This is an article I wrote for merton-l on June 24th, 1995
A few years ago I did some research on self-referential systems, originally in the field of computer science but more generally applicable to any system (such as a mind or a society) that contains and manipulates information.
I have continued to ponder this area (although now moving further from computer science as such) and have reached some ideas growing from that work seem relevant to the ongoing discussion on cosmology and contemplation.
One idea that struck me as particularly significant, is that manipulation or alteration (such as evolution) of an information-handling entity cannot raise such an entity to self-awareness from not having (potential) self-awareness. The (potential) self-awareness must be provided from outside (or beyond) the entity -- from the creator of the entity. I believe it is possible to demonstrate or prove this rigourously. (However, I am not yet so sure where to place our being within the framework provided by this structure -- elucidation thereof will require more contemplation on the nature of contemplation!)
When I first read Beatrix's excellent articles on de Chardin's cosmology, one of de Chardin's ideas seemed to contradict this: that the attainment of consciousness was the result of a stage in the evolution of humanity. (I can now see that these two ideas are not in conflict. A non-self-aware entity can be transformed into a self-aware one if the creator of the entity has included the potential for self-awareness into the structural field within which the entity exists. A transformation taking non-realized (potential) self-awareness to realized self-awareness may occur through processes such as evolution.)
I have written about this in general terms (and can post that as an essay, if wanted and appropriate; or those with web browsers can read it at http://www.cb1.com/~john/thoughts/essays/tower.html ) but the most concise way to describe it (even to non-computer-scientists) is probably to fall back to computer science and simple maths, to form a simple example of something that is not self-aware and cannot transform itself to self-awareness; and which furthermore can neither contemplate nor transform itself into something that can contemplate... but, interestingly, could spawn something that can contemplate its parent within computer science!
So please excuse a brief excursion into a rigourous science, on the way back to contemplation; I cannot see how else to transform a mixture of a theologian and a logician into that stable compound, the theologician!
Consider the use of a simple arithmetical function -- something
which ``does something to a number that has been given to it''. A
suitable example is the square root, commonly abbreviated to
sqrt
. We say that we `apply' the square root function to
a number, and write such an application thus:
sqrt(4)
(which, of course, yields the result 2
). Such an
application can be put into action by pressing the keys of an
electronic calculator.
Such functions may be applied to more than one parameter, for example
divide(6,2)
which yields 3
.
As represented above, the `application' of `sqrt
' to
`4
' is in some sense ``behind the scenes''. If, however,
we regard the implementation (`intension' or `representation' are the
terms used in this field) of `sqrt
' as being a pattern in
the computer / calculator's memory, just as `4
' is also
represented as such a pattern, we may see it as more appropriate to
write this application explicitly:
apply(sqrt, 4)
or, for an example with more than one parameter
apply(sum, [1 4 2 0 7])
(where I write a list of things in [ ]
)
Now we can see that `apply
' is also a function within
the computer, and, having answered the question `what makes
sqrt
do something?' with `apply
makes it
work', we must ask `what makes apply
do something?' and
try to answer it by looking at
apply(apply, (sqrt 4))
{That's probably the hardest part of this argument... if I haven't lost you so far, the rest should follow naturally!}
We can now see that a tower of `apply'
applications
is part of the answer; we can go back any number of levels without
reaching any more conclusive answer, and must posit that for all or
any of these `apply
's to work, there must be a computer
for them to run on... the computer is the ground of the
meaning of this tower of applications. (I am using the term "ground"
formally here.)
At this point, it becomes interesting to project from the special
back to the general, and to look at the idea of meaning in context. In
the example, `apply'
gives meaning to
`sqrt
', the computer / calculator gives meaning to
`apply'... and you, the user of the calculator, give meaning to the
result of the calculation. For example, you might be calculating the
length of the side of a square, given the area. But what gives meaning
to your interpretation of that number?
Now let us procede with one foot on the specialized but rigourous bank of the stream, and the other on the general but non-rigourous, and see whether we reach a point at which the parallel banks of the stream converge... (will it be at the alpha of the stream, or at the omega? or are they one?)
Having seen that within a structural field (such as the
memory of a computer) there can be `values' to which functions may be
applied, and that functions are also values (which may be applied to
values, and to which function values may be applied), let us posit the
existence of such a function value that is capable of some form of
reasoning (such as modus-ponens deduction). Any value may be referred
to by a name (if the structural field containing the structural field
containing the value also contains names, and allows their association
with values in the structural fields which it contains). For easy
reference, we will call this function Anselm
.
We can now represent the application of Anselm
to a
value (such as the number pair [1, 3]
) either as
Anselm([1, 3])
or as
apply(Anselm, [1, 3])
the values of either of these applications, of course, being the
result of Anselm
's deliberations about the number pair
[1, 3]
.
Moving on to more interesting deliberations, we can consider self-reference:
Anselm(Anselm)
or
apply(Anselm, Anselm)
and we can also consider forms of consideration of elements of the structural field in which the reasoner reasons:
Anselm(apply)
or
apply(Anselm, apply)
and, more fully,
Anselm([apply, Anselm])
or
apply(Anselm, [apply, Anselm])
It should be clear that such applications are possible only if
permitted by the structural field in which the values exist. A
structural field which allows the above applications will not
necessarily permit Anselm
to consider the structural
field itself: that is possible only if the structural field containing
Anselm
also contains itself. Furthermore, by the same
reasoning that showed us that no furthering of the chain
...(apply(apply(apply(apply(sqrt, 4)))))....
there is no amount of reasoning that can be done by
Anselm
, even about the chain
...apply(apply(Anselm, [apply, Anselm, [apply, Anselm, [ .... ]]]))....,
that will allow Anselm
to consider the structural
field itself, if the structural field has not allowed for the
possibility of Anselm
considering it.
So, non-self-aware information-handling entity cannot be transformed by an information-handling process (such as reasoning or evolution) into a self-aware one.
However, an information-handling entity may create structural
fields embedded within itself which do allow such field-reference (but
only within those embedded fields). For example, I, as such an entity,
have created the field of discourse above, and can choose whether to
make that field within which a value (such as Anselm
) can
refer to the field containing that value.
Thus, a value in a structural field may be the creator of embedded structural fields, to which it is the structural metafield. It is obviously possible to move in a dimension (not a linear one, but a partial order, mathematically speaking) in which the directions are `creatorwards' and `creaturewards'. The field in which this dimension is a value is the structural hyperfield of the original fields; it is of course a field in its own right, embedded within a metafield system embedded within a hyperfield... and then we can make two such transitions at once, but find we have just made the same kind of transition in another hyperfield... we can do this infinitely many times... we can do this omega times {in ordinal theory, omega is the first number that cannot be reached by counting from zero and adding one any number of times}... we can do this omega-squared times... or make a corresponding level shift again... where does the real context come from? I posit the existence of an absolute ground field, the omega field, which we cannot reach by our actions; but all fields are embedded in, and part of, the omega field, and so can be reached from the omega field, not in transfinitely many steps, but in none! Transfinitely far, and yet more than transfinitesimally close, the omega field is also the alpha field!
At this stage in the development of my thoughts on this topic, it seems most appropriate for me to let my readers form their own views on what light these ideas shed on the process or being of contemplation. I will however add the personal note that when I realized the significance of the non-emergence of self-reference of structural fields, my mind took on a blank grey state quite unlike anything else I had ever experienced, for a period of twenty minutes or so... a frightening state at the time, partially aware at once of both our size in the scale of the universe, and at the same time of the significance of a single idea that can be passed from the Mindscape into a mind... an extraordinary awareness that the thought I had just had was more significant than anything I had thought before...
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