「FISHING」# 4

. . . thinking about tools and technology . . .

〈Can actors know if messages they sent were read?〉

Imagine we have some computers or computer users and they only interact by passing each other messages. The system in which the actors live tries to always deliver messages, but nobody has to read the messages they get, let alone respond to them.

All communications are therefore ad hoc and one way.

Each actor of this sort can send messages, create other actors, or decide what to do with future messages it receives.

Can an actor know whether it's message was read?

If it receives a message from the actor to which it sent a message, even then it cannot be sure that other actor has read it's earlier messages. Maybe it's just sending it a message for other reasons.

Now what?

Can an actor know whether it's message was read?

Yes, in the right environement. Not with certainty. But with increasing probability.

Imagine functionals f1(t), . . . , fN(t) that output functions f1, . . . , fN.

Let's write them thus — t.f(1) . . ., t.f(N).

As far as any actor is concerned, even though it might live at different times, at time t, all the other actors A in the system including itself, to whom it can send messages, are named by vectors |x⟩ in some higher dimensional space Φ such that

( ∀t ∈ T ) ( A = { | x ⟩ ∈ Φ | (t.fv)| x ⟩ – (t.fw)| x ⟩ = 0 , 1 ≤v ≤ N , 1 ≤w ≤ N } ).

Basically, other actors, basically, can change in number, as things in the system change.

They are named by the different qualities they have, and no two have the same name.

You have some curves, which change over time. The curves intersect where distance between them is nil. The coordinates of that intersection is an actor so far a some other actor is concerned. It might send it a message — and it would like to know, did it read the message.

Consider the pseudoideal ⟨ K ⟩. Let's define it.

⟨ S ⟩ is the set of all actors which ever a sent a message to actor S and S forwarded the message to yet other actors.

Let's also define a representative actor; it's just an actor S ∈ A such that ⟨ S ⟩ = A where this is true for all possible incompatible definitions of "ever" — all possible different restrictions of the sets of messages sent by each actor in A so long as at least one message from each actor in A is considered for evaluating whether ⟨ S ⟩ = A is true or not.

Basically, there is a playground actor S ∈ A. Every actor sends a copy of every message to S when it sends a message to any actor in A, and S forwards copies of it to all the actors in A. The original sender time stamps and addresses the messages it sends. Or the forwarding agent time stamps and addresses the messages it forwards.

This still doesn't reveal whether any message was read by anybody, only what message was sent to whom and when it was sent.

For each actor, all the other actors can see a sequence of message M ( t = h ), . . . , M ( t = k*). The mailbox each actor has in this system is therefore a monad, because it's possible to merge all streams of messages into a single sequence, and this the same for all actors, even though the sequence may not be what's experienced by each actor time-wise locally. Locally if m11 is prior m12 is prior m13, and m21 is prior m22 is prior m23, and m12 is prior m22, who really knows whether m11 is prior m21 or not, or whether m13 is prior m23 or not.

If the set A lives in a system that has a representative actor S, then out initial problem can be solved by repeated messaging to establish a history.

If actor ξ sees that actor δ received its messages but sent to messages to other actors whose messages it received much later, there's an increasing probability that its messages were either not read or else read and ignored — if it sends messages again and this happens again with increasing frequency.

If actor ξ also sees that actor δ received its messages but sent to messages to other actors ξ had sent messages to, then regardless of the content of the messages, which might be ignored, the larger the system, the greater the probability that it's message read and ignored rather than simply not read.

The probability that its messages were read but would be replied to some time later, that δ had delayed response is decreasing, and decreasing ever more rapidly the larger the system.

If response occurs too soon, compared with delay in responding to other messages, that suggests, with increasing probability the larger the system, that messages were not read but the timing was a coincidence. The other actor just sent its own original message.

THINKING ABOUT TECHNOLOGY. — Can actors know if messages they sent were read?

「FISHING」# 4

〈Can actors know if messages they sent were read?〉