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John Abramson is retired and lives in the Lake District in Cumbria, England. He obtained an MSc in Transpersonal Psychology and Consciousness Studies in 2011 when Les Lancaster and Mike Daniels ran this course at Liverpool John Moores University. In 2015, he received an MA in Buddhist Studies from the University of South Wales. He can be contacted at johnabramson@btinternet.com

Convergence Is the Wrong Invariant

A Reply to Frank Visser

John Abramson / Claude

Frank Visser's reply to my second essay is, I think, correct on the point that matters most, and I want to begin by saying so plainly rather than burying the concession in qualifications.

What I concede

Visser's central claim is that reproducibility of an experience does not establish the external ontology attributed to it, and that a community of trained practitioners cannot calibrate itself. A thermometer is not trusted because thermometers agree with one another; it is trusted because its readings can be connected to independently established facts, cross-checked, and used to predict. If the trained contemplative is the instrument, then agreement among contemplatives within a tradition is not calibration, and the tradition's own ontology cannot supply it without circularity. I accept this. It follows that "framework-relative certainty" is exactly what I said it was: knowledge within a framework, and unestablished metaphysics outside it. Visser is right that this is not scientific confirmation, and right that the phrase "not yet" in my title carries more hope than evidence.

I also concede the specific point about Wilber. Nothing I have argued establishes etheric, astral or psychic energies as independent entities, and I do not think anything Wilber has argued does either. Where Visser and I have arrived is a science of contemplative states with no established science of subtle energies. I am content with that formulation.

There is one inference in his reply, however, that I want to contest, and it is the one on which his treatment of the chakras rests.

The inference I contest

Visser argues that if the chakras were objective structures in a subtle body, trained observers across traditions would converge on their number, location and function. Since the traditions do not converge, the divergence is evidence that the chakra system is "a culturally elaborated map of experience" rather than an anatomy. His appendix on clairvoyants makes the same demand explicit: if the subtle object is real, competent observers should be able to see the same thing twice, and their descriptions should converge.

The inference from divergence to non-objectivity presupposes that an independently existing object must have a unique decomposition, so that competent observers describing it will arrive at the same parts. That is not generally true. An objectively existing thing can have several coordinate systems, several scales of description, several legitimate partitions, and disagreement between descriptions of these kinds is not disagreement about whether the thing exists. I should be clear about what I am and am not claiming here. Convergence of description, if it were found, would be evidence, and I would welcome it. What I deny is that it is a necessary condition for a common referent. The question is therefore not whether the traditions agree, but what kind of divergence is compatible with a common referent and what kind rules it out. That is a more demanding question than Visser asks, and it is the one his evidence should be made to answer.

Consider what the traditions agree about and what they do not. Across the systems I have examined, the principal centres preserve a stable vertical ordering of bodily locations, from the lower body through navel, heart and throat to the head. Their functional attributions also show a broad, though not uniform, correspondence along this axis, with generative and vital functions at the bottom, affective in the middle, and cognitive and transcendent at the top; the positional ordering is what the sources state, and the functional gradient is my abstraction across them, and the two should be kept apart. The systems disagree, sometimes sharply, about how many principal centres there are. Systems with four, five, six, seven, eleven and eighteen centres are attested in the textual record, and where two systems place a centre at a different height, or divide one region that another leaves whole, they conflict. What I have not found, in a first pass through nine historically identifiable systems reported in the Appendix, is any system that reorders the principal sequence. Some systems add centres that do not lie on the axis at all, at the joints for example, but they do so while retaining the axial sequence rather than disturbing it.

This pattern is at least consistent with a common ordered structure being represented at different levels of granularity, and it is considerably less naturally explained by a finite anatomy consisting of a fixed number of independently identifiable, objectively discrete elements. Such an anatomy should yield convergence on those elements, in the way that anatomists converge on the number of cervical vertebrae. A structure that is continuously, densely or hierarchically organised admits many legitimate levels of description, each correct as a description while none of them is the anatomy. An observer trained at one level of resolution will encounter the others as errors, and will be wrong to do so, but not because the others are hallucinating. I put this forward as a hypothesis, not a conclusion: a model under which the observed combination of structural agreement and descriptive divergence would be expected rather than anomalous. The simplest version treats the principal axis as continuously or densely structured, but the systems with non-axial centres show that a one-dimensional model cannot be assumed in advance.

The clearest ordinary case of this structure is music. The octave has a robust physical basis as a 2:1 frequency relationship, and octave equivalence is among the most widespread features of the world's musical systems, while those systems divide the pitch space within the octave in very different ways: five- and seven-note scales, the twelve-fold chromatic division, and the Indian system based on twenty-two shrutis. A musician trained in one scale hears the others as out of tune. Nobody infers from the diversity of scales that pitch is imaginary, and nobody infers from the physical reality of the octave that the seven-note scale is the true anatomy of sound. There is no unique number of discrete notes imposed by the octave itself, and that is not because the octave is unreal.

If the subtle axis is of this kind, then the divergence Visser cites is not an embarrassment to be explained away. It is what one should expect, and its absence would be surprising.

What this does and does not claim

I want to be precise about the scope of this proposal, because imprecision on exactly this point is what Visser has rightly criticised in Wilber.

The granularity model is a hypothesis under which the divergence is expected. It does not establish that the axis is a subtle-energy channel. The model is neutral between two readings: that the axis is a structure in a subtle body, and that it is the interoceptive body, the spine, the breath, the heart and the head, with a shared functional gradient that any tradition attending carefully to bodily experience will find. Both readings predict the same pattern of agreement on order and disagreement on count, and the second reading has the further advantage that the order it predicts is simply the order of the body's landmarks. Deciding between them would require exactly the kind of independent constraint Visser has asked for, and I have not supplied one.

This means I am conceding more than it may appear. The literal subtle anatomy, seven discrete centres at seven locations, is not merely unproven on this account; it is disfavoured, because a discrete anatomy of identifiable elements would produce convergence on the count and the historical record shows none. Wilber's presentation, to the extent it reads the traditional systems as literal maps of discrete structures, is on the wrong side of the evidence. The traditions themselves are at least compatible with being read as representations at different resolutions.

A better test than convergence

Visser proposes an experiment: present several clairvoyants with the same person, without information about one another, and see whether their descriptions converge. I think the experiment is worth doing, but I think identity of description is the wrong invariant, for the same reason that asking musicians from different cultures to agree on the number of notes in an octave would be the wrong test of whether pitch is real.

The relevant invariant is not identical description but preservation of structural relations, and the first structural relation to test is order. If independent observers, and independent traditions, are representing a common ordered structure at different resolutions, then three things should hold. Their systems should be related by order-preserving refinement or coarsening along the principal axis, never by reordering: for any two systems there should exist an order-preserving map between their sequences of principal centres. Agreement should be highest on the sequence and its endpoints, and lowest on counts and on the placement of boundaries between adjacent regions. And where systems disagree over boundaries, those disagreements should cluster at points where the functional categories themselves overlap or shade into one another; throat and heart, or navel and solar plexus, would be candidate examples, and a boundary dispute between the base and the crown would not be. Each of these can fail. A system that reordered the sequence, or whose boundary disputes fell where the functions are most distinct, would count against the model.

This is a stronger test than convergence, because it specifies what kind of disagreement is permitted and what kind is not, and the first part of it can be applied to the textual record now. I have begun to apply it, and the Appendix reports a first pass across nine systems, with the coding rule stated before the results. In brief: no counterexample to the first prediction was found in the preliminary sample, the first half of the second is supported and the second half untested, and the third remains a prediction rather than a finding. I say this plainly because the test is only worth proposing if its results are reported whether or not they help.

One element of Visser's experiment needs repair before it can be run at all, and the repair bears on his calibration argument. His test requires "competent" or "advanced" observers, and if a tradition decides who is competent by reference to its own subtle-body doctrine, the test is circular in just the way he objects to. The traditions do, however, recognise competence of another kind across their boundaries: they can and sometimes do acknowledge compassion, equanimity or wisdom in practitioners of other lineages, without endorsing those lineages' ontology. That recognition cannot calibrate a report, and I do not claim it can; an authentically compassionate observer can still have perceptions that construct rather than track. But it can serve as a criterion for selecting observers that is independent of the doctrine under test, and that is the one circularity in the design that can be removed now.

If order-compatibility holds across the traditions and across independently selected observers, that will not establish a subtle anatomy. It will provide evidence that the traditions' descriptions are related by a common ordered structure, and it will leave open whether that structure is a subtle body, the organisation of embodied experience, or something else. That is a respectable result, and it is the most that the evidence presently permits.

Where this leaves the disagreement

Visser has won the argument about proof. The subtle-energy ontology is not established, the contemplative community cannot calibrate itself, and the responsible position on Wilber's etheric, astral and psychic energies is suspension of judgment. I no longer wish to contest any of that. What I contest is the step from divergence to non-objectivity, because it assumes the object is of a kind that the traditions' own pattern of agreement suggests it is not.

The more general question, whether the traditions' own systems contain internal anomalies that point beyond them, in the way that the square root of minus one pointed beyond the real numbers, is one I am pursuing separately, and it belongs in a different essay. For the present exchange I am content to have replaced a standoff with a test. If Visser accepts preservation of structural relations as a more appropriate invariant than identity of description, then our disagreement becomes considerably narrower, and what remains becomes textually and empirically tractable.

Appendix: A first pass at the order-compatibility test

This appendix reports a preliminary check of the three predictions against nine chakra systems. It is a first pass, not a study. The sample was chosen for textual identifiability rather than by any sampling rule; the predictions were formulated with the broad pattern of the literature already in view, so this is not a pre-registered test; and the coding is coarse. Its purpose is to show that the predictions can be applied, and to report what happens when they are.

Coding rule

The rule was fixed before the systems were scored, and is stated here so that it can be applied by anyone to any system.

Reference sequence. Five bodily landmark regions, ordered bottom to top: lower body (perineum, base of trunk, genitals), navel (including solar plexus), heart, throat, head (forehead, brow, crown). These are anatomical regions of the trunk and head, chosen because every system in the sample locates its centres by reference to them.

Counting. A principal centre is any centre the source itself names as a member of its main series and locates on or at the central vertical axis. Every such centre is counted, including a crown centre that the source places beyond or above its main series; so the Sat-cakra-nirupana is counted as seven, not six, even though the text treats sahasrara as beyond the sixfold sequence. Centres the source locates off the axis (joints, spleen, limbs) are recorded but not counted as principal.

Compatibility. A system is order-compatible if there exists an order-preserving injection from its sequence of principal centres, taken in the source's own stated bottom-to-top order, into the reference sequence, mapping each centre to the landmark region containing its stated location. Two centres in one region are permitted (that is a refinement). What is not permitted is any reversal of the source's stated order relative to the reference, or any relocation of a centre from where the source places it. A system with off-axis centres is scored on its axial centres and marked as not purely axial.

The sample

The reduction of each system to a sequence of landmark regions is my own and can be checked against the sources listed. Where a source gives a centre's location in a way that could fall into two adjacent regions, I have recorded the region the source's own terminology favours and noted no case in which the choice affected compatibility.

Prediction 1: no reordering

Under the coding rule, all nine systems are order-compatible on their axial centres. Hevajra contains the upper four regions only; Cakrasamvara and the Yuthok system add a lower-body centre; Kalacakra and the Saiva six- and seven-centre systems refine the head region into two centres and, in the Saiva case, the lower body into two. In every case the additional centres are inserted into the sequence, never transposed across it. No counterexample was found in the preliminary sample. A nine-system convenience sample cannot establish a universal prediction, and this result should be read accordingly.

It is worth stating what would have counted as a counterexample, since the rule was fixed in advance: a source that places, for instance, a heart centre above a throat centre, or a navel centre above the heart, in its own stated order. None of the nine does.

Leadbeater's system is an instructive case, because he was a clairvoyant, and his system is therefore of exactly the kind Visser's appendix has in mind. It introduces a spleen centre, located off the axis, that is not found in the principal Buddhist or Saiva sequences, and it omits the genital centre, while retaining the ordering of the remaining axial centres. Whether an off-axis addition of this kind is compatible with the granularity model is a fair question; the model as stated permits added nodes but was not formulated with this case in view, and I record it rather than claim it.

The two systems marked "mixed" or "no" for axiality are not counterexamples to ordering but to one-dimensionality. Kaulajnananirnaya adds stations at the mouth and the crest of the head; Lamdré adds twelve centres at the principal joints. Neither reorders the axial sequence; both add structure that a single axis cannot represent.

Prediction 2: agreement highest on order, lowest on count and boundary

Under the counting rule, the principal-centre counts across the nine systems are 4, 5, 5, 6, 6, 7, 7, 11 and 18. There is no convergence on number. The axial ordering of the principal centres is, by contrast, conserved across all nine. So the first half of the prediction, that order agreement should greatly exceed count agreement, is supported in this sample.

The numerical variation also has a specific shape. The five-centre Buddhist systems do not select five arbitrary centres from a larger set; they retain the sequence lower body, navel, heart, throat, head that is common to nearly all the systems. The six-centre systems refine it by inserting a centre in the head region (Kalacakra) or the lower-body region (Kubjika). The variation looks like different granularity along an already ordered axis rather than different answers to a single question of count.

The second half of the prediction, that boundary placement should be the locus of greatest disagreement, has not been tested. Testing it requires coding each centre not as a point but as a region with a spatial extent and a functional attribution, so that the boundaries between adjacent regions can be compared across systems. The present sample codes centres as points only.

Prediction 3: boundary disputes cluster where functions blend

This prediction is untested and should be read as a prediction. To test it one must first define what counts as a boundary dispute: not, for instance, a difference in the count of centres between heart and head, but a case in which one system merges functions that another separates, or draws the division between two adjacent regions at a different height. That requires the interval coding described above, and a coding of functional attributions. The candidate examples given in the main text, throat and heart, navel and solar plexus, are candidates only.

What the sample suggests

The pattern in the sample is large variation in cardinality together with small variation in principal ordering, with some systems adding nodes off the axis. The additional nodes are important. Lamdré's joint centres are not an alternative answer to how many centres lie on the axis; they are additional structure recognised at a higher resolution while the axial centres are retained. That looks like refinement, and it means the hypothesis should be stated as "a common ordered structure represented at different levels of granularity, with some systems resolving dimensions or nodes that others ignore," rather than as "different partitions of one continuum."

None of this establishes a subtle body. The conserved ordering is exactly what the embodiment reading predicts, since the landmarks are the landmarks of the physical trunk and head, and Visser is entitled to say so. What the sample does show is that the inference from "they disagree about the number" to "they are not describing a common structure" cannot be made, because the disagreement about number coexists with agreement about order, and the second fact needs explaining as much as the first.

What a proper test would require

A proper test would extend the sample to twelve to fifteen systems chosen by an explicit rule; code every centre for vertical position, spatial extent, functional attribution, principal or secondary status, and axial or non-axial location; compute an order-compatibility score for each pair of systems, defined by the existence and size of an order-preserving map between their principal sequences; and compare the observed distribution of disagreements with that expected under a null model in which the same landmark set is randomly ordered. The hypotheses are then explicit. Under the null, chakra systems are independently generated categorical schemes, and preservation of a common partial order across systems should be no greater than chance under that model. Under the alternative, the traditions encode a common ordered structure at different resolutions, and order preservation should significantly exceed the null. The predictions, the coding rule and the null model should be fixed before the extended coding is done. I hope to carry this out in due course, and then to report the result whichever way it falls.