Functional Equivalence

Revision as of 14:20, 17 September 2025

Functional Equivalence is when two or more possibilities are different in method, action, or constitution but remain equivalent or indistinguishable in crucial aspects.

Penrose Tilings

One way to understand Functional Equivalence is by considering Penrose tilings which are type of aperiodic tiling:

The Penrose tilings, being non-periodic, have no translational symmetry – the pattern cannot be shifted to match itself over the entire plane. However, any bounded region, no matter how large, will be repeated an infinite number of times within the tiling. Therefore, no finite patch can uniquely determine a full Penrose tiling, nor even determine which position within the tiling is being shown. ^[1]

Despite the total tiling never matching 100% when shifted, the longer the Penrose tiling goes, the more any patterns and larger patterns will arise that match one another.

To put this in terms that are more easily accessible, imagine that you have two simple experiences where someone enters a store. You live through both and cannot determine any difference between the two. As far as you can tell, they are a matching pattern. However, the stars in the cosmos above may be in a different order which you cannot tell, or memories and empirical knowledge about the world that are not being accessed during the experience may differ.

In other words, the total pattern in its entirety does not match between the compared experiences, but the experience itself if still functionally equivalent

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 == Penrose Tilings ==
-One way to understand [[Functional Equivalence]] is by considering [[wikipedia:Penrose tiling|Penrose tilings]] which are type of [[wikipedia:Aperiodic tiling|aperiodic tiling]].
+One way to understand [[Functional Equivalence]] is by considering [[wikipedia:Penrose tiling|Penrose tilings]] which are type of [[wikipedia:Aperiodic tiling|aperiodic tiling]]:<blockquote>''The Penrose tilings, being non-periodic, have no translational symmetry – the pattern cannot be shifted to match itself over the entire plane. However, any bounded region, no matter how large, will be repeated an infinite number of times within the tiling. Therefore, no finite patch can uniquely determine a full Penrose tiling, nor even determine which position within the tiling is being shown.'' <ref>Wikipedia contributors. (2025, August 30). Penrose tiling. In ''Wikipedia, The Free Encyclopedia''. Retrieved 14:10, September 17, 2025, from <nowiki>https://en.wikipedia.org/w/index.php?title=Penrose_tiling&oldid=1308631319</nowiki></ref></blockquote>Despite the total tiling never matching 100% when shifted, the longer the Penrose tiling goes, the more any patterns and larger patterns will arise that match one another.
+To put this in terms that are more easily accessible, imagine that you have two simple experiences where someone enters a store. You live through both and cannot determine any difference between the two. As far as you can tell, they are a matching pattern. However, the stars in the cosmos above may be in a different order which you cannot tell, or memories and empirical knowledge about the world that are not being accessed during the experience may differ.
+In other words, the total pattern in its entirety does not match between the compared experiences, but the experience itself if still functionally equivalent
 == See Also ==