Lachesis, computation and desire to explore (Ancient Turing machines III)

This post continues the previous:

– “Ancient Turing machines (I): the three Moirai

– “The three Moirai, continued

– “Graphic beta move extended, to explore“.

In the fiction of the Moirai performing as an ancient Turing machine, destiny  is akin to computation:

– it might be anyhow, like the Turing machine which could do anything,

– but once threaded by Clotho, Atropos and Lachesis, destiny is fixed (as in greek tragedies), like the outcome of a computation is fixed once the program and the data are given (by the gods  holding the keyboard).

Where is the part of exploration here? Where is the free will to leave the destiny’s path and take a walk on the field, towards that distant glitter from the mountain, far away…

Exploration is not computation, like (trying to understand something and) formulating problems is not solving problems.

Let’s get pragmatic and suppose that Lachesis is capable of doing the extended beta move instead of the more limited graphic beta move. Is this enough for allowing exploration into one’s destiny? Yes, if we interpret exploration (as done before) as being governed by the emergent algebra gate \varepsilon.

In the previous Moirai posts I showed how the three fates may construct any graph representing a lambda calculus term, starting from an initial loop. What the Moirai could not do, was to construct a \varepsilon gate. Now, with the extended beta move available, here is how they could do it:


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