Events and Causal Dependence

**Updating Events and Causal Dependence**. wolframphysics

[…] Another feature of our Models is that every element can be thought of as having a unique “Lineage” [⇒ LineupJournal], in that it was created by a particular updating Event, which in turn was the result of some other updating event, and so on.

When we introduced our models in section 2, we just said that any element created by applying a rule should be **new and distinct from all others**. If we were implementing the model, this might then make us imagine that the element would have a Name based on some global counter, or a UUID.

But there is another, more deterministic (as well as more local and distributed) alternative: think of each new element as being a kind of encapsulation of its Lineage (analogous to a chain of pointers, or to a hash like in blockchains or Git).

In the Evolution above, for example, we could describe element 10 by just saying it was created as part of the relation {2,10} from the relations {{2,4},{2,5}} (as the second part of the output of an Update that uses them)—but then we could say that these relations were in turn created from earlier relations, and so on recursively, all the way back to the initial state of the system:

The final expression here can also be written as:

Roughly what this is doing is specifying an element (in this case the one we originally labeled simply as 10) by giving a symbolic representation of the Path in the Causal Graph that led to its creation. And we can then use this to create a unique symbolic name for the element. But while this may be structurally interesting, when it comes to actually using an element as a Node in a Hypergraph, the name we choose to use for the element is irrelevant; **all that matters is what elements are the same, and what are different**. [⇒ Being the Same]


⇒ The Formal Structure of Multicomputation Here’s the result for a single step:

There are two possible events because the two initial hyperedges given here can in effect be consumed in **two different orders**. Continuing even one more step things rapidly get significantly more complicated: […]


Milan Tomeš, The Pile System. pdf

> Abstract: The Pile system brings new alternative, progressive and especial look at data. It works with relations instead of data, and that is why storing it without redundancy. This paper describes basic features, principles and possible applications of this system.

# Two Different Orders

Different Orders

There is the two trees, black line we call **normative system**, blue arrow we call **associative system**. Each node from the normative system is identified with a node of a tree from the associative system.

KRIEG P. Assimilative Computing: A Radical Relationist Approach. [online], 2005, [cit. 3.4.2007], ppt

Peter Krieg reinvents artificial intelligence in his book, »Die paranoide Maschine«. See also one of the book reviews, *Haufen mit Richtung*. post (de)

Pile Systems Inc