What's a Turing machine?

Question

What is a Turing machine and why do people keep mentioning it? My IBM PC is all I need to do my computation! Why does anyone care about these machines?

Answer 1

There are actually examples of Turing Machines in nature. Specifically, the ribosome, which translates RNA into proteins, implements a Turing Machine.

First, some background:

1. RNA is composed of a string of nucleotides ("bases") which define the letters of the genetic alphabet.
2. There are 4 bases in the RNA alphabet - A, C, G, U.
3. Bases are directional: by convention the ends are called five-prime and three -prime (5', 3')
4. A base in an RNA string can attract a base on another RNA string in "anti-parallel complementary pairs", where A sticks to U and C sticks to G.
5. The bases are combined in groups of 3 to form "codons" (words).
6. There are 64 possible combinations for the codons (4^3).
7. each codon can match an "anti-codon". for instance AUG <-> UAC
8. there are special carrier molecules ("tRNA") which have particular anticodons and are attached to specific amino acids (proteins).

The operation of the ribosome is simple:

1. transcription initiates at a "start codon", which defines the "reading frame"
2. transcription always proceeds in the 5'->3' direction
3. the codon under the reading frame is matched with a specific tRNA containing a specific amino acid
4. the start codon always encodes the amino acid Methionine.
5. the new amino acid is attached to the growing protein
6. the frame then advances 3 bases to the next codon, and the protein is continuously extended
7. upon encountering a "stop" codon, translation is terminated, no amino acid is attached and the ribosome dissociates from the mRNA.

As you can see, this is a very simple Turing Machine that performs the most complex operation - nature itself!