“Some amount of redundancy is necessary” (WIP)

• ratio of entropy of potential states (\(H(X)\)) (i.e. statistical ensemble) and its max possible entropy value (\(\log |{\mathcal {A}}_{X}|\)) (i.e. uniform prob)

  why

  • \(H(X)\): entropy of a system ensemble
  • \(\log |{\mathcal {A}}_{X}|\): max possible entropy value of such a system ensemble
    • \(\mathcal {A}_{X}\): all possible alphabets of ensemble \(X\), and \(|\mathcal {A}_{X}|\) is the alphabet size
  • \(H(X)\) value is the largest when \(X\) is uniformally distributed
    • i.e. each symbol in \(\mathcal {A}_{X}\) has probability of \(1/|\mathcal {A}_{X}|\), hence \(\max H(X) = \log | \mathcal {A}_{X} |\) by definition of information entropy

• “Informally, it is the amount of wasted ”space“ used to transmit certain data.”

• Although we now know that the two hemispheres of the brain perform vastly different functions, redundancy within the two hemispheres is still held as a viable theory of functional recovery

• the brain is at least twice as large as is needed for immediate survival, and the extra baggage of the normal brain simply replicates functions already present.

• RPR: (representational redundancy) redundant encoding of information
  • non-orthogonal scheme of information representation
    • hence favour non-homogeneous system design
  • every entry of information can be encoded by numerous distinct system configurations, including the conventional one; aka. system microstates
  • i.e. so that when some entries went missing, other entries could still loosely represent missing ones in-place
• ETR: (entangled redundancy) practical implementation of redundancy
  • microstates must have some correlation: distribution of the microstates with respect to error cannot be independent, but partially correlated or entangled

• Biological processes overcome this challenge by harnessing the computational capacity of the nervous system, which is exceptionally adequate at approximation (e.g. visual and musculoskeletal system)

e.g.: redundant sensing system design

fig

• (figure from the paper above)

• (RS) the amount of computational power required to process redundant information increases rapidly with the number of sub-arrays.
  • Two sub-arrays or two eyes is the minimum number necessary to create a redundant structure.

• It is therefore conjectured that binocular vision effectively creates a form of static redundancy allowing the brain to collect sufficient information to remedy the error and produce the images we perceive.
• During microsaccades, the field of vision of each eye is sampled multiple times by different spatial configurations of photoreceptors, which resemble entangled redundant microstates and facilitate visual acuity.
  • microsaccades: small, rapid eye movements that occur when a person is attempting to fixate their gaze on a stationary object

e.g.: human musculoskeletal system (HMS)

• The HMS has more muscles and joints than the necessary mechanical degrees-of-freedom even though are energetically expensive to produce and maintain

fig

• (figure from the paper above)

• (a,b) sagittal view of a human leg’s mechanical model consisting of 14 muscles and muscle groups
• (c) Any specific movement trajectory and force can be achieved by multiple distinct muscles and joints combinations