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Kanerva's proposal is based on four basic ideas:<ref>Mendes, Mateus Daniel Almeida. "Intelligent robot navigation using a sparse distributed memory." Phd thesis, (2010). URL: https://eg.sib.uc.pt/handle/10316/17781</ref>
*1.# The boolean space <math> \{0,1\}^n</math>, or <math>2^n</math> points in <math>10^0 < n < 10^5</math> dimensions, exhibits properties which are similar to humans' intuitive notions of relationships between the concepts. This means that it makes sense to store data as points of the mentioned space where each memory item is stored as an n-bit vector.
*2.# Neurons with n inputs can be used as address decoders of a random-access memory
*3.# Unifying principle: data stored into the memory can be used as addresses to the same memory. Distance between two points is a measure of similarity between two memory items. The closer the points, the more similar the stored vectors.
*4.# Time can be traced in the memory as a function of where the data are stored, if the data are organized as sequences of events
===The binary space N ===
The space N can be represented by the vertices of the unit cube in n-dimensional [[Euclidean space]]. The vertices lie on the surface of an n-dimensional sphere with (Euclidean-metric) radius <math>\sqrt{n}/2 </math>. This gives rise to the [[sphere]] analogy. We will call a space spherical if
*1.# any point x has a unique opposite 'x,
*2.# the entire space is between any point x and its opposite 'x, and
*3.# all points are "equal" (meaning that for any two points x and y there is a distance preserving [[automorphism]] of the space that maps x to y, so that from any of its points the space "looks" the same).
The surface of a sphere (in Euclidean 3d-space) clearly is spherical. According to definition, N is also spherical, since y ⊕ x ⊕ (…) is an automorphism that maps x to y.
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