Asked about this, I spent a bit thinking and I arrived at this very brute answer:
What I have in mind can be split in two.
There is a first part concerning graphic lambda calculus seen as it’s about real molecules interacting in space. For this part I would like to construct graphs which are like a Turing machine (or other computing devices) then, the important step is to eliminate everything which is due to our human 1d writing conventions (see details in the rant from the first part of this post) and thinking and simplify such “machines”, in the same way, for example, like I saw it’s possible
- when it comes to the currying procedure and lists
- see also Sets, lists and order of moves in graphic lambda calculus
- as well as Combinators and stickers
- or in the case of the connections controlled by other connections in neural networks described in the second part of this post.
A serious tool for doing this would be, for example, a program which allows to visualize and perform moves (automatically and from the keyboard) on graphs in .
The second part, which goes in parallel, would be to try to find in the real world (here DNA origami looks like a possible tool) ways to construct chemically, physically, such machines, which are naturally adapted to the real world because they are geometrical (an object or a property is geometrical if it can be described, or it’s invariant to an arbitrary change of parametrization, in our case, an arbitrary renaming). For this part I want to understand first how DNA origami works, to the level of being able to absorb information and understand some of the hurdles. This leads to applications, which are still vague in my head, but I was impressed by this video
as well as by research of Jean-Pierre Banatre and Daniel Le Metayer.
In conclusion, I can’t imagine what a syringe with 10^9 nano
geometrical turing machines graphs representing lambda terms [see UPDATE] can’t do.
UPDATE: Corrections to this post are made in Chemical concrete machine not algorithmic self-assembly of DNA, nor Turing machine , where it is stressed that the “chemical concrete machine”, even if it has Turing universality property, it is not intended to be a Turing machine, (nor an automaton), as is wrongly suggested in this post.