Abstract
There exists a dynamic interaction between the world of information and the world of concepts, which is seen as a quintessential byproduct of the cultural evolution of individuals as well as of human communities. The feeling of understanding (FU) is that subjective experience that encompasses all the emotional and intellectual processes we undergo in the process of gathering evidence to achieve an understanding of an event. This experience is part of every person that has dedicated substantial efforts in scientific areas under constant research progress. The FU may have an initial growth followed by a quasi-stable regime and a possible decay when accumulated data exceeds the capacity of an individual to integrate them into an appropriate conceptual scheme. We propose a neural representation of FU based on the postulate that all cognitive activities are mapped onto dynamic neural vectors. Two models are presented that incorporate the mutual interactions among data and concepts. The first one shows how in the short time scale, FU can rise, reach a temporary steady state and subsequently decline. The second model, operating over longer scales of time, shows how a reorganization and compactification of data into global categories initiated by conceptual syntheses can yield random cycles of growth, decline and recovery of FU.
Similar content being viewed by others
References
Anderson JA (1972) A simple neural network generating an interactive memory. Math Biosci 14:197–220
Anderson JA (1995) An introduction to neural networks. MIT Press, Cambridge
Arbib MA (2003) The handbook of brain theory and neural networks, 2nd edn. MIT Press, Cambridge
Ashby WR (1956) An introduction to cybernetics. Wiley, New York
Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512
beim Graben P (2014) Contextual emergence of intentionality. J Conscious Stud 21:75–96
beim Graben P, Rodrigues S (2014) On the electrodynamics of neural networks. In: Coombes S, beim Graben P, Potthast R, Wright J (eds) Neural fields: theory and applications. Springer, Berlin, pp 269–296
Berry MW, Browne M (2005) Understanding search engines: mathematical modeling and text retrieval. SIAM, Philadelphia
Borges JL (1964) Labyrinths. New Directions, New York (Spanish version in Borges, J. L. Obras Completas, EMECE, Buenos Aires, 1974)
Brown SR (2013) Emergence in the central nervous system. Cogn Neurodyn 7:173–195
Coombes S, beim Graben P, Potthast R, Wright J (2014) Neural fields: theory and applications. Springer, Berlin, pp 47–96
Cooper LN (1974) A possible organization of animal memory and learning. In: Proceedings of the Nobel symposium on collective properties of physical systems. Aspensagarden, Sweden
Cooper LN (1980) Sources and limits of human intellect. Daedalus 109(2):1–17
Cowan J (2014) A personal account of the development of the field theory of large-scale brain activity from 1945 onward. In: Coombes S, beim Graben P, Potthast R, Wright J (eds) Neural fields: theory and applications. Springer, Berlin, pp 47–96
Damasio AR (1999) The feeling of what happens. Harcourt Brace, New York
De Regt HW (2009) Understanding and scientific explanation. In: de Regt HW, Leonelli S, Eigner K (eds) Scientific understanding, Chap. 2. University of Pittsburgh Press, Pittsburgh
de Regt HW, Leonelli S, Eigner K (eds) (2009) Scientific Understanding. University of Pittsburgh Press, Pittsburgh
Deerwester S, Dumais S, Furnas G, Landauer T, Harshman R (1990) Indexing by latent semantic analysis. J Am Soc Inf Sci 41:391–407
Dehaene S (2014) Consciousness and the brain: deciphering how the brain codes our thoughts. Viking, New York
Edelman G (1989) The remembered present: a biological theory of consciousness. Basic Books, New York
Érdi P (2015) Teaching computational neuroscience. Cogn Neurodyn 9:479–485
Friston KJ (1995) Functional and effective connectivity in neuroimaging: a synthesis. Hum Brain Mapp 2:56–78
Friston KJ (2011) Functional and effective connectivity: a review. Brain Connect 1(1):13–36
Huth AG, Nishimoto S, Vu S, Gallant JL (2012) A continuous semantic space describes the representation of thousands of object and action categories across the human brain. Neuron 76:1210–1224
James W (1911) Some problems of philosophy. Longmans and Green, New York
Kandel ER, Schwartz JH (1985) Principles of neural science. Elsevier, New York
Kohonen T (1972) Correlation matrix memories. IEEE Trans Comput C-21:353–359
Kohonen T (1988) Self-organization and associative memory, 2nd edn. Springer, Berlin
Landauer T, Dumais S (1997) A solution to Plato’s problem: the latent semantic analysis theory of acquisition, induction and representation of knowledge. Psychol Rev 104:211–240
Lipton P (2009) Understanding without explanation. In: de Regt HW, Leonelli S, Eigner K (eds) Scientific understanding. University of Pittsburgh Press, Pittsburgh
McClelland JL, Rumelhart DE, PDP Research Group (1986) Parallel distributed processing. Explorations in the microstructure of cognition, volume 2: psychological and biological models. MIT Press, Cambridge. https://mitpress.mit.edu/books/parallel-distributed-processing-0
Mizraji E, Lin J (2011) Logic in a dynamic brain. Bull Math Biol 73:373–397
Mizraji E, Lin J (2015) Modeling spatial-temporal operations with context-dependent associative memories. Cogn Neurodyn 9:523–534
Newell A, Simon HA (1972) Human problem solving. Prentice-Hall, New York
Newman M, Barabási A, Watts DJ (2006) The structure and dynamics of networks. Princeton University Press, New Jersey
Reeke GN Jr, Edelman GM (1987) Real brains and artificial intelligence. Daedalus 117:143–173
Robinson PA, Wright JJ, Rennie CJ (1998) Synchronous oscillations in the cerebral cortex. Phys Rev E 57:4578–4588
Sporns O (2010) Networks of the brain. MIT Press, Cambridge
Valle-Lisboa JC, Mizraji E (2007) The uncovering of hidden structures by latent semantic analysis. Inf Sci 177:4122–4147
Valle-Lisboa JC, Pomi A, Cabana A, Elvevåg B, Mizraji E (2014) A modular approach to language production: models and facts. Cortex 55:61–76
Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442
Wright JJ, Bourke PD (2014) Neural field dynamics and the evolution of the cerebral cortex. In: Coombes S, beim Graben P, Potthast R, Wright J (eds) Neural fields: theory and applications. Springer, Berlin, pp 457–482
Acknowledgments
This work was partially supported by PEDECIBA, CSIC and ANII, Uruguay (EM) and a Grant from Washington College, MD, USA (JL). The authors thank Juan C. Valle-Lisboa for stimulating discussions during the preparation of this work.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Let us illustrate how FU evolves with a minimalist example.
-
1.
In the first step we have a large data vector \({\text{V}}_{\text{D}}^{\text{S}}\) = (…, A, …, B, …, C, …), where A, B and C are clusters of data associated with singular topics. This data vector induces a concept vector \({\text{V}}_{\text{C}}^{\text{S}}\) = (…, Ca, …, Cb, …, Cc, …) with clusters of concepts Ca, Cb and Cc. In the binary model, clusters A, B, C, Ca, Cb and Cc are mapped onto 1’s and the inter-cluster spaces are mapped onto 0’s, giving vectors \({\text{V}}_{\text{D}}\) and \({\text{V}}_{\text{C}}\). Let us then imagine a miniature 12-dimensional space where \({\text{V}}_{\text{D}}\) = (001000100100) and \({\text{V}}_{\text{C}}\) = (001000100100). In this ideal situation the initial correlation coefficient K is equal to 1.
-
2.
The subsequent accumulation of data increases the number of 1’s in \({\text{V}}_{\text{D}}\) = (011101100111) but leaves \({\text{V}}_{\text{C}}\) temporarily unchanged. This activity is similar to the process of augmenting the number of nodes in the knowledge graphs illustrated in “Knowledge networks” section and Fig. 2. Therefore, the value of K decreases (K < 1). The dynamics of this scenario for high-dimensional vectors are modeled by Eqs. (15)–(16) and their behavior are depicted in Figs. 4 and 5.
-
3.
To simplify to the maximum the complex interactions between data and concepts, let us imagine that concepts are enriched and data are reconstituted. Then we may have, \({\text{V}}_{\text{D}}\) = (001101100110) and \({\text{V}}_{\text{C}}\) = (001101100110). In this stage, the correlation K will reach again a maximum value of 1. After this process, we follow a new path to the first step (1) with reconfigured vectors. The evolution of high-dimensional vectors follow Eqs. (17)–(18) and their behavior are sketched in Figs. 6 and 7.
In real situations the sparseness of data and concept vectors create new filling niches of 1’s while maintaining the clusters distant from each other.
Rights and permissions
About this article
Cite this article
Mizraji, E., Lin, J. The feeling of understanding: an exploration with neural models. Cogn Neurodyn 11, 135–146 (2017). https://doi.org/10.1007/s11571-016-9414-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11571-016-9414-0