An Important Mathematical Oversight

The original intention for this website was to encourage public awareness of an historical medical crime, one that has remained a tightly-kept British state secret now for more than five decades. The matter is of enormous public interest, not least because the motivation behind the crime itself was that of advancing scientific research into areas that would come to provide the seminal knowledge behind much of the technological progress of the last half-century. My investigation into the matter inspired a parallel enquiry into some of the fundamental principles that underpin that scientific and technological impulse.

There are therefore two principle concerns of this website, and if there is acknowledged to be a substantive connection between them, that has inevitably to do with late 20th Century developments in science and information technologies, and more broadly with the idea of an burgeoning technocracy – the suggestion of a growing alliance between corporate technology and state power – one which might be judged to have atrophied the powers conventionally assigned to liberal-democratic institutions. This link therefore serves as a segue to emphasise the equal importance, to my mind, of what is going on in the X.cetera section of the site, so that that section should not appear, from the point of view of the other, as some kind of 'afterthought'.

X.cetera is concerned with a problem in mathematics and science to do with the way we think about numbers. As a subset of the category defined as integers, elements in the series of the natural numbers are generally held to represent quantities as their absolute, or 'integral', properties. On the page: The Limits of Rationality I have made a criticism of this standard definition of integers as indices of self-contained values, on the basis that the definition obscures the fact that the relations of proportion between integers is derived from their membership of a restrictive group of characters as defined by the decimal rational schema; and that those ratios of proportion cannot be assumed to apply to the the same values when transcribed into alternative radical bases such as binary, or octal, or hexadecimal, for instance.

This means that, while the values of individual integers so transcribed will be ostensibly equal across those alternative radices, the ratios of proportion between groups of those values will not be preserved, as these must be determined uniquely according to the range of available digits within any respective radix (0-9 in decimal, 0-7 in octal, for instance); one consequence of which of course is the variable relative frequency (or 'potentiality') of specific individual digits when compared across radices. This observation has serious consequences in terms of its implications for the logical consistency of data produced within digital information systems, as the logic of those systems generally relies upon the seamless correspondence, not only of 'integral' values when transcribed between decimal and the aforementioned radices, but ultimately upon the relations of proportion between those values.

Information Science tends to treat the translation and recording of conventional analogue information into digital format unproblematically. The digital encoding of written, spoken, or visual information is seen to have little effect on the representational content of the message. The process is taken to be neutral, faithful, transparent. The assessment of quantitative and qualitative differences at the level of the observable world retains its accuracy despite at some stage involving a reduction, at the level of machine code, to the form of a series of simple binary (or 'logical') distinctions between '1' and '0' – positive and negative. This idea relies upon a tacit assumption that there exists such a level of fine-grained logical simplicity as the basis of a hierarchy of logical relationships, and which transcends all systems of conventional analogue (or indeed sensory) representation (be they linguistic, visual, sonic, or whatever); and that therefore we may break down these systems of representation to this level – the digital level – and then re-assemble them, as it were, without corruption.

However, in the X.cetera section I am concerned to point out that the logical relationship between '1' and '0' in a binary system (which equates in quantitative terms with what we understand as their proportional relationship) is derived specifically from their membership of a uniquely defined group of digits (in the case of binary, limited to two members). It does not derive from a set of transcendent logical principles arising elsewhere and having universal applicability (a proposition that will come as a surprise to many mathematicians and information scientists alike).

It follows that the proportional relationships affecting quantitative expressions within binary, being uniquely and restrictively determined, cannot be assumed to apply (with proportional consistency) to translations of the same expressions into decimal (or into any other number radix, such as octal, or hexadecimal). By extension therefore, the logical relationships within a binary system of codes, being subject to the same restrictive determinations, cannot therefore be applied with logical consistency to conventional analogue representations of the observable world, as this would be to invest binary code with a transcendent logical potential that it simply cannot possess – they may be applied to such representations, and the results may appear to be internally consistent, but they will certainly not be logically consistent with the world of objects.

The issue of a failure of logical consistency is one that concerns the relationships between data objects – it does not concern the specific accuracy or internal content of data objects themselves (just as the variation in proportion across radices concerns the dynamic relations between integers, rather than their specific 'integral' numerical values). This means that, from a conventional scientific-positivist perspective, which generally relies for its raw data upon information derived from discrete acts of measurement, the problem will be difficult to recognise or detect (as the data might well appear to possess internal consistency). One will however experience the effects of the failure (while being rather mystified as to its causes) in the lack of a reliable correspondence between expectations derived from data analyses, and real-world events.

So that's some of what X.cetera is all about.. If you think you're 'ard enough!

2nd MRI Head Scan (March 2013)

In January 2013 I asked my GP if I might be referred for a second opinion on the Brain MRI scan previously conducted at St Thomas' Hospital, and possibly further scan investigations. I was referred to the National Hospital for Neurology and Neurosurgery ('NHNN'), at UCLH NHS Trust in London. I attended a preliminary appointment there, and an arrangement was made for a further MRI scan of my head to be conducted on 06/03/2013. Although I have yet received no consultation following these scan results, I obtained a copy of the scan from the Medical Records Dept. of the hospital. A selection of details of three images from this scan is displayed below (click on the individual images to open slideshow):

MRI Head sagittal section1

1. MRI Head sagittal section (detail) – 20.0mm to the right of the central axis

The image detail above is one of a series of 128 vertical (sagittal) sections of my head. The sections show a sideways view, progressing from right to left of the skull. Sequential slices are 1.6mm apart. The image above is the 52nd image in the sequence, and is a section of the skull offset 20.0mm to the right from the central axis. The superimposed arrows point to two square or box-like structures, approximately 1cm square (see adjacent sections below for additional clarification), although the rearmost of these objects is less clearly defined across the three images selected here. These items are positioned behind the back of my throat, close to the brain-stem, i.e., in a position immediately below the foramen magnum – the large aperture at the base of the skull. The objects are clearly not of biological origin, appearing to be of a rigid rectilinear construction.

The second image below is 1.6mm to the left of the first image (i.e., 18.4mm right of the central axis). The forwardmost of the two objects is shown with slightly better clarity:

MRI Head sagittal section2

2. MRI Head sagittal section (detail) – 18.4mm to the right of the central axis

The third image below is 1.6mm to the right of the first image (i.e., 21.6mm right of the central axis). The forwardmost object therefore remains clearly identifiable through a depth of 3-4mm in the scan sequence.

MRI Head sagittal section3

3. MRI Head sagittal section (detail) – 21.6mm to the right of the central axis

Prior to my GP making the referral to NHNN, I had contacted the hospital independently by letter in October 2012, enclosing a copy of the earlier MRI scan from St Thomas', and requesting a second opinion on that scan. No private consultation had followed from that enquiry, but my concerns were addressed to my GP in January 2013 resulting in the NHS referral. I had also reported some symptoms of faintness, and pressure in my left occipital region, unconnected to my specific concerns over the images from the first scan, which added weight to the referral.

During my consultation with Dr Heaney, consultant neurologist at NHNN, on 08/02/2013, I presented him with a copy of the earlier scan, and asked him to explain the aspects of the images 7.13-7.15 which were giving concern. However, Dr Heaney was noticeably reluctant to discuss the items I referred to in any meaningful detail, and appeared nervous and impatient at my request. He was unable or unwilling to identify the specific items I pointed out from the scan. So I did not get the second opinion I had been seeking. His recommendation for a second scan was made ostensibly to assess if there had been any deterioration in the mild ischaemia previously reported in 2008 by Dr Hawkins at St Thomas' Radiology sufficient to explain the recent symptoms of occipital pressure.

I received the following copy of Dr Heaney's letter to my GP dated 18/03/2013:

NHNN's report on the 2nd scan – 18/03/2013 [pdf – 45KB]

In his letter Dr Heaney interprets NHNN's radiological report on the second scan simply thus:

"I am reassured that there has not been significant deterioration in the radiological appearances, and that there is no acute lesion to account for his symptoms."

This statement is highly specific in that it relates only to a comparison of any potential difference (deterioration) between the first and second scans, and to the absence of any acute lesion which might explain the symptoms of occipital pressure. It makes no commitment to any statement about the absence of anomalies in general (compare, for instance, with the final sentence of Dr Hawkins' report on the first MRI scan, which had concluded with the statement: "No significant intracranial abnormality identified") or to any statement intended to allay the concerns that had evidently led me to seek a second opinion over the findings of the earlier scan. The radiological report quoted in his letter consists also of a list of specific exclusions – it makes no inclusive statement about the absence of anomalies in general.

I received the copy of the 2nd MRI scan from UCLH Medical Records Dept. two months after Dr Heaney's letter of 18 March. After studying the scan I became aware of the apparent anomalies as highlighted in the images above. At this time I was awaiting a response to my complaint against Guy's & St Thomas' NHS Trust (GSTT), so I did not immediately raise an issue with NHNN over their failure to report anomalies from the 2nd scan. However, at the time of referring the complaint against GSTT to the Health Service Ombudsman, I sent an email to Jill Rayfield, Dr Heaney's secretary, on 26/09/2013, attaching copies of the three images above, and asking for Dr Heaney’s corroboration of the fact of the self-evident anomalies revealed in those images. I received the following response from Dr Heaney, dated 03/10/2013:

Dr Heaney's response to my email enquiry – 03/10/2013 [pdf – 92KB]

In his reply Dr Heaney refutes the existence of two box-like structures of non-biological origin in the scan images, suggesting that the two superimposed arrows point only to: "the posterior aspect of the foramen magnum and the lateral mass of C1" (i.e., the large aperture at the base of the skull, and the first cervical vertebra), and declaring them as "entirely normal". This statement however can only be interpreted as a deliberate refusal to acknowledge the reality of the specific anomalies indicated by the two arrows; as it is plainly self-evident that the rigid rectilinear character of the two objects could not occur biologically, and that their presence in my neck must therefore have resulted from a surgical implantation, however sinister and distasteful such a conclusion might be to an ethically-minded medical professional. While I accept that Dr Heaney would not have had the knowledge or information required to accurately identify the objects in question, resulting as I allege they do from an unprecedented surgical implantation, without official medical approval or publicity, it is inconceivable that he could honestly have not noticed these items, simply because they do not conform to any existing diagnostic paradigm.

In response therefore to the appearance of a further cover-up of medical evidence at NHNN, I submitted the following complaint to UCLH Governance Dept. on 11/11/2013:

Complaint to UCLH NHS Trust – 11/11/2013 [pdf – 64KB]

UCLH's response to this complaint was received on 17 December 2013, i.e., promptly following the '25 working-day' prescribed response window. The response includes a covering letter from the Trust's Chief Executive Sir Robert Naylor, dated 16/12/2013, together with a report on the complaint investigation from Prof. John Duncan, Divisional Clinical Director of the Queen Square Hospitals, dated 12/12/2013:

Response from UCLH NHS Trust – 16/12/2013 [pdf – 95KB]

The covering letter from Sir Robert Naylor is fairly formulaic in that it probably differs very little from his standard response to any other complaint addressed to the Trust, though it is perhaps significant that he should offer his personal apologies for any distress caused by the issues raised by my complaint. However, the attached investigation report from Prof. Duncan does nothing at all to address those concerns.

Prof. Duncan states that he has himself reviewed the MRI scan made at NHNN on 06/03/2013, and has also sought the opinion of Dr Katherine Miszkiel, Senior Consultant Neuroradiologist at NHNN. He quotes Dr Miszkiel's report to say that the "anatomy of your neck is normal", with "no signs of any foreign body or device whatsoever". He refutes my observations of the self-evident anomaly indicated in the three images reproduced above with the statement: "[W]e see no box like structure behind the back of your throat".

The rectilinear structure of the anomaly revealed in these images is perfectly self-evident, and confirms the non-biological origin of the anomaly beyond reasonable dispute – it does not require any specialist training in neuroanatomy to be able to perceive it. For instance, in the enlarged detail of the third section above (shown below with elevated tones), one can quite clearly perceive the internal rectilinear 'G' structure of the forwardmost of the two objects, confirming beyond doubt its artificial construction:

MRI Head sagittal section3 - detail

Detail of the third section above, shown with elevated tones

The statements of Prof. Duncan and Dr Miszkiel can only be interpreted therefore as blatant mistruths. Prof. Duncan has not addressed the details of my complaint that refer to the institutional context of the implied covert research program responsible for these illicit surgical implantations (i.e., that it occurred controversially within an NHS Hospital), and which may provide an explanation for why Dr Heaney found himself compelled to conceal his awareness of them; he merely denies having seen the anomaly, thereby avoiding any further discussion. One might paraphrase Prof. Duncan's denial ("We see no box like structure..") as: "We do not 'see' the box-like structure, because it is not one that is predicable within accepted diagnostic paradigms" – in effect the equivalent of his saying "no comment" to a question of highly sensitive medical and legal importance. His investigation (and Dr Miszkiel's report to which it refers) has clearly been subject to the same systemic constraints that inhibited the initial reports on the scan. It is simply the case that no single NHS department, and no individual NHS clinician, dares (for reasons of their own personal security) to take on the responsibility for unilaterally disclosing the evidence. To do so would be to reveal a medical atrocity of extraordinary and horrific proportions, and one which is likely to challenge anyone's faith in ethical medicine, and risk bringing the reputation of the entire medical profession into disrepute.

I saw little point in asking UCLH to look again at my complaint, the initial complaint investigation having so stubbornly avoided addressing the issues it raised. The only hope for a satisfactory resolution lies within the route of an independent investigation. Therefore I referred this complaint, as with the previous complaint against GSTT, to the Parliamentary & Health Service Ombudsman, on 18/12/2013:

Complaint to the Parliamentary & Health Service Ombudsman – 18/12/2013 [pdf – 58KB]

Within three weeks I received the following decision from the PHSO in agreement to investigate the complaint:

PHSO decision to investigate my complaint – 09/01/2014 [pdf – 91KB]

The summary of the complaint described in the PHSO's decision contained some inaccuracies, and limited its evaluation of the complaint to Dr Heaney's failure to disclose the anomalies in his initial reporting on the scan results from 18/03/2013. It does not acknowledge the fact that both Dr Heaney (in his response to my email of 03/10/2013), and Prof. Duncan (in his report on the investigation of the complaint of 12/12/2013) had both evidently lied in declaring the absence of items of non-biological origin in my MRI Head scan, when asked to comment on the specific images represented above. In order to point out these inadequacies, I sent the following email in response to the PHSO's decision:

Comments in response to the PHSO's summary of my complaint – 13/01/2014 [pdf – 20KB]

Eight weeks following the PHSO's decision to investigate the complaint, on 05/03/2014, I sent them an email seeking an update on the progress of their investigation. I asked that they provide evidence of their independent medical evaluation of the MRI scan and, if that expert opinion confirmed the presence of items of non-biological origin as highlighted in the images referenced above, to also confirm that they had referred the suspicion of a cover-up of evidence by the Trust to the police. I received a reply from Tracy Hancock, Allocation Manager at the PHSO, on 06/03/2014, to say that the case had not yet been referred to an investigator and that only at the investigation stage would they be able to respond to my request for information. Eight days after this I received the first communication from the investigator Paul Farrell, including an introductory letter and copy of the PHSO's draft investigation report:

PHSO's draft investigation report – 14/03/2014 [pdf – 102KB]

Rather surprisingly, the decision of the draft investigation report was not to uphold my complaint against the Trust. The report is rather brief, and the decision hinges upon the evidence of the PHSO's medical advisor, quoted only indirectly in the report, who apparently had concurred with the opinions given by the three specialists at NHNN that the images: "do not show evidence of artificial structures in your neck". The report included no copy or verbatim statement of the medical advisor's findings from his examination of the scan however, nor any details relating to the advisor's specialism, qualifications, or identity. The report is ambiguous as to the extent of the medical advisor's examination – whether it had involved an examination of the original MRI scan itself, or only of the three modified image-details I had attached to my email to the PHSO of 13/01/2014. There appeared therefore to be little substance to the advice quoted in the report and, in view of the fact that the investigation had been completed within six working days of its being allocated to an investigator, I suspected it had been conducted with the aim of peremptorily dismissing the complaint. I sent the following comments to Paul Farrell in response to his draft investigation report:

Comments in response to the PHSO's draft investigation report – 25/03/2014 [pdf – 315KB]

In those comments I reiterated my understanding of the systemic constraints inhibiting disclosure of the evidence, and which seemingly had influenced the reports of the three specialists at NHNN. In light of the PHSO's draft investigation report, I suggested that the same constraints now appeared to be affecting the attitude of the PHSO towards its own investigation, i.e., including the advice of its medical advisor; since, on any frank and honest perception of the MRI images (with or without specialist training in neuroanatomy) the evidence of items of non-biological origin in my neck is plainly irrefutable. I had also pointed out the existence of a catalogue of evidence – in the form of my report (already in the PHSO's possession) – supporting the allegation that I had been the victim of a medical crime in my early childhood, and which had been the occasion of the illicit surgical implants.

The final investigation report of the PHSO followed 10 days after my letter, on 04/04/2014:

PHSO's final investigation report – 04/04/2014 [pdf – 127KB]

The final investigation report does not change the decision of the draft report not to uphold the complaint. The only essential difference between the two reports is that in para.3 Mr Farrell has added some information regarding the specialism and qualifications of the medical advisor in response to my comments. This does not fully answer my request on this point, as we are still without any explicit and verbatim statement of the advisor's examination findings – the report still only quotes him indirectly. Mr Farrell's accompanying letter to the report states that: "[W]e only looked at the MRI scan images you sent to us", suggesting that the advisor has considered only the modified image-details sent to the PHSO by email attachment on 13/01/2014, and has not examined the original MRI scan itself (which was however already in the PHSO's possession). Such a cursory inspection of the derived image-details hardly constitutes an objective medical examination of the evidence in question.

After speaking to Mr Farrell on the telephone, on the 09/04/2014, he informed me that the medical advisor in question was a regular ('internal') advisor employed by the PHSO, and had conducted his examination of the MRI images on one of his routine visits to the PHSO offices, during a discussion with Mr Farrell at his desk. His opinion had been given informally that is, by word of mouth – there is no documentary or signed declaration of his advice for which he might later be held accountable. Neither do we have any idea of his identity; we are only told that he is an "orthopaedic & trauma surgeon" whom Mr Farrell is satisfied (for the purposes of his peremptory investigation) "has suitable experience to examine and understand MRI images". In response to my question if the advisor might be simultaneously employed by the NHS, Mr Farrell informed me that he is employed by the NHS and therefore "not entirely independent of the NHS", but that this did not affect his contractual duty in giving medical advice 'independently' to the PHSO.

The PHSO's investigation has been conducted with deliberate disregard for the arguments made throughout my complaint of the self-evident nature of the MRI scan evidence, and that the refusal to disclose this evidence amongst the various medical professionals involved can only be explained therefore in terms of systemic and institutional constraints operating against its disclosure across the broad institution of the NHS. These arguments, and the reasoning behind them, have simply been ignored, in preference for the informal verbal opinion of a medical advisor whose specialism (orthopaedic & trauma surgery) is not even relevant to an expert opinion on the evidence concerned. Even if it could be claimed that the quoted advisor has quasi-independence from the NHS (despite being principally employed by that organisation), how likely is it that he would have the professional confidence to overturn the opinions of three specialists in the area of neuroradiology, which is not his own specialism?

In spite of the claims of the PHSO to be 'independent of the NHS', it clearly felt compelled to conduct an intentionally crude and blinkered investigation, for the sake of its own administrative convenience, at the same time refusing to conduct a thorough, formal, and independent evaluation of the medical evidence in question. Its actions in response to this complaint therefore reveal the PHSO's structural inability to offer any effective regulation in the context of the most serious ethical transgressions conducted within the NHS.1

During April 2014 I submitted a Freedom of Information Request to the PHSO in which I requested details of the specialisms of the PHSO's contracted medical advisors, as well as details of the contracts required between the advisors and the PHSO. The response to the FOI request revealed that the PHSO employs 42 such 'internal' medical advisors, none of whom are specialised in neurology or neuroradiology.2 It also maintains contracts with 102 'associate' advisors, including one neurologist and three neurosurgeons. The contractual agreements maintained between associate (and 'external') advisors and the PHSO specify that it is an obligation for the advisor to provide signed copies of their advice reports within 15 days of receiving the case file. There is no such specific contract however which applies to the PHSO's internal advisors – they must sign the standard PHSO employment contract signed by all PHSO employees, which includes no specific clause relating to internal advisors’ reports. During our telephone conversations Mr Farrell had informed me that there was no medical report submitted by the advisor in question, and that the only written record of his advice is a note written by Mr Farrell himself.

In the light of the information received from the FOI Dept. I sent the following request for a review of its investigation decision to the PHSO's Review Team on 30/06/2014, approaching the 3-month deadline for the submission of a review request:

Request for a review of the PHSO's investigation decision – 30/06/2014 [pdf – 377KB]

I received the following response from the PHSO, dated 17/07/2014:

PHSO's response to my review request – 17/07/2014 [pdf – 65KB]

The response from Nicola Bubb is to say that my request for a review does not meet the PHSO's review criteria for the reasons that I have not identified any factual errors in their decision letter, submitted any new information, or explained which evidence they have overlooked. However, in order to satisfy the review criteria, it is not necessary for me to point out evidence which has been overlooked in the PHSO's investigation, only that the PHSO has overlooked or misunderstood my complaint (see the postscript on p.2 of Mr Farrell's decision letter of 04/04/2014, which details the review criteria).

In my review request it was necessary for me to reiterate the two substantial features of my complaint, well represented in all of my complaint correspondence, and which had not been acknowledged, discussed, or refuted in the PHSO's investigation report. These had emphasised: a) the self-evident nature of the anomalies revealed by the MRI scan; and: b) the systemic constraints operating against disclosure of the evidence across the broad NHS institution, and which were likely therefore to be affecting the quoted advice of the PHSO's own medical advisor (himself an NHS employee). As Mr Farrell had rigidly ignored any discussion of these two factors in his investigation report, the PHSO cannot honestly claim that it has not overlooked these major elements of my complaint.

Ms Bubb's response to my remarks on pp.4-6 of my review request, with regard to the poor quality and immaterial nature of the medical advice quoted in the investigation report, is to defend the validity of that advice on the basis that the notes made by Mr Farrell from his discussion with the medical advisor had been "approved" by the advisor himself. Ms Bubb states that the PHSO is not required to obtain a medical report or to use an external (or associate) advisor. However, she has not answered the allegation implicit in my review request that the choice of an internal advisor in this case was made specifically to exclude the obligation to provide a material report. A formally objective investigation ought to have chosen an advisor with a specialism that matched those of the three specialists from NHNN under investigation (i.e., in neuroradiology), and the only available advisors with such a specialism are associate or external advisors, who are contractually obliged to provide such a material report. The choice of an internal advisor therefore has avoided the submission of a medical report from an advisor with an appropriate specialism, so as to enable the PHSO's investigation to proceed on the basis of immaterial advice against which no legal challenge could be made.

During a telephone conversation with Mr Farrell he informed me that the decision to use an internal advisor was made between himself and Maria Leader (the "lead clinician" referred to in para.4 of Ms Bubb's letter). I am informed that Ms Leader has a nursing qualification; Mr Farrell, I understand, has no medical qualification. The claim that the advisor had approved Mr Farrell's notes from their discussion does not save the quoted advice from the charge of hearsay made on p.6 of my review request, for the reason that the advisor has not himself written the advice and cannot therefore be held legally accountable for any indirect quoted instance of that advice.

Furthermore, and in addition to these objections, the PHSO's response to my request for a review does not address the fact, made clear on p.5 of my review request, that the PHSO has not actually conducted an independent medical evaluation of the original MRI scan material – the quoted advice was given following a cursory examination only of the three modified image-details I had attached to my email to the PHSO of 13/01/2014. It is not acceptable that an independent medical evaluation of the scan should be conducted by the advisor looking at the derived image-details (only) that have been copied from the original scan material and modified by the patient.

There is no further option to appeal the PHSO's decision, save for that of an independent Judicial Review. However, as any independent legal process would involve my representative enquiring into matters invoking issues of national security, my experience so far has shown that no lawyer is currently prepared to represent me in the case.

September 2018


  1. The intractability with which the PHSO maintained the findings of its draft investigation report, through to its final report, in ignorance of evidence and arguments raised against the draft findings, compares with that of its sustained decision not to investigate my earlier complaint against Guy's & St Thomas' NHS Trust – see: PHSO decision not to investigate Guy's & St Thomas' NHS Trust. [back]
  2. For reference purposes, the PHSO's response to my FOI request is available as a ZIP archive (5.17MB) from cloud source: I have highlighted some of the text in the file "annex c", which is the contractual agreement between the PHSO and its 'associate' advisors. The specialisms of the PHSO's 'internal' and 'associate' advisors are listed in "annex f". [back]

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