「FISHING」# 2
thinking about technology
〈Tools For Productive Thought〉
@dan's post relates to a subject that is rather interesting.
This essay expands on a comment I had made yesterday.
DEFINITIONS?
Do we need them? John Wheeler often said that sometimes we do not.
Furthermore, sometimes we do not want them; I think he was right.
To illustrate why, consider security. I'd written yesterday:
I am unsure that we need to use any definition of security. We might take it as something to be solved for in the relevant problem context. We might not need to define our terms in advance. (Wheeler suggested this approach.) We might ask questions about decentralized systems without narrowing scope by using tacit definitions. ("N" is secure if "N interacting with M" is secure when "M" is also secure. That sort of thing.) We discover our proper scope in the relevant problem context gestalt.
The simplest examples are from music theory and theoretical biology. A sound is not music if the result is not also music when this sound is combined with other sounds which are music (Strutt, 1896). Two organisms are not the same species if they cannot mate and produce offspring that can themselves mate and produce offspring.
Observe that what is the fundamental unit is not explicitly defined.
Notice also that it can therefore be modal — it can vary with its context.
This is one way of thinking more productively about interacting structured disaggregated systems.
An interesting theme; I will comment further on it.
It has significant implications of the practical kind.
If I was not who I am, I would have different problems to solve. If I was not where I am, I would have different problems to solve.
The same is true for most systems. The concept of problem for a complex system is a modal one.
Different systems generally have different problems; but what each system is varies with its internal organization and what other system it is part of.
Wertheimer argued, discussing apparent motion as resulting from phenomenal identity. That two points which are the same if considered in isolation, are different when parts of different systems. Yet different points are the same in different wholes. We see the result as motion. The whole determines how the parts functionally behave; this is the difference between piecemeal identity and functional identity, according to Wertheimer.
In the last chapter I informed you exactly when I was born
— but I did not inform you how.
No; that was reserved entirely for a chapter by itself.
--- Laurence Sterne, 1760, Tristram Shandy, vol. 1, cha. 5
The definition of a problem for a complex system depends on the whole problem context. However all the different modes and types of behavior of the system are staggeringly many and the vast space of all that we do not comprehend in advance. For systems that have interacting units which can be organized it is infeasible to comprehend all that space at once. Each part of it is very large itself. Requires its own analysis. Yet much of it also is not relevant. Most contexts never occur in fact. If we start with defining problems we'd like our system to solved we typically miss what is significant and focus on that which is not significant. We rarely guess or anticipate the one proper whole situation that is significant to us in our situation and misidentify the units and therefore the problems and solve the wrong problems. Formulating problems for the system to solve rather than first making a system and identifying problems typically misses a majority chunk of what the system can do and will do but spuriously includes what it will not do. (George Friedman, 2005).
Exists generally no clear shortcut for finding out what a complex system shall do exactly — if by shortcut we mean something less than constructing the system and letting it run to see where it will go (Stephen Wolfram, 2002). Which was known in the special case as a no simulation theory for markets and other economic systems (Ludwig Mises, 1949).
The problems we identify and define in advance are usually the wrong problems. Both too narrow and too broad in different senses. We have generally no idea what our complex systems will do in advance. So how do we define its problems in advance? They seems to have happened frequently with various coins.
Exist many different undecidable logics whose axioms are finite and decidable (Goldblatt, 1992). We can reason about these systems by guessing and combining axioms. The terms in the axioms are vague and define themselves as axioms produce behavior when combined.
So the units mutate with they system they are part of. First we construct the system; then we learn what is each unit. At that point we solve for our problems and their scope is neither too narrow nor two broad; just right. Then we solve these problems and get what we actually want.
Consider a complex system like a network of actors. That is a social network.
Things with structure are not associative; they have internal organization (Miller Galanter Pribram, 1960).
So this network has a monad. Such as a monetization algorithm that flattens the interactional complexity of this system into a single dimension that the actors in it can associatively and easily reason about.
The platform on which this essay appears is an obvious example. The units of the network are constantly being changed, because the network they are part of changes.
In turn, the units operate on the network. Flow of change is the result.
The different actors face generally different problems in the different circumstances.
We cannot proceed by defining our terms first of all and then posing problems to solve in these terms.
Summarizing, rather than a system solving a problem, there is simply the system. It has several, different problems in different contexts. Also the problems it solves are different, varying with the contexts in which the system exists.
We solve for problems in the context that interests us. Then we solve those problems.
The strategy is common for studying networks and other complex systems, but for coins I have not seen it much used.
(Image: tibra; photography is useful for illustrating concepts.)
Thinking in a more roundabout way often gets you nearer your goal.
I feel like I am talking in somewhat of a circle. That is, however, exactly how we narrow down what is important and what is not if we start with axioms that are sharp containing terms which are vague.
We might consider systems in the form of an invariance relation.
X = B(B(A_1, . . . , A_N),X)=B(B(A_1, . . . , A_N)).
Now suppose we introduce the As in a sequence. (So we have an operad.)
X would often change once we add the next A.
It would be all the same be consistent with all the previous forms it had.
I predict that ultimately people will treat security and trust like a species, treat money like a species. And so on. Mathematically speaking our problems are not entirely intrinsic. Only partly that.
(Image: tibra; crystals ten microns thick. — Nature up close.)
Nature is mostly order arising from disorder. That we can directly see. And then what? Then we think about it. Some things are relevant. Others are not.
The relevant ones are those which organize the others.
So order from disorder (in the sense of Weizaecker and Foerster).
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