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## Re: [ontolog-forum] Axiomatic ontology

 To: "[ontolog-forum]" "John F. Sowa" Sat, 09 Feb 2008 17:16:07 -0500 <47AE2627.9080805@xxxxxxxxxxx>
 ```Rob,    (01) Pat was using the word "random" in a precise technical sense. But like any technical term, it can also be used in an open-ended variety of metaphorical senses of varying degrees of usefulness.    (02) > At the very least we need to think about it more and should > not simply dismiss information sources (like the Web) because > their elements are related randomly (=unpredictably.)    (03) The info on the web is definitely *not* random, and there are very important kinds of patterns that can be found it in. The patterns that have been found so far are an insignificant fraction of the extremely important patterns that are out there.    (04) > It would be interesting to know if it is possible to compress > a hologram without losing resolution. If the analogy of > randomness holds, then it should not be possible.    (05) A hologram is definitely *not* random. A hologram is a representation in frequency space of an image in a 2-D or 3-D Euclidean space. If you recall from an old math course, a sound wave can be represented as a time-varying function f(t). The Fourier transform of f(t) is another function F(w), where w (actually a lower-case omega) represents frequency.    (06) Far from being unpredictable, such transformations are very widely used for *detecting* many kinds of patterns that are easier to find in the transformed frequency coordinates.    (07) One example is a pure tone of a fixed frequency w1. For that tone, f(t) is very simple:    (08) f(t) = A sin(w1 t)    (09) which is a sine wave of amplitude A. The Fourier transform of that f(t) is even simpler:    (010) F(w) is a constant C for w=w1 and 0 for all other values of w.    (011) This pattern can be compressed to just two numbers, w1 and C, which can detect and predict the original pattern with superb accuracy.    (012) There are the usual caveats about floating-point arithmetic, but the usual precision on a digital computer is more than adequate to store and reproduce sound and spatial information with a precision that is far beyond what the human eyes and ears can detect.    (013) In short, holograms (and related kinds of transforms, such as wavelet transforms) are far from random, and they can be very useful for both detecting patterns and reproducing them.    (014) John    (015) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (016) ```
 Current Thread Re: [ontolog-forum] Axiomatic ontology, (continued) Re: [ontolog-forum] Axiomatic ontology, Barker, Sean (UK) Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Schiffel, Jeffrey A Re: [ontolog-forum] Axiomatic ontology, Sharma, Ravi Re: [ontolog-forum] Axiomatic ontology, Schiffel, Jeffrey A Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Bill Andersen Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Message not availableRe: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, John F. Sowa <= Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] language ambiguity (was: Axiomatic ontology), Jakub Kotowski Re: [ontolog-forum] language ambiguity, John F. Sowa Re: [ontolog-forum] language ambiguity, Schiffel, Jeffrey A Re: [ontolog-forum] language ambiguity, John F. Sowa Re: [ontolog-forum] language ambiguity, Sharma, Ravi