To quote important observations by Vladimir ShCherbak:

shCherbak VI.

**Arithmetic inside the universal genetic code**.

*Biosystems*. 2003 Aug;70(3):187-209.

“…one may assume that natural computing can exist as well. For instance, such a computing could be essence of exact gene processing and scrambling (Landweber and Gilbert, 1993; Landweber et al., 2000). If that is the case,

**some cell organelles should work as biocomputers**. Thereby, we have to discover the number systems with which they work.” “…the genetic code is connected more closely to abstract notions of arithmetic than with notions of physics or chemistry.”

**The Arithmetical Origin of the Genetic Code **http://www.springerlink.com/content/t85w0h771510j187http://tinyurl.com/y9w5gfj“There seems to be but one conclusion:

**the genetic code is itself a unique structure of arithmetical syntax**. The arithmetical syntax is

**separated from natural events by the unbridgeable gap between the fundamental laws of nature and the abstract codes of the human mind** (Barbieri, 2005). Chemical evolution, no matter how long it took, could not possibly have stumbled on the arithmetical language and initialized the decimalization of the genetic code. Physics and chemistry can neither make such abstractions nor fit the genetic code out with them. It seems that

**the genetic code appeared as pure information like arithmetic did**.”

“

**There is no plausible chemical logic to couple directly the triplets and the amino acids. In other words, the principles of chemistry where not the sought essence of the genetic code**”

“

**The zero is the supreme abstraction of arithmetic. Its use by any alphabet, including the genetic code, can be an indicator of artificiality**.”

“The place-value decimal system represented through digital symmetry of the numbers divisible by prime number (PN) 037. This arithmetical syntactic feature is an innate attribute of the genetic code. The PN 037 notation with a leading zero emphasizes zero’s equal participation in the digital symmetry. Numbers written by identical digits are devised by PN 037 x 3 =

**111 **and 1 + 1 + 1 = 3 and appear regularly [from the figure: 037 x 6 =

**222 **and 2 + 2 + 2 = 6, 037 x 9 =

**333** and 3 + 3 + 3 = 9, 037 x 12 =

**444** and 4 + 4 + 4 = 12, 037 x 15 =

**555** and 5 + 5 + 5 = 15, 037 x 18 =

**666 **and 6 + 6 + 6 = 18, 037 x 21 =

**777 **and 7 + 7 + 7 = 21, 037 x 24 =

**888 **and 8 + 8 + 8 = 24, 037 x 27 =

**999 **and 9 + 9 + 9 = 27].”

“The feature not only excites our sensation of beauty but may simplify some computational procedures too. Moreover, decimalization of the genetic code may be a special case of the general computational power of genomics and their molecular machinery. In fact,

**the only reason for a number system to appear is for arithmetic calculations**.”

“In fact, there is no way to write or read any gene when no code is available. Thanks to its immutability,

** the universal genetic code is the most accurate information messenger from the time of genesis to the present**.”

“

**First, a general and the most forcible argument: it has been found that the genetic code is governed directly by the arithmetical symbol of zero. This striking fact is verified simultaneously by several independent orderlinesses – logical, arithmetical, and semantical… Incidentally, such an acting zero alone might be sufficient to assume an artificial nature of the genetic code**.”

“

**There is a complete set of information symbols** utilizing the decimal syntax 111, 222, 333, 444, 555, 666, 777, 888, 999 in the genetic code. Each of these symbols consists uniformly of a carrier (balanced nucleons) and a meaning (the decimal syntax).”

“As a rule,

**possible consequences of the mutations such as an abrupt change of hydrophobicity are, to some extent, weakened** (e.g. Sjostrom and Wold, 1985; Figureau, 1987; Knight et al., 1999).”

“…

**when amino acids are replaced through mutation the change of hydrophobicity is generally weak, while that of size is strong**.”

“

**If a point mutation occurs, the code amino acids are to a certain extent protected against an abrupt change of their hydrophobicity but not of their geometric size**.”

“

**Arithmetic is the only tool for producing information systems of extremely high efficiency. Life, being an information phenomenon, could use arithmetic for control, integrity, and precise alterations of its genetic texts**.”

“One can speculate that

**some regular arithmetical background may “underlie” genetic sequences without limitation to their biological context. Analyzing its own arithmetic, such background might check, restore, and alter superimposed biological context by means of calculations omitting translation**.”

“Almost half a century ago, the idea of chemical evolution determined a stochastic (random) approach to the origin of the newly deciphered genetic code.

**The molecular machinery of genetic coding revealed however a baffling complexity. It is common practice to criticize the stochastic approach because the likelihood that this machinery could have been produced by chance is extremely low if not negligible**. But, on the other hand, the basic premise of the stochastic approach is that billion years and countless natural events could realize, nevertheless, practically impossible things. This vicious circle exists because both these opposing opinions appeal to the same concept – to the assessment of chances of natural events.

**One needs therefore properties of the genetic code that eliminate any possibility of a dual interpretation or overlapping of the arguments. In these terms, only the facts whose essence cannot be reduced to natural events can solve the original problem. We believe that a part of these facts have been presented and discussed above**.”

I just found another compilation on

*sh*Cherbak's work, by Craig Paardekooper:

http://www.craigdemo.co.uk/circleoflife.pdfWhere it was concluded:

"The existence of such

** perfect mathematical balance within the genetic code** may be taken as

**evidence of Intelligent Design**. As ShCherbak states,

**the only conceivable way for the summation to have appeared would be by some arithmetical process**.

**Did arithmetic precede life?**"