Mathematics, BioFusion and Reflexive Control




Sentient Machines



By:  John D. Norseen





Presentation for International Reflexive Control Symposium




Russian Academy of Sciences – Institute for Psychology


17 – 19 October 2000     Moscow, Russia












     Copyright © 2000 Lockheed Martin Corporation – USA.  All Rights Reserved.
     May not be reproduced for commercial purposes without the express written permission of the copyright holder.




Mathematics, BioFusion and Reflexive Control for Sentient Machines

by John D. Norseen, Intelligent Systems,
Lockheed Martin Aeronautics Company. 




Sifting and culling through the combined works of Charles Sanders Peirce, Karl Pribram, William Calvin, John Sowa, Stuart Hameroff, Manfred Clynes and others well known in the domain of neuroscience, logic, mathematics and philosophy, the author, John D. Norseen puts forth a staggering set of principles for the onset of the era of Sentient Behavior in Machines.  Using mathematics as the formation of what he calls semiotic reality, he describes emergent mathematical properties of information interacting with neural structures – the results of which we call thought.  Norseen does a masterful job of describing this basic construct analogous to the Bernoulli’s equations of airflow over an airfoil producing lift.  He calls such an emergent process of biochemical induced, electromagnetic E & H field mediated interaction of information with uniquely configured neural structures, and expressed into work via protein reconfiguration, under the term BioFusion.  And he does an equally good job of putting forth examples of how Biofusion and the Russian work in Reflexive Control can be used for the development of the first generation of Sentient Machines, for which Norseen has a patent pending.  From semiotics, to brain mapping, to concepts for information operations in both cyberspace and the biosphere, Norseen even explores the concept of the human condition as a steganographic ‘biomark’ capable of recording and playback in Krylov Space.


From before Sun Szu, encompassing the famous Admiral Gorshkov, and extending well beyond future INFO-CYBER warriors, the dictum:  Control the Electromagnetic Spectrum and Victory is Promised as your Reward - will be the mandate for success and survival in the coming dawn of the Age of Automated Reasoning, the advent of Synthetic, Sentient Species.  Accordingly, this paper is presented:  Mathematics, BioFusion and Reflexive Control for Sentient Behavior, subtitled:  Control of the Inverse Function is the Key to Control of Information Injection.


Presented in this paper is an original portfolio of both hierarchical and ergodic constructions that suggest pathways to lead to the eventual development of sentient behavior in machines and new synthetic species that will come to dominate earth, and earth related systems, by converting information not into more information (IKI) but where information itself, expressed in Reflexive Control, will be converted into work performing energy (IKE).


BioFusion is the increasing complexity of one part of the brain to share, mathematically, its information with other parts of the brain in a common, emergent family of mathematical operations, to which the inverse function, the ability to recreate or trigger stored information by using the inverse mathematics is allowable.  Panum’s fusion space, horopter operations, dreams, and the distinct linkage of either end of the invariant versus holistic storage continuum of object recognition in the posterior inferior temporal gyri (ITG) as opposed to the more pure prosopopoeia in the fusiform gyrus (FG) are very nice examples of BioFusion in the visual perception modality.  The ability to blend vision and verbal modalities in the Temporal Cortex, TC-22 and Broadmann’s Area 44, for example are also fine indications that BioFusion is taking place in more and more complex, adaptive regions of the brain.


Accordingly, the common family of interacting mathematics of BioFusion would appear to account for how the entire brain can act independently yet in concerted fashion from moment to moment for many years producing for us a relatively stable mental picture of semiotic reality and a useful, purposeful repertoire of Reflexive Control circuits, our ‘Portfolio of Life’ called the Human Condition. 


In building block fashion, Norseen shows that the perception of objects, faces and voices as an emergent mathematical operation, can lead to larger, more complicated, mental thought domains of strings, spirals, knots and geometric patterns that can form into cooperating sets of ‘phase locked’ behavioral circuits or reflexive channels.  Norseen also explores the need for error, and the ultimate impact on Synthetic Life Forms/Sentient Systems engaged in Synthetic Reality created by the inverse mathematical injection of recording and playback of information interacting with discrete linkages of human neural structures across such diverse life-death/survival situations as the influence of the nucleus accumbens (NA) in sexual behaviors and the superior colliculus (SC) in suicidal actions.  The full range of human emotions, or as Clynes would call, Sentic Forms, could well be ensconced in recording and playback devices – the human condition captured in automated Krylov Space.  Having only one brain, our internal display, our inner TV, if you will, has many channels, but seemingly only one display.  This would suggest that our inner scope is really the ability to filter at different signal to noise thresholds different just noticeable difference (JND) patterns of information – the Steganographic ‘Biomark.’ 


Steganography is the ability to hide information within information until that information layer is exposed or filtered.  The author suggests that the brain is engaged as a measurement and mapping device to expose or filter in Krylov Space various complete and incomplete neurophsyiological patterns or channels as mathematical expressions from within the complete information field provided by the environment, and stored, compressed memory patterns within the orchestrated reduction of the twisted folds of the protein microtubulin, locked and unlocked by the movement of biochemical mediated electromagnetic information criss-crossing across the dendritic fields and neuropils of the brain at specific brain frequencies.  Crick, early co-founder of the DNA double helix, and now pursuing the coding sequence of thought, seems also to suggest such a process in his most recent works.


Keywords:  Peircian Semiotics, Reflexive Control, BioFusion, Gabor-Like Functions in Hilbert Space, Krylov Space, Sentient Values (SV’s), Inverse Function, Information Injection, Information converted Information (IKI), Information converted to work Energy (IKE), Protein Microtubulin (MT), Orchestrated Reduction (OR), Steganography



Copyright © 2000 Lockheed Martin Corporation - USA.  All Rights Reserved.




SENTIENT VALUES:  Sentient Value (SV) number one:  Identification.  It is nice to be recognized by someone, a smile or even a gentle wave of the hand.  It makes you feel alive.  Getting a machine to respond to you, to recognize you, to ‘identify’ you is an important beginning step toward sentient behavior in machine systems.  Will it really be so hard to put Identification into a Machine?  It would not appear too hard to incorporate the following techniques into a machine based on various biological paradigms using multiple, independent sensory/perception modalities fused into a complete pattern, an emergent behavior, which appears to be a mathematical function…”A Gabor-like Function in Hilbert Space.”  From this completed math function, regionally dispersed in the brain, such math functions can then be compared to a stored, compressed memory of prior experiences. Again, the fusion of new experience with old experience produces new emergent behavior.  Once this new emergent behavior gets generated, the older less useful Reflexive Control dies out  - replaced by a new emergent Reflexive Control circuit.  The onset of Reflexive Control is a precise mathematical event of engaged neural circuits.  Importantly, something else also happens to facilitate the ‘Identification’ process of math functions and changes in Reflexive Control states of awareness:  And that answer is – ‘Motion.  Motion is required to match up the Invariance of the New Situation with the Stored Invariants of Prior Experience.  Multiple forms of Motion are required to solve the complex adaptive system of mathematical domains, to let each sensory modality make independent, then fused hermeneutics (interpretation) of external information, and to help in internal rotation of stored images.  So the first lessons for getting Sentient Machines to Identify you and respond to you is that they must also begin to ‘MOVE,’ in order to internally produce ‘Invariant Patterns’ of you matched to prior patterns in memory storage.  Hence SV # 2 is Motion.  Importantly, and as a necessary extension of Motion, Sentient Machines must be able to stop and let you move in concert with them.


Another important element of identification process in Sentient Machines is ‘Direction.’ Sentient Value # 3 is Direction.  Just as moss grows on the north face of a tree and can provide semiotic direction, somewhere in sentient machines must be located some set point, some origin, by which all other movement, hence invariant identification, can be measured.  This may very well be taking place in E and H field vector information, the Electromagnetic Compass setting, in the 10/13 type protein microtubulin/calpain interaction to environmental and biological stimuli in the protein structures in the brain or equivalent neural structures in other living or sentient beings.   Accordingly, Measurement is Sentient Value # 4.  The brain may be regarded as an interferometer to changes in the environment, but with the ability to control the inverse function of perception via internal mechanisms, or ‘irritants,’ and thus exerts its own influence upon the measurement of the environment.  Pierce would have the environment made up of actual things, ideas/concepts, and everything else as ‘in between-ness.’  In fact, the incorporation of invariants, memory, sensors, identification, movement, and direction all conspire to provide measurement of information.  Sentient beings are truly measurement devices, with the measurement in Krylov Space as Semiotic Reality.  And the set point for such measurement and which would allow for inverse function control would be the Electric (E) and Magnetic (H) field vectors at the instantaneous interaction of information with neural structures when a sufficient ‘Energy Wall’ or Energy Moat, or Energy Hump, is crossed – its protective threshold overcome allowing some other structure to perform work (IKE).  In this case, protein orchestrated reconfigurations carry out the measurement, mapping, and work (IKE) execution of signal-to-noise information interacting with unique arrangements of neural structures.  Perhaps what makes us human is that we possess the right group of neural structures to allow us to control the ability to crawl up and over in any direction these energy walls, moats and humps. 


With such ability, a sentient being can begin to understand the entire past by merely looking at an object or event in the present or future.  This is pretty powerful computation and may have provided a very significant evolutionary advantage for humans, but at some internal energy dissipation cost negatives.  But the outcome of further controlling the inverse function and even of injecting energy in from external sources to super pump, jump over walls, moats and humps, may yet allow Sentient Machines to operate in other mathematical domains, other than just Gabor-Like Functions in Hilbert Space, such as maybe Walsh Transforms in Chu Spaces, etc.  The question and the research paradigm would then become:  Can Sentient Machines, or artificial neural emulation systems, experience Perception in altered mathematical domains?  The answers will most likely be, No, To Some Degree, and Why Yes, In Fact – In A Most Powerful and Truly Unique Fashion.  But remember, once you are in the middle of the energy well, or the center of the moat, you are temporarily, or perhaps permanently, caught up in the local inktomi and maelstrom of the local energy swirls.  It takes additional energy to climb back out and over into the next neural/mental topology.  Dipping into information pockets and the associated energy costs to deal with the vagaries of the orchestrated reduction and quantum factors of mixed photons, phonons, electrons, and tensors is the cost of Perception and the Control of the Inverse Function.  One need only look at the bright, deep contrast peaks in Positon Emission Tomography (PET) scans and in fMRI color displays of energy utilization to see such walls, moats, and humps, and the associated binding frequencies that keep the emergent fields together.


Just as wind under an airfoil produces lift at the right settings producing Bernoulli’s equations, then at the right brain settings of biochemicals, and temperature, and brain state, information from internal or external sources, interacting with brain structure, will produce emergent mental, mathematically precise activity, which we call thought. 

·       Thought, then, is described as mathematical operations, in particular Gabor-Like Functions in Hilbert Space *


The accumulation of many of these Gabor-Like Functions in Hilbert Space would establish the threshold for operations of an entire system, an entire human or synthetic being, in a larger realm, or Krylov Space.

See illustration of Gabor Functions below:


Just as airplanes can be built that can be highly stable to highly unstable, so too it would appear that different parts of the brain, based on their neural ensemble arrangements, engage in a range of highly stable or unstable thought processes when interacting with different information structures.  Given that these values can be instilled in a machine, what can one then expect from a sentient machine?  Sentient Value #5 is when the machine begins to ask you, repeatedly calls for, demands, and begins to go chaotic in the request for resources, before it sets out on its own to resupply itself.  SV # 5 is the Search and associated Anxiety for Resources/Resupply.  Are we there yet in terms of Artificial Intelligence (AI), and all the other recent intelligent sciences such as reasoning by analogy, to expert systems (ES), to neural networks (NN), to predictive statistics, to neurophysiological engagement index packages, to accomplish Identification, Motion, Direction, Measurement and Resourcing in engineering terms?  The answer is Yes!


The Intelligent Architecture (IA) known as (SOAR), States, Operators and Results, is developing intelligent behavior schemes along similar lines to the Sentient Values expressed in this paper, with activation of symbol sets at the neural-circuitry level which can lead to forms of accelerated learning using eight basic principles: 


1. Problem Spaces,

2. Long Term Memory,

3. Attribute-Values,

4. Preference Memory,

5. Decision Procedures,

6. Perceptual-Motor Subsystems,

7. Goal-Directed Behavior, and

8. Chunk Based Learning.


We can even generate suspicion in machine intelligence.  Consider that a ‘Machine’ with multiple sensors can be programmed to be suspicious if one of its sensors detects information, then other sensors also pick up similar or different inputs that could all statistically lead to an intruder.  There are various AI look up tables, and programs that concern reasoning by analogy, and quick search databases that a machine, thus startled, can instantly begin to ‘Interpret the Suspicious’ nature of the external input.  The NN machines of today can even use rudimentary Reflexive Control…a growl or a bark, if you will.  “Stop, I detect an intrusion…I am processing now if you are a threat or friendly event.”   Why we can even begin to program ‘Loyalty’ parameters into machines, just allowing the current predictive statistics and outcome regimes to be relaxed a bit more in time and space or resource accounting.  Loyalty and Suspicion are but elements of emotional states that come to characterize sentient behavior patterns.  Therefore, and using Sentic Forms as an example, Emotions are SV # 6. 


Interestingly, in the human, there appear to be only about 30-50 emotional qualities that make up the human condition.  According to Norseen there are only about 30 to 50 semiotics that make up the visual alphabet.  Study after neurolinguistic study also shows that there are only about 40 or so sound types that the Human Brain can process in any culture anywhere in the world.  So maybe the alphabet size for the regional compartmentation of the human brain into Visual, Auditory and Kinesthetic areas is each supported by its own Brain Language sustained by upwards of 30 to 50 signs or symbols in its alphabet.  Three Brains in One, the I the Me and the Agent, each capable of independent, yet limited operations, but better off in synergistic, combined emergent “BioFused” activity – almost as if we were born with the capacity to talk to the world in at least three survival languages of the visual, auditory and emotional, that as we grow into a more complex sentient being, all begin to blend together into the emergent being we call the Conscious Soul.  This premise of innate brain languages would support why episodes of Synesthesia, or the criss-crossing of the perceptions, can take place using overlapping yet underlying cognitive, linguistic, semantic, syntactical, pragmatic, logical and emotive meaning.  From the right to the left brain, from the frontal lobes to the imagery domain at the back of the brain, to the cerebellum with its own firing mechanisms, to the top of the cortex versus the "bottom's up" deep brain, to the now described three language centers in one, it is obvious that the brain is in reality ‘Many Brains In One!’ – But still with apparently only one steganographic internal display mechanism (mental imagery).  Sentient Value # 7 is to develop a machine with such multiple, independent, yet interacting emergent BioFusion – the ability to mathematically separate or mathematically smooth emergent neural level circuits, as well as the inverse function, presented in some form of cognitive display.  See Alexander Zenkin’s work in Cognitive Graphics, which can be found at on web search engines.  This will be a much more difficult engineering task, but is not intractable.  Sentient Value # 7 is in fact BioFusion, containing emergence and display.



Illustrations depict the rich topology of emergent visual perception in the occipital area being ‘smoothed’ out in the coexisting BioFusion of the parietal area.


In order to understand the system-size tradeoff that brain evolution is undergoing, let’s take a moment to ‘percentage-wise’ partition the brain into its functions:  50% or more goes to hand-eye coordination, with another 10-15% for incorporation of verbal thinking that specifically allows the individual to word think complete hand-eye/body actions at faster than real time speed.  There are projections that word thought is at about 700 or more words per minute, while actual execution in speech is an order of magnitude slower.  Another facet of why humans are so well endowed with mental capability is the mental ability for such faster than real time rehearsal and incorporation into motor control for actual execution of elements within the portfolio of the human condition.  Given that 25 % or so of the brain is operating at very low levels of signal to noise, non-cognitive control of metabolism – leaves only about 10 to 15 % of the brain for what we could call Emergent Human Behavior.  Consider also the cerebellum for the rapid execution of learned motor firing circuits, in concert with the spinal cord and well extended central nervous system autonomic functions, and the brain is yet again seen as marvelously configured to operate in many independent, yet complimentary domains of action.


The time scale for BioFusion action is remarkably short.  The vast majority of the brain executes its portfolio of actions in seconds to tenths, to hundredths of seconds.  It is very hard for the brain consciously to concentrate for minutes or hours on end, almost as if in the striatum, our sense of time to dwell, our biochronicity is preset for the sub-second regime.  Can this be reset?  The answer would appear to be yes, if only at least from episodic documentary from periods of altered states and periods of time loss due to dissociative or fugue events.  This also does not preclude that the brain may be engaged in very long term, but non-conscious, mathematical processing.  So what would happen if suddenly, instantly, in fit of advanced, catastrophic evolutionary rage, that our brain would suddenly operate on a far more distant Time Slope of not seconds and partial seconds, but thought domains of hours, days, years – allowing Sentient Machines to handle the routine reasoning tasks of the lesser Time Limits?  Such time-thought testing is now available in Cortical Emulation Research (CER).  And where is the dark matter of the brain, the untapped regions that will provide for our future, perhaps even Accelerated Rates of Evolution?  The answer may exist at the layer in the anterior cingulate between the older brain, deeper brain and the outer folding top cover of the cortex, as well as in the less knotty, less complicated realm of the right side of the brain – ‘The God Spots!”  Just as the brain goes into bizarre periods of radical growth, then consolidation, and then massive pruning several times in its lifetime, maybe a new coding sequence can be triggered to shift Pre-Frontal evolution into the more mystical Life-Death interface of the Anterior Cingulate or the Ineffable, Kinesthetic Spiritual world of the right temporal cortex.  Sentient Value # 8 is to couple ineffable regions of the Sentient Machine with the faster than real time language rehearsal capability of the inverse function operating within BioFusion communication portions of the Sentient Machine.


Sentient Value # 9 is Reflexion.  Just as we spend a portion of our day in contemplation or reflection, reviewing events and making summations and forming lessons learned, even non-cognitively down to seven or even higher sigma classifications, so also must a sentient machine begin to probe its own data bases, and dream, and day dream, if you will.  Reflexion will begin the process of personality development in sentient machines.


A vital extension of Reflexion, which will further develop personality in sentient machines is play and exploration, creativity and imagination.  While we are engaged in reflecting upon our day, or week, or life – we almost spontaneously embark on wistful flights of play, exploring, creating, doodling, and imagining.  When this mental activity is seen as merely manipulating the internal measurement and direction and energy moats of our brain by streaming along, back and forth and across the Inverse Function, then it becomes apparent that even Sentient Value # 10, the combined features of play, exploration, creativity, and imagination, are all-ascertainable in engineering terms via advancements in BioFusion understanding.


Sentient Values #8, #9 and #10 combine to produce a wonderful facet of the human condition, and also a condition that most likely provided humans with an exceptional ability over other lesser intelligent competitors – the ability to look into a block of stone or a log of wood and perceive a beautiful statue or pleasing carving – the ability of controlling the inverse function in the future which is the key to Tool Making and Manipulation of the Environment.  The ability to look into a block of stone and see a face that is pleasing would involve the following neural reflexive circuit at a minimum, connections among the fusiform gyrus, nucleus accumbens, and amygdala, and then spreading out from this circuit.  Again, remember, more than fifty percent of the brain is geared to hand-eye coordination to execute the logic functions of abduction (spreading) but more importantly, adduction (selection-gripping, finger pointing, choice, free will).

But we still need to understand that Sentient Behavior is based on Mathematical Domains of interest.  So even the loyal and the growling machine will still need to move or have the information presented to it moved in such a way that stored invariant patterns can be matched to known mathematical domains.  This is the machine equivalent to satisfaction of Incomplete Neurophysiological Patterns that takes place in the human brain…this mathematical process can be represented synthetically in Krylov Space, named after the noted Russian non-linear mathematician Krylov.  



Illustration depicts regional functions of the brain, which could be also converted into a Krylov Space.


We all have a homunculus sitting in our heads.  In fact our brain does a very good job of taking our entire body from the head to the feet, to include our lips and hips, and flips them basically upside down and inside out, and voila, right under the tip of my finger or your finger right on the very top of my or your skull, a very interesting brain map of who I am, whom you are, is laid out in our cortex.  Studies indicate that various parts of our body get more or less of a ‘Shakespearean’ role in our various homunculi, with a great concentration of brain structure oriented to our hands, eyes, and mouth.  This would seem to make sense, since more than fifty percent of our brains are geared to hand-eye coordination and the ability to silently practice speaking to ourselves about the state of our human condition, or to faster than real time practice of hand eye-body movements.


Dr. Alenka Brown-VanHoozer would state that this represents the Visual, Auditory, and Kinesthetic (V, A, & K) parts of us, forming into circuits and belief systems that program us into our everyday actions.  Her arguments are that we process the world visually, that we also process the world in auditory terms, and those we also process the world with the rest of our brains, which she combines into the generalized term kinesthetic.  Each of us uses our own pattern of V, A and K in differing combinations to make interpretations of reality.  If our use of patterns is different from one another, then we measure differently, and as a result we have different belief sets and act differently to different Reflexive Controls.  But she also strongly suggests that information can itself be used to shape the belief patterns, to set up similar patterns and types of V, A, & K.  Given this, then Information Operations can be designed to create patterns of V, A, & K to orient a person, group or culture toward reflexive control in a desired belief set. 


Couple this to a finer understanding of Semiotic Reality and Inverse Mathematical programming in E and H field electromagnetics, and the stage is more fully set to engage in transforming the mental processes of humans in society via the internet and other transmission and communications devices such as the Next Generation Internet (NGI), as well as the augmentation of human society with reprogrammable V, A & K belief sets in the first generations of sentient machine societies.  Such an internal map of mental regions and even exact landmarks of sulcus and gyri on the brain where we expect certain thoughts to reside, or at least emanate, and the associated energy humps necessary to make and maintain such thoughts in the intense signal-to-noise competition for information in the human brain, will allow societies in future cyberspace and biospheres to precisely, scientifically, and to a firm legalistic determination, know the complete factors of ‘Truth Verification’ and even the complete portfolio of what makes something humorous, or artistic, even ethical and moral in the brain.  So Sentient Value #11, which can now begin to be incorporated into Machine Intelligence includes:  Truth, Justice, Humor, Art, Ethics and Morality.  It is important to note that brain scans already show that telling the truth requires less energy and tends to formulate along the outside edges of the cortex, while the development of falsity requires a greater energy flow and larger region(s) of the brain to ensemble to maintain deception action circuits.  At some point this will cross over from nice neurological findings to court admissible justification/probable cause legal action involving ‘Truth Verification – Truth Maintenance.”


The last Sentient Value is the concept of Fear or Death.  This can be programmed as the opposite of work - the cessation of purposeful work.  Such a concept of death and the lack of productive functioning may explain why humans have a strange central nervous system (CNS) where the afferent pathways are so much more qualitative, almost fiber optic like or wave division multiplex in operation, as opposed to the lesser quality, highly error prone efferent nervous pathway, or output motor control pathway.  We take in wonderful amounts of information but we do a very poor job of output of feedback to the environment.  Why would this be so?  Could there be some teleological or purposeful inclusion as an emergent byproduct of such an antinomy?  Perhaps we have fear and the ultimate fear of death, as a very precise signal coding sequence in our hippocampal structures.  Such fear of death would be close to our hormonal, circaddian, and emotional centers of our hippocampus, our sexual and reward centers around the nucleus accumbens, and our life-death focii in the anterior cingulate and superior colliculus.  The fear center is directly in our amygdala, that wonderful set of almond shaped fear generators at the end of a precisely tuned horseshoe shaped magic wand, the hippocampus, that can convert our life in an instant into raging terror and the fear of death, the complete cessation of IKE.  Suicide studies that map the brain during reenactments of the visualization process of past suicide attempts show a most interesting neural level circuitry that begins to form and then locks into almost a phase locked loop just before the memory of the actual suicide act fires.  Blood flow to the left prefrontal and right prefrontal splits, one going up and the other going down, with a concomitant energy spike in the superior colliculus, an evocation of mental imagery as opposed to external visual sources, and spurious signal sets in the nucleus accumbens.  When this pattern is locked in, the person recalls this as the moment when the final act of suicide kicked in.  If there is indeed such a death circuit in humans, can such an off switch also be emplaced in sentient machines for the cessation of IKE?  What would such an on-off switch look like?  Perhaps the following fMRI scan of an easily hypnotizable person can provide a viable brain illustration of such “On-Off” patterns in the brain.



Fear of Death, and its opposite No Fear, is an essential antinomy continuum as Sentient Value #12.  The reason we make mistakes is because our central nervous system is designed that way.  Because we make mistakes, we are then forced to seek out novel ways to fix things, or to seek out other people or machines to help fix our difficulties.  Making a machine that makes mistakes and is fearful of the death consequences will ensure that a machine with control of the inverse function will try to fix things.  Accordingly, we need to program sentient machines with random, chaotic, ‘can’t be fixed alone’ errors.  We must force the Machine to face death, thus prompting it to seek help to correct certain errors,  to join with other machines or humans, or face the inglorious cessation of IKE.  But maybe there is more than just a representative map of our body laid out in the cerebral cortex by which our intelligent actions and even our metabolism seem to take direction.  What if the brain itself is a mathematical topology, a multidimensional game table, a tableux upon which our many perceptions of reality are literally mathematical functions?  Pribram (91) suggested that perception would be found to be neural structures interacting with information to produce a Gabor-Like Function in Hilbert Space.  This would accommodate both classical and quantum computational aspects of life in the natural world.  The gabor represents a Shannon’s Law like element or compressed signal spike in a domain akin to what mathematician Hilbert in the late 1890’s was seeking, a mathematical expression, a place where a string or a spiral would most rapidly fill up the space that it was to occupy.  Hence, to find a Gabor-Like Function in Hilbert Space as the operant mathematical operation where neural structure interacts with information compressing it from the environment would be the precise math structure that one could use to define the exact moment when Perception occurs from the general state input from or of the Sensory Modalities.  A specific gabor function could then be assigned to each object perceived in the brain.  A data base could be built up, a thought code of mathematical expressions that literally is what the brain actually sees when information, like a bernoulli’s code, passes through neural structure.  Just as wind under an airfoil produces lift, a gabor function is the moment when information entering neural structure creates a thought.  Such a ‘Eureka’ moment was discovered in Pavlov’s Laboratory in 1996, by Dr. Juri Kropotov and his team.  They found that just as Pribram predicted, when you look at neural structure interacting with signal to noise information from the external environment, that a Gabor-Like Function in Hilbert Space emerges at the exact moment of perception from the sensory field.  Based on the work described in this paper, BioFusion R&D findings strongly suggest earlier predictions that human brain perceptual processes represent, at a minimum, an n-dimensional family of interacting Gabor-Like Functions in Hilbert Space (Pribram-91).


Even more extraordinary, Dr. Kropotov was able to capture the complex adaptive rules of mental functions, perceptual activity across sensory modalities, into software to produce Cortical Emulation Research, by which the same math functions that appear in brains, can now be made to emerge in software.  This finding of extreme importance leads us to Information Injection via the introduction or playback of the Inverse Function of the Gabor in Hilbert Space, or whatever other mathematical domain that also may be workable in various species’ brains. Thoughts then could be categorized as either culturally dependent, or when synthetically produced, as culturally independent.  Both culturally independent and dependent thought means that machines could be produced that could conceivably never be able to communicate with a human.  It/they would exist in its/their own perceptual world made up of its/their own mathematical thought structures.  But more likely is that some common, semiotic language of human-machine interests will arise that can universally transform to some degree each particular species, to include synthetic species, into emergent mathematical thought domains.


Below is taxonomy of other Mathematical Domains that perform Space-Time-Frequency-Accuracy functions.



Nature is rich in complex adaptive systems (CAS), and can provide suitable biologic models for developing improved closed and open system intelligent control.  Results of such research will allow for improved Crew/Vehicle developments generating direct interface systems level engineering packages for inclusion in advanced aerospace technology applications and programs.

The twelve sentient values are then:


1.  Identification

07.  BioFusion (overlap/emergent S:N Math

2.  Motion

08.  Couple Ineffable States to Comms

3.  Direction

09.  Reflexion – Daydreaming

4.  Measurement

10.  Play, Exploration, Creativity (Make Tools)

5.  Resource Supply

11.  Truth, Justice, Humor, Art, Ethics, Morals

6.  Emotion

12.  Fear of Death / Cessation of IKE


Personality will not need to be a Sentient Value.  Personality will arise as an emergent property of these twelve SV’s, and most likely as a function of values 9,10, 11 and 12.


By way of comparison and contrast, here are the properties that William Calvin suggests are important.  William H. Calvin picked about six (6) to (9) Darwinian aspects to intelligent behavior - slightly expanded here to capture the full gamut:


  1. Pattern
  2. Copy
  3. Change/Edit
  4. Compete
  5. Environmental Stress
  6. Survive to Copy
  7. Search Images - Invariant Structures, Play, Practice, Groove Brain
  8. String Things Together
  9. Plan Ahead, Rehearsal

…and, underlying all this is Inverse Functions.  



The concept of injection of information for Information Operations from one human into another human, or from a machine generation of information into a human, the inverse function is utmost and vital.  In order to trigger, or refine, or replace, or sharpen an old perception in the human, or to create brand new perceptions, the exact inverse function must be known, or very close to it, in order to fool the brain into accepting it as real.  And this inverse injection must also very closely model the exact E and H fields, the electromagnetic field shapes that the original Gabor-like Function in Hilbert Space occupied. The inverse function is pure mental deception, but when one considers the role of medicine and its efficacy, what does it lead from?  Medicine works because it Burns You, Cuts You, Poison You, or Fools You!  Information in this case will be used to Fool You into believing that what you perceive is indeed real.  Now our brains do this all the time.  We possess Mental Imagination.  We can close our eyes and call forth all kinds of images, sound types, voices, and even feelings, emotions, kinesthetics of all kinds, mostly emanating from the Fusiform Gyrus in the case of prosopopoeia and from the left temporal sulcus for auditory manifestation of voices.  Actors and Actresses do this all the time; stimulate the elucidation of the internal circuits, and quite well.  So do people with some forms of brain damage or other mental incapacity, such as schizophrenia. 


In fact, study after study is showing that the internal brain circuits, ’The Internal Irritants of our Psyche,’ are really two thirds or more the same circuits that fire from the external cortex, but in this case are the inverse agonistic and antagonistic circuits from the deep internal brain regions firing stored information outward – (the inverse function).  It is as if outside reality is matched one for one by deep internal reality, compressed information coming in, meeting compressed information unleashed from within.  The result, new brain patterns, reinforced circuits, modified memory fields, and complete brain regions producing emergent mathematical operations that are even more complex than before. The inverse function is the key to human action, the key to reflexive control for sentient machines.  The inverse function of what?  The answer is the inverse of Gabor-Like functions operating in Hilbert Space, and ultimately the ability to record and store the complete Krylov Space, the steganaographic ‘biomark’ of an individual, for future playback to another individual or sentient receptive machine.  IBM's Blue Gene is already looking at proteins in their original pristine Orchestrated Reduction state, before they begin to reconfigure, to IKE, to include the exact inverse functional states – giving insight into quantum states, and electromagneticE/H fields -- The mathematics of proteins that underlay the mathematics of thought - the onset of the era of Sentient Machines.



Copyright © 2000 Lockheed Martin Corporation - USA.  All Rights Reserved.



Additional  References:


Web Sites:


See Norseen, Semiotics.




Go to Bulletin Vol. 20 #2  See C.S. Peirce, Nozawa.


See Famous Curves Index.


See BioSemiotics Home Page.


Go to WMD  See The Mind Has No Firewall, by Tim Thomas.


Alpha Rhythm Emerges.




See History/Survey of Krylov Methods.


See Science Vol.281 07 Aug 98 pgs. 814 – 818, Callosal Window Between Prefrontal Cortices:  Cognitive Interaction to Retrieve Longterm Memory.


See Decision and Control.



See Orchestrated Reduction – Protein Microtubulin Cytoskeletal Structures.



See emergent intelligence research in SOAR concepts.



See John F. Sowa work in conceptual graphs, intelligence/knowledge engineering.



See William H. Calvin work in emergent intelligence.


Copyright © 2000 Lockheed Martin Corporation - USA.  All Rights Reserved.




Additional Written Materials:


Burch, Robert W., The VINITI Program, Army Research Laboratory, ARL-CR-212, June 97.


Calvin, William H., “The Emergence of Intelligence,” Scientific American 271(4): 100-107, Oct. 1994.  See website:


Clynes, Manfred, “Time Forms, Nature’s Generators and Communicators of Emotion,” Keynote Paper, IEEE International Workshop on Robot and Human Communication, Tokoyo, Japan, September 1992.  See the following website:


Coombs, Mike and Sulcoski, Mark, Control Mechanisms for Complex Systems:  Issues of Measurement and Semiotic Analysis, Proceedings of the Las Cruces, New Mexico 1996 International Workshop, December 8-12, 1996.


Dickhaut, Richard H., Neuroelectric Activity and Analysis in Support of Direct Brainwave to Computer Interface Development, Office of Naval Research Grant # N00014-97-1-0926, June 29, 1998.


Miller, L.D., and Sulcoski, M.F., Reflexive Models of Human Behavior:  Variations on a Lefebvre Theme, Proceedings of the Los Alamos, New Mexico Workshop on Multi-Reflexive Models of Agent Behavior, 18-20 August 1998, Army Research Laboratory, ARL-SR-63, August 1998.


Montgomery, L.D. and Gleason, C.R., “Simultaneous Use of Rheoencephalography and Electroencephalograhy for the Monitoring of Cerebral Function,” Aviation, Space, and Environmental Medicine, April 1992.


Pribram, Karl H., Brain and Perception:  Holonomy and Structure in Figural Processing, Erlbaum Publishing, 1991.


Pospelov, Dimitri, in Proceedings of March 20-29, Columbus, Ohio Workshop on “Russian Situation Control and Cybernetic/Semiotic Modeling,” by Battelle, Edit. Stohl, Robert J.,  March 31, 1996.


Copyright © 2000 Lockheed Martin Corporation - USA.  All Rights Reserved.



Other Information:




BioFusion For Intelligent System Control, Norseen, Kropotov, Kremen, Proceedings of SPIE, Sensor Fusion: Architectures, Algorithms, and Applications III, pages 411-417, 7-9 April 1999.


BioFusion R&D Report, Norseen, Contract #N66001-97-C-8605, WO 31-1856, 29 September 1999.


Visual-Spatial Ability of Pilots, I. Dror, S. Kosslyn, W. Waag, Journal of Applied Psychology, pgs. 763-773, 1993.


Journey to the Center of My Mind, S. Hall, New York Times, Section 6, page 122, column 1, 06 June 1999.


Workshop on Multi-Reflexive Models of Behavior, V. Lefebre, ARL-SR-64, May 1999.


Reflexive Control in Multi-Subjective and Multi-Agent Systems, V. Lepsky, ARL-SR-64, May 1999.


Using Ketamine to Induce the Near-Death Experience:  Mechanisms of Action and Theraputic Potential, K. Jansen, 1996. BioFusion R&D  Peircian Semiotics  Dr. Dror – Pilot Mental Skills


http://  Dr. J. H. Downs III  NeuroVisualization  Dr. Crawford  Pain-Hypnosis  Dr. Kropotov   Pavlov’s Lab CER Software  See Alenka Brown-VanHoozer for her work in Auditory, Visual and Kinesthetic intelligence.  Time Forms – Sentic Forms, Sentic Mouse, Manfred Clynes – Emotional Alphabets   Norseen International, Yardley, PA.  See Alexander Zenkins conceptual graphs, number theory of intelligence transfer.  See Victor Finn’s work in Quasi-Axiomatic Theory, being reproduced in the Texas A&M Laboratory of Dr. Robert Burch.



Copyright © 2000 Lockheed Martin Corporation - USA.  All Rights Reserved.