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.