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 167-page
report: Special Operations
in Medical Research

[pdf – 1.88MB]:

Download my Open Letter to the British Prime Minister & Health Secretary
[pdf – 363KB]:

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


Applications to the European Court of Human Rights

This page forms a logical continuation to the account given in the page A Miscarriage of Civil Justice. That account detailed the conduct of my legal defence in the London county courts against a claim for possession of my flat brought my landlord during October 2017. Possession had been granted to the landlord at Clerkenwell & Shoredith County Court on 04/10/2018 through what I allege to have been a miscarriage of justice. I spent the next two years trying to appeal that judgement on the basis that my genuine defence against the claim had been intentionally denied a fair hearing in court, with the consequence that I had been rendered homeless by the action and had also lost possession of the entirety of my belongings held in the flat. I had been finally refused permission to appeal against the possession order by an order of Mayor’s & City of London Court, without the option of an oral hearing, on 01/12/2020.

On 23/02/2021 I submitted an application to the European Court of Human Rights (‘ECtHR’) alleging violations of Articles 6 and 8 of the European Convention on Human Rights against the UK; i.e., in respect of the conduct and outcome of the housing possession case against me, and also with regard to the conduct of the courts in wilfully obstructing my attempts during 2019-20 to appeal the judgement of 04/10/2018 which had originally granted possession to the landlord. The application involved allegations against various offices of the UK Ministry of Justice, including several London county courts as well as the office of the Official Solicitor and Public Trustee.

I received a response from ECtHR dated 18/03/2021 rejecting the application as ‘incomplete’ (reference: 12776/21), for the reason that I had not included within the bundle of supporting documents copies of the transcripts of the various court judgements referenced within the application. At that time I possessed only one of the missing transcripts, while ECtHR identified five such transcripts required to complete the application. I was determined to submit a complete second application, and so I then made requests to the relevant courts in London by email on 12/04/2021 for the outstanding transcripts. After having eventually received all but one of these (the court in question had responded to say that the relevant case file “cannot be located”), I then submitted a ‘complete’ second application to ECtHR dated 19/05/2021. [ZIP archive – 41MB]

The material submitted to ECtHR in each of the two applications (with the exception of the 330-page bundle accompanying the first), including the response letter from the Court of 18/03/2021, is included in the ZIP archive linked above. That material had been submitted by email to the Channel4 News Team in the UK on 15/06/2021, as part of the series of my 39 email statements sent to that team between October 2018 and June 2021, and which is frequently referenced in the page: A Miscarriage of Civil Justice.1 The difficulties and resistance I met with from the London courts in response to my four transcript requests of 12/04/2021 was described in detail in my subsequent email to the news team of 21/06/2021. The documents involved in those requests, including correspondence with three London courts and the transcription company Marten Walsh Cherer, is included in three PDF folios as attached to that email.2 There are potential allegations of fraud which may transpire from this material, with regard to the interactions between the transcription company and Central London County Court, and which echo those remarked upon at A Miscarriage of Civil Justice in relation to an earlier transcript request I made to Clerkenwell & Shoreditch County Court during May 2019.3 It had chiefly been my awareness of the sensitivity implied by my allegations in relation to that earlier transcript which had encouraged me to exclude it from my first application to ECtHR of 23/02/2021, in the expectation that this somewhat controversial material could ultimately be submitted to the European Court at a later date, following (so I anticipated) its initial acceptance of the first application.

ECtHR’s eventual (backdated) dismissal of my second application

On 27/05/2021 I received acknowledgement from ECtHR during a telephone call that it had received the second application on 25/05/2021 and was given the reference: 26495/21. The second application had been sent from Sweden, and included the address of the hostel where I stayed in Stockholm – Interhostel – as my address for correspondence. I waited for a response from the Court, occasionally checking the progress of the application at the Court’s searchable online State of Proceedings web facility (‘SOP’).4 The first entry to appear there in relation to the application was dated 21/06/2021, and showed the state of proceedings as: “Application awaiting first judicial decision”. In comparison, the Court’s response to my first ‘incomplete’ application had been its dismissal letter of 18/03/2021, before any information was recorded at the online database (there remains no information either at the SOP facility or at the Court’s online HUDOC database in relation to that first application).

Following the events of 12/07/2021 at Interhostel described on the page Swedish Asylum Applications (2018-2021), I was hospitalised for a period of ten weeks, although I had limited day-to-day mobility outside the ward where I stayed. In a decision which I understand to have been largely driven by the disturbance of those events, the hostel was compelled to finally close for business on 31/08/2021. It was necessary therefore for me to inform ECtHR of a change in my correspondence address, and so on 26/08/2021 I sent a letter to the Court advising it that correspondence should now be addressed to a poste restante address in Stockholm instead of the hostel address given in my application form.

I had anticipated that the hostel premises at Kammakargatan 46 would be inaccessible following its planned closure on 31/08/2021. However, it transpired that the hostel management were to conduct a ‘firesale’ of the hostel’s domestic equipment at the premises for the duration of September 2021, meaning that the premises remained accessible for that period and I was able to telephone the staff there to check for any mail that might arrive from ECtHR. This I continued to do, in addition to checking for mail at the poste restante address, until I finally departed Sweden on 24/09/2021. No mail was received from the Court however during that period at either of the given addresses.

From my new location in Novi Sad, Serbia, I sent a further letter to ECtHR on 29 September to change once more my correspondence address with the Court, nominating the main post office in Novi Sad as a poste restante address. In that letter, I tried to emphasise to the Court the point that the UK’s alleged violation of Article 8 §1 of the Convention on Human Rights, as detailed within my application, should be regarded by the Court as a “continuing situation” with respect to Article 35 §1 of the Convention; and that as such the application demanded a more urgent response from the Court than was apparent from its delay at that point of four months in arriving at its initial judicial decision (the state of proceedings at this time recorded at the SOP facility remained unchanged from that of 21/06/2021 – as: “Application awaiting first judicial decision”).

After waiting a further two weeks, with no response from the Court, and no change in status of the application at the SOP facility, on 16/10/2021 I decided to publish the web page referencing my correspondence with the Channel4 News Team regarding my allegation of a miscarriage of civil justice in the London county courts. At that time the page: A Miscarriage of Civil Justice contained the information in the current page describing my applications to ECtHR as its final section (the sections were divided in to separate pages on 30/04/2023). This was the occasion of the first online publication of each of the two ZIP archives containing the combined correspondence to Channel4 News [ – 143MB], and the two applications to ECtHR [ – 41MB].

Between 19/10/2021 and 27/10/2021, I made three further updates to this website. The first of these was to include the additional page describing my asylum applications in Sweden. The fourth update, dated 27/10/2021, included some minor textual revisions to the page: A Miscarriage of Civil Justice, which also included for the first time a link to the ECtHR’s SOP online facility, together with my remark that the Court’s apparent delay in providing a more effectual response to the application than the one recorded at the SOP facility was “unacceptable” in view of my allegation regarding the “continuing situation” of the UK’s violation of Article 8 §1 of the Convention. Naturally, immediately prior to making that update I had researched the link itself to check the current status of the application, which – on 27/10/2021 – showed no change to the status recorded on 21/06/2021 – i.e., that of: “Application awaiting first judicial decision”.

I continued to wait for a response from the Court to my most recent letter of 29/09/2021. Ten days after my update to the current page of 27/10/2021, on 06/11/2021 I checked the Court’s SOP facility for the latest status of the application. I was surprised to find that a new current state of proceedings was now recorded as: “Application finished”, and there appeared a second entry in the list of major events: “Decision to declare a case inadmissible” showing the date “02/09/2021”. It appeared therefore that this entry had been added to the database after my publication of the application documents online – in the period between 27/10/2021 and 06/11/2021 – and that the decision had been in effect backdated to appear as if it had been made eight weeks previously on 02/09/2021.5

I telephoned ECtHR on Monday 08/11/2021 to query the timing of this recorded decision, and to verify the Court’s receipt of my two letters of 26/08/2021 and 29/09/2021 notifying it of changes to my correspondence address. I was informed during this call that a letter notifying of the decision had been sent from the Court to me “on 09/09/2021” at the address given in my application form (the Interhostel address), and that the Court had “not received” the information regarding my changes of correspondence address. I was advised that if I wished to receive a copy of the decision I should fax that request to the Court. I then sent the fax request to the Court on 09/11/2021, after searching several hours for a fax service.6 During a telephone call to the Court later that day it was confirmed the Court’s receipt of the faxed request.

I then waited for a response from the Court at the poste restante address in Novi Sad given in my faxed letter. Having received no such response at that address by 19/11/2021, I telephoned the Court once more to query whether a response had yet been issued by the Court. On this occasion the call-handler stated that no information could be given by telephone and that any such request for information must be put in writing to the Court. This was inconsistent with the fact that exactly that kind of information had been readily given to me in response to my earlier calls.

I telephoned the Court again on 25/11/2021, giving my reference number and explaining that I had still received no response from the Court to my faxed request of 9 November, and asking for information whether the Court had yet sent a copy of its decision letter in response. The call-handler stated again – inconsistently with the responses to my earlier calls – that she was unable to access the details of the case in order to confirm whether or not any letter had been sent from the Court.

No mail was received at the Novi Sad poste restante address by the 03/12/2021. As I was planning to depart that location the following week, on 7 December I telephoned the Court once more requesting the same information. I was told during this call that a response had been sent from the Court to the address given in my fax “on 19 November”. Why then could that information not have been conveyed to me during my call on 25 November? I checked at the post office on 8 December (the day of my departure for Albania), but there was no letter from ECtHR addressed to me – if the letter had not reached its destination within this 19-day period, then it was effectively ‘lost in the post’.

From this account of events there inevitably arises the suspicion that the Court has falsely represented the date of its decision to dismiss my second application – that suspicion is reinforced in view of the Court’s most recent failure to provide a response to my faxed request for a copy of its decision. In particular, it is not at all credible that all four of the letters sent by regular post – my two letters to the Court notifying it of the changes to my correspondence address, plus the two copies of the decision letter purportedly sent by the Court, the first on 09/09/2021 to Kammakargatan 46 in Stockholm, the second on 19/11/2021 to the Novi Sad address – have all been similarly ‘lost in the post’ (however, this is necessarily implied if we accept the information given by the Court as truthful). The Court’s first letter ought to have reached its destination by the 17/09/2021 at the latest, where I would have been able to receive it, as I visited the hostel premises on 23/09/2021, and I also had an arrangement with the staff there to email me with the news of any post arriving in my absence; so that had the letter arrived at any time during September I would have been informed of the fact.

The suspicion that the Court has falsely claimed both to have made and communicated its decision to dismiss my second application between 2 and 9 September 2021 is consistent with the observation that no entry in relation to that decision appeared upon the Court’s SOP database until after 27/10/2021, following my somewhat controversial publication of the application documents online, together with a link to the SOP facility itself. It is inferred therefore that the Court was wise to the event of that publication and was provoked as a consequence into invoking a decision to dismiss the application, not for the reason of any inherent inadmissibility in the application itself, but essentially because the Court lacked the judicial will to proceed to a fair judgement of that application.7

Since my departure from Serbia for Albania, I have had no address consistent for a long enough period to make further requests to the Court. It is apparent anyway that the Court does not wish to comply with that request, and has exploited the temporary status of my previous correspondence addresses in order to evade reasonable compliance with it. In not acknowledging or responding appropriately to any of my three letters (the two sent by regular post, and the third sent by fax) the Court is applying a policy of selective opacity with regard to its decision to dismiss my second application, and is to all intents and purposes refusing to communicate the content of that decision or its justification to me.8 The same policy of selective opacity has also been employed by its reception staff in response to my enquiries over correspondence, as on several occasions those staff have freely given the information requested, but with notable inconsistency on the occasions of my calls on 19/11/2021 and 25/11/2021 explicitly refused to convey that information.

It is essential that ECtHR should communicate the reasons for its decision to find my second application “inadmissible”, and its failure to respond to reasonable requests for an explanation of those reasons means that its justification remains opaque. That it should have effectively refused to communicate its reasons suggests that the Court’s decision has been made arbitrarily, i.e., with positive disregard to the merits of the application. I am also unaware of the category of decision supposedly made by the Court (whether it is the decision of a single judge, a Committee of 3 judges, or a decision made by a Chamber of 7 judges). I understand however that a decision on inadmissibility is final and unappealable in all three categories. To compare with the timing of the decision in the case of my first application dated 23/02/2021, the inadmissibility of that application was established by the Court (presumably by a single judge) within three weeks of the Court’s receipt of the application (it is assumed that the Court received that application around 02/03/2021, while its letter rejecting the application followed dated 18/03/2021). In the case of the second application however, even if we accept the purported date of 02/09/2021 for that decision as ‘truthful’, it is clear that ECtHR deliberated for more than 14 weeks in arriving at that decision. As that decision did not appear at the SOP database until after 27/10/2021, the effective delay by the Court in notifying of its decision (excluding its reasons) was more than 22 weeks following its receipt of the second application.

It is reasonable to conclude from the above that the ECtHR finds that it is simply unable to act according to its mandate in response to my application and has been compelled into a decision of ‘inadmissibility’ while being unable to provide substantive reasons for that decision. The behaviour of the Court in applying selective opacity in the case of my application, both with respect to its material correspondence and to its published case law (re: footnote 8 below), merely replicates a pattern of behaviour well established by the London county courts during 2019-20, in their responses to my efforts to appeal the possession claim, and which formed a substantial part of my allegation against the UK over its violation of Article 6 §1 of the Convention. In this case therefore the ECtHR appears incapable of acting to redress either that violation or the continuing situation of the UK’s violation of Article 8 §1 – the Court’s failure of judicial will serves to perpetuate both violations. This failure to respond with judicial rigour by an office of the Council of Europe, in the context of these quite egregious domestic European human rights violations, is consistent with that already observed following my approaches to the Council’s Commissioner for Human Rights between 2013-2016, as discussed within the later sections of the introductory page to this website.

30 April 2023

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  1. The series of my emails to Channel4 News, together with their attachments, is available to download as the additional archive: (143MB). The 39 emails are presented in the form of a PDF folio (Emails_C4-News_folio.pdf), with their listed attachments as a series of accompanying numbered and dated ZIP files. My email to Channel4 News of 15/06/2021 mentioned here is item 38 in the series – however, for reasons of economy the attachments to that email are not included in the larger archive, but are available here as the dedicated archive: (41MB). [back]
  2. My email to Channel4 News of 21/06/2021 is item 39 of Emails_C4-News_folio.pdf in the archive:, which includes the attachments to that email. [back]
  3. See my email #15 to Channel4 News of 12/06/2019 in the archive: for further details regarding these earlier allegations. [back]
  4. The URL for ECtHR’s State of Proceedings online searchable database is: [back]
  5. My correspondence with ECtHR following its receipt and verbal acknowledgement of my second application, beginning with my letter of 26/08/2021, is contained within a PDF folio comprising 4 items: ECtHR_folio.pdf (1.95MB). This folio is also included within the archive: The third item within this folio is a document showing two pasted screenshots from the ECtHR’s online SOP facility – the first representing the state of proceedings as viewed on 27/10/2021; the second that viewed on 06/11/2021. [back]
  6. The faxed letter is item 4 of the folio described in note 3 above. [back]
  7. After all, the violations of Rule 47 on admissibility criteria that were identified by the Court in its dismissal of my first application had all been resolved in the second application by the inclusions of the missing transcripts – the absence of the fifth transcript had been justified in terms of Rule 47 §5.1(a), by providing evidence of Mayor’s & City of London Court’s response that the case file relevant to that judgement “cannot be located”. [back]
  8. As a further evidence of this policy, it is not possible to find a reference to either of the decisions relating to my first (ref: 12776/21) or second (ref: 26495/21) application at the Court’s searchable HUDOC database (accessible at:, which is a transparent repository of all judgements and decisions made by the Court, i.e., including decisions of inadmissibility, and representing even those cases in which the applicants have requested anonymity. It appears therefore that the decisions in response to both my applications have been intentionally sequestered by the Strasbourg Court from its HUDOC database. [back]