Mauro, the digital vs analogue question was the topic of the essay two years ago so it is not my emphasis in this essay. There as here I take the view that quantised information made of qubits has analogue as well as digital features. It has never been my position that the foundations of physics are based on pure digital information in the form of bits.
The analogue side comes from the uncertainty which is realised through quantisation or multiple-quantisation. I think I could not have made the importance of this clearer given the title of the essay. If I had to give my own short slogan it would be more like "it from qubit" or even "it from ...quququbit"
The "It from Bit" question is not so much about digital vs analogue as about emergence. This has also been a common theme in all my previous essays where I have discussed emergence of locality, causality, space and time. My contention is that the foundations of physics take an purely algebraic form where space and time are emergent. I have argued in this essay that the holographic principle implies a large redundancy of information when physics is viewed as a theory in space and time which suggests that a "complete" symmetry plays a role in the emergence. My fundamental formulation is therefore in terms of pure algebras defined by multiple quantisation but independent of space and time. These are infinite dimensional Lie-algebras defined over the complex numbers so there is an analogue nature to physics already at this level. I do not expect the analogue nature of physics to be purely emergent.
As for the reference to string theory you should be aware of the modern view that string theory is just part of the larger framework that includes quantum field theories. It is of interest because of its ability to bring gravity into the picture. I do not adhere to the view that it will provide a conveniently unique formulation of particle physics. I think that is a view which is fading in popularity. We now have to accept that such a theory is a long way off and concentrate instead on the underlying principles to understand the relationships coming from dualities and how these lead to emergence. Hoefully when new experimental BSM data is forthcoming we will be in a position with the theory to understand it.
I have been looking at necklace lie algebras in this way for nearly twenty years and have seen many new ideas appear in the mainstream that follow the same principles. Permutations of the qubits extend to larger infinite dimensional symmetries which should resolve to diffeomorphism invariance as space and time emerge. You can compare this to what happens in quantum graphity for example. More recently we have seen new work on scattering theory in planar 4D SYM where permutations of states are of fundamental importance. The super conformal symmetry in space-time is joined by a new dual superconfirmal symmetry in momentum space and the completion of these symmetries defines an infinite dimensional Yangian symmetry which is similar to a necklace lie algebra. It is natural to turn this round and assume that the Yangian symmetry is the fundamental idea and that space and time are emergent along with locality, causality and unitarity. In the last few years this has become a very active field of research which is philosphically and mathematically very similar to what I have been looking at for many years.
Iterated integration also arises in scattering theory as a process that recursively generates the polylogarythmic amplitudes. I have recently learnt that the free Lie algebra is a simple form of necklace algebra that can be mapped to a continuous space using iterated integrations. This is what I have described in my essay. It is just a small part of the whole picture which is too big and as yet incomplete to describe in more detail. The hope is that similar mappings could be used on my earlier necklace lie algabras in the same way.
I hope this gives you a better picture of how my ideas fit in to the bigger picture. I am sorry that you seem to have gotten a completely upside down impression of what I was trying to say. Others have graciously complemented me on the clarity of my exposition so perhaps you just need to read it again more carefully.
