive at, perhaps two conclusions. One, is that most of the pictures are lousy (not up to the standards of this blog). Two, is that the pictures are here, pure random, and have nothing to do with each other except for that last scan of a little girl’s bedroom slipper.

Les Wiseman and Randall Carpenter

I think you would be right about one. Yes these pictures are lousy. But there is a reason (poor excuse, I might add). I took these pictures sometime in the mid 80s and I had just been given a very cheap opportunity to acquire a brand new Minolta CLE. The camera, a rangefinder camera using the Leica mount came with a 28mm, a 45mm and a 90mm lens. This camera was supposed to be ahead of its time as it boasted an off the film plane flash measurement and adjustment. In fact the flash system did not work very well. I was also quite used to focusing a single lens reflex camera and trying to match two images in the viewfinder as one (that’s how a rangefinder works) was not good in a dark environment. To make it all worse I had placed in the Minolta a roll of Kodak Technical Pan which at an ISO of 25 meant that I had to shoot almost wide open most of the time.




Maddalena


Having seen Orson Welles's A Touch of Evil just a few minutes before writing this I could weave a story of a drug bust in Piedras Negras by Licenciado Felipe Ferrer Junco the DA for the State of Coahuila who may have been my friend (he actually was and is my friend but he was the head of the Federal Police in Acapulco not a DA). The man with the bare back (once I lightened the scan revealed a De Havilland Beaver float plane. That could have been a story. But what would you make of the picture of Red Skelton showing off his bull? And then there is the picture of Les Wiseman with Randy Carpenter. And there is the picture of  Maddalena Di Gregorio with Kristine. For years Les Wiseman and I thought that Kristine was the most beautiful woman in Vancouver. She was our icy blonde who would coolly enter punk or English band concerts at the Commodore, swishing her way in like Catherine Deneuve in The Hunger. All Wiseman and I could do was to stare silently at the apparition. When I met her I thought she was not quite as perfect as I thought she had been. She seemed to have a lisp. But it was quite a few years later that I found out that her last name was indeed Thimsen.

Art Bergmann and Soli

There are two more photographs besides the one of my young daughter (was she 12 or 13?) Hilary with those sheep slippers (precursors of Uggs?). One of the pictures is of Art Bergmann and Soleadad. We all called her Soli and some of us knew (I did) that Bergman was the love of her life. The other picture with the odd bare concrete landscape is one that I took in the train that took passengers from one terminal to another in the Dallas airport.




Maddalena di Gregorio & Kristine Thimsen


What is the link to all these pictures? I took them in one 36 exposure roll that I found filed under Di Gregorio, Maddalena. I believe that the Wiseman, Bergmann, Kristine and Maddalena pictures I took in a rock and roll boat cruise. At about that time I was taking pictures for a CBC drama series in Egmont to which I flew in a Beaver every weekend. The Dallas airport picture came from the fact that I went to Houston to visit my friend Stephen Burdick, a high school friend who lived in Houston. In Houston he took me to see some bulls as he informed me that Red Skelton would be present.

Last night Ale, my eldest daughter was helping us get rid of stuff. She showed me the sheep slippers and asked me about them. I said nothing. She put them in a recycling bag.  Just a while ago I retrieved them as I think they should be kept in the family. Thanks to a collapse of linearity they are back to our fold. Will Lauren wear them? I am sure she will.

Egmont, BC

Dallas Airport

Hilary Waterhouse-Hayward

Red  Skelton & his bull in Houston