Thursday, October 15, 2009

What do a Chinese room and a cat have in common

They are both indeterminate! As much as you can’t tell if the computer or person in the other room knows Chinese, or if the cat is alive or dead or both, as one is blurred into the other, however, you can find a solution by direct observation (if you know what goes behind closed doors). 




The image on the left is taken from http://www.macrovu.com/CCTMap4ChineseRm.html. The picture is Searle's argument against the hubris of the Strong AI project that conflates the ability to perform a particular analytical task with understanding.








Picture on the right is from http://n2.nabble.com/Schrodinger-s-Dusty-td2118011.html







 The paradox of the cat is a small paragraph from the English translation of Erwin Schrodinger's paper, The Present Situation in Quantum Mechanics.
"That it is in fact not impossible to express the degree and kind of blurring of all variables in one  perfectly clear concept follows at once from the fact that Q.M. as a matter of fact has and uses such an instrument, the so-called wave function or psi-function, also called system vector. Much more is to be said about it further on. That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message. At all events it is an imagined entity that images the blurring of all variables at every moment just as clearly and faithfully as does the classical model its sharp numerical values. Its equation of motion too, the law of its time variation, so long as the system is left undisturbed, lags not one iota, in clarity and determinacy, behind the equations of motion of the classical model. So the latter could be straight-forwardly replaced by the psi-function, so long as the blurring is confined to atomic scale, not open to direct control. In fact the function has provided quite intuitive and convenient ideas, for instance the "cloud of negative electricity" around the nucleus, etc. But serious misgivings arise if one notices that the uncertainty affects macroscopically tangible and visible things, for which the term "blurring" seems simply wrong. The state of a radioactive nucleus is presumably blurred in such a degree and fashion that neither the instant of decay nor the direction, in which the emitted alpha-particle leaves the nucleus, is well-established. Inside the nucleus, blurring doesn't bother us. The emerging particle is described, if one wants to expain intuitively, as a spherical wave that continuously emanates in all directions and that impinges continuously on a surrounding luminescent screen over its full expanse. The screen however does not show a more or less constant uniform glow, but rather lights up at one instant at one spot - or, to honor the truth, it lights up now here, now there, for it is impossible to do the experiment with only a single radioactive atom. If in place of the luminescent screen one uses a spatially extended detector, perhaps a gas that is ionised by the alpha-particles, one finds the ion pairs arranged along rectilinear columns,[5] that project backwards on to the bit of radioactive matter from which the alpha-radiation comes (C.T.R. Wilson's cloud chamber tracks, made visible by drops of moisture condensed on the ions).

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.


 It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks."(Excerpted from http://www.tu-harburg.de/rzt/rzt/it/QM/cat.html#sect5)

I thought I'll just leave a thought discovered in the course of my presentation yesterday. Too brain-dead to analyze now. More later.


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