The following one-liner (beware of wrapping!) plots three dragons: plot 1j1 }.@:(] ^~ (2 ^~ 2&o.)@:(3.1415926535897931 % +:))@:>:@:((#. #:)"0 _) i.2^2 15 [ require 'plot'
I thought that some members of this forum might find it interesting. Does it mean anything? The part of the sentence, near the front, ( prob=. ] ^~ (2 ^~ (cos=. 2&o.)) @: ((PI=. o.1) % +:) f. ) ] ^~ (2 ^~ 2&o.)@:(3.1415926535897931 % +:) corresponds to the probability that a photon will emerge a 2-level system in a particular way as a function of the number of its components. Examples of 2- level systems include a series of polarization rotators with certain orientations and a series of perfect Mach-Zehnder interferometers connected in a particular form (see, http://njsas.org/projects/light_polarization/Interaction-Free-Measurements.htm for more details). The schemes are based in the Zeno quantum effect, a.k.a. Turing paradox. The Zeno quantum effect refers to situations in which an unstable particle, if observed continuously, will never decay; thus, evoking Zeno's famous (infamous?) arrow. (According to Sudarshan, E. C. G.; Misra, B. (1977). "The Zeno's paradox in quantum theory". Journal of Mathematical Physics 18 (4): 756–763. ) The part of the sentence, near the end, (#. #:) is the Cantor function and its arguments( 1j1 and i.2^2 15) correspond to four dragons (see, http://www.jsoftware.com/pipermail/programming/2011-November/025165.html and the first issue of the Journal of J for more details). Four dragons can be plotted by, plot 1j1 ((Cantor=. #. #:)"0 _) i.2^2 15 The these equally sized dragons (reportedly Zeno was fond of talking about a half, a half of a half, etc.) can depict the distortion due to the quantum probability, as a function of the complex components of 2-level systems (>: is used to avoid calculating the probability of an empty system; that is, a system with zero components). The distorted four dragons, representing systems up to 131071 components, can be plotted by, plot 1j1 prob @: >: @: Cantor i.2^2 15 The plot of the three dragons was merely zooming on the last three dragons by dropping (}.) the first dragon. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
