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von Neumann’s deduction that biological reproduction is digital
We now know that the reproduction and growth of organisms is driven by DNA and proteins. The DNA contains the instructions which proteins execute.
If we travelled back in time, what arguments might we use to convince people that ‘our’ model for how organisms reproduced and grew was correct?
The General and Logical Theory of Automata is a talk given in 1948 by John von Neumann, four years before the discovery of the structure of DNA.
In this talk, von Neumann deduces from first principles:
- that the mechanism for organism reproduction must be digitally based, rather than analogue. His argument is based on error rates. The performance of the recently invented computers showed that it was possible for digital systems to return correct results for calculations requiring at least
operations; while for analogue systems the signal/noise ratio is often 
, with 
to 
sometimes being possible.
Prior to 1940s valve based electronic computers, relays were used to build what were essentially digital devices.
Relays go back to the mid-1800s, which is when Boolean algebra was created. The Jacquard weaving loom takes us back to the start of the 1800s, but there is not yet any digital mathematics to cite,
- it is possible for a simple machine to build a much more complicated machine. Twelve years earlier, Turing had published his results around the universal capabilities of a Turing machine, i.e., Turing completeness, the ability of any Turing machine to perform any calculation that any other Turing machine can calculate.
Turing completeness is a surprising result. An argument that it is possible for simple machines to build more complicated, prior to Turin, would have to rely on evidence such as ship building,
- a conceptual algorithm for a self-reproducing machine; this uses two Turing machines, and a mechanism for sequentially controlling operations.
A talk on automata obviously has to say something about organic computers, i.e., the brain. The von Neumann paper intermixes the discussion of neurons and reproduction. McCulloch, of McCulloch & Pitts neurons fame, was in the audience, as was the psychologist Karl Lashley, and neuroscientist Lorente de Nó. The recorded post talk discussion was mostly ‘brain’ oriented.
Team DNA-impersonators create a business plan
This weekend I was at the Hack the Police hackthon, sponsored by the Metropolitan Police+other organizations. My plan was to find an interesting problem to help solve, using the data we were told would be available. My previous experience with crime data is that there is not enough of it to allow reliable models to be built, this is a good thing in that nobody wants lots of crime. Talking to a Police intelligence officer, the publicly available data contained crimes (i.e., a court case had found somebody guilty), not reported incidents, and was not large enough to build allow a good model to be built.
Looking for a team to join, I got talking to Joe and Rebecca. Joe had discovered a very interesting possible threat to the existing DNA matching technique, and they were happy for me to join them analyzing this threat model; team DNA-impersonators was go.
Some background (Joe and Rebecca are the team’s genetic experts, I’m a software guy who has read a few books on the subject; all the mistakes in this post are mine). The DNA matching technique used by the Police is based on 17 specific sequences (each around 100 bases, known as loci), within the human genome (which contains around 3 billion bases).
There are companies who synthesize sequences of DNA to order. I knew that machines for doing this existed, but I did not know it was possible to order a bespoke sequence online, and how inexpensive it was.
Some people have had their DNA sequenced, and have allowed it to be published online; Steven Pinker is the most famous person I could find, whose DNA sequence is available online (link not given; it requires work+luck to find). The Personal Genome Projects aims to sequence and make available the complete genomes of 100,000 volunteers (the UK arm of this project is on hold because of lack of funding; master criminals in the UK have a window of opportunity: offer to sponsor the project on condition that their DNA is included in the public data set).
How much would it cost to manufacture bottles of spray-on Steven Pinker DNA? Is there a viable business model selling Pinker No. 5?
The screen shot below shows a quote for 2-nmol of DNA for the sequence of 100 bases that are one of the 17 loci used in DNA matching. This order is for concentrated DNA, and needs to be diluted to the level likely to be found as residue at a crime scene. Joe calculated that 2-nmol can be diluted to produce 60-liters of usable ‘product’.
There was not enough time to obtain sequences for the other 16-loci, and get quotes for them. Information on the 17-loci used for DNA matching is available in research papers; a summer job for a PhD student to sort out the details.
The concentrate from the 17-loci dilutes to 60-liters. Say each spray-on bottle contains 100ml, then an investment of £800 (plus researcher time) generates enough liquid for 600-bottles of Pinker No. 5.
What is the pricing model? Is there a mass market (e.g., Hong Kong protesters wanting to be anonymous), or would it be more profitable to target a few select clients? Perhaps Steven Pinker always wanted to try his hand at safe-cracking in his spare time, but was worried about leaving DNA evidence behind; he might be willing to pay to have the market flooded, so Pinker No. 5 residue becomes a common occurrence at crime scenes (allowing him to plausible claim that any crime scene DNA matches were left behind by other people).
Some of the police officers at the hack volunteered that they knew lots of potential customers; the forensics officer present was horrified.
Before the 1980s, DNA profiling was not available. Will the 2020s be the decade in which DNA profiling ceases being a viable tool for catching competent criminals?
High quality photocopiers manufacturers are required to implement features that make it difficult for people to create good quality copies of paper currency.
What might law enforcement do about this threat to the viability of DNA profiling?
Ideas include:
- Requiring companies in the bespoke DNA business to report suspicious orders. What is a suspicious order? Are enough companies in business to make it possible to order each of the 17-loci from different company (we think so)?
- Introducing laws making it illegal to be in possession of diluted forms of other people’s DNA (with provisions for legitimate uses).
- Attacking the economics of the Pinker No. 5 business model by having more than 17-loci available for use in DNA matching. Perhaps 1,000 loci could be selected as potential match sites, with individual DNA testing kits randomly testing 17 (or more) from this set.
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