This article continues a series of two previous articles on femtotechnology and femtocomputing.

Computing at the femtoscale – using elementary particles directly as computing elements – should be possible, according to physical law as we now understand it. Hugo de Garis has begun working out some of the details, and has outlined some basic relevant ideas in a recent H+ Magazine article. Obvious caveats abound here – our knowledge of physics at that scale is still dodgy and incomplete; even “mere” nanotech remains largely speculative; quantum uncertainties (and possibly even more peculiar quantum-gravity undercertainties) may make it hard to extract information from femtoscale computing systems. But still, the train of thought is a natural one, and it’s compelling to explore femtocomputing conceptually and mathematically, as far as current science allows.

Indeed, this sort of thinking verges on “hi-fi sci-fi” – but then, it’s well documented that a large percentage of real science and engineering ideas appeared first in science fiction!

Hugo De Garis’s recent article shows, at a moderate level of technical detail, how one could carry out basic computing operations using quarks and gluons. This specific approach has potential problems with quark confinement — because quarks can never be observed in isolation, according to current physics theories. However, Hugo has subsequently pointed out (in a private communication not reflected in that article) that a similar thing could be done in other ways as well — e.g. via using the fact that a W particle can interact with a lepton (e.g. electron, muon or tauon) and convert it into a neutrino, allowing one to implement logic operations by observing whether the output is an electron or a neutrino. It seems there are many ways to extract the basic logic operations from the rich algebraic structure of particle interactions.

These are fascinating observations, but they pertain solely to a single computational operation – they don’t give any clues about how one might make a complete computational system at the femtoscale. My goal in this article is to give some highly speculative — but hopefully interesting! — hints as to how this might be done.

De Garis’s femto-scale logic gate involves interactions of very small particles that are difficult to localize and manipulate. It’s difficult to imagine pinning a bunch of these particles down on a circuit board to make a computing circuit analogous to a contemporary laptop’s motherboard! However, this is not the only computing hardware paradigm available. It seems to me that a better metaphor for designing femtocomputing systems might be DNA computing. We already know how to do simple kinds of DNA computing using special computing fabrics built using DNA nanotechnology. And DNA is not pinned down and precisely positioned like the circuitry on a laptop’s motherboard – it’s wet and messy and wiggly and often imprecise, though rigorous in its coding scheme. My suggestion, in this article, is that it might be possible to build a femtocomputer along lines vaguely similar to current DNA computers – and to the more powerful DNA computers that have been been envisioned in detail but not yet built.

DNA Computing via DNA Nanoengineering

DNA computing may sound like science fiction – but it’s actually real science and engineering, right now in 2011. Using DNA for computing is not yet of any practical value – the computing systems built using DNA so far are very slow and carry out very simple operations. But they demonstrate the viability of the principle of engineering and operating computing systems via utilizing molecular-biology components, connected in novel ways.

DNA is, of course, a natural substance that plays a key role in biological organisms, encoding the information needed for their growth and ongoing maintenance. DNA nanotech involves using DNA and other nucleic acids to engineer novel nanostructures – including, in some cases, nanocomputers. DNA computing can be done using DNA nanotech, but it can also be done via leveraging the properties of DNA in simpler ways, without building new nanostructures out of DNA. If you’re not familiar with the basics of DNA and genetics, you may want to look at a tutorial like this one (or, for a more thorough treatment, this one), before reading any further.

One of the many approaches to DNA computing is based on the engineering of tile-like structures using DNA. “Tiles” in this context are DNA-based constructs where there is very tight binding within the tile, and looser binding between tiles. This allows the building of a variety of structures via piecing the tiles together. The figure below (from this article) shows one example of this, the DX tile:



The top row of the figure shows the theoretical structure; the latter shows actual microscopic images of real DX tiles.

Most of the work with DNA tiles has involved two-dimensional tiles, but recently three-dimensional tiles have been created as well. Rothemund, Pappadakis and Winfree have shown how to use these tiles to do computing. Their work draws on prior research using DX tiles to implement Wang tiles, a method of implementing computation using graphical tilings developed in the early 1960s. The practical example that Rothemund et al have implemented is fairly simple – the computation of a simple fractal structure called the Sierpinski Gasket, shown in its mathematical form below:

The following figure gives a computer simulation of Sierpinski Gasket type formations as their DNA computing approach was foreseen to create them:

and finally, the following figure shows actual microscopic images of similar formations produced in their experiments:

The production of Sierpinski Gasket formations using DX tiles may seem quite a specialized achievement. However, the underlying method is quite general and could be used to implement any 2-dimensional cellular automaton (any set of computational rules determining what happens at one point in a 2D lattice, based on the state at neighboring positions in the lattice). And it’s well known that some 2D cellular automata have universal computing power – the capability to simulate any possible computational process. (For a lengthy and erudite discourse on this point, see StephenWolfram’s book A New Kind of Science.) Thus we can do universal computing using DNA – using what Rothemund et al poetically term “algorithmic crystals.”

Femtocomputing via DNA-Like Femtoengineering?

DNA lives at the nano scale, not the femto scale. However, as Jinfeng Liao and Edward Shuryak pointed out in a 2010 paper, there is reason to suspect the existence of polymer-like structures at the femto scale – for example, chains of quarks and gluons, occurring in quark-gluon plasmas when the underlying parameters have the right values. They look at chains of the form quark-gluon-…-gluon-quark, and a few other similar forms — but it seems that similar mathematics could be used to explore a variety of more complex, similar structures. Of course these are very different in their physical underpinnings than DNA sequences like AGCTTTAA…CTG — but computing theory has taught us repeatedly that the encoding of information in symbols is independent of the specific infrastructure used to create the symbols.

And so, speculatively at least, this research on polymer-like structures in quark-gluon plasmas opens the door for the possibility of something broadly similar to DNA computing at the femto scale. So far, our evidence for the existence of these polymer-like femtochains is purely indirect and mathematical – based on mathematical extrapolation from the theory of quark-gluon plasmas, which has been validated using other experiments not involving such chains. We don’t have direct observation of these chains — even the simple ones explicitly explored by Liao and Shuryak, let alone more complex ones. And making direct observations of such chains is a dicey matter due to the principle of quark confinement. Isolated quarks can’t be observed, according to current physics theories, though various scenarios involving observing “partially isolated” quarks are being considered in the literature. So, the use of these femtochains for femtoengineering and femtocomputing is certainly speculative. But, it’s interesting!

What might an analogue of DNA computing at the femto scale look like? The first step would be to construct a femtoscale analogue of the DX tile – some sort of chain of elementary particles with complementary “sticky” ends. The precise polymer-like femtochains that Liao and Shuryak describe would not necessary display this property, but it seems feasible that similar mathematics could lead to something of this nature – either in quark-gluon plasmas or in some other kind of degenerate matter. Once we have femto DX tiles, then, we could potentially engineer these tiles to work like Wang tiles, as in the DNA computing case. This would give us the capability for executing arbitrary computable functions, in a cellular automaton like manner.

Of course, the femto analogue of a DX tile might have a significantly different geometry than DX tiles, and might rely on a different mathematics than Wang tiling. The key point is that, in the vision presented here, femtocomputing is not about building circuit boards where elementary particles are laid down in the fashion of metallic wires, but rather about engineering the formation of fundamental femtocomputing units that are designed to self-assemble into complex distributed structures, whose natural dynamic iteration carries out desired computational processes. So, one would have degenerate matter whose dynamics approximates a cellular automaton (or other similar discrete dynamical system) carrying out specified computations.

Onward and Upward!

In the style and speculativeness of these considerations, we are perhaps closer to a Greg Egan novel than to a Physical Review article. (Egan fans may recall that in his novel Diaspora, Wang tiles are used to create complex and intelligent computational structures via patterns of molecules.) I’m well aware of the amount and type of difficult mathematics that would need to be done to create rigorous theories in the direction of these hand-wavy speculations. And then there are the experimental and engineering breakthroughs that would be needed to actually build anything along these lines, even after all the theory is worked out.

It may well be that femtocomputing is a post-Singularity technology, rather than something we traditional humans carry out ourselves. Perhaps it will require powerful AGIs implemented on nanotech based quantum computers, to figure out how to build the femtocomputers on which their descendants will run – who knows!

In any case, it is interesting – and, I think, important – to scope out the boundaries of our scientific understanding, and get a concrete sense of where future technologies may lead.