The example with the marbles

In a discussion about the possible advantages for secure computing with the  GLC actors model, I came up with this analogy, which I want to file here, not to get lost in the flow of exchanges:

Mind that this is only a thought  experiment, which might not be accurate in all aspects in it’s representation of the kind of computation with GLC or more accurately with chemlambda.

Imagine a large pipe, with a diameter of 1 m say, and 3 m long, to have an image. It is full of marbles, all identical in shape. It is so full that if one forces a marble at one end then a marble (or sometimes more) have to get out by the other end.

Say Alice is on one end of the pipe and Bob is at the other end. They agreed previously to communicate in the most primitive manner, namely by the spilling  of a small (say like ten) or a big (for example like 50)   marbles at their respective ends. The pipe contains maybe 10^5   or 10^6 marbles, so both these numbers are small.

There is also Claire who, for some reason, can’t see the ends of Alice and Bob, but the pipe has a window at the middle and Claire can see about 10% of the marbles from the pipe, those which are behind the window.

Let’s see how the marbles interact. Having the same shape, and because the pipe is full of them, they are in a local configuration which minimizes the volume (maybe not all of them, but here the analogy is mum about this). When a marble (or maybe several) is forced at Alice’s end of the pipe, there are lots of movements which accommodate the new marbles with the old ones. The physics of marbles is known, is the elastic contact between them and there is a fact in the platonic sky which says that for any local portion of the pipe the momentum and energy are conserved, as well as the volume of the marbles. The global conservation of these quantities is an effect of those (as anybody versed in media mechanics can confirm to you).

Now, Claire can’t get anything from looking  by the window. At best Claire remarks complex small movements, but there is no clear way how this happens (other than if she looks at a small number of them then she might figure out the local mechanical ballet imposed by the conservation laws), not are Alice’s marbles marching towards Bob’s end.

Claire can easily destroy the communication, for example by opening her window and getting out some buckets of marbles, or even by breaking the pipe. But this is not getting Claire closer to understanding what Alice and Bob are talking about.

Claire could of course claim that i the whole pipe was transparent, she could film the pipe and then reconstruct the communication. But in this case Claire would be the goddess of the pipe and nothing would be hidden to her. Alice and Bob would be her slaves because Claire would be in a position which is equivalent to having a window at each end of the pipe.

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Comments:

  • each marble is a GLC actor
  • they interact locally, by known and simple rules
  • this is an example of signal transduction
  • which encrypts itself, more  communication makes the decoding harder. It is the same problem which is encountered when observing a living system, for example a cell. You may freeze it (and therefore kill it) and look at it but you won’t see how it functions. You can observe it alive, but it is complex by itself, you never see, or only rare glimpses of meaning.
  • the space (of the pipe) represents  an effect of the local, decentralized, asynchronous interactions.

Beneath under there is just local interaction, via the moves which act on patterns of graphs which are split between actors. But this locality gives space, which is an emergent, global effect of these distinctions which communicate.

Two chemical molecules which react are one composite molecule which reduces itself, splitted between two actors (one per molecule). The molecules react when they are close is the same as saying that their associated actors interact when they are in the neighboring relation.  And the reaction modifies not only the respective molecules, but also the neighboring relation between actors, i.e. the reaction makes the molecules to move through space. The space is transformed as well as the shape of the reactants, which looks from an emergent perspective as if the reactants move through some passive space.

Concretely, each actor has a piece of the big graph, two actors are neighbours if there is an arrow of the big graph which connects their respective pieces, the reduction moves can be applied only on patterns which are splitted between two actors and as an effect, the reduction moves modify both the pieces and the arrows which connect the pieces, thus the neighbouring of actors.

What we do in the distributed GLC project is to use actors to transform the Net into a space. It works exactly because space is an effect of locality, on one side, and of universal simple interactions (moves on graphs) on the other side.

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