Pythagorean,
I can't know any one thing.
No disturbance here!
There is an interesting discussion of the Pythagorean Theorem and Heisenberg's uncertainty principle in Bart Kosko's Fuzzy Logic.
Speaking of Heisenberg, one of my favorite quotes (and often cited on the Web) is "What we observe is not nature in itself but nature exposed to our method of questioning." It turns out that in the source, Physics and Philosophy (1958), this is actually not a complete sentence, but actually part of a much longer one. Which goes as follows:
"This again emphasizes a subjective element in the description of atomic events, since the measuring device has been constructed by the observer, and we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning." (fourth to last sentence in Chapter 3, Copenhagen Interpretation of Quantum Theory)
If one thinks of perceiving as a method of questioning, or vice versa, the following quote from Kant is also of interest:
"... all our intuition is nothing but the representation of phenomena; that the things which we intuit, are not in themselves the same as our representations of them in intuition, nor are their relations in themselves so constituted as they appear to us; and that if we take away the subject, or even only the subjective constitution of our senses in general, then not only the nature and relations of objects in space and time, but even space and time themselves disappear; and that these, as phenomena, cannot exist in themselves, but only in us. What may be the nature of objects considered as things in themselves and without reference to the receptivity of our sensibility is quite unknown to us. We know nothing more than our mode of perceiving them, which is peculiar to us, and which, though not of necessity pertaining to every animated being, is so to the whole human race." (Kant, Critique of Pure Reason, SS 9, section I)
Here's a less wordy version of the quote:
"... if we take away the subject, or even only the subjective constitution of our senses in general, then not only the nature and relations of objects in space and time, but even space and time themselves disappear.... What may be the nature of objects considered as things in themselves ... is quite unknown to us. We know nothing more than our mode of perceiving them...."
I first saw this quote (attributed to Kant but unreferenced) in Maurice Nicoll's Living Time.
Heisenberg gives a sympathetic account of Kant's position in Chapter 4 of Physics and Philosophy, but disagrees with it. Regarding the idea expressed in the previous quote:
"The "thing-in-itself" is for the atomic physicist, if he uses this concept at all, finally a mathematical structure; but this structure is-- contrary to Kant--indirectly deduced from experience.
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