Computation by Interaction


The presence of meaningful electrical patterns in spikes (spike directivity) challenges the spike timing dogma and temporal coding models. In order to understand the new model of computation a significant departure from  Turing Machine is required

The Turing Machine and Connectionist Models

Any computational system has to access the “memory “to write (code) and read (decode) information




 
The Turing machine reads a symbol from the tape and moves the head one cell to the left L or to the right R depending on the internal states s(k) and received input i(k). While the computations are carried out the Turing machine does not accept any inputs from the external environment. Each output o(k+1) is determined only by inputs and internal machine states.

 
The spike timing neurons compress temporal information.  While the model neglects fundamental information processing that occurs in the neuron, the main  focus is on (synaptic) transmission of information between neurons. In order to be implemented on  current computers  (e.g.Turing machine) the entire framework  is buried  in a connectionist model of computation. The connection weights approximate only "weak" interactions between neurons [3].

Interactive Computation 

Interactive computation  describes a more general process of computation. Recently Dina Goldin and  Peter Wegner have challenged  the paradigm in computer science.    Interactive computation is presented as a distinct non-Turing  form of computation that involves intrinsic communication with the external world during the computation [1,2].
In fact God was  unaware of Turing's work and has put forward a better model beyond limitations of Turing Machines as a formal mathematical model of the real-world.

Computation by Physical Interaction 


The Turing Machines can be seen as an approximation of a general  model of computation (GMC) carried on by physical interactions.

 
The electric charges are represented in blue color and the  molecular structure in magenta color (e.g protein structure)
  1. The processing and exchange of information during spikes (action potentials, synaptic spikes) is first performed by interactions at molecular level, intracellularly;
  2. Neurons do not compress information in temporal domain, they process, communicate and store information;
  3. Schematic representation of computing by biophysical interaction, the protein structure in the cell, the flow of electric charges and electric interactions provide ‘direct’ access to stored "memory" to "read" and "write" information
  4. Information can be quickly "read" and "written" during electric interactions and becomes available due to electric field propagation; 
  5.  During the process of computation  the inputs from the external environment are considered and can entirely change the outcome;
  6. Therefore, during biophysical interaction information from multiple sources can be easily instantaneously  integrated.
  7. The structural arrangement at molecular level  inside neurons provides the “memory” that  is shaped  and re-shaped continuously by biophysical  interaction
  8. The image presented at http://neuroelectrodynamics.blogspot.com/p/spike-directivity.html proves this phenomenon.

    NeuroElectroDynamics - Computation by Biophysical Interaction

    Computation  by physical  interaction is the fundamental model of computation developed at molecular level in neurons and represents the hallmark  of computation in the brain described in NeuroElectroDynamics (NED).
    Biophysical interactions  are continuously maintained under normal conditions in the brain. At least  three  regulatory interconnected  systems are present at the neuronal level and extend to  the whole brain scale


During spike activity “strong” interactions intracellularly occur within dendrites, soma, axon while ‘weak’ forms of interaction between neurons can be described by synaptic and non-synaptic interactions (e.g electric field). These interactions that intracellularly occur can be related to the mechanism of neurotransmitters action or different activities in astrocytic glial cells. The general framework of temporal coding and connectionist models approximates only a small part of "weak" interactions and ignores strong interactions that occur within cells [3,4]. In fact, the interaction between neurons (connectivity) is a result of information processing in the cell, it can change during every generated spike (see spike directivity).Typical connectionist weights approximate only  weak interactions. Therefore, all  connectionist models [5] have partially  neglected the ability of cells to process information.  The fundamental parallel distributed process of computation by interaction occurs inside the neuron [6], [7] and can lead by itself to intelligent action in single cells [8],[9][10].
The NED  model integrates molecular computation  in a general framework to achieve a better understanding of the brain and neurological diseases in computational terms.

References  


1.Peter Wegner, 1997, Why interaction is more powerful than algorithms. Communications of the ACM, May , pages 81–91. Computation Theory
2.Dina Goldin, Peter Wegner, 2008, The Interactive Nature of Computing: Refuting the Strong Church-Turing Thesis”. Minds and Machines, v.18, n.1, p.17-38,
3.Dorian  Aur, 2011, From Neuroelectrodynamics to Thinking Machines, DOI: 10.1007/s12559-011-9106-3,  Cognitive Computation,  http://www.springerlink.com/content/x1l7388475323758/
4. Dorian Aur and Mandar Jog 2010, Neuroelectrodynamics- Understanding The Brain Language , IOS Press, http://dx.doi.org/10.3233/978-1-60750-473-3-i
 5.James L McClelland and David E Rumelhart., 1988, Exploration in Parallel Distributing Processing., Brandford Books, MIT Press, Cambridge, MA.
6. Stuart Hameroff, Nip Alex, Mitchell Porter, Jack Tuszynski, 2002, Conduction pathways in microtubules, biological quantum computation, and consciousness. Biosystems 64, ,  pp. 149–168.
7. Nancy J. Woolf,  Avner Priel Jack A. Tuszynski,  2009, Nanoscience:Structural and Functional Roles of the Neuronal Cytoskeleton in Health and Disease,  Springer Verlag
8.Brian J Ford, 2010, The secret power of the single cell, The New Scientist, Volume 206, Issue 2757, 21,  Pages 26-27
9.  Brian J Ford, On Intelligence in Cells: The Case for Whole Cell Biology,2009, Interdisciplinary Science Reviews, Vol. 34 No. 4,  350–365
10. Jack Copeland, Hypercomputation Minds and Machines, vol. 12 (2002), pp. 461-502.
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