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My son suffers from a communication and cognition disorder known as autism, a condition in which his world does not fully overlap with ours. His world appears to orbit a sun outside of our own, one we cannot see nor follow, one of immense joy. He is often the embodiment of bliss, moving and giggling, swallowed in a light of his own making; and that is his problem: He rarely drops from his heavenly realm to receive instruction from this one.

Autistic children show deficits in sociability, communication, and imaginative play as well as exhibiting stereotypical motor behaviors. My son is uniquely hyper-social, constantly seeking interaction with everyone he finds, making few distinctions between people, calling girls boys and by the names of babysitters they resemble. When we are out and about and I warn him not to "stranger talk", he approaches everyone just the same, taking a stranger's hand, hugging "Grandma" at the supermarket, because to him there are no such things as strangers.

In actuality, his world orbits not a sun but a black hole, an infinite collapse, a darkness built not of evil but of loss, separation, and ultimately isolation, and he continues to be drawn inwards. He is in his 9th orbit around our sun but spiraling ever faster away from it. When he was 3, he underwent 20 sessions of SMR uptraining. I was fortunate to train him incorrectly on the first day so I knew immediately how much impact the training had -- all in the wrong direction. We trained 12-15 Hz up and he wet his bed that night for the first time in a year and became aggressive in school. SMR was his beta rhythm and we had aroused or disinhibited him. So we lowered the frequency in later training sessions and some inhibition returned to his nature. [Wrong-training is a useful lesson for anyone who thinks neurofeedback is a placebo. A session or two in the wrong direction -- compel someone into a neurochemical depression (e.g., downtrained alpha F4, uptrained alpha F3) -- will open their eyes to the power of rhythm training.]

I trained him in a car seat, a helpful restraint, but after 20 sessions on the Neurocybernetics system, he stared at a filing cabinet instead of the computer monitor. He had burnt out on the games, which led to a multi-year hiatus from training as I invented a set of "Infinite Content" games for him. Last year a student of mine (Justine Paoletti) trained him another 20 sessions, mostly to induce rhythmicities in his temporal poles. He shows very little dominnt frequency, making the term "dominant frequency" oxymoronic. Soon after his initial set of training we discovered that his sleep spindle, and presumably sensorimotor rhythm, was in the 10-12 Hz range, overlapping his alpha range -- and this may be common to autistics.

Autism involves severe disturbances of attention, often with evidence of compromised temporal lobe function (Gendry et al., 2005). A careful QEEG assessment of my son's data showed elevated delta in his right temporal lobe. Delta activity is perfectly normal -- for an infant, for cortex prior to subcortical connection. Apparently this part of his brain never joined the thalamocortical confederacy that governed the rest of his cortex; it never matured past infancy. And it is this area of the temporal lobe which is important in the formation of episodic memories, so I suspect his autobiographic sense of himself is infantile, like a schizophrenic's. His sense of experience often collapses to self-referentiality, which is why he laughs inappropriately, treats others as objects, and generally has difficulty with social information. His internal mental representations shout while the sensory stream from the outside world remains a whisper. We have to train him to shush his auto-relational representation and grab hold of those provided from without, so he can expand his world.

Neurofeedback training has been shown to be beneficial for seizures, hyperactivity, attention problems, anxiety, and sleep disturbances (Egner & Sterman, 2006; Monastra et al., 2005; Hammond, 2005; Hauri 1981). We evaluated the impact of operant conditioning of temporal lobe activity on behavioral, psychophysiological, and neurocognitive function. The goal was to induce greater rhythmicity to his anterior temporal poles, especially right sided.

Method
My son was diagnosed at three years of age with autism and recent training used a 2-channel system. Feedback images included animals, ocean life, children playing, and family members. Audio feedback included statements by his mother such as "you can do it" or his brother exclaiming "Perfect!" and other comments and sounds. A Neuro-ABC (Autism Behavior Checklist), Autism Treatment Evaluation Checklist (ATEC), and WISC digit span were administered pre and post training.

He underwent 20 half-hour neurotherapy sessions and was evaluated pre- and post-training. Training montages were C3-to-contralateral ear for the first 4 sessions and T3-T4 bipolar training for the remaining 16 sessions to address emotional lability. As the subject's SMR rhythm was atypically slow (cf. Kaiser, 2002), reward band was set at 9-14 Hz, with 2-7 Hz and 22-30 Hz inhibit bands to control artifact. Jarusiewicz (2002) also began with a slower SMR reward band, 10-13 Hz or lower depending upon the child's condition.

Results
Cognitive & Behavioral Assessments: Forward digit span improved from 4 items to 5 items after training (i.e., 35th to 69th percentile improvement for his age) although the Neuro-ABC and ATEC assessments were inconclusive.

Behavioral Observations: He was highly engaged by images and voices of family members. He became much calmer and less talkative during sessions when familial stimuli were used as rewards. In addition to images, the client screen presented filtered EEG signals and he attended to these complex signals as he discovered how to alter his breathing to produce SMR bursts, with subsequent reward, by the 3rd session. After 19 sessions he showed signs of improved self-regulation by cleaning up and washing his hair on his own. Greater rhythmicity was evident across EEG sites after training.

Operant conditioning of temporal lobe activity produced signs of EEG and cognitive normalization: there was increased EEG rhythmicity during baseline recordings and improvement in memory span performance. Social functioning was specifically targeted by temporal lobe training and the use of social and emotional rewards (e.g., pictures of children playing, faces, and emotional expressions) and some improvements were observed in this domain, although a quantitative assessment of sociality was not performed. That symptom changes were observed after only 20 sessions is remarkable and additional training sessions are recommended as most clinical studies for this population involve 30 or more sessions. (This work was part of my student Justine Paoletti's Senior project for Psychology at RIT.)

In my experience autism is a disorder of agency: too much agency, too little reception, probably due to too much testosterone and too little estrogen, a neuroendocrine disorder with neuroanatomical and physiological consequences. Inhibition training (along with connectivity training) ought to be very useful in addressing hyper-agency, especially if the area of the cortex disconnected from subcortical influence can be identified. After a modicum of training (40 sessions), and a many other interventions, my son was recently diagnosed with P.D.D. by one psychiatrist who worked with him briefly. But this is wishful thinking as my son's world still orbits that black hole and he may collapse into infinite auto-relation at any given moment. Our goal is to slow and reverse his collapse but only time will tell if we are successful and he can join the expanding universe.

References

Egner T, & Sterman MB (2006). Neurofeedback treatment of epilepsy: from basic rationale to practical application. Expert Review of Neurotherapeutics, 6, 247-57.

Gendry I, Zilbovicius M Boddaert N, Robel L, Philippe A, Sfaello I et al. (2005). Autism severity and temporal lobe functional abnormalities. National Library of Science Medicine, 58, 466-900.

Hammond DC (2005). Neurofeedback with anxiety and affective disorders. Child and adolescent psychiatric clinics of North America, 14, 105-23.

Hauri P (1981). Treating psychophysiologic insomnia with biofeedback. Archives of Gen. Psychiatry, 38, 752-758.

Jarusiewicz B (2002). Efficacy of neurofeedback for children in the Autistic Spectrum: A Pilot Study. Journal of Neurotherapy, 6, 39-49

Kaiser DA (2002). Rethinking Standard Bands. Journal of Neurotherapy, 5, 87-96.

Monastra VJ, Lynn S, Linden M, Lubar JF, Gruzelier J, & LaVaque TJ. (2005). Electroencephalographic biofeedback in the treatment of AD/HD. Applied Psychophysiology and Biofeedback, 30, 95-114.

Paoletti JL & Kaiser DA (2006). Neurotherapeutic Assessment and Training of an Autistic Individual. Presented at 37th Assoc. Applied Psychophysiology & Biofeedback, Portland, OR, April 7.

-DK

News & Reviews NEW BOOKS

Rhythms of the Brain
by Gyorgy Buzsaki
Mechanisms and functions of neuronal synchronization. --www.amazon.com/exec/obidos/ASIN/0195301064/eegspectrum

Epilepsy: A New Approach
by Adrienne Richard, J Reiter
Medical and self-help techniques from a writer with epilepsy and a physician. --www.amazon.com/exec/obidos/ASIN/0802774652/eegspectrum

Head Injury: The Facts
by Dorothy Gronwall, P Wrightson, P Waddel
Stages that a TBI patient undergoes after the injury is described. --www.amazon.com/exec/obidos/ASIN/0192627139/eegspectrum

Is This Your Child
by Doris Rapp
Unrecognized allergies may be the source of a "problem" children. --www.amazon.com/exec/obidos/ASIN/0688119077/eegspectrum

Computational Explorations in Cognitive Neuroscience
by RC O'Reilly, Y Munakata
Basic neural computation mechanisms from individual neurons to neural networks to learning mechanisms up to large-scale brain areas. --www.amazon.com/exec/obidos/ASIN/0262650541/eegspectrum

Living with Brain Injury: A Guide for Families
by RC Senelick, Karla Dougherty
Updated edition discusses neuroplaticity and experimental rehabilitation research. --www.amazon.com/exec/obidos/ASIN/1891525093/eegspectrum

Dancing with Fear: Overcoming Anxiety in a World of Stress and Uncertainty
by Paul Foxman
Written for professionals treating anxiety disorder. --www.amazon.com/exec/obidos/ASIN/0765701502/eegspectrum

Promise of the QEEG of Treatment for Major Depressive Disorder. : Neurophysiologic function of frontal lobe before treatment and after antidepressant treatment begins correlate with clinical outcomes. www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=17362807

EEG neurofeedback: peak alpha frequency training for cognitive enhancement : Double-blind controlled design determined that peak alpha frequency NF improved cognitive processing speed and executive function, but no clear impact on memory. www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=17366280

Cortical Connectivity Reflected in EEG Coherence in Autism. : Locally elevated theta coherence was found for ASD adults, especially within left hemisphere frontal and temporal lobe. www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=17336944

Hemodynamic response of the alpha rhythm: An EEG/fMRI study. : EEG coregistered with fMRI scanning found inconsistent results with alpha activity. www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=17336548

Developmental transition to alpha band in developmental disabilities. : Developmental transition of EEG spectra to alpha band takes additional years in the developmental disabled. www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=17326512

Opioid withdrawal results and functional connectivity at alpha and beta bands. : Withdrawal increased functional cortical connectivity in 13 opioid-dependent patients and this correlated with severity. www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=17320230

Mind does really matter: neuroimaging studies of emotional self-regulation : Neuroimaging data shows how subjectivity and intentional content influence brain function at various levels. www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=17349730

Brief motivational intervention with psychophysiological feedback for cocaine abuse. : EEG/ERP feedback for cocaine abusers found effectiveness of neurofeedback on relapse. www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=17347121

Every Friday in 3rd grade math class (35 years ago) we would play a game of competitive flash cards. Two children would stand up and Mrs Thurston, our teacher, would turn over a flash card with a problem such as "8x7" If you answered "56" before the girl or boy standing next to you could, you continued your turn and stepped to the next row while your opponent took the open seat beside you. Some minds break out earlier than others and math is where my mind emerged. My mental world was individuated at an early point in development and I suspect much of my sense of self remains shaped by such early individuation. I was not able to hide in plain sight as some children do.

As of late I've returned to 3rd grade, becoming more mathematically-minded, less narrative minded. I've been corresponding with a few mathematicians and physicists via the ArXiv, an online repository of p/reprints for math, physics, and all things quantitative. Many of the scientists who work at uncovering the contours of our universe speak of God matter-of-factly, without reserve, as they attempt to look over His/Her shoulder to crib answers off the Test, this universe, as it were.

Autism, as the name implies, is a severe form of auto-relation, an inertness, like the noble gases Argon or Helium which rarely mix with other gases. We all have degrees of autism in that we all live within a world of our own making, unshared in the details, though the gross sweep of events are communal. Like turtles we all live in our own shell. Some of us poke our legs and head out very far while others retreat at the slightest provocation. My autistic son thinks we inhabit his shell, which is a nice thought, but not always easy to deal with.

So my brief proof is about auto-relation. Auto-relation is my term for a number raised to a power, a number multiplied by itself over and over again. The most interesting auto-relation is 1 raised to any power as it remains itself (1) forever.... or so we thought. I show that it doesn't in my little proof. (This is not like saying 2+2 = 5 for large values of 2, but actually using the rules of mathematics to punch a hole into auto-relation.)

Fortunately my mathematics rarely venture into concepts beyond the 12th grade level but in this case I need a little Cantor, which is college sophomore math (i.e., his work on infinities). And for those who hate math, rest assured, language is a stronger form of math than math, as it possesses causality and agency whereas math is impotent on these matters. Everything math can do so can language, although math is often more economic in expression. Language allows higher forms of relation, as shown by its location in the brain (i.e., more of its operations are performed in the front of the brain than math).

I shopped this paper around to a handful of old-guard mathematicians, which has been interesting. None said it was wrong (yet?), only that it is unconventional and enigmatic. Mathematical formulations can be as beautiful as a sonnet, or more so, given their universality. My mathematical proof uncovers an until-now hidden point of creation, and makes a commentary on autism, although that is hidden in the equations. An autistic limits his auto-relation and in doing so, fails to create anything but himself. Only by making all things you, transfinite auto-relation, do we make all things.

I can forward my brief paper to whoever cares to read it, but I can summarize it here.

Entitled "Infinite auto-relation and dimensionality", using a simple technique of identifying dimensions or number planes: square-root of -1 = i, square-root (-i)=j;, sqr (-j)=k, etc., until we've run the square-root(-...) infinitely so. Now start on i, the imaginary plane, and ask at what point do we hyperdimensionally rotate to get to 1, the real plane. Think of it like a circular table setting, with your father sitting at your right side, and he asked to you to pass the potatoes to him, but you can only pass objects to the left side of the table. Now the table is infinite in size, infinite place settings, just like those family clan dinners on Thanksgiving. My proof looks at how many people or passes will it take until the potatoes reach him. Taking the square-root (-(square-root(-x)) is a trick which forces only leftward passing. And those who encountered complex math in 11th grade know that the real and imaginary planes are adjacent, square-root (-1) = i, which in this analogy means adjacent to the right.

There are five possibilities for passing the potatoes leftward to reach my father at my right side: Either (1) the potatoes can never reach him (the table is endless but in a way which doesn't include him, which isn't fair or correct), or (2) the potatoes reach him and continue leftwards and onwards to me, which mean they did reach him at some point in the passing, or (3) the potatoes fall short and remain a few passings away from him, which means infinity ran out of gas which it is not allowed to do, or (4) the potatoes reach me and I am my father, but I am not him so that's cheating (and doesn't meet the orthogonality requirement), so what remains is an infinite amount of passes (called Aleph_0 by Cantor) to reach him.

Simple, but it now places i and 1 in "bidirectional" relationship with each other, which for some reason no one took the time in doing. Either one pass to the right or an infinite amount to the left. Now the passes (dimensions) were based on my square-root(-...) trick, and we can rewrite the formula so (sqr-(sqr-...sqr(-i) = 1 becomes -i = 1 [squared raised to infinity], which means 1 raised to Aleph-1 + i = 0, so when 1 is multiplied by itself an infinite number of times (the infinity of the continuum), it becomes imaginary (i.e., equal to -i).

1^c + i = 0

I've sent it around and no one has found the flaw (yet?). As my wife would ask, so what? Well, here is my conclusion:

Infinite auto-relation of a mathematical nature (1 multiplied by itself and itself ...) features orthogonal extension of similar magnitude. Does a similar principle of dimensionality and auto-relation underline nature? Does physical reality necessarily feature non-physical dimension of comparable magnitude? Or conversely, does mental auto-relation necessarily attain physicality at some point? Further understanding of auto-relation and dimensionality may shed light on the mind-brain problem, such as how neurophysical events are associated with qualia (i.e., mental experience).

Metaphorically, the 1^c is seen by me as God thinking "I am what I am" an infinite number of times, and then an infinite number of times beyond that, and in doing this S/He manifests Him/Herself orthogonally, with equal strength, as a new plane of existence which we experience as the universe. More amazing is when our minds and all those around us are doing exactly the same thing.