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 that 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. It is argued that this conventional understanding of integers, which is the one widely held amongst mathematicians and scientists adopting mathematical principles, is the cause of a significant oversight with regard to changes in the relations of proportion between numerical values, i.e., when those values are transposed out of the decimal rational schema into alternative numerical radices such as those of binary, octal, and hexadecimal, etc.

On the page: The Limits of Rationality it is argued that the relations of proportion between integers are dictated principally by their membership of the restricted group of characters (0-9) as defined by the decimal rational schema; and that corresponding ratios of proportion cannot be assumed to apply between otherwise numerically equal values when transposed into alternative numerical radices having either reduced (as in binary or octal, for instance) or extended (as in hexadecimal) member-ranges.

This is shown to be objectively the case by the results published at: Radical Affinity and Variant Proportion in Natural Numbers, which show that for a series of exponential values in decimal, where the logarithmic ratios between those values are consistently equal to 1, the corresponding series of values when transposed into any radix from binary to nonary (base-9) results in logarithmic ratios having no consistent value at all, in each case producing a graph showing a series of variegated peaks and troughs displaying proportional inconsistency.

These findings are previously unacknowledged by mathematicians and information scientists alike, but the import of the findings is that, while the discrete values of individual integers transposed into alternative radices will be ostensibly equal across those radices, the ratios of proportion between those values will not be preserved, as these ratios 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. While the assessment of quantitative and qualitative differences at the level of the observable world necessarily entails assessments of proportion, the digital encoding of those assessments ultimately involves 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. The process 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. Logic is assumed to operate consistently without limits, as a sort of ‘ambient’ condition of information systems.

In the X.cetera section I am concerned to point out however 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 limited to two members. It does not derive from a set of transcendent logical principles arising elsewhere and having universal applicability (a proposition that, despite its apparent simplicity, may well come as a surprise to many mathematicians and information scientists alike).

As the proportional relationships affecting quantitative expressions within binary are uniquely and restrictively determined, they 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!

[ PDF version ]

[ PDF version ]

[ PDF version ]

[ PDF version ]


Download my 165-page
report: Special Operations
in Medical Research

[pdf – 1.86MB]:

Download my Open Letter to the British Prime Minister & Health Secretary
[pdf – 230KB]:

The Limits of Rationality
(An important mathematical oversight)


Radical Affinity and
Variant Proportion in
Natural Numbers


Mind: Before & Beyond Computation

Dawkins' Theory of Memetics – A Biological Assault on the Cultural

Randomness, Non-
Randomness, & Structural Selectivity


Special Operations in Medical Research: MRI Evidence

Click on the MRI scan images displayed below to enlarge as a slideshow:

Brain MRI image 7.13

MRI image 7.13

Brain MRI image 7.14

MRI image 7.14

Brain MRI image 7.15

MRI image 7.15

Brain MRI image 7.13 (detail)

Detail of above

Brain MRI image 7.14 (detail)

Detail of above

Brain MRI image 7.15 (detail)

Detail of above

The images displayed above are a sequence of 3 vertical (coronal) sections from Series 7 of an MRI scan made of my brain on 02/10/2008 at St Thomas’ Hospital, London. Each image is also shown in enlarged detail. Series 7 of the scan comprises 26 such vertical sections, beginning from the front of my skull and progressing rearwards. The images are transposed as in a mirror, so that the right half of the images represent the left side of the skull. Sequential slices are approximately 6mm apart.

The three selected images begin at a midpoint between front and rear and include the spinal column. A close look at these images reveals a foreign object to the left of the spinal column, just below the base of the skull. The object appears in cross-section as a small circular object with a cylindrical or torpedo-shaped projection, of at least 12-15mm in depth. In the enlargement of section 7.13 (7.13d) there appear to be two armatures or linkages associated with this object which proceed upwards toward the base of the skull. In the enlargement of section 7.14 (7.14d), approximately 6mm to the rear of 7.13, one gets a distinct impression of the internal ‘C’ structure of this object, and which indicates perhaps some clue as to its functional composition. In the enlargement of section 7.15 (7.15d), which is the furthest rear image in which the object is visible, it appears somewhat narrower and less circular than in the previous two images.

Download zip archive containing all Series 7 images [1.46MB]

It is understood that the object revealed in these scan sections has been placed in my neck through an incision in the back of my throat, by surgeons at the North Staffordshire Infirmary (now the University Hospital of North Staffordshire) during a tonsillectomy operation I underwent at the hospital on 09/04/1967 – a week before my sixth birthday. Further evidence of additional items situated in my neck area was subsequently revealed in a 2nd MRI scan conducted in 2013. In addition to these items revealed in my neck, there is also now evidence of a further device (or device-part) located in my thorax – see: Further Evidence, and the latest MRI scan of my cervical/thoracic spine discussed at: CSPINE MRI Scan (July 2020). Until the year 2001, I had no knowledge of the existence of these implants, or of the true purpose of my ‘tonsillectomy’ at age five. At the page: Technological Imperatives I have offered some speculative discussion on what I undertand to have been the technological determinants behind this covert ‘special operation’.

As referred to in Part 2 of my personal report (pp.48-59), I received a consultation over the 2008 scan from Dr. Thomasin Andrews, a neurologist at Guy’s Hospital, in April 2009, during which nothing anomalous was disclosed to me. The six-month delay before the consultation was due to the scan results not being sent back to the referring physician at the South London & Maudsley NHS Trust (‘SLaM’), for a period of eleven weeks after the date of the scan itself, and it was not possible to make arrangements for a consultation until these were produced, in December 2008. It was not until December 2010 that I obtained my own copy of the scan. Since that time I have tried to obtain medical corroboration of this evidence, both through the NHS and privately, but the highly controversial nature of the evidence has meant these attempts have so far proved unsuccessful, as no doctor has been prepared to take initial responsibility for its disclosure (see: Complaint to the GMC for further remarks).

Following the scan procedure, Dr. Crews at the SLaM Trust informed me that he was having considerable trouble locating the scan results, but eventually the Radiology Dept. at St Thomas’ Hospital sent a report of the MRI findings to the SLaM Trust on the 23/12/2008, i.e., eleven weeks following the date of the scan itself. I have seen the notes made by the SLaM Trust which relate to this report, which transcribe the findings as:

  • “Ventricles normal.
  • There are a few small periventricular and subcortical sulci consistent with minor small vessel ischaemia.
  • There are tortuosities of the left vertebral artery leading to slight mass effect on the dorsal aspect of the medulla.
  • No evidence of trauma, brain injury or space occupying lesion.
  • Conclusion: Minor small vessel ischaemia. No significant intracranial abnormality identified.” (my emphasis)

There is nothing in these findings which alerts to any cause for concern, in view of my age, and nothing that identifies the significant anomaly revealed in the images above. In an attempt to locate a copy of the original report made by the Radiology Dept. at St Thomas’ Hospital, I made a subject access request under the Data Protection Act to St Thomas’ Hospital Information Governance Dept. on 29/06/2012. I eventually received copies of my Guy’s & St Thomas’ NHS Trust (‘GSTT’) medical records from the IG Dept. on 02/10/2012. However these did not include a copy of the MRI findings report. I then made an arrangement to view my records in person at the hospital on 13/11/2012. I also filed a complaint with the Information Commissioner’s Office (‘ICO’) to address the failures in the IG Dept.’s response.

On viewing the online copy of my MRI scan at the hospital, in the relevant Reports section, the only written information was “no reports found”. I insisted to the manager that there must have been a report, as one had been sent to the SLaM Trust on 23/12/2008. She said she would make enquiries with the Radiology Dept. I later received a call from the manager to say she had found the report, and I should return to the hospital to collect it.

I now have a copy of the missing MRI findings report (verified by Dr. Scott Hawkins on 06/10/2008; first typed by “RJ1RANV” on 02/10/2008). The content is essentially the same as that transcribed into the SLaM notes, i.e., concluding with: “No significant intracranial abnormality identified”.

In an update to my complaint to the ICO I asked that they consider the following issues:

  • Why was there a delay of eleven weeks between the writing of the MRI findings report, and its being forwarded to the referring physician at the SLaM Trust?
  • Why was the findings report not attached to the online copy of my MRI scan?
  • Why did it take four-and-a-half months from the date of my subject access request, three separate visits to the IG Dept., and numerous telephone calls, for the IG Dept. to fulfil my request for a copy of the MRI findings report?

My own conclusion must be that, as the item revealed in the scan images above is significantly anomalous and highly controversial, the physician who wrote the report deliberately omitted to disclose the anomaly in order to occlude any further attention to it. I further conclude that the MRI findings report was then intentionally sequestered from my online record, in an attempt to obscure the identity of the reporting physician.

The ICO advised me, on 14/03/2013, that it did not fall in the remit of the Data Protection Act 1998 to address either the issue of the eleven week delay in the initial forwarding of the MRI findings report, nor my wider suspicions regarding the reasons for the failure to attach that report to the online scan record. However, the ICO requested that GSTT explain the ‘filing system’ under which the MRI findings report was stored, and the reason it was not attached to the online record of the MRI scan. They advised me that in order to address my concerns falling outside the remit of the DPA, and if I was subsequently dissatisfied with GSTT’s response to the ICO’s enquiry, that I should complain separately to GSTT itself.

The response from GSTT to the ICO’s enquiry, which was sent to me on 12/04/2013, included the following explanation:

“When a patient has a radiology exam at the Trust the images are taken and stored in the image application Picture Archiving and Communication System (PACS). The image is then reported on by a radiologist and that report is written in another application called Computerised Radiology Information System (CRIS). If the digital stamp that is created by PACS for the image is not the same as for the report, then the report cannot be attached to the image in PACS. Therefore, when the Information Governance staff were looking for the report as an attachment to the image in PACS, it was not found and an assumption was made that one did not exist.”

This explanation does not however explain under what circumstances the ‘digital stamps’ respectively created under ‘PACS’, and under ‘CRIS’, would permit a report ever to be successfully attached to the online copy of the scan, which we must expect to be the standard requirement. If the respective digital stamps are required to be identical, or to have some additional digital association, then why were they not so in the case of my scan images and report?

In view of my dissatisfaction with GSTT’s response to the ICO, I submitted a complaint to GSTT’s Complaints Office, on 19/03/2013. For the progress of this complaint, see: Complaint to GSTT.

September 2020

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