An Expedient Mind: The Representation of CAUSAL LINKS

AN EXPEDIENT MIND

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CAUSAL LINKS

The Basic Causal-Link
The mechanism of Mind - The Representation of Causality

The diagram above shows the basic structure representing a causal-link. Note that the two #states involved in this relationship (S1 and S2), are represented by two separate (unlinked) structures. The causal-link between them is represented by a third separate structure. We must resist the temptation to represent the link by placing a pointer in S1 pointing at S2 and/or vice versa. The causal-link is not part of the observation of either S1 or S2. No reference to the link should appear in either. The relationship is something observed independently of both. The causal-link is the relationship of their occurrence together and repeatedly. That "togetherness" is not a property of either. It was not observed at either time T1 or at time T2. It was an observation made over a period of time spanning T1 and T2. That is represented by the annotation "ext(T1,T2)" meaning "an extension from T1 to T2". By convention, in this notation, "ext(T1,T2)" includes T1 but stops just short of including T2. This arrangement ensures that there are no unintended overlaps or gaps, when we are dealing with contiguous time intervals or distance measurements.
Giving the causal-link a separate representative structure of its own has beneficial consequences. It is now possible represent the circumstance in which the #states are each involved in several different causal relationships. S1, for example, could have several different causal consequences represented by several different #states. It is also possible for S2 to be only one of several #states caused by S1. But these individual #states do not and need not "know" that they are involved that way. Here I am using the term "know" in a metaphorical sense - shorthand for the presence or, in this case, the absence, of information stored within the #states themselves. The existence of the relationships was something spotted by the compression algorithm and the causal-link is therefore a structure created by the process of consolidating that compression chunk into a concept.

Representing Expectations
I have argued (or insisted) elsewhere that a causal-link is nothing more than a confident expectation. #State S1 has been found by experience to be a reliable predictor of S2. So when S1 is observed, S2 is expected. When that prediction is made, S2 will not yet have been observed. We should therefore extend the representation of the causal-link to include two extra bits of information. The first is the status of S2. At time T1, or, more correctly, over the time interval ext(T1,T2) (which does not include T2), S2 has not yet been observed. During that time interval, S2 is only an expectation. During this period of anticipation, #state S2 has the status "pending".
Another item of information which should be included in the causal-link structure, is an indication of the degree of confidence associated with the expectation. We shall avoid giving numerical values to this quantity. Instead the degree of confidence will be given a "standard" value denoted by some unique token or symbol. More particular information can then be provided in the form of a relationship to that standard. Greater than, smaller than, very much greater than, and so on. We can also have a value which we will denote as "negligible" and another which, for convenience, we can call "certain". It should be noted, however, that "certain" does not mean absolutely certain. It means, in effect, "a racing certainty". i.e you can put your money on it with confidence, but do not lose sight of the fact that in rare circumstances, the confidence may be misplaced.

The diagram above shows an alternative abreviated way to illustrate a causal-link. Most of the information stored internally in the structures has been omitted. This form of illustration allows me to explain the way the structures can be used to represent various kinds of additional causal relationship.

The diagram illustrates the representation of a causal chain of events. The series of #states have been given time-stamps (T1,T2,T3,T4,T5). The #states involved in a causal-link must always be in chronological sequence. That is a consequence of the way a causal-link is recognised and formed by the compression algorithm. It follows that, in this chain, the #states are all part of an extended chronological sequence. In addition, according to this diagram (and presumably for other reasons) we know that T3 = NOW. That means that #state S3 is currently being observed. The two previous #states (S1 and S2) have already been observed, while the reamining two (S4 and S5) have not yet been observed, but are anticipated. For that reason, the three #states S1, S2 and S3 each have a status = "real", while the #states S4 and S5, each have a status = "pending".

Multiple Consequences

The diagram above shows a single causal precursor #state "causing" four successor #states. These consequences are independent of one another, so while all may be anticipated, some may be prevented while others are observed to happen. An example might be a storm which causes trees to fall over and ships to sink. The fact that one of these consequences may be avoided does not mean that that is so for the others. To be able to represent this set of circumstances, we need the various causal-links to be represented separately.
Contrast that with the situation we have when the various consequences are consequent on one another. For example if a storm causes large waves and the large waves sink ships. We cannot prevent the large waves without also stopping the sinking of ships. The proper way to represent that would be with a causal-chain.
Contrast the multiple cpnsequences representation also with the alternative consequences representation which is shown below.

Alternative consequences

Here we see a single #state (S1) causing another (S2). S2 can take one of several alternative forms (S3, S4, S5, or S6). These are mutually exclusive. If S2 takes the form of S3 (i.e. has all the properties of S3, then it does not take the form of any of the others. For example, If I kick a ball, the ball might fly through the air or it might roll along the ground. It cannot do both. Note that if we want to introduce the possibility also that the ball might burst, then that would be represented as one of a set of multiple-consequences since the ball could burst are roll along the ground. If the bursting of the ball affects the way in which the ball rolls, then that would be introduced by a subordinate causal-link.

Multiple Causes
The representation of Multiple Causes and Alternative Causes are not illustrated, but it is obvious that a similar arrangement would suffice.

Prevention

The diagram above illustrates the representation of "prevention". For this we need to introduce the concent of negative #states. If we have a #state S then we can also have a #state or condition NOT(S). Since S could have many properties, it is not possible to say which, and how many of these, are not present in NOT(S). All we can say, is that there is somethiing missing, or there are extra properties present, and as a consequence there is a sufficient difference between the properties of S and NOT(S) for NOT(S) to be so designated. The diagram above illustrates just one way in which prevention can be represented. Here the #state S1 causes the #state S2. A third #state (S3) causes a condition which is labelled NOT(S2). NOT(S2) by being labelled as such, refers to S2. If NOT(S2) has the status "real" then the status of S2 must switch from either "real" or "pending" to "potential".
It is important that in any representation of "prevention", that we retain a full representation of what might have happened if the prevention had not occurred? How else would it be possible to understand the significance of a preventative action. How else can the system represent the concept of "danger"?
In the example illustrated the prreventative action prevented the occurrence of the #state S2. Prevention can also occur if the new condition S3 prevented the occurrence of S1 or of the causal-link between S1 and S2. All these possibilities can occur and all can be represented depending upon circumstances.

The Inherent Multiplicity of Causes and Consequences
There is a mutiplicity of conditions (causes and consequences) involved in every causal connection. We might, for example, say that "a lighted match caused a forest fire". What is not often mentioned however, is that this circumstance would not have been possible but for the presence of oxygen in the air, the absence of a wind to blow the match out, the absence of rain to extinguish the fire, the relative closeness of the burning match to the flamable grass or whatever. When we discuss causal connections, we usually ignore everything which can usually be taken for granted. That is, we make assumptions about what other people are likely to know, or assume, and we inform them only of the non-standard aspects. That is another reason why there can never be absolute certainty about any causal effect. One of these normal extra factors might be missing or an exceptional one might be present. The representation of causal-links always has to be open-ended. There always has to be scope for the addition of extra factors under exceptional circumstances.

Causing a Cause
The way in which a causal-link is represented as a concept structure in its own right, allows it to become involved in additional causal-links in which it may play the roll of causal precursor or consequence. The various ramifications which that permits, will not be illustrated, because there are so many possibilities. The complexities of structure which are possible however, allow us to find a representation for (for example) "enabling", "the prevention of a prevention", "permitting" and so on.

Representing Expectations
When we are dealing with alternative or with multiple consequences, each of the various consequences can be given its own measure of expeectation. The facility for representing expectations is very important when we deal with language because the meanings of many words in the language are expressions of anticipation. Consider, for example, what meanign we may attach to the words "BUT", "THEREFORE", "SURPRISINGLY" and "NEVERTHELESS". All of these express conditions which either confirm expectations or the converse. Once again, these useful extra properties will not be given numerical values. They will, instead, be given identifiers and these identifiers given relative values.

{REALITY}

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