What is *X*?

You might well be wondering what it is this 'logo' represents.. I mean what does an '*X*' in a box within a circle have to do with exposing an historical medical atrocity? So to begin with let's be clear about one thing – I'm not in business, and there's nothing for sale here..

But there are *two* things going on on this site, and circumstances dictate that both get given some space here together, though I'm not sure I've fully worked out what the connection is – if there is a substantive connection, it has to do with Science.. Information.. *Technocracy*..

So this 'device', 'logo', 'icon', call it what you will, is by way of a segue to what is going on (perhaps incongruously, on a first impression) in the *X.cetera* section..

*X.cetera* is concerned with a problem in mathematics and science to do with the way we think about numbers – are numbers best described as logical *concepts*, or as logical *objects*? – at least that's one way of approaching the problem.. and it happens that something very significant has been overlooked (even amongst experts in those fields).. well, for at least 400 years or more – an oversight which has serious consequences in terms of its implications for the logical consistency of data produced within digital information systems (generally speaking)..

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.. The implicit assumption here is that there is 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 (which will come as a surprise to many Mathematicians and Information Scientists alike).. To illustrate this, the research now revealed at: *Radical Affinity etc.* shows that the proportional (logical) ratios between particular values expressed in binary do not correspond seamlessly to the ratios between *the same values* when expressed within decimal or octal for instance (or to those within any other number radix from *ternary* (base3) to *nonary* (base9) – the key factor referred to above as being previously overlooked within Mathematics and Science), as these must be determined uniquely according to the member-ranges of their respective permitted digit groups (0-9 in decimal, 0-7 in octal); one consequence of which of course is the variable *relative frequency* (or 'potentiality') of specific individual digits when compared across radices..

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 (and hence digital) system of codes, being subject to the same restrictive determinations, cannot therefore be applied, with logical consistency that is, to conventional or analogue representations of the observable world, as this would be to invest binary code with a transcendent logical potential which 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 which 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).. Which 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!

But back to my 'X-box' (as I like to call it).. It is a highly schematic depiction of a relationship, or a *ratio* – '*X*' is the typical unknown variable of mathematics.. It takes a value, and that value is something that we *know* about things in the world.. The box is the form through which we represent that knowledge – a 'unit' of information, which obeys the rules of rationality, proportionality and, in the case of visual images via screen-pixels, the rules of *perpendicularity*.. The circle is everything else about the object described by '*X*', including what we don't know, or perhaps are just unconscious of in the act of representing..

If we take the side of the box as the unit value '1', the ratio of the box to the diameter of the circle (the square's diagonal) is 1:√2.. Mathematics defines √2 as an *irrational* number.. Which means that it cannot be expressed as the exact ratio of any two whole numbers, and therefore does not resolve to a finite number of decimal places, or to a settled pattern of recurring digits (there are always more – possibly infinitely more – digits behind the decimal point which can be added, as in the case of π).. This ratio indicates to me something about the limits of knowledge.. And of representation..

Generally speaking, instrumental scientific discourse assumes the 'facthood' of its representations and judgements – a form of quantitative identity between its concepts and objects in the world (which is why the distinction between numbers as concepts or as objects is an important one), which is to fashion the ratio described above instead as a 1:1 relationship.. Our diagram therefore provides a numerical ratio – a standard – with which to destabilise this illusory identity – the 'absoluteness' of a representation of fact entails a degree of opaqueness towards its object expressed by this ratio.. The finitude of the singular, as a proposition, is differentiated in actuality by the infinitude – the *irrationality* – of √2..