This is a really short post that is a random thought I had while discussing genetics with a friend over dinner. Here’s the idea: DNA has 4 nucleotides that pair up thus as AT and CG. Now, there are 4 possible nucleotides, so lets use modular arithmetic (yep 
If we randomly pick one of the nucleotides, e.g. A, and assign it some element in {0,1,2,3}, say 3. We then assign a weight 1 to T so the sum A+T=1+3=0 mod 4.
We consequently have C and G have weights 0 and 2 (it doesn’t matter which gets which). Observe its sum is C+G=0+2=2 mod 4.
Now DNA is a sequence of such pairs, but we have reduced it to a sequence of zeros and twos. If we normalize these values, we get a sequence of ones and zeros. Holy cow, this looks like a binary string!
Of course, DNA is such a huge source of data, you’ll probably end up with stuff like lines from Shakespeare translated to ancient Greek backwards, or some other phenomenal coincidence like that.
Just a random thought that I thought was interesting…what is also interesting is that the quadratic residue of each sequence is zero mod 4. That is:
Remember that if we have a number squared it is 0 or 1 mod 4. Why? Well, suppose we have an even number 
What does this mean? It means that this numerological DNA thingy involves squares of even numbers!
Perhaps if we treat it as a sort of code, there is an error-correcting mechanism built into it? Perhaps if it’s a Reed-Muller code, we can bust out some Galois theory and do some finite group analysis. Or if we treat it as a lattice, sphere packings could get involved. Or we could treat it as a sort of binary continued fraction? There’s quite a bit one can do from here!
Well, I’m exhausted, but I thought this random coincidence was worthy of note…
Post Script A thought just occurred to me too, if we treat every e.g. 16 digits (more generally 
where 
Remark: Next time I’ll ramble on about the floating point arithmetic as a formal algebra, or whatever it is. I’ll try to provide some pseudo-rigorous proofs…
