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November 13, 1996

Dr. Philip J. Corr, Ph.D.
Lecturer in Psychology
Psychology Department
GOLDSMITHS COLLEGE
University of London
New Cross, LONDON  SE14 6NW
ENGLAND,  U.K.

Dear Phil:

 I have had a chance to study your three 1995 papers with Jeffrey Gray, Glenn Wilson et al.  We have a great deal to talk about on the topics of Eysenck's Arousal/Activation, Gray's BIS/BAS and the Cartesian Theory. Much of this discussion is detailed, specific and experimentally based and involves much experimental data from the literature.
 It is reported that when Freud first met Jung they talked for 14 hours;  I have the feeling that we could easily duplicate that... but obviously not in a single letter!

 So, rather than write you a lengthy communication; launching right into a discussion of how the Cartesian Theory explains Arousal/Activation, identifies Gray's BIS/BAS as the two lateralized halves of the SHS and reconciles Eysenck's and Gray's biological models etc., I have decided that it would be more to the point to answer the few essential points you have raised in your letter of October 18th.

 You raise the fundamental issue in that letter; that:

 "Apart from gross morphological features, why should
 Cartesian space determine neuropsychological space?"

 First, let me underscore and emphasize most strongly, that it is precisely an understanding and comprehension of this point that is the sine qua non of the entire Cartesian Theory!  Furthermore, it is precisely an understanding of this point that, in general, is preventing Psychology from comprehending the Cartesian Theory.  I have briefly discussed this matter with Hans Eysenck himself in Montreal, and its clear that he doesn't understand it; to wit, when I tried to impress on him the axiomatic nature of the fact that E, N and P originate biologically in the first 3 cleavages of the egg (cf. Roux 1888; Conklin 05, 06) he said to me:  "I don't see the relevance of it."  Well, unfortunately I was so sick and exhausted by the time I reached Montreal that I wasn't able to respond adequately with something like; "it demonstrates that E,N,P have biological parity." or some such technically concise answer.  Anyway, upon subsequent reflection, I'm rather glad that our meeting remained rather on the personal wavelength than on the technical; because I don't think it proper in the first place for someone like me to be engaging someone like Hans Eysenck on the technical/argumentative level... I think its more appropriate that other technical experts take a look at it and form an opinion first.  That's where I think someone like you comes in, because apparently you are an experimentalist.  I notice that your Ph.D. thesis was on an investigation of the biological bases of the Structural Model of Personality.  Such a topic could not be more appropriate to this discussion.  I have only discussed this theory at length with one other person, Paul Barrett, and despite his association with the Biosignal Laboratory he strikes me as more committed to psychometric questions than experimental.
 At any rate, here we are, and I would like to see if it is possible to explain to you "why real Cartesian space causes psychometric Cartesian space".
 the first thing I notice is that in your statement (quoted above) you do allow as how the "gross morphological features" of the vertebrate body and brain are apparently 3-axis Cartesian.  At least that's my reading of your statement; when you say "Apart from gross morphological features, ..?".  I interpret this to mean that while you do allow as how the "gross morphological features" of the brain appear to be de facto 3-axis Cartesian... your question really is; why should Psychometry be 3-axis Cartesian as a general stand alone scientific rule in its own right?  I gather at least, that that is your question.
 Well, let me insist that there is an answer to this question and that the trouble lies in the fact that the answer derives from (theoretical) Physics and not from (empirical) Psychology; that's the problem!
 The "simple" answer to the question is this:  That the "gross morphological features" of the vertebrate body and CNS are not simply de facto 3-axis Cartesian; they are axiomatically 3-axis Cartesian.  There is a world of difference between "de facto" and "axiomatic".
 O.k., so let me dispose of this "axiomatic issue" before I get into the micro-mechanics of how, phenomenologically, Cartesian space causes Cartesian psychological space.  This latter discussion I'm  sure you'll find more interesting; probably being better versed in "Natural Science" while the former "axiomatic question" involves axiomatic science, that is, Theoretical Physics.
 Anyway, taking up the "axiomatic" issue first:  There is a fundamental law of Physics (wch. is not something we would expect Psychologists to be generally aware of) that may be paraphrased as follows:

 Any machine designed to freely operate in
 (or span) N-dimensional space, must have a minimum of N
 orthogonal mechanical axes of structure (i.e. must have N
 mechanical degrees of freedom).

Now, for the human body, N=3 (three dimensions), because we are designed to operate in (or fully span) 3-dimensional space.
 A typewriter and T.V. are examples of N=2 (scroll and carriage return; horizontal and vertical hold).  An airplane has N=3 (pitch, roll and yaw), and so does the vertebrate body (the 3 semicircular canals detect
pitch, roll and yaw along the 3-cartesian body axes in the human); Figure 1.

 Figure 1

 Now since is an "axiomatic law" of classical mechanics, we see that the "3-mechanical axes" of the human body are not accidental, fortuitous or de facto... no, they are preordained by an axiomatic mechanical law from classical Physics.  the body must have 3-orthogonal mechanical axes, no less than 3, no more than 3, and precisely 3.  This is a primary law of Physics and it can be accurately said that it is a law of Physics that "man is created in the image of the Cartesian coordinate system".
 All right, so much for the elementary mechanical structure of the human body; it's axiomatic, but how do we get from there to the psychometric structure of man?  That turns out to be a very interesting Natural Science story; the story I shall embark on next.

 As I have pointed out, a fish, is the simplest example of this (now axiomatic) 3-axis biological structure, but it turns out that the "generalized vertebrate body plan" clearly manifests this structure (Fig. 2):
 

 Figures 2 and 3

In this diagram we see the medial, lateral and transverse septums defining these 3-Cartesian axes in the gross anatomical structure of the vertebrate animal.  Note that the hypaxial and epaxial muscles (esp. in a fish) clearly highlight the "axial quadrature" of the vertebrate body plan.  So the primitive vertebrate body plan may be reduced to a simple 3-axis diagram thus (Fig. 3):
 

X = dorso-ventral axis
Y = left-right axis                 (see Fig. 3)
Z = cranio-caudal axis
 

 Now, so far we haven't said anything about the nervous system, and in order to do so we have to survey the entire evolutionary history of zoology (I will attempt to do this in a few paragraphs).
 all animals begin as a single cell, the egg.  This egg, itself, has a 3-axis Cartesian structure.  You can in other words, draw a 3-axis "Cartesian homunculus" right inside the egg itself with the head at the "animal pole" and the feet at the "vegetal pole" (Fig. 4):

 Figures 4 and 5

 The egg begins expressing this body structure through "binary Cartesian cell division" and the first 3-cleavages are precisely along the 3 body axes of the homunculus x,y,z in Fig. 4.
 Shown in Fig. 5 are the first 3 orthogonal (Cartesian) cleavages; producing the 2,4 and 8 cell stages of the embryo.

Fig. 5 (above)

 Now next, I am about to describe one of the most important scientific discoveries in the history of biology, namely Wilhelm Roux's celebrated discovery of 1888.  This experiment rocked the scientific world and earned Roux the title of "Father of Modern Embryology".  Roux was watching a frog's egg collected from a local pond with a magnifying glass.  He observed it make the first cleavage to the 2 cell stage.  On what impulse Heaven only knows, he took a common pin and heated it in the candle flame and stuck one of the cells... pssst!  He then let the thing continue to cleave and grow.  The result was astonishing... it grew into half a frog!  Only the right half of the tadpole emerged.. the left half was entirely missing.  Roux had discovered that the first cell cleavage of life produces the bilateral symmetry line of the human body (including notably the medial fissure of the brain).
 Conklin in 1905, 06 continuing this research on Styela also confirmed that if you separate the front two cells from the back two in the 4 cell stage (dorso-ventral separation instead of left-right separation) you will produce 2 "half embryos", only this time a front half and a back half!  A sketch of all this is shown in Fig 6.

 Figure 6

Now what does this prove?  It proves that the vertebrate body is "theoretically" an axial quadrature which is isomorphic with the first 3 Cartesian cleavages of the egg.  It shows that the first 3 cleavages of the egg are isomorphic with the 3 Cartesian axes of the "generalized vertebrate body plan" shown in Fig. 2.
 In particular it shows that the Sperrian and Bell-Magendian divisions of the brain derive from the same elementary biological mechanism- namely the first and second orthogonal Cartesian cleavages of the egg.

 Now, leaving embryology for a minute, we have to turn to zoological evolution; mainly to elucidate the history of the geometric origin (structure) of the CNS.
 The most primitive animals (sessile animals) only display clear Cartesian structure in the early Cartesian-binary formative stages of embryology (which we have been discussing above).  Until they are subject to the Cartesian dynamics of movement (moving animals), this initial Cartesian influence on body form may peter out as the animal gets larger.. but it is evident even in such primitive sessile animals as the Hydra or certainly in bivalves (clams).  However, once we proceed up the evolutionary chain to moving animals, the Cartesian axiom takes over and transforms the original formative Cartesian structure (wch. in itself is a static formative Cartesian necessity; probably deriving from molecular Cartesian structure bonding structure itself; the p-orbitals are Cartesian) and Cartesian structure is reimposed on the macroscopic "gross anatomy" form of the body itself.  A longitudinal axis develops first and immediately thereafter bilateral symmetry appears.  By the time we get up into the cephalopods, chordates and vertebrates, the 3-axis macroscopic body form is fully established (Fig. 2).
 O.k. so we have seen that 3-axis Cartesian structure is used in the formative stage of  all animals and is continued directly up to the gross anatomy stage in moving animals... manifesting its most fully expressed degree  in the vertebrates.
 On the subject of moving animals, quite a bit more has to be said vis a vis 3-axis Cartesian structure... wch. I will only briefly outline here.  Moving animals immediately adopt a "longitudinal" body plan.  While a sponge or a jellyfish may simply be a blob, a worm, a fish, and insect or any animal engaged in active travel, immediately adopts a "lengthwise" body plan with the body axis pointing in the direction of motion and with the head and mouth at the front and the aboral end at the back.  This "travel" axis corresponds to the "z-axis" in the egg (cf. Fig. 4).  O.k. so we now have a bilateral, longitudinal, prone animal.  The only axis left of the 3 is the dorso-ventral axis, which now corresponds to the top and bottom (back and belly) of the animal.  This is now coincident with the up vs. down direction in the terrestrial Cartesian coordinate frame of reference.  The 3-body axes have now permanently aligned themselves with the "horizontal, vertical and forwards-backwards" axes of the terrestrial environment.  This body axis orientation first becomes firmly established in the Cambrian invertebrates, chordates (primitive fishes), insects, vertebrates and finally the tetrapod vertebrates (4 legged animals, including man).
 Alright, we have seen the axiomatic origin of the 3-axis Cartesian vertebrate body plan, and we have seen the evolutionary orientation of the 3 body axes to the 3 terrestrial Cartesian axes of the environment.  This process has created the physical, geometric, appearance of the higher tetrapod life forms e.g. a cow, a horse or a dog.  From there to man, with the well known 90 degree rotation of the longitudinal axis for bipedal gait is simply a trivial final step in this 4-billion year saga.
 But we have yet to mention the geometry of the CNS... where does the structure of the nervous system enter into the evolutionary picture?
 The main purpose of the nervous system is the motor-sensory reflex.  This reflex predates even the evolution of the neuron.  An Amoeba exhibits motor-sensory reflex- if you touch it, it moves away, and yet, there isn't a single nerve cell in an Amoeba!
 A study of zoological evolution shows, first, the development of motor nerves, especially in connection with locomotion.  Fig. 7 shows an elementary invertebrate animal with both legs and eyes.

 Figures 7 and 8

This simple animal has a ventral nerve cord (called the "pedal" nerve cord) wch. consists of motor nerves controlling the legs.  Dorsally, the eyes are connected o two (bilateral) sensory ganglia.  The pedal nerve cord is connected to two "motor ganglia"..  These 4 motor-sensory ganglia are connected in a ring surrounding the esohoogus.  Here we already see a dorso-ventral separation of the motor and sensory nerves; simply because the legs are ventral and the eyes are dorsal.  Obviously we can attribute this dorso-ventral geometry to the fact that the D-V body axis is aligned with gravity and causes the legs only to appear on the ventral side of the body.
 Now, as animals get more advanced they start developing sensory nerves, as well as motor nerves, connecting the muscles to the brain.  A Lamprey for instance (a primitive jawless fish still extant) has a full blown "spinal cord" consisting of motor and sensory nerves situated now dorso-ventrally (Fig 8):

Fig.8 (above)

 Now, with the ever increasing number of nerves and a concomitant increasing "cephalization" of the CNS in the evolution of animals; the next thing that appears out of necessity, is a body/brain map or neurological homunculus in the brain, in order to organize and coordinate these thousands or millions of nerves.
 The first requirement of this homunculus is that it must be "mirror symmetric" between the motor and sensory maps; this because the most elementary m-s action is the reflex, i.e. a mirror symmetric motor-sensory reaction.
 Now, all I can do in this letter is touch on the highlights, less the thing become a book!  It encompasses 15 years of study.  So allow me to present a somewhat heuristic/illustrative description of how the vertebrate "motor-sensory homunculus" of the cortex came into being.
 It stems originally from the fact that the "neural tube" (embryological spinal cord) itself derives its structure; like the other axial tubes of the body (alimentary canal and spinal column)- directly from the 4-cell stage.  The reason that the spinal column and the neural tube manifest 3-axis geometrical symmetry, is because they are homologous with the first and second cleavages of the egg.  The crossection of the neural tube is shown in its relation to the 4-cell stage in fig. 9:

 Figure 9

 So the 2-axis mirror symmetric substrate of the neural tube derives from the first two mirror symmetric cleavages in embryology.  I will spare you the details of involution, gastrulation and generation of the neural tube in embryology, other than to cite a classic paper in the field in which vital stain (dye) was injected into the 4-cell stage and traced all the way to the 4-quadrants of the crossection of the neural tube; demonstrating conclusively this Cartesian morphology (Hirose & Jacobsen 1979).
 At any rate, the CNS in embryology begins as the neural tube which is 3-axis Cartesian, Fig. 10:

 Figure 10

 These 3-axes are shown above.  The alar plate and the basal plate, are also known as the sensory and motor plates because the crossection of the neural tube shown in Fig. 10 becomes the familiar "butterfly" crossection of the adult spinal cord in wch. the ventral half is motor and the dorsal half sensory Fig. 11:

 Figure 11

 Also shown in Fig.11 is the Telencephalic end of the neural tube (CNS) in the adult.  Here we see the "butterfly" has turned into the full blown mirror symmetric m-s "map" that we mentioned earlier.  Now this map is taken directly from Gray's Anatomy (38th edition, p.  1155,  Fig. 8.260) and is experimentally accurate.  The two maps are mirror symmetric across the Medial and Central fissures of the brain.  The Central fissure corresponds morphogenicall to the Sulcus Limitans in the neural tube.  The 2 images are "face to face" symmetric across the Central fissure.
 Now, we are concerned here with how and why this mirror symmetric map came into being and why it is astride the Medial and Central fissures of the brain and how this is related to the fundamental Cartesian geometry of the vertebrate body.  The basic question is:  what has motor-sensory function got to do with Cartesian geometry?  Particularly; what has it got to do with the embryological formative Cartesian geometry of the CNS neural tube?
 Well, there is an answer to this question and you won't find it in a book; I have had to discover it!  We have the following facts:

1. The esophagus, spinal column and neural tube are all morphologically 3-axis Cartesian and derive this geometry from the 3-axis Cartesian structure of the first 3-cleavages of the egg.

2. The question then is basically this- why would the motor-sensory function decide to take up residence in a dorso-ventral position in this tube with the motor legs pointing "foot to foot" with the sensory legs in the m-s homunculus; as we see in Fig. 11?

 Well, the answer to this derives form the evolutionary history of the animal, and in particular to the fact that we have already mentioned, that in evolution the 3-ontogenetic body axes become "oriented" to the 3-terrestrial Cartesian axes (horizontal, vertical and forwards-backwards).  Of  particular significance is that (in "prone" animals) the dorso-ventral axis is aligned with the gravity axis, Fig. 12:

 Figure 12

 Now, the significance of this, is that the legs of the animal appear only on the ventral side; to support it against gravity (Fig. 12).  These legs are positioned in the L-R ventral quadrants of the vertebrate body plan.  This is a dorso-ventral asymmetry imposed on the body by the unidirectional force of gravity.  Gravity is the principal and largest geometric asymmetry in the terrestrial Cartesian coordinate system.
 Now the brain and the body, as we have seen, is an ontogenetic axial quadrature.  Now, therefore, the simplest structural scheme for connecting the brain to the body, is a direct 1 to 1 (isomorphic) correspondence, Fig. 13:

 Figure 13

 Now, in this diagram I have drawn a hypothetical animal with symmetric dorsal and ventral legs; in order to preserve the "axially symmetric vertebrate body plan".  In this scheme the 4-quadrants of the brain controlling these 4-legs are supposed to be entirely motor... this is a simple "open loop" animal with no sensory nervous system.  This might correspond to a simple eyeless primitive invertebrate with a 4-way "pedal nerve cord" mentioned earlier.
 Now this model although theoretically simple does not correspond to reality because we have 2 facts to deal with:

1. Legs are only ventral because of gravity.

2. The CNS of higher animals is a reflex system with both motor and sensory nerves.

As we will now see, the simple "theoretical" model of Fig. 13 is exactly suited to accommodate these 2 facts.  The reason is this; unlike the theoretical animal (Fig. 13), the real animal has only ventral legs- and this leaves the 2 dorsal quadrants of the brain with nothing to do.  However, this is where the matter of the "reflex" system comes in; Fig. 14:

 Figure 14

Here we have an actual animal with only ventral legs (horse, dog, cat etc.).  These legs support the animal against gravity for the purpose of locomotion.  Now the sensory nerves in the legs sense the force of gravity and the motor nerves cause an equal and opposite force so that the animal remains in equilibrium (i.e. "stands").
 Now, one way to visualize this, is that the animal is walking on a mirror, and there is a "gravity reflexion" animal walking against it "foot to foot" (Fig. 14).  The nerve output of this "gravity reflexion" animal would be exactly equal to the sensory nervous output in the legs of the actual animal!  So, biologically speaking, the force of gravity has turned our "ventral legs only" animal into an animal that "thinks" it has both dorsal and ventral symmetric legs because of gravity and the existence of both motor and sensory nerves.
   Now, as we have seen, the two hypothetical dorsal legs of the "theoretical symmetric animal" are actually missing, but the body "knows" that they could exist  because of symmetry (note that in a fly, Fig. 13, all 4 quadrants are used; the wings becoming the "dorsal legs")... but now because of gravity and sensory nerves, it HAS two mirror symmetric legs that it has to place somewhere in the brain.  Obviously it simply places these two sensory (and now gravity reflex) legs in the two empty dorsal quadrants of the brain.  Thus it is, that the Bell-Magendie symmetry map, or motor-sensory homunculus of the cortex comes into being ( Fig. 15).  Note that the "dorsal and ventral" rami of the (mised motor and sensory) spinal nerves still serve the original 4-axial Cartesian quadrants of the body; with the ventral rami controlling the legs.

 Figure 15

 O.k., so what does all of this tell us?  Well, the first thing it tells us is that the Bell-Magendie symmetry and the L-R Sperrian symmetry are NOT UNRELATED.  In fact, what it tells us is that they stem from an absolute structural/mechanical equivalence.  They have biological equivalence because they (structurally) originate in primary cleavages of the egg (namely the 1st and 2nd primary orthogonal cleavages).  They have mechanical (functional) equivalence because they both originate in a transverse structural/mechanical mirror symmetry due to the legs (L-R and D-V).  They are certainly NOT two disparate and unrelated neurological systems.

 O.k. then, we are still on the road to answering your original question:

"Why would the Cartesian structure of space cause a Cartesian structure of psychometry in Personality."

We have certainly come a long way.  We have in fact started with the Cartesian structure of space, seen how it dictates the Cartesian mechanical structure of the body (the Cartesian axiom) and then proceeded through zoological evolution and embryology to see how this causes the B/M and Sperrian symmetries (and the neuraxial cephalization gradient too).  We are now therefore on the doorstep of modern experimental and psychometric research in Personality psychology.
  The foregoing exposition has shown, clearly, how the Cartesian structure of the body has caused the B/M and Sperrian symmetries.  To complete the answer to your question then, I simply assert that modern psychology research shows that the B/M and Sperrian dichotomies cause Eysenck's E and N Personality dimensions.  If this can be shown, we have an unbroken chain of causality from the "Cartesian structure of the brain to the Cartesian structure of Psychology".  Indeed, from the Cartesian structure of real space to the Cartesian structure of Personality space!  A truly historic scientific revelation.
 Now, the evidence connecting B/M and Sperry to E and N lies squarely in modern psychology research and gets us immediately into your research on Arousal and Activation.
 As far as the E dimension goes, the argument runs as follows:  Eysenck's Arousal thesis is known to have substantial experimental validity as a neuropsychological explanation of E-I.  Basically Introverts are more Aroused than Extraverts.  However, as Eysenck points out, there is still a fundamental ambiguity in the Arousal Hypothesis; he says:

"Furthermore, there are two possibilities concerning Arousal differences.  It is possible that introverts are more sensitive to incoming stimuli and become more aroused as a result of stimulation; or they may have high tonic arousal anyway, and their response ... may reflect this basic arousal difference."
    Eysenck, in Handbook of Personality
    Ch. 10, p. 259; Guilford Press, 1990

This suspicion is testified to by the fact that many researchers, ignoring Arousal theory, simply state without qualification that:

"Introverts are more sensitive to sensory stimulation than Extraverts".

  (cf. Powell, Gray, Claridge etc.)

 Eysenck cites particularly Stelmack's research in this connection (1990 p. 252) where he says:

"As they point out, these results provide some evidence of individual differences in physiological responsiveness at the level of the auditory nerve and the brain stem.  The findings are not easy to explain in terms of a simple arousal theory, and the authors (Stelmack & Wilson 1982) argue that their findings may require the development of new conceptions of the neurophysiological bases of individual differences in E ..."

    Eysenck, (ibid 1990, p. 252)

 A year later Stelmack and Plouffe (1983) followed up on this discovery with a major experimental thesis entitled:

 Introversion-Extraversion: The Bell-Magendie Law Revisited

    (Stelmack & Plouffe 1983)

In this paper Stelmack advances directly, based on experimental evidence that "the case can be made" that E-I is caused by the Bell-Magendie dichotomy at the neurophysiological level of the properties of the motor and sensory nerves.
 Anyway, I take Stelmack's finding to be absolutely fundamental to the Cartesian Theory.  According to his research and the Cartesian Theory, what we see is that Eysenck's "Arousal" is mainly "higher sensory sensitivity" which underlies Introversion.  At the other end of the scale, (and also according to Stelmack) we see that Extraversion is caused by enhanced motor cortex activity- thus the fully bipolar psychometric dimension of E-I.
 On the question of N, as Eysenck states in his 1990 Chapter, there has been a lot less work done on N and the experimental measurement of "Activation".  Given this, it seems more productive here for me to work backwards from the Cartesian Theory to the experimental data rather than, as in the case of E-I starting with the experiments (Stelmack) and working forward to the Cartesian Theory.
 The main reason for this is the following:  According to the Cartesian Theory N is caused by Sperrian Lateralization; the left-brain vs. the right-brain.  This is entirely similar to the situation for E-I which is caused by the motor cortex vs. the sensory cortex (front brain vs back brain).  But this immediately tells us that "N" should be a major strong "bipolar" psychological dimension like E-I.  Extreme E or extreme I are pathological, so that E-I has pathology at both ends and "normality" in the middle.  This is not so with Eysenck's N formulation (or P for that matter).  Eysenck's N has "above normal" on one end, pathology at he other end and normal in the middle.  This, if explained by Sperrian Lateralization would tell us that the R-hemisphere is "above normal" and that the L-hemisphere is neurotic.  That's obviously ridiculous.  No; what we immediately see is that N should have pathology on both ends and normality in the middle of the scale just like E-I.
 O.k., so if this latter idea is true, what the heck is Eysenck's N really measuring?  Well, a little investigation soon produces an answer.  First of all, "emotionality" apparently is the principal psychometric marker of Sperrian Lateralization in Personality.  There undoubtedly are a lot of other "Sperrian related features" in this second orthogonal dimension, but "emotionality" seems to be the most immediately visible.  What we suspect now however is that there is "R-hemisphere emotion" and "L-hemisphere emotion" which would, if properly assessed in a written questionnaire, produce a strong bipolar Neuroticism scale with normal in the middle.  Classic "Neurosis" would still be where it is (since I surmise this is principally L-brain emotionality).  However, I think we are going to "rediscover" that there exists R-brain emotion (basically Mania) which is going to be at the opposite end of the scale.
 So o.k., what is Eysenck's-N measuring?  Well, it's measuring |N|; i.e. "absolute value of N".  In other words Eysenck is measuring "absolute level of emotionality" irrespective of whether its Left or Right (e.g. Manic or Neurotic).  Eysenck's N is the magnitude of a vector quantity!  Eysenck's N scale in other words, essentially folds the True-N scale in half so that normality (non-pathology) which should be in the middle is now at one end.
 Now I'm not the first one to suspect this.  The reverend Professor Leslie J. Francis has actually empirically detected this in Eysenck's N-scales:

 The dual Nature..............

    (Francis 1993)

 In this paper, Francis has discovered the obvious, that women score higher on N than men (note it is well known that men score higher on P, so this in itself is not unprecedented).  However, Francis has gone further, he has separated out the sex (female) biased items from the non gender items in all of Eysenck's tests, calling the first group NEUROS and the second group NEUROA (see Francis 1993, p. xx).
 My interpretation of these two scales is that NEUROS contains only classic Neurosis items (e.g. loneliness, despair, hurt feelings etc.) while NEUROA contains items descriptive of generalized emotionality that could occur on either the right or the left (e.g. either manic or neurotic emotionality); such as "fed up, annoyed etc.".  Therefore NEUROS is measuring "True-N" (classic Neurosis) and NEUROA is measuring Eysenck's |N| ("absolute" N).  I have proposed elsewhere that running a test of NEUROS and NEUROA along with a simple written test to determine R-L brain preference (lateralization) would show NEUROS to be significantly correlated with L-brain preference and NEUROA to be correlated with "absolute magnitude" of lateralization irregardless of left or right.
 Now, what makes me so confident of all this?  Well, first of all, it is already established that Trait Anxiety (highly related to N) does correlate with L-brain preference in exactly this kind of testing procedure (Tucker xx; Tucker & Tyler xx).  Moreover there is a large literature on the Lateralization of Emotion (see Silberman & Weingartner 19xx for a review).  Included in this summary is the widely cited work of Flor-Henry on focal epilepsy (N.Y. state health department).  This work shows conclusively that Manic depressive illness is associated with R-brain activation in contrast to (Neurotic) Schizophrenia which is associated with L-brain activation; in focal epilepsy.  This is very strong evidence for the existence of the two poles of a reformulated N-dimension.
 Of interest here also is something that I recently heard from Paul Barrett to the effect that M.W. Eysenck and Fahrnberg have recently uncovered some "disconcerting" evidence that the N-dimension is in need of a major reassessment.  I haven't gotten the details of this, but given Hans Eysenck's rather dismal report on the current state of experimental research on N:

"As regards the N construct, the position is clearly unsatisfactory.  We have to consider the reasons why this might be so; perhaps future research, taking into account the objections to current methodologies, will give more positive results than are available at present."

    (Eysenck 1990, Ch. 10, p. 270)

It seems quite likely that N which was formulated some 50 years ago (Eysenck 1947), that it is highly likely that Eysenck's classic N is only a "first approximation" to True (bipolar) N.
 So o.k., there it is, the final step in the process; relating B/M and Sperry to E-I and N.  As I say the connection between B/M and E-I is quite strong (vis a vis Stelmack).  The evidence connecting N with Sperrian Lateralization is certainly; new, but even that has not gone unsuspected.  On p. 266 of Eysenck's 1990 Handbook of Personality article he devotes a paragraph to the work of Lolas (1987) who has detected a "lateralized EEG result" which correlates strongly with N, and has also surmised on the basis of this that N is caused by Sperrian Lateralization!
 Well then, with the experimental identification of B/M and Sperry with E-I and N, we have finally arrived at the "Cartesian structure of Psychometric space" (i.e. we refer to Eysenck's E,N,P as "Cartesian" because they are linearly independent, and we now see that this linear independence does originate in geometrical orthogonality of the B/M and Sperrian divisions of the brain).
 We of course haven't mentioned "P" so far, but lets face it, if we prove that the brain has 3-axes and 2 of them cause E and N, it's 66 2/3 % sure that the 3rd axis is causing P!
 There is in fact little if any experimental evidence proving this, but that is not surprising considering that even Eysenck has yet to propose any definitive biological (at least neuropsychological) basis for P.  His 1967 biological model you will recall only explains E and N.  Eysenck says (ibid 1990 p. 270):

"Regarding the P dimension...... What is clearly needed in this field is some more inclusive theory.."

 In line with that suggestion, we see that according to the Cartesian Theory it is now evident that P is associated with the "cephalization gradient" along the neuraxis itself.  This simply because there are 3 and only 3 primary orthogonal cleavages of the egg (the 1st 3).  If the first causes N and the 2nd causes E-I, it would follow that the third simply causes P.  This is supported by the fact that the 3rd cleavage (and all subsequent cleavages parallel or isomorphic to it) account for the somites of the embryological body; including the vertebrae, the ribs, and the cephalic neuromeres (segmentation of the cephalic end of the neural tube) which is the morphological origin of the "diencephalon, mesencephalon and telencephalon".  It is surmised then (not to say intuitively obvious) that the "3rd cleavage" causes a bipolar cephalization gradient, say stem-limbic-cortex; which causes yet a 3rd bipolar neuropsychological dimension corresponding to Eysenck's P.
 This, incidentally, immediately tells us that Eysenck's P probably is suffering from the same "absolute magnitude" problem as N!  According to the Cartesian Theory, all 3 dimensions in the Structural Model are strongly bipolar in precisely the same sense that E-I is.  This because all 3 dimensions originate in 3 (nominally) identical biological mechanisms- namely the 3-primary Cartesian cleavages of the egg!
 O.k., so we have identified Mania (frustrated/sublimated emotion) as the missing negative pole of N (+N still being classic hysteric/paranoid emotion; classic Neurosis)- but what now could be the missing negative pole of Eysenck's P?  Well, just looking at the "cephalic gradient" from stem to cortex, we see that we have a gradient from vegetative to intellectual (or in the egg from vegetal to animal).  Taking our que from the fact that "psychotics" (especially the classic diabolical types) have a reputation for cleverness and energy (consider the Unibomber for instance who entered Harvard on full scholarship at the age of 16) we assume that +P must be at the cortical end of the neuraxis.  This means the missing negative pole of P must lie at the lower end of the brain; the limbic to brainstem level... we are looking then for the virtual human vegetable.  This immediately suggests Mental Retardation (MR) as the missing negative pole of Eysenck's P dimension!
 Now all I can do with respect to P, other than suggest that someone write a revised bipolar questionnaire for P and factor analyze it with EPQ-N and EPQ-E and see if it substantially increases the variance explained (i.e. produces a much more robust P)... is to note the following piece of relevant evidence.
 The DSM-IV has adopted a "two-category classification of all mental illness".  These two categories are called AXIS-I and AXIS-II (axis here simply means category).  AXIS-I contains all of the "florid mental disturbances" namely the acute psychoses.  Now this I say is suggestive of "+P".  AXIS-II contains mainly MR with the inclusion of long term mild dependency disorders referred to as "Personality Disorders".  The main clinical features of these Personality Disorders  seem to be things like "learned helplessness, dependency, etc.".  AXIS-II therefore, since it contains all of the MR cases, I suggest is simply Eysenck's missing negative pole; "-P".  Thus the DSM-IV itself provides an immediate "bipolar reformulation" of Eysenck's P.  What we see is that 50 years of experience by the World Health Organization has come to the same conclusion that Eysenck has; that all mental illness is classified first and foremost according to its location on the "Psychosis" dimension.  The WHO however, having a much larger empirical base than Eysenck has apparently identified both poles of the dimension.
 Neuropsychologically then, the Cartesian Theory indicates that (classic) Psychosis is caused by an (abnormal) cortical shift and that -P, classic MR and dependency disorders, are caused by just the opposite.. a lower brain stem shift.  Experimental research then would be looking for cortical vs. lower brain activations correlating with a psychometric scale running from "pathological dependency to pathological autonomy" or "MR to Psychotic" in clinical terms.  This would be True-P now running from -P to +P with normal in the middle.
 

 O.k. then, that completes an outline of the full story and explanation of:

"How Cartesian mechanical/biological structure CAUSES Cartesian Psychometric structure; or simply put, how real Cartesian space causes Psychological Cartesian space."

 Now, needless to say this letter as long as it is, is but a brief outline of the full detail of this theory.  I have had to resort to illustration and heuristic devices in this letter in order to condense the story to something manageable.  A rigorous and detailed treatment would require a book or a dozen papers with 1,000 bibliographic citations from half a dozen scientific disciplines.  Numerous supporting studies have not even been mentioned.  The Cartesian Theory for instance explains theoretically the existence of "simple structure" empirically discovered by Thurstone in 1935 and to this day still a theoretical enigma.
 I have not mentioned Gray's theory, even though my published paper (Hammond 1994) is subtitled Unification of Eysenck and Gray.  Nor have I mentioned the Big-5 and Cattell's second order factors -all immediately explained by the Cartesian Theory (The Big-5 is the subject of my Montreal address; audio tape enclosed).  Hopefully we can get to a discussion of these results once we get the (considerable) challenge of reaching a conclusion on the basic scientific bona fides addressed in this letter.

 In closing this letter let me say that I think our discussions may present a very unique opportunity regarding this scientific theory.  As I have mentioned I have already had a somewhat comprehensive discussion of this theory with Paul Barrett on Idanet.  Unfortunately that was a public discussion and not a private one.  One cannot of course conduct a state of the art and forensic scientific discussion in public.  This simply because public matters take precedent and science (especially professional level topics) become secondary.
 Our discussion however, is private and purely scientific and taking place in the venue of competent academic discourse (as opposed to public discourse).  This will be an absolute first for the Cartesian Theory.  As I say I have also discussed this theory briefly with Hans Eysenck, again however that was at an international Psychology congress and again was more of a public policy sensitive discussion than a technical one.
 I am hopeful that a young Ph.D. like yourself, obviously of superior academic/research achievement who might still have the time and the inclination to make a purely academic/scientific assessment of this question, will be able to provide not only me, but other more beleaguered scientists like Hans Eysenck, Jeffrey Gray, M.W. Eysenck, Paul Barrett and many others with a purely formal, academic assessment of this theory, according to the contemporary standards of formal academic research in Personality.  That inquiry and that judgement is what the senior people need before they can even consider how this new piece of the puzzle might fit into the larger currents in Psychology research.
 I suggest we move methodically at whatever speed we can muster given the eternal restraints on time and resources; in this direction.

 In the meantime I have studied your 3 1995 papers with Jeffrey Gray, Glenn Wilson et al. and I am gratified and immensely relieved to find that they are of the highest order of formal academic research, flawlessly and powerfully conducted and expressed.  I therefore have unqualified confidence in your scientific judgement and will not have to spend time negotiating around any major scientific deficiencies on your part- after studying these papers at length I find none.

 Finally, I'm sorry I've taken so long in responding, as I have other demands on my time.  I expect that you likewise are busy and I don't expect a reply from you right away.
 I am presently working on several papers at once, one of which will contain some of the material contained in this letter.  At the rate I'm going I probably won't have them ready until next spring.

 I am looking forward to hearing from you, and I would appreciate it if you could email me a short note when you receive this letter just so I will know that you have received the materials.
 

Sincerely yours,
 
 
 

George Hammond

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