There is a certain sort of random process called a Markov process.
"The characteristic property of this sort of process is that it retains no memory of where it has been in the past. This means that only the current state of the process can influence where it goes next....
The process can assume only a finite or countable set of states, when it is usual to refer to it as a Markov chain." [1].
"Markov chains are the simplest mathematical models for random phenomena evolving in time. Their simple structure makes it possible to say a great deal about their behaviour ... this makes Markov chains the first and most important examples of random processes. Indeed, the whole of the mathematical study of random processes can be regarded as a generalization in one way or another of the theory of Markov chains." [2]
"Chains exist both in discrete time... and continuous time..."[3]
Note that in these distinctions discrete time manifests a particular, object bias in thinking, whereas continuous
time manifests a more general, relational bias in thinking. In other words, based on distinctions
made elsewhere on this site, continuous time is a SECONDARY concept whereas discrete time is a PRIMARY concept
as far as our species is concerned.
In the context of meaning, Markov chains with their lack of feedback manifest pure genetic responses to a given moment. Thus concepts such as 'compensatory behaviour' are where 'out-of-context' behaviours manifest themselves since the gene program is running and a context has emerged that is not in the program and the nature of the gene means that there is no immediate context sensitivity and so the gene-context 'flow' is broken.
Discrete time - object-like with no begin/end, just 'is'. Thus the use of numbers to count includes the setting of an arbitrary start point. The use of numerals is there merely to differentiate for us 'this' moment from 'that' moment.
Generalise this process and you chunk-up. Thus the 1-2-3 is grouped in, for example, 24-hour time frames but these come from *relational* considerations and so feedback processes and so continuous time where the dynamics lose sight of the particular elements.
This moves us from the stimulus/response-like nature of discrete time to the context sensitive, feedback bias of continuous time where the lack in precision at the quantitative level is replaced by a qualitative precision that includes general 'begin/end' distinctions.
It is important to recognise that in the context of "meaning", which means feedback, so continuous time Markov chains are SECONDARY in that secondary processes deal with relational space and so dynamics.
This said. there will be PRIMARY meanings that are meanings that have been embedded at the gene level. These meanings are manifest in the form 'instinct' behaviours. These manifest archetypal meanings but are not 'sensed' in that they manifest pure 'stimulus/response' behaviour where responses lack any link to conscious or even unconscious intent; 'mind' is totally unaware of these sort of behaviours and can do little but react by trying to control or guide these sorts of behaviours and at best let them run their course.
In monkey studies of infants, surrogate mothers can be created made from fur and foam rubber etc. We also see this in other lifeforms in the form of imprinting. Imprinting is a sort of 'one-shot' memorisation process that, like firmware in computer systems, becomes 'hard-coded'.
It is important to recognise that the lack of memory in Markov chains is identical to the lack of memory in primitive genetic programs where there is no sensitivity to feedback from the context. A lifeform has no recognition of context and only functions as coded, thus survival is upto the context, there is a strong REACTIVE bias in this sort of 'behaviour', pure absolute stimulus/response.
The presence of this sort of behaviour implies that it is possible for a behaviour to be 'random' in that there is no intent behind it, the behaviour can be due to a hardware or firmware problem (e.g. ADD problems where the forgetfulness etc does not manifest 'passive/aggresive' behaviour, it just 'happens'.) This leads us to the area of psychotherapies where, since the emphasis is on relational processes, so everything is given 'meaning' but without understanding of PRIMARY processes, which include 'random' moments, so there is no chance of a 'random' moment being interpreted as such. (see comments on randomness and dreams).
Reflecting on the requirement that Markov chains have no memory, it become apparent that any form of consciousness would be at best 'fleeting'; perhaps a sort of 'awareness' that cannot go past the moment. If you try to put this in the form of a context series using discrete time concepts so a Markov chain is expressable as a sequence of 1s:
1,1,1,1,1,1,1,1,1
where each moment, regardless of scale, is always 'new', always 'now'. (Interestingly, many religions try to achieve this state -- Taoism, Zen etc)
If you now add the ability to distinguish one moment from the previous we see the emergence of a primitive mind-set in the form of remembering sequence. Thus our 1,1,1,1,1 becomes:
1,2,3,4,5,6
Where each moment is added to the previous. We see a form of this in territorial mappings where the sequence method is used in the form of waypoint mapping to mark-out territory (A to B to C ...) and this sequence, when brought around back to the beginning creates a sense of 'ownership', of 'mineness'.
Now let us consider what happens when we consider the previous TWO contexts, whenever we do this, where we add the previous two contexts together to give us the current, we find ourselves dealing with one of the most basic manifestions of feedback processes used for development. This is in the form of a Fibonacci sequence:
1,2,3,5,8,13,....
This pattern is extremely common in life and seems to manifest the basic minimum required for development with a minimum use of energy.
As we increase the number of contexts to add together to give us 'meaning' we find that when we go back to the beginning of anything, to the FIRST instance and then sum ALL contexts from that point, we end up with an emerging binary sequence:
1,2,4,8,16,32,.....
At this point something 'interesting' happens in that to go beyond this level we enter the realm of complexity/chaos and the concept of emergence. But how? The answer is to add more feedback than is already there. A classic example of this is in the human mind where, seeing someone walking down a street our memories map that person to someone we know and immediately a flood of feelings can emerge that will influence us if we meet that person, we put more into the meeting than is actually there and so lead to an 'emergence' that is a direct result of the addition of feedback beyond just 'the moment'.
Verhulst showed that going beyond 2 leads into these unstable areas (using a number line. Mandelbrot does the same thing using the imaginary number plane giving us the Mandelbrot Set).
What we are seeing in these sequences are the basic building blocks of developing a memory and so the patterns that come with these processes. In a pure object oriented frame of reference, the one favoured by mathematicians, there is NO link AT ALL from one moment to the next other than in time. Thus there is no way that last week's lotto draw can affect this week's draw. Every draw is a unique moment, a '1' as we find in Markov Chains; there is no memory. The moment you start to use memory what you are doing is comparing contexts, 'this' with 'that' and the more you do this the more you approach a level where 'emergence' can happen and so the development of a memory system followed by the emergence of concepts of 'self', 'others' and consciousnessin general, and all from 'basic' feedback processes.
frame 1 2 3 4 5 6 7 8 9 10 12 ....
system
1 frame 0 1 1 1 1.... (independence)
2 frames 0 1 1 2 3....(Fibonacci sequence)
3 frames 0 1 1 2 4 7....(Tribonacci sequence)
4 frames 0 1 1 2 4 8 15....
5 frames 0 1 1 2 4 8 16 31...
6 frames 0 1 1 2 4 8 16 32 63...
..
n frames 0 1 1 2 3 8 16 32 64 128 256 512 1024 etc
Fig 1. Emergence of the binary sequence from a Fibonacci sequence
when concidering previous contexts.
[1] page iii, Norris, J.R.,(1997) "Markov Chains" CUP.
[2] p vix, ibid.
[3] p xiii, ibid.
[4] Chaitin, G.L., (1999) "The Unknowable" Springer