Biting the Big One (part 2)
September 21st, 2007 Fred McVittie
When we extend our categorisation outward to its utmost extent, we arrive at a point where everything is contained within this ultimate category. We might call this category ‘the Universe’, or ‘Everything’, or ‘All’, or ‘the One’ (capitalising the word for added emphasis). For Plato this category was ‘Being’, and for the neo-Platonic Christians it was synonymous with the concept of ‘God’ (again capitalised for emphasis). The ultimate category has nothing beyond it and there is no place ‘outside’ it from where it can be regarded. It contains every material entity, every iota of space and every moment of time; past, present, and future. It contains every planet, inhabited and uninhabited, all of the inhabitants of those planets, every cell in the body and electrochemical signal in the brain of those inhabitants, and every thought in the minds supervenient on those brains: real, imaginary, true, false, glorious, pitiable, good, evil, enlightened or dismally dark. Every God that has ever been conceived, and all those that have not, and indeed all those that could not, are contained within the boundless bounds of Everything, along with every scientific hypothesis and theory, including of course, innumerable theories of everything.
Symbolising the ultimate category in the form of a mark, on paper for example, presents certain difficulties. One could, of course, use any arbitrary mark, a word for example, and simply accept that this chicken scratch somehow ’stands in’ for the concept, just as the small geometrical shapes of these letters stand in for the ideas in this writing, or a street sign that shows a number 30 on a white background, indicating the maximum legal speed limit. This ’symbolic’ relation between the mark (the signifier) and the idea (the signified) is fine, provided of course we know the language. This is necessary since the mark and the concept are associated by convention only, and such conventions have to be learned. Without a knowledge of numbers the speed limit sign is meaningless, as indeed is this writing without a knowledge of letters. There is no way you can look at a text written in a language that is unfamiliar to you and guess what it might mean. Words, numbers, and other marks of that kind do make even the vaguest appeal to intuition, to get the meaning you really have to know the language. With symbolic signifiers the lack of a connection between the mark and the idea, the signified, means also that the form of the mark makes no contribution to the understanding of the concept referred to. In order to understand what the mark means you have to already have full knowledge of the referent. Even if you are fully conversant with the English language for example, there is nothing about the word ‘tree’ that adds to your understanding of what a tree is; the mark simply points you to what you already know.
In our search for a mark for the ultimate category it would be nice if we were not so locked in to language and convention, and our choice did not have to appear so random and disconnected from the thing itself. Also, ideally, we would find a mark which more closely mirrored the condition of the category itself, an ‘iconic’ signifier in which the relation between the mark and the idea was one of recognisable similarity, like the drawing of house that shares some features of the actual house (the outline on the page is similar to the perceived outline of the actual house formed on the retina, albeit upside down), or the icon of a folder on the desktop of this computer in some way resembles a real folder, or like the street sign for ‘national speed limit applies’ which (in the UK) shows a black diagonal band on a white background, almost as if someone had taken a large pencil and crossed the number out. This type of signifier, whilst it does have a tendency to calcify into convention, does have a much closer, non-arbitrary relationship to the ideas represented. We do not have to have any specific knowledge to see a drawing of a house as representing an actual house; our familiarity with the use of folders in the real world allows us to understand the folder icon and its use in organising digital information intuitively, we need to learn the convention of the Arabic numeral system to feel the logic of the strike-through mark on a street sign; who amongst us has never crossed out something that no longer applied, or slashed with a machete at a section of redundant foliage?
Our mark for the category of ‘Everything That Is, Ever Was, And Ever Will Be, Real Or Imagined,’ (’Everything’, for short) should be of this type, but since Everything does not, by definition, have an outline, and certainly does not form an image on the retina,we cannot use the same strategy for the making of such a mark as we might when making the mark for a house, or designing an icon for my laptop. The other strategy, that which is used by the sign for ‘national speed limit applies’, is available to use however. Such signs are not pictures of the ideas they signify, nor are they totally arbitrary symbols which only acquire meaning within the language of a particular society, they are instead visual metaphors which capture the way we understand those ideas. We understand the street sign because of the embodied experience we have of removing something which was previously relevant by making a slashing motion through it with our arm. The act of wielding the machete through thick undergrowth, the act of striking out the words on the page with a bold stroke of the pen; both these actions physically perform the function of laying waste the stuff we no longer need, and it is this action, transformed into the visual metaphor of a diagonal line, which we use to stand for the cutting away of the previous thirty mph limit. Even if we had never come across this sign before, with a little bit of thought we could probably make a reasonably good guess at its meaning simply by ‘feeling’ the action it seems to be asking us to make. This guesswork would be even easier in some European countries where many signs are ‘cancelled’ by later signs on the road which duplicate them, but with the addition of a strike-through. The signs announcing the names of towns and villages in Spain which appear on the road into those towns, for example, are duplicated on the roads out but with a cancelling double slash. The signs seem to say that, should we be thinking we are still in that town, we should at this point cross out that redundant idea from our minds. This type of mark differs from arbitrary symbols not only in that it informs us of the idea that is stands in for, but because it also contributes toward the understanding of the idea in a way that symbolic signs cannot. In the UK the national speed limit is seventy mph so the exact same meaning should be conveyed by replacing the strike-through mark with another symbolic sign that simply had the number 70 on it. However, I would suggest that the feel of these two signs would be very different. When we see the strike-through mark on a street sign we intuitively understand it as the removal, possibly even the forceful removal, of something. Some restraint that was previously placed on our behaviour is being cut away like a blade through the ropes of a captive, and when we see the sign we understand it partly (albeit unconsciously) in those terms. After chugging along at a frustratingly slow 30 mph we suddenly feel licensed to cut loose and put the pedal to the metal. For this reason, the ‘national speed limit applies’ sign is very often incorrectly referred to a the ‘no limit’ sign. Rather than reading it as the imposition of a particular (higher) speed limit it is intuitively interpreted as the removal of the speed limit which previously applied, with no substitute put in its place. This incorrect interpretation is completely reasonable given the contribution made to our understanding of the sign by the metaphorical action implied.
This type of iconic signifier, a mark which stands metaphorically for some important aspect of the idea, which allows for a relatively intuitive grasping of that idea, and which also, ideally, contributes appropriately to the understanding of that idea, is the type we are seeking for the distinctly abstract idea of the ultimate category or Everything.
The most common mark of any category is the bounded space, usually drawn as a circle.
This mark as representative of the general concept of ‘category’ is found in a wide number of contexts, but most evidently in mathematics, where it features in Venn diagrams, set theory, Spencer-Brown’s ‘primary algebra’ and other systems of Boundary Math, etc. It also appears less formally in organisational charts, mind-maps, and in the pictures on the back of cereal boxes showing which foods constitute the major food groups. In each case the line of the circle represents a boundary within which are to be found the members of the category, and outside of which is anything which does not belong to the category. The intuitive success of this image as a mark for the concept of a category is due to its ability to function as a visual metaphor or iconic signifier. Although it may, at first pass, appear as arbitrary and abstract as a number or letter, this mark is grounded in embodied experience in much the same way as the strike-through mark on street signs. It can be seen as minimally representative of a container into which we may be placed all the members of a particular category. With almost no imaginative effort it is easily recognisable as the bird’s eye view of a basket into which we put all of the apples, and out of which we throw all of the oranges. Or alternatively we can effortlessly see it as the fence which we use to corral all of the sheep and exclude all of the goats. The experience of dealing with such bounded spaces as containers (and perhaps less so corrals) in the routine of daily life has created in us an intuitive grasp of this form or ’schema’ which we can, and do, apply in our understanding of categories. The bounded space of the circle is a highly successful and practical mark of the general concept of the category, intuitively accessible through being grounded in embodied experience.
Returning to our search for a mark which represents the ultimate category, the mark of Everything, we need to ask ourselves whether the bounded space of the circle is up to the task. Immediately we see that it is not. As discussed above, the strength of the circle is that it represents not only a category which contains, but also one which excludes. We separate apples from oranges only partly by keeping the apples together in a basket, we also throw the oranges out of that basket into the space beyond. Similarly, the fencing off of sheep in a corral is effective only if we have a space outside that corral to chase the goats into. In other words, the circle as a mark of categorisation is also a mark of separation. There is an inside and an outside to the category represented by the circle just as there is an inside and an outside to any container. When we are trying to refer to the ultimate category, by definition, there can be no ‘outside’, and everything must be on the ‘inside’. (including, paradoxically, the very idea of an ultimate category itself, or ‘the set of all sets that contains itself’. The category of Everything must also contain the category of Everything). There is no space ‘beyond’ the boundary of Everything.
One possible way to resolve this problem, which might lead us to producing a satisfactory mark for the ultimate category is by looking again at the circle. As we have already found, the ability of the circle to serve as a visual metaphor for a category depends upon the existence of a space outside the boundary line which defines these entities which do not belong in the chosen category. So, for example, the space outside the apple barrel does not just contain oranges but also contains everything that is not an apple. The vast prairie beyond the corral where we keep our sheep is defined not only by the presence of a few goats, but also by the presence of everything else that is not a sheep; it is marked, in a way, by its total sheeplessness. In a very real sense, the space outside the barrel, the corral, or the mark of the circle, is itself a category, albeit one which is defined in the negative. Also, the space outside the boundary of the circle is immense, as it would need to be to contain everything in the entire Universe apart from apples, whilst the space inside the boundary is comparatively small. We could, therefore adopt some version of the circle as a mark for the ultimate category if we place our attention not on the interior space but on the exterior space. When we do this we find that Everything (apart from apples, say) is indeed contained by this space. The boundary line of the circle on the page still represents the outermost limits of this large space as it excludes all that is not contained in this almost-ultimate category of ‘Everything minus apples’.
We still do not have a mark for absolutely everything,but having got this far, the next step is very easy. We can simply define the contents of the ‘exterior’ space where the apples are more closely, drawing the line around Everything corresponding larger. When we enlarge the category of ‘Everything minus apples’ to include the skin of apples we find that less is left outside and the mark on the page shrinks.
The inclusion of pips and the juicy flesh of the apples again increases the size of the ‘Everything but’ category.
At this point, or almost point, we are one bite away from the ultimate act of inclusion and the realisation of the mark of Everything. We reach out and, taking hold of the core, we pull it into ourselves, consuming it in a final act of border-crossing. At this point, and now we really are at this point, nothing is left out, not even nothingness. There is no space except the space that Everything embraces and the line around everything becomes infinitely short, infinitely curved. And we can represent this with the mark at the end of this sentence.
Here it is again, in case you missed it that time
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