or you could have a pet which embeds and run a copy of the whole Internet.
The story from this post starts from this exploratory posting on Google plus from June 2nd, 2015, which zooms from sneakernet to sneakernet delay-tolerant networking to Interplanetary Internet to Nanonetworks to DNA digital data storage to molecular computers.
I’ll reproduce the final part, then I’ll pass to the Internet as you pet thing.
“At this stage things start to be interesting. There is this DNA digital data storage technique
which made the news recently by claiming that the whole content of the Net fits into a spoon of DNA (prepared so to encode it by the technique).
I have not been able to locate the exact source of that claim, but let’s believe it because it sounds reasonable (if you think at the scales involved).
It can’t be the whole content of the net, it must mean the whole passive content of the net. Data. A instant (?) picture of the data, no program execution.
But suppose you have that spoonful of DNA, how do you use it? Or what about also encoding the computers which use this data, at a molecular level.
You know, like in the post about one Turing Machine, Two Turing Machines https://plus.google.com/+MariusBuliga/posts/4T19daNatzt
if you want classical computers running on this huge DNA tape.
Or, in principle, you may be able to design a molecular google search …
molecule, which would interact with the DNA data to retrieve some piece of it.
Or you may just translate all programs running on all computers from all over the world into lambda calculus, then turn them into chemlambda molecules, maybe you get how much, a cup of molecular matter?
– it executes as you look at it
– you can duplicate it into two cups in a short matter of time, in the real world
– which makes the sneakernet simply huge related to the virtual net!
Which brings of course molecular computers proposal to the fore
Let’s develop this a bit! (source)
The following are projections about the possible future of biochemical computations with really big data: the whole, global data produced and circulated by humans.
They are based on estimates of the information content in the biosphere from the article  and on a proposal for life like molecular computing.
Here are the facts. In  there are given estimates about the information content of DNA in the biosphere, which are used further.
One estimate is that there are about 5 X 10^11 tonnes of DNA, in a biomass of about 2 X 10^12 tonnes, which gives a proportion of DNA in biomass of about 1/40.
This can be interpreted as: in order to run the biochemical computations with 1g of DNA there are needed about 40g of biochemical machinery.
From the estimate that the biomass contains about 5 X 10^30 cells, it follows that 4g of DNA are contained (and thus run in the biochemical computation) in 10^13 cells.
The Internet has about 3 X 10^9 computers and the whole data stored is equivalent with about 5g of DNA [exact citation not yet identified, please provide a source].
Based on comparisons with the Tianhe-2 supercomputer (which has about 3 X 10^6 cores) it follows that the whole Internet processes in a way equivalent as a magnitude order to 10^3 such supercomputers.
From  (and from the rather dubious equivalence of FLOPS with NOPS) we get that the whole biosphere has a power of 10^15 X 10^24 NOPS, which gives for 10^13 cells (the equivalent of 4g of DNA) about 10^17 NOPS. This shows that approximately the power of the biochemical computation of 4g of DNA (embedded in the biochemical machinery of about 160g) is of the same order with the power of computation of the whole internet.
Conclusion until now: the whole Internet could be run in a “pet” living organism of about 200g. (Comparable to a rat.)
This conclusion holds only if there is a way to map silicon and TM based computers into biochemical computations.
There is a huge difference between these two realms, which comes from the fact that the Internet and our computers are presently built as a hierarchy, with multiple levels of control, while in the same time the biochemical computations in a living cell do not have any external control (and there is no programming).
It is therefore hard to understand how to map the silicon and TM based computations (which run one of the many computation paradigms embedded into the way we conceive programming as a discipline of hierarchical control) into a decentralized, fully asynchronous, in a ransom environment biochemical computation.
But this is exactly the proposal made in , which shows that in principle this can be done.
The details are that in  is proposed an artificial chemistry (instead of the real world chemistry) and a model of computation which satisfies all the requirements of biochemical computations.
(See very simple examples of such computations in the chemlambda collection https://plus.google.com/u/0/collection/UjgbX )
The final conclusion, at least for me, is that provided there is a way to map this (very basic) artificial chemistry into real chemical reactions, then one day you might have the whole Internet as a copy which runs in your pet.
 An Estimate of the Total DNA in the Biosphere,
Hanna K. E. Landenmark, Duncan H. Forgan, Charles S. Cockell,
 Molecular computers,
Marius Buliga, 2015