wittgenstein wrote:
Actually, Schrodinger's cat is a thought experiment. It is a way of showing how the paradox at the quantum level ( A does not =A) would manifest itself at our macro level unless we create a new logic where
http://en.wikipedia.org/wiki/Principle_of_explosion is avoided by simply creating a new logic. Physicists recognize that A does not always = A at the quantum level. Because of
http://plato.stanford.edu/entries/logic-paraconsistent/ ( the new logic that was invented) we supposedly do not have to worry about
http://www.exfalsoquodlibet.com/.
However, even if we accept paraconsistent logic that still does not rid us of the paradox ( A does not =A) at the quantum level. True, we do not have to worry about it being proven that the queen of England eats gerbils. However, a square circle ( metaphor for something self contradictory) that exists at any level of magnification still astounds me!
Yes, I was trying to explain that in another thread, but it does have interesting application as a model for other things.
A square circle is not necessarily self-contradictory if we're thinking about the difference between an actual, true circle versus a
representation of it. A digital representation of a circle, for instance, would visually show it pixilated, basically "rounded off" or "quantized" in square or rectangular patterns. Obviously, the greater distance you are from the graphic and the more pixels used, the more accurately the circle appears as compared to a true circle. The closer you get to the edge of the circle, the more you realize how jagged the edge is due to quantization error. Reduce the bits used to represent the circle and you end up with a square.
I own a Synclavier, which is an advanced computer synthesizer built back in the 1980s. The designers of the FM synth cards didn't really know what they were doing, so the synth ended up with some interesting eccentric behavior compared with other digital synths. The FM synth is only 8-bit. If you reduce a sine wave to near-0 volume level, the synth voice card renders the result normalized so that no matter what level you tell that one sine operator to sound, it will stay at full volume--to get actual variation in volume, there is a separate amp EG on the output of each voice such that there is no bit loss in the output of the signal. That doesn't mean, however, you can't stop it from degrading the signal if you WANT that. Since it's only 8-bit based on the available technology at the time, it's possible for a user to reduce the sine operator level, thus increasing the amount of quantization error from a musically acceptable sine wave to something resembling an analog pulse wave. The voice cards are unaware that anything less than a sine is hitting the output, but in reality all you're getting is some variation on a pulse wave. A square circle.
07 Dec 2013, 12:00 am
