Irreversible
Suppose we have two entities p and q, having the respective states P and Q, and an operation O that effects a difference in both p and q, taking them to new states P’ and Q’. We will say that O is an observation by q of p if the difference that it makes to the state of q varies as the state P’ of p varies, such that O produces in the state Q’ of q a representation of the state P’ of p.
In other words, given two possible initial states P1 and P2 of p, there are two possible “observed” states P1’ and P2’ of p, and two possible “observing” states Q1’ and Q2’ of q. O is an observation by q of p if there is a correlation between P1’-P2’ (the difference between P1’ and P2’) and (Q1’-Q)-(Q2’-Q) (the difference between the two “delta”s effected in q by O). For the sake of argument we’ll assume it’s a perfect correlation, which means that deltas in q are isomorphic to values of P’ (if you know what difference the observation O makes to q, you know all there is to be known about the observed state P’ of p, and vice versa).
Note also that in this terminology, the observation O is not necessarily an action carried out by q; it is just something that occurs that involves both p and q in such a way that this particular correlation obtains. We may say for convenience that “q observes p”, but q may be an entirely passive and unwitting party to this event, like a light sensor detecting the sunrise. Agency is not excluded – p may strive to bring itself to the attention of q, which in turn may crane its metaphorical neck to get a better view of p– but neither is it in any way essential.
Now, in this scenario, the operation O forms in q a representation (in terms of its new state Q’) of the state of p-as-observed-by-q (or p operated on by the operation O). Is there then another operation that can form in q a representation of the state of p as unobserved by q – that is to say, can q in state Q’ be taken to a state Q’’ which is similarly representative of the initial state P of p?
Let’s start with the maximal and minimal cases. In the case that P’ is equal to P (that is, the operation O makes no real difference to the state of p), the representation that Q’ makes of P’ is equally a representation of P, and so Q’’ just is equal to Q’. The photons bouncing off the table into my retina make no real difference to the table, so insofar as my perceptual system forms within itself a representation of the table as observed by me, this representation is equally a representation of the table as unobserved by me (it’s remarkable how much difficulty some people have with this entirely banal equation). That’s the “maximal” case, where a representation of P is instantaneously accessible from a representation of P’. The minimal case would be that in which the operation O completely obliterated the entity p, so that its state was completely destroyed. There would be no way to infer from a representation of the “ruined” state P’ what the “prelapsarian” state P might have been: whatever P was, Q’ would always correlate with the “ground zero” state of an obliterated p.
Between these two cases is an interesting range of possible effects of O on p. O might induce a very slight random variation between P and P’, such that q could form a representation of the approximate state of p-as-unobserved-by-q. Or P’ might be a subtly degraded version of P, from a representation of which a representation of P could be almost but not quite perfectly reconstructed (as when, for example, a digital sample of an analogue signal is used to recreate the original signal). There are various degrees to which a representation of the unobserved state P of p might be inaccessible to the observing entity q; it all depends on the reversibility of the difference O makes to P. Some operations are totally reversible – multiplication by two, for example, can be reversed by dividing by two. Some operations are totally irreversible – there is no operation that can reverse multiplication by zero, or obliteration – while others are partially reversible: for example, having raised a number to the power of two, taking the square root will return the original “magnitude” of the number but erase the sign. Many other degrees and kinds of irreversible “degradation” are possible.
Let us now call “ancestral” an entity p such that the operation O – the observation of p by q – includes the construction of q itself (the state Q of q prior to O is null, or “inexistent”). The unobserved state P of p is the state of p in a universe without q; p is thus q’s “ancestor”. It follows, given an operation that creates q, that the observed state P’ of p is necessarily the state of p in a universe in which q also exists. Can q form a representation of P – that is, of the state of p prior to q’s existence? The question would seem to turn on the degree to which the operation which took P to P’ was reversible – as would the veracity of those scientific statements which seek to infer the early history of the cosmos from contemporaneous observations.
However, one could object that an entity q in a “null” state (or in its birthday suit), entirely lacking in attributes, is not the same as no entity q whatsoever: the coming into being of q cannot therefore be an operation O taking some q from the state Q (inexistent) to Q’ (existent, and containing a representation of the state P’ of p). For q to have some state Q, it must already exist, and so the operation O (which presupposes such a state) can only commence after q has in some sense come into being (even if only minimally, with no attributes to speak of). Even if it is possible to infer Q’’ (a representation of the state of p-as-unobserved-by-q) from Q’ (a representation of the state of p-as-observed-by-q), this still does not give q access to a representation of the state of p-prior-to-q’s-existence.
We saw in our discussion of the “minimal” case of the representability of p-as-unobserved-by-q that an observation that completely devastated p would render its unobserved state forever unrecoverable in representation by q. This “complete devastation” is a voiding of attributes, a reduction to a “null” state; but it results in an obliterated entity rather than no entity at all. On both sides, therefore, observation is constrained to be the observation of and by entities, be they perilously newborn or irreversibly decrepit, rather than of and by nothing. To the extent that the ancient fossil is contemporaneous with the earliest existential precursor of the human cosmologist, be it an infinitely dispersed handful of cosmic dust, it is not truly “ancestral” in the sense demanded by Meillassoux. But perhaps only an entity pre-existing the rest of the material universe could truly be “ancestral” in quite that sense.
January 15th, 2009 at 5:20 am
“The photons bouncing off the table into my retina make no real difference to the table, so insofar as my perceptual system forms within itself a representation of the table as observed by me, this representation is equally a representation of the table as unobserved by me (it’s remarkable how much difficulty some people have with this entirely banal equation).”
That may be because this is not a logical inference?
It is conceivable that there is no representation of the table as unobserved by you, or at very least, not one that at all resembles the ones as observed by you.
January 15th, 2009 at 7:43 am
Yes, but how is it conceivable? It’s conceivable that the observing operation O which forms in me a representation of the table-as-observed-by-me also modifies the table in such a way that this representation in no way correlates to the table-as-unobserved-by-me. But it’s also conceivable that the operation O largely leaves the table alone, so that the set of attributes (the state P’) of the table to which my representation of the table correlates is pretty much the same as the set of attributes (the state P) the unobserved table (the table on which O has not operated) would have had. And I think that when it comes to things like tables, this is usually the case. They’re sturdy enough to be eaten off – looking at them doesn’t usually bother them very much.
Note that the representation is still a representation, formed in me. It isn’t a table. It may not even be a particularly good representation of a table (Q’ may correlate rather weakly with P’, registering only a few of the possible differences between tables – and those rather vaguely and inconsistently). But it looks just as much or as little like an unobserved table (p in the pre-O state P) as it does an observed one (p in the post-O state P’).
January 15th, 2009 at 7:14 pm
Somewhat trivial point: To observe is to mediate. We can conceive of multiple representations of one table that are not the same or even remotely similar to that table when unobserved based upon whom or what is doing the initial observing-into-representation of the table.
In human observers, representations of objects like tables are entirely contingent on the optimal functioning of all systems within the human body, but in particular the optic nerve and the visual cortex.
For example, a man who is red-green color blind looks at a table that’s painted with an orange and green pattern, and the representation of that table in his mind after the photons hit his retinas and this image is processed by the visual cortex looks nothing like the representation of an unobserved table, because the colors orange and green are not represented as distinct colors in the brain of the color blind person, while they are reflected differently in the light spectrum. (You could easily substitute in this example a human observer with glaucoma, macular degeneration, or one who is blind, schizophrenic, or under the influence of hallucinogenic drugs…)
Given that all possible observers do not represent the table in exactly the same way that the unobserved table is known to be represented, it is not logical to infer that any one representation of a table (even yours) must/will accurately represent the unobserved table. It is impossible to know whether all observers (including you) are able to represent the table as it is when unobserved by any observer.
Of course, even if we’re not talking about nervous systems observing and we’re talking about bits of information being stored that represent the table, it’s still not so clear that representations made mechanically by picture-making devices of various types would look the same as a representation of a table that is unobserved. In fact, we know for certain that different cameras will represent the table using differing numbers of megapixels stored at different rates of compression, with different saturation, brightness– their representations of the table bear little resemblance to the actual table in size, color, dimension.
Somewhat more trivial point: Sure, most possible observers aren’t going to affect the table in observing it, but that doesn’t mean there aren’t conceivable observers who might inadvertantly (some kind of camera that gets so hot it burns the table) or intentionally (an animal who attacks the table and scratches or breaks it because the animal mistakes the table for a predator) do so.
January 15th, 2009 at 7:28 pm
Meant to write “…nothing like the representation of the unobserved table” even.
I also tried to avoid the word actual but it found its way in despite my best intentions.
January 15th, 2009 at 8:03 pm
Strike out “accurately.”
January 15th, 2009 at 10:23 pm
Right, let’s see if we can sharpen this up a bit.
An operation O is called (by me) an observation of p by q if:
* Both p and q have a state which is changed by O, from P and Q to P’ and Q’ respectively.
* The way in which the state of q changes from Q to Q’ varies to some degree as the state of P’ (the state of p after O) varies.
I call the difference between Q and Q’ a “representation in q” of P’ (the state of p as modified by O).
If Q is taken by O to Q’ in a way that has no relation whatsoever to P’, then O is not an observation by p of q, and q cannot be said to have formed a representation of P’ – it is just confabulating, or varying its state at random.
In the “perfect” case, there is no possible difference between two values of P’ that does not result in a corresponding difference in the delta between Q and Q’. In this case, the function from P’ to delta-Q is injective. Additionally, it never happens that O takes Q to Q’ differently for the same values of P’, so the function from delta-Q to P’ is also injective. There is thus a bijection between P’ and delta-Q, which makes them isomorphic.
We can construct plenty of cases where such an isomorphism obtains (like backing up your hard drive), but they all tend to be rather artificial. Human and other animals trying to get a fix on other objects generally miss all sorts of things about the different ways those objects might have of insisting in the world, and sometimes see differences where there are none; unaided human perception is a lamentably bandwidth-restricted and probabilistic endeavour.
However, the question I was discussing was not whether a “perfect” isomorphism obtains between delta-Q and P’, but whether the state P of the object before the operation O was any different from its state P’ after it.
In the case that it isn’t (and there are cases, some of which I also discussed, where it is), then a weakly-correlated representation of P’ (p-as-observed-by-q) just is a weakly-correlated representation of P (p-as-unobserved-by-q), just because P’=P. In neither case does q get to apprehend the “in-itself” of p; it’s just that its caricature (to borrow Graham Harman’s term, without I hope misusing it too egregiously) of P’ is also perforce a caricature of P.
I contend that when a representation of the state of a table is formed within me, that representation is also perforce a representation of the state of the table before the representation was formed: the table’s state hasn’t been changed by the operation which formed the representation. Which might seem like a tremendously boringly obvious thing to assert; but, as I say, people have a quite mystifying ability to find it dubious.
January 15th, 2009 at 11:01 pm
Now, some more contentious assertions:
i) It is false to say that P’ can never be equal to P. Some observations have no effect on the thing observed.
ii) It is false to say that P can never be inferrable from P’. Some operations have a fully reversible effect on the thing operated upon.
iii) It is false to say that delta-Q can never be isomorphic to P’. Entirely faithful transliterations are possible, as we indeed hope when we back up our hard disks.
iv) Even if delta-Q is not a wholly faithful transliteration of P’, we can still sometimes obtain a delta-Q’ that is a more or less equally (un)faithful transliteration of P (that is, a “fuzzy” representation of p-as-unobserved-by-q). We can always do so in the case that P’=P, and sometimes do so in the case that P->P’ is reversible. We can never do so in the case that P->P’ is completely irreversible, for example if O completely destroys p so that P’ is null.
January 15th, 2009 at 11:54 pm
I’m never quite sure where people want to go from this level of generality.
If by “… my perceptual system forms within itself a representation of the table as observed by me, this representation is equally a representation of the table as unobserved by me” you’re simply saying that a representation of a table in an observer’s view is always a representation of the table and continues to be a representation of the table whether the observer is here, there, or somewhere in nebulous the future and nowhere near the table–this seems a teensy bit tautological.
Can’t decide if this is a proof blowing correlationism out of the water or what. The so-called problem of ancestrality itself seems trivial in a way–if there are beings who think and there were other things that were around before those thinking beings (observers) came along to observe them, to what extent were those pre-observed things really thinkable at all? To what extent are these pre-observed things thinkable as something other than a magical/transcendental sum [of metaphysical relations between thinking beings and their pre-observed ancestor-things] greater than the parts of its whole? (This is how I’ve understood ancestrality, although I’d love to be corrected if I am wrong.)
Seems a little disingenuous to try to claim that science isn’t fully aware of this “problem”–but science is never a totalizing, universalizing, metaphysical endeavor. Should it be? How can anything that trades in absolutes be properly speculative? Something doesn’t sound right here, though I’m not sure I can put my finger on it just yet. I’m certainly not at all sure that the absolute is what needs to be revived–or that we need to radically re-enact the Enlightenment– in order to save “philosophy” (which sounds almost cute, invoked without a shred of irony, anymore) from science and/or itself.
I can’t help but hear these pleas for a renewed metaphysical rigor as the last gasps of “Western” culture in its death throes, clinging to its traditions for dear life.
Maybe this is cynical, maybe it’s naive, maybe it’s ignorant.
January 16th, 2009 at 7:45 am
I think there’s usually an assumption lurking around somewhere in correlationist arguments that only thinking about things or observing them makes them have definite attributes – that the unobserved thing, the thing just floating around with no observers to observe it, is just a sort of miasma of indescribable pre-stuff. I think this assumption is completely unwarranted, and causes great philosophical misery – nothing obliges us to make it, and we’d be much better off without it.
January 16th, 2009 at 10:51 pm
Aha. Well, this is probably true, but I think the more pressing problem for science is the one posed by the mediation of representations of things that is inherent to the observation function– which is not an entirely metaphysical problem.
To be done with correlationism, on the other hand, seems an entirely metaphysical, and hence philosophical, problem. Not sure what role science would have to play in this, unless (as Meillasoux suggests) we are to radically revise science so it can do something other than what it can already do.