Steven Lehar

PhD Graduate (1994) Cognitive and Neural Systems
Research Fellow in Ophthalmology, Harvard University
Post-doc at Schepens Eye Research Institute
former Professor of Cognitive Psychology at Salem State College


My Story:

I am an independent researcher with a novel theory of mind and brain, inspired by the observed properties of perception. These observations are confirmed by some peculiar anomalies in phenomenal perspective. The implications of these observations are that the foundational assumptions of neuroscience are fundamentally in error, and that an alternative paradigm of neurocomputation will have to be formulated to account for the properties of consciousness and perception.

Summary of My Research
Proposal for Future Research

The Central Insight Behind My Work:

The Epistemology of Conscious Experience

A brief illustrated presentation of the epistemology of conscious experience, and its implications for the computational function of visual processing. The idea of Indirect Perception, or Epistemological Dualism, was the central inspiration for much of Gestalt theory.

A Cartoon Epistemology

An informal cartoon presentation of the central epistemological debate between naive realism and representationalism.

The Dimensions of Visual Experience: A Quantitative Ananlysis


A narrated PowerPoint presentation of a plenary talk given at the Tucson 2006 consciousness conference showing that visual experience is spatially structured, and thus, a model of visual experience must also be expressed as a spatial structure. Theories of direct perception, and projection theory are refuted.

See also the Representationalism Web Site.

My Books:

The World In Your Head: A Gestalt View of the Mechanism of Conscious Experience

Publisher: Lawrence Erlbaum Associates

This book presents a modern reformulation of Gestalt theory based on the philosophy of indirect realism, i.e. that the world you see around you is not the world itself, but merely an internal replica of the external world generated by perceptual processes in your brain. This reveals the primary function of visual perception to be the generation of a fully spatial virtual-reality internal model of the external world.

The Boundaries of Human Knowledge: A Phenomenological Epistemology.

This book explores the boundaries of human knowledge, beginning with the root of all human knowledge which is our conscious experience of the world.

[Download whole book in PDF format]

My Principal Papers:

The Constructive Aspect of Visual Perception: A Gestalt Field Theory Principle of Visual Reification Suggests a Phase Conjugate Mirror Principle of Perceptual Computation

Many Gestalt illusions reveal a constructive, or generative aspect of perceptual processing where the experience contains more explicit spatial information than the visual stimulus on which it is based. The experience of Gestalt illusions often appears as volumetric spatial structures bounded by continuous colored surfaces embedded in a volumetric space. These, and many other phenomena, suggest a field theory principle of visual representation and computation in the brain. A two-dimensional reverse grassfire algorithm, and a three-dimensional reverse shock scaffold algorithm are presented as examples of parallel spatial algorithms that address the inverse optics problem in perception. The principle of nonlinear wave phenomena and phase conjugate mirrors is invoked as a possible mechanism.

Gestalt Isomorphism and the Primacy of the Subjective Conscious Experience: A Gestalt Bubble Model. (2003) Behavioral & Brain Sciences 26(4), 375-444.

[Download pdf file]

The world of visual consciousness appears in the form of solid volumes, bounded by colored surfaces, embedded in a spatial void. The retinal input on which it is based however is two-dimensional. (in the monocular case) Visual processing therefore computes a solution to the inverse-optics problem, i.e. it performs a transformation from the two-dimensional retinal input to the three-dimensional spatial percept. But the inverse-optics problem is underconstrained, and has no unique solution. I propose that perception resolves this fundamental ambiguity by way of a unique kind of emergent field-like computation as suggested by the Gestalt soap bubble analogy.

Harmonic Resonance Theory: an Alternative to the "Neuron Doctrine" Paradigm of Neurocomputation to Address Gestalt properties of perception

[Download pdf file]

The properties of the world of visual experience appear to be inconsistent with contemporary concepts of neurocomputation. For phenomenology presents the mind as a three-dimensional colored structure, while neurophysiology presents the brain as an assembly of discrete local processors in a massively parallel network. Where in that mass of neural circuitry are the three-dimensional volumetric real-time moving pictures that we know so well in conscious experience? A Harmonic Resonance theory is presented as an alternative to the Neuron Doctrine, to account for the holistic global aspects of perception identified by Gestalt theory which are so difficult to account for in conventional neural network terms.

Computational Implications of Gestalt Theory I: A Multi-Level Reciprocal Feedback (MLRF) to Model Emergence and Reification in Visual Processing

[Download pdf file]

Computational Implications of Gestalt Theory II: A Directed Diffusion to Model Collinear Illusory Contour Formation

[Download pdf file]

This is a two-part paper that discusses the computational implications of Gestalt theory. I propose a perceptual modeling approach, i.e. to model the subjective experience of vision rather than the corresponding neurophysiological state. I propose specific computational interactions to account for the Gestalt properties of perception, and to explain the role of feedback in vision with a specific computational model that replicates a number of visual illusory phenomena. Part II of the paper demonstrates how the more subtle second order properties of illusory contour formation can be modeled computationally with a dynamic feedback model, as an alternative to the hard-wired receptive field embodied in the neural network approach.

Directional Harmonic Theory: A Computational Gestalt Model to Account for Illusory Contour and Vertex Formation. (2003) Perception 32(4) 423-448.

[Download pdf file]

Neural network models have been proposed to account for the formation of collinear illusory contours as seen for example in the Kanizsa figure. There are however a number of illusory grouping effects which involve perceived vertices defined by the intersection of two, three, four, or more illusory contours that meet at the vertex. A neural network approach to this kind of perceptual grouping leads to a combinatorial explosion in the number of required receptive fields. A Directional Harmonic theory is presented to account for all of these diverse grouping effects by way of a single simple mechanism that involves harmonic resonances, or patterns of standing waves in the neural substrate. A single resonance mechanism replaces a whole array of different receptive fields in a computationally equivalent neural network model. I propose that harmonic resonance is the long-sought and elusive computational principle behind the holistic emergent aspects of Gestalt theory.

The Dimensions of Conscious Experience: A Quantitative Phenomenology

A short paper on the structure of conscious experience and its implications for the nature of consciousness.

The Function of Conscious Experience: An Analogical Paradigm for Perception and Behavior

[Download pdf file]

A short paper on the function of conscious experience as an analogical representation of the external world.

Clifford Algebra: A Visual Introduction

Geometric Algebra: Projective Geometry

Geometric Algebra: Conformal Geometry

My latest discovery is Clifford Algebra, a most extraordinary reformulation of all of mathematics that reveals algebra to be actually a branch of geometry. It converts all algebraic relations into spatial relations between spatial structures. It is simultaneously a geometrification of algebra and an algebrification of geometry.

David Hestenes (pron. "Hes-ten-es"), who single-handedly rediscovered Clifford Algebra and brought it back to life from complete obscurity, then proceeded to improve on it with two most extraordinary extensions, the projective geometry and the conformal geometry, concepts that are not exclusive to Geometric Algebra, but are very simply expressed in it. These remarkable extensions reveal the intimate connection between mathematics and perception, revealing mathematics to be an artifact of how our brain makes sense of spatial reality.

David Hestenes prefers the term "Geometric Algebra", which is the term proposed by Clifford himself, because "Clifford Algebra" sounds like "just another algebra", whereas in fact Geometric Algebra is the radical discovery of the geometric roots of all of algebra.

Double Conformal Mapping: A Finite Mathematics to Model an Infinite World

[Download pdf file]

David Hestenes' conformal mapping in Geometric Algebra suggests an intimate connection between mathematics and perception, especially in the handling of infinity.

Submitted to Advances in Applied Clifford Algebras Special Issue From Signals, Images, Transforms, to Consciousness. Review, Author's Response Review round 2 Author's Response Round 2 Final Rejection Author's Response to Final Rejection

The Perceptual Origins of Mathematics

A WordPress book on the origins of mathematics through the mechanism of perception.

Chapter 1: The Perceptual Origins of Mathematics

Chapter 2: The Schema As A Mental Image

Chapter 3: Amodal Perception

Chapter 4: The Language Of The Mind

Chapter 5: Ray-Tracing Algorithms

Chapter 6: Let There Be Light!

Chapter 7: The Inverse-Optics Problem

Mathematics And Mind

Mathematics is not a human invention, mathematics is a discovery of a pre-existing system of laws and geometrical structures, and those laws and structures are themselves innate properties of the human mind, located in the human brain. We can reverse-engineer the computational principles of human perception and cognition by examining the laws of mathematics. This video demonstrates some of the remarkable properties of mathematics that reveal the operational principles of the mind and brain.

Mathematics And Mind

All My Papers in Chronological Sequence

Including my PhD thesis, all of my journal submissions, and some unpublished essays.

Some of My Creations:

Exerpts from Some of My Papers

Gallery of Miscellaneous Pictures

Quotes from various books:

General Quotes from various sources

More Quotes

Rudolf Arnheim (1969) Art and Visual Perception
Alfred Binet (1905) Mind and Brain
J. J. Gibson
D. E. Harding (1960) On Having No Head.
Stephen Harrison (1986) The Mind/Brain Problem
Gaetano Kanizsa (1979) Organization in Vision
Immanuel Kant (1781) Critique of Pure Reason
Thomas Kuhn (1970) The Structure of Scientific Revolutions.
Wolfgang Köhler (various selections)
Jose Luis Marroquin (1976) Human Visual Perception of Structure.
Ramachandran & Blakeslee (1998) Phantoms in the Brain.
Bertrand Russell
Arthur Schopenhauer
Sir Charles Scott Sherrington
John Smythies (1994) The Walls of Plato's Cave.
Tom West(1997) In the Mind's Eye.
Edward O. Wilson (1998) Consilience.


Web Resources:

Web Search

My Favorite Links: