Is Programmable Matter A Direct Star Trek Like Consequence of Wolfram Physics?
If underlying spacetime is a constantly evolving graph like network of nodes, is it possible to deliberately rewrite the network to fashion, literally, anything?
The Concept of Nanotechology
In the recently debut of the third series of Star Trek: Discovery we see a 32nd century Federation using programmable matter in many forms from customer user interfaces to detached warp nacelles.
The canon explanation reveals its nature as “consisting of minute nano-molecules, the matter had the abilities of redistributing and redesigning itself into pre-programmed shapes.”
This idea has been popular in science fiction for some time with nanomachines or nanobots being a popular trope for the low level construction and repair of both organic and inorganic matter.
Indeed, research is already well underway with regard to nanotechnological applications in everything from the repair of arteries in the human body, to the diagnostic of medical conditions in human biology and dentistry¹.
Prototype nanomachines already exist that can propel “DNA, proteins, quantum dots, and other nanoparticles” through tiny nanoscale corridors.
Going Deeper and Smaller
However, with nanotechnology in its current form we are effectively manipulating what already exists in terms of matter be it existing molecular substances down to atoms themselves — with increasingly smaller and smaller machines — or some kind of localised field effect such as electro-magnetics.
Matter was being naively rearranged on smaller and smaller scales until the ability to rearrange atoms themselves was realised, as in IBM’s 1989 letter writing with individual Xenon atoms. From here it’s a matter of time (no pun intended) until accessible machines will be developed to perform this process on demand.
This is the level of technology, and scale, at which devices in the Star Trek universe such as the replicator (rearranges atoms to produce desired goods, usually food and drink) and the transporter (rearranges you, sends you somewhere, puts you back together) are envisaged to operate.
However, what if we could go deeper, what if we could rearrange the underlying spacetime, the underlying structure itself that manifests matter, and energy, as we know it?
With a graph an edge connects exactly two vertices.
With a hypergraph an edge may connect any number of vertices
Not so easy to show on a flat page, in the hypergraph to the left the edges are shown in colour and the vertices as points.
A rule, or set of rules, is then repeatedly applied to this hypergraph that rewrites relations between vertices and thus alters the hypergraph itself.
(I imagine this methodology to be somewhat akin to an iterated function system, something I’ve studied in detail myself and part of the reason I’m fascinated by the Wolfram Physics Model, where repeated iteration of set of rules (which are usually contractive) arrive at some final, fixed point.)
Without getting into too much detail, as the project itself describes this far better than I could in a few paragraphs, it is the structure of the hypergraph itself that gives rise to elementary particles, or fluctuations in fields if you wish, and subsequently through larger and larger scales, the manifestation of matter around us. (Energy is a slightly different facet of the hypergraph in the model, but arises as a consequence of its rewriting).
“…for example, a particle like an electron or a photon must correspond to some local feature of the hypergraph”²
The quote above from Stephen Wolfram describes how local features, or arrangements, of the hypergraph give rise to elementary particles. On the left, a simple arrangement contains a highlighted graph that demonstrates this concept. Perhaps this is how an electron appears in the hypergraph.
Of course, in the Wolfram Model the hypergraph would be much more complex. Work continues on all aspects of the model including as to ascertain the possible complexity.
Given that the rules may be extremely complex and how many iterations may have already taken place in our universe (Wolfram estimates possibly “over 10⁵⁰⁰”, “or even more”²) any elementary particle would have a far more complicated arrangement in the universal hypergraph!
In a previous article I touched on how Wolfram’s ideas are akin to a universe that’s continually computing, that all reality is in effect some vast ongoing computation. If we were to get a handle on the fundamental rules that govern the evolution of spacetime then is it valid to consider that we may alter them to rewrite reality?
Perhaps this is what will become the programmable matter of Star Trek.
Considering the engineering challenges involved is somewhat speculative at the moment as the model research continues. But, should the universe be evolving through both rapid and vast computation it has to be considered if the computing capacity in terms of both storage and speed could possibly exist to perform the necessary calculations involved and in a suitably accessible period of time.
I have neglected to mention the concept of computation irreducibility³, which not only puts limits on our ability to make predictions of the model but also may restrict, fundamentally, our ability to utilise our knowledge about it effectively. But, that’s for another time.
So, apart from the challenge involved in actually developing a workable model, there are those which invoolve devloping a method to access and manipulate the underlying hypergraph of spacetime.
What tools can be imagined that can directly manipulate reality at this level? They would surely be generations of complexity away from simple atomic manipulation involved in such Star Trek devices as a replicator or transporter that trivially manipulate already existing atoms!
Perhaps that’s why, at least in the Star Trek timeline, it takes until the 32nd century to get a real handle on reality…
 Mehta, M., Subramani, K., “Nanodiagnostics in Microbiology and Dentistry”, Emerging Nanotechnologies in Dentistry, 2012, Pages 365–390, https://www.sciencedirect.com/science/article/pii/B9781455778621000213
 Wolfram, Stephen, “Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful”, “How It Works”, Stephen Wolfram Writings April 14th, 2020 https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/
 Wolfram, Stephen, “A New Kind Of Science (Online)”, 2002, Chapter 12 https://www.wolframscience.com/nks/p737--computational-irreducibility/