Piero Scaruffi(Copyright © 2013 Piero Scaruffi | Legal restrictions )
These are excerpts and elaborations from my book "The Nature of Consciousness"
A Fuzzy Physics?
Unlike Probability theory, Fuzzy Logic represents the real world without any need to assume the existence of randomness. For example, relative frequency is a measure of how a set is a subset of another set.
Many of Physics' laws are not reversible because otherwise causality would be violated (after a transition of state probability turns into certainty and cannot be rebuilt working backwards). If they were expressed as "ambiguity", rather than probability, they would be reversible, as the ambiguity of an event remains the same before and after the event occurred.
Fuzziness is pervasive in nature (everything is a matter of degree), even if science does not admit fuzziness. Even Probability Theory still assumes that properties are crisp, while in nature they rarely are.
Furthermore, Heisenberg's “uncertainty principle” (the more a quantity is accurately determined, the less accurately a conjugate quantity can be determined) can be reduced to the” Cauchy-Schwarz inequality”, which is related to “Pythagoras’ theorem”, which is in turn related to the “subsethood theorem”, i.e. to Fuzzy Logic.
One is tempted to rewrite Quantum Mechanics using Fuzzy Theory instead of Probability Theory. After all, Quantum Mechanics, upon which our description of matter is built, uses probabilities mainly for historical reasons: Probability Theory was the only theory of uncertainty available at the time. The result is that Physics has a standard interpretation of the world that is based on population thinking: we cannot talk about a single particle, but only about sets of particles. We cannot know whether a particle will end up here or there, but only how many particles will end up here or there.
The interpretation of quantum phenomena would be slightly different if Quantum Mechanics were based on Fuzzy Logic: probabilities deal with populations, whereas Fuzzy Logic deals with individuals; probabilities entail uncertainty, whereas Fuzzy Logic entails ambiguity. In a fuzzy universe a particle's position would be known at all times, except that such a position would be ambiguous (a particle would be simultaneously "here" to some degree and "there" to some other degree). This might be viewed as more plausible, or at least more in line with our daily experience that in nature things are less clearly defined than they appear in a mathematical representation of them.
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