Talk:Dichotomy
The two domains article needs to focus on their generic nature - that they conceptually underpin all disciplines of knowledge and percevable comtexts, and identifying the two domains is key to structuring concepts within a given context. It's not the dichotomy of the small and the large, but of frequency vs time, momentum vs position, pattern vs instance, current vs voltage, change vs state, polar vs rectangular, wave vs particle - uncertainty, fourier analyasis, entropy are principles relating these two domains and so are applicable to all contexts that exhibit the two domains. --Nad 21:48, 29 Aug 2006 (NZST)
Section zero removed, needs massive clarification
The normal world, according to the way we learn maths at school, exists on a continuum of infinitesimally small to infinitely large. There are instantaneous and eternal concepts, but one doesn't hear much of them: this is because time inheres in the structure of what we all perceive to be the world of objects moving through time as a one-way arrow into the future.
In the Fourier domain that axis is radically shifted away from space to become one of time, where infinitesimally short moments become the ultimate of fine-grainedness in the perception of the frequency spectrum, and the infinitely long period being the biggest window, or, if you like, the standing wave of the universe (see Hubble constant).
Given that the Heisenberg Uncertainty Principle, or at the very least observer error, seems to defy all attempts to inquire into the nature of things, it is instructive to know where our observations must be incomplete. In the Fourier domain, our information is going to be limited both by an inability to fine-grain the frequencies enough (can't plot infinitesimals) or to observe over a sufficiently long wavelength (window problems). In the space-time world, these roughly equate to the problems respectively of quantum mechanics and cosmology.
Dealing with the continuous Fourier transform, though alien at first, does not pose any special problems that are not normally present. Continuous observation in spacetime requires a perception that does not reduce the content into the spacetime artifacts of things in time - continuous observation of the Fourier domain requires that we do not grade frequencies.
While it is customary to note that the trick of continuous perception is easier said than done, in either case it is not so - it absolutely cannot be said (by its very nature) and hence can only be done! It is instructive to note that each visual perception actually constitutes a reverse Fourier transform,
For a person, however we look at the world, we are constrained perception-wise by the sum total of knowable local information. The beauty is, of course, that our species has developed the capacity to generate information by description (incomplete though that must necessarily be) as well as the ability to theorise about such things.
